ELEKTROENERGETSKE MREŽE - eihp.hrmmajstro/Elektroenergetske_mreze-Radni_materijal_1.pdf · - 1 - ELEKTROENERGETSKE MREŽE PRORAČUN NAPONA ČVOROVA I TOKOVA SNAGA . vježbe s pripadnim

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ELEKTROENERGETSKE MREŽE PRORAČUN NAPONA ČVOROVA I TOKOVA SNAGA

vježbe s pripadnim teoretskim podlogama Prof dr sc Matislav Majstrović

Split 2009 god

Primjer Na slijedećoj slici prikazana je jednopolna shema elektroenergetske mreže nazivnog napona 110 kV Potrebno je odrediti napne sabirnica (čvorova) koristeći Gauss-Seidelov-u iterativnu metodu Zatim odrediti tokove snaga po elementima mreže

Slika 1 Jednopolna shema elektroenergetske mreže

Poznato je Snaga elektrana (trofazna)

Cv1 Pg1 = 40 MW Qgmin1 = -15 Mvar Qgmax1 = 15 Mvar

Cv2 Pg min 2 = 10 MW (teh min) Pg min 2 = 50 MW Qgmin2 = -20 Mvar Qgmax2 = 20 Mvar Snaga potrošača (trofazna)

Cv1 Pp1 = 20 MW Qp1 = 5 Mvar

Cv3 Pp3 = 50 MW Qp3 = 20 Mvar

- 2 -

Podaci vodova

Vod od Cv1 do Cv3 (Cv1-Cv3) lv1 = 50 km Rd = 018 Ωkm Xd = 04 Ωkm Gd = 00 μSkm Bd = 26 μSkm

Vod od Cv2 do Cv3 (Cv2-Cv3) lv2 = 30 km

Rd = 018 Ωkm Xd = 04 Ωkm Gd = 00 μSkm Bd = 26 μSkm

Regulacijska elektrana je u čvoru 2 (Cv2)

Fazni napon na sabirnicama regulacijske elektrane kV03

110V o2 =

Željeni iznos faznog napona na sabirnicama elektrane u Cv1 kV3

110

Za početne vrijednosti faznih napona u iterativnom procesu uzeti

Cvor 1 (Cv1) kV03

110V o)o(1 =

Cvor 3 (Cv3) kV013

107V o)o(3 minus=

Dozvoljeno odstupanje vrijednosti napona između dvije iteracije je

realna komponenta napona 3

U10 n4re sdot= minusε

imaginarna komponenta napona 3

U10 n4im sdot== minusε

gdje je Un ndash nazivna vrijednost linijskog napona Rješenje Analiza će se provesti u metodi jediničnih vrijednosti U skladu s tim odabrat će se

- 3 -

Iznos baznog napona (linijski) kV110UB =

odnosno faznog baznog napona kV3

110003

110V oB ==

Bazna snaga (trofazna) odnosno jednofazna MVA100SB = MVA3

100SBf =

Dozvoljeno odstupanje vrijednosti napona u jediničnim vrijednostima između dvije iteracije je

00010110

11000010

3110

3U10

V

n4

B

rere =

sdot=

sdot

==ε

minus

εrealna komponenta napona

00010110

11000010

3110

3U10

V

n4

B

imim =

sdot=

sdot

==ε

minus

εimaginarna komponenta napona

Odavde je bazna impedancija za 110 kV naponski nivo

Ω==B

2B

Bf

2B

B SU

SVZ (11)

( )

Ω=sdot

sdot= 121

1010010110Z 6

23

B (12)

Odnosno bazna admintancija za 110 kV naponski nivo

SZ1Y

BB = (13)

S00083121

1YB == (14)

Parametri vodova u jediničnim vrijednostima su Vod Cv1 ndash Cv3 Uzdužna impedancija

- 4 -

B

1vdd31u Z

)XjR(Z

lsdot+=minus (15)

01653j + 00744121

50)40j180(Z 31u =sdot+

=minus (16)

Uzdužna admitancija

31u31u Z

1

minusminus =y (17)

03125 - j2640216530 + j07440

131u ==minusy (18)

Poprečna admitancija

B

1vdd31p Y

)BjG( l+ sdot (19) =minusy

01570 +j000830

50)1062j00( 2

31p =sdotsdot+

=minus

minusy (110)

Vod će se prikazati pomoću π ekvivalentne sheme

Slika 2 Ekvivalentna shema voda Cv1 - Cv3

Vod Cv2 ndash Cv3

- 5 -

Uzdužna impedancija

B

2vdd32u Z

)XjR(Z

lsdot+=minus (111)

00992j + 00446121

30)40j180(Z 32u =sdot+

=minus (112)


32u32u Z

1

minusminus =y (113)

38538 - j7734309920 + j04460

132u ==minusy (114)


B

2vdd32p Y


00940 +j000830

30)1062j00( 2

32p =sdotsdot+

=minus

minusy (116)


- 6 -

Snage elektrana u jediničnim vrijednostima su Cv1

B

1g1g S

P=P (117)

4010040

1g ==P (118)

B

1ming1ming S

Q=Q (119)

150100

151ming minus=

minus=Q (120)

B

1maxg1maxg S

Q=Q (121)

15010015

1maxg ==Q (122)

Cv2

B

2ming2ming S

P=P (123)

100100

1002ming ==P (124)

B

2maxg2maxg S

P=P (125)

5010050

2maxg ==P (126)

B

2ming2ming S

Q=Q (127)

200100

202ming minus=

minus=Q (128)

- 7 -

B

2maxg2maxg S

Q=Q (129)

20010020

2maxg ==Q (130)

Snage potrošača u jediničnim vrijednostima su Cv1

B

1p1p S

P=P (131)

2010020

1p ==P (132)

B

1p1p S

Q=Q (133)

050100

51p ==Q (134)

Cv3

B

3p3p S

P=P (135)

5010050

3p ==P (136)

B

3p3p S

Q=Q (137)

2010020

3p ==Q (138)

Naponi čvorova u jediničnim vrijednostima su Cv1

- 8 -

B

)o(1)o(

1im)o(

1re)o(

1(o)

1(o)

1 VV

jV =+=δang= VVV (139)

00j01001

3110

03

110o

o

(o)1 +=ang=

ang=V (140)

Cv2

B

22im2re22 V

VjV =+=δang= VVV2 (141)

00j010001

3110

003

110o

o

+=ang=ang

=2V (142)

Cv3

B

)o(3)o(

3im)o(

3re)o(

3(o)3

(o)3 V

VjV =+=δang= VVV (143)

01700 - j972600197270

3110

013

107o

o

(o)3 =minusang=

minusang=V (144)

U konkretnom primjeru ukupni broj čvorova je N = 3 Općenito je veza između struja i napona čvorova dana slijedećom jednadžbom

[ ] [ ] [ ]VYI sdot= (145) gdje je - stupčana matrica struja čvorova [ ]I

- matrica vlastitih i međusobnih admitancija čvorova [ ]Y (ova matrica se može odrediti jednom od metoda prezentiranih u [1])

- 9 -

- stupčana matrica napona čvorova [ ]V Dakle za konkretni primjer gornja matrična jednadžba će biti

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡sdot

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

3

2

1

VVV

YYYYYYYYY

III

(146)

Odnosno

3132121111 VYVYVYI sdot+sdot+sdot= (147)


3332321313 VYVYVYI sdot+sdot+sdot= (149) Sve varijable u ovim jednadžbama su kompleksni brojevi U skladu s tim one se mogu prikazati pomoću realne i imaginarne komponente ili pomoću modula i kuta Slijedi da je

1im1re111 jV VVV +=δang=

2im2re222 jV VVV

(150)

(151) δang = +=

3im3re333 jV VVV

(152) δang = +=

1111111111 jY BGY

+=Θang=

1212121212 jY BGY

(153)

(154) = Θang = +

3333333333 jY BGY +=Θang= (155) Poznato je da je snaga čvora 1 (Cv1) jednaka

1p1g1 SSS minus= (156)

gdje je Sg1 - prividna snaga koju elektrana daje u mrežu (čvoru)

- 10 -

Sp1 - prividna snaga koju potrošač uzima iz mreže (čvora) Ovdje je potrebno istaknuti da snaga koja ulazi u čvor (snaga elektrane) ima preznak + a snaga koja izlazi iz čvora (snaga potrošača) predznak - Snaga elektrane je

1g1g1g j QPS += (157) gdje je Pg1 - radna snaga koju elektrana daje u mrežu (čvoru) Qg1 - reaktivna snaga koju elektrana daje u mrežu (čvoru)

(Qg1 je reaktivna snaga koju daje elektrana mreži u ovom čvoru da bi održala zadani iznos napona ako je moguće)

Analogno je snaga koju uzima potrošač

1p1p1p j QPS += (158) gdje je Pp1 - radna snaga koju potrošač uzima iz mreže (čvora) Qp1 - reaktivna snaga koju potrošač uzima iz mreže (čvora) Jednadžba (156) jednaka je

( ) ( ) (159) 1p1g1p1g111 jj QQPPQPS += = minus + minus

Analogno je i snaga čvora 2 (Cv2)

( ) ( ) (160) 2p2g2p2g2p2g222 jj QQPPSSQPS =+= minus = minus + minus

Budući da u ovom čvoru nema potrošača s pripadnom radom (Pp2) i jalovom (Qp2) snagom gornja jednadžba postaje

2g2g222 jj QPQPS +=+= (161) Snaga čvora 3 (Cv3) je

( ) ( )3p3g3p3g3p3g333 jj QQPPSSQPS minus+minus=minus=+= (162)

Budući da u ovom čvoru nema elektrane s pripadnom radom (Pg3) i jalovom (Qg3) snagom gornja jednadžba postaje

3p3p333 jj QPQPS minusminus=+= (163)

- 11 -

Nadalje snaga čvora (S) jednaka je umnošku napona čvora (V) i konjugirano kompleksne vrijednosti struje čvora (I) U skladu s tim je snaga čvora 1

111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)

Iz gornjih jednadžbi slijede struje čvorova

1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)

Uvažavajući jednadžbe (159) (161) i (162) gornje jednadžbe postaju

1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)

Uvrštavajući ove jednadžbe u jednadžbe (147) (148) i (149) dobit će se

- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)

Odavde su naponi čvorova

⎟⎟⎠

⎞⎜⎜⎝

⎛sdotminussdotminus

minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)

Uvažavajući jednadžbe od (150) do (152) gornje jednadžbe izgledaju

( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛δangsdotΘangminusδangsdotΘangminus

δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus

minus+sdot+minusminus

minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)

Budući da je čvoru 2 (čvor u kojem je priključena regulacijska elektrana) poznat iznos (V2) i kut (δ2) napona to znači da nam jednadžba (177) odnosno (180) ili (183) u gornjim sustavima jednadžbi nije potrebna U skladu s tim sustav jednadžbi za izračunavanje nepoznatih vrijednosti iznosa (modula) i kuta napona čvorova je

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)

Pri tom treba imati na umu da je u čvoru 1 za sada poznat iznos napona (V1) a nepoznat kut napona (δ1) te da su poznate sve snage (Pg1 Pp1 i Qp1) osim reaktivne snage koju daje elektrana u mrežu (Qg1) Ovaj čvor se naziva čvor s kontrolom napona ili PV čvor (oznaka PV znači da je poznata radna snaga (P) i iznos napona(V)) U čvoru 3 nepoznat je iznos (V3) i kut napona (δ3) a poznata je radna (Pp3) i jalova (Qp3) snaga Ovaj čvor se naziva čvor snage ili PQ čvor (oznaka PQ znači da mu je poznata radna snaga (P) i reaktivna snaga (Q)) Nadalje poznati su elementi matrice vlastitih admitancija čvorova ( 1111Y Θang i 3333Y Θang ) i međusobnih admitancija čvorova ( i 1212Y Θang 3113Y Θang 3131Y Θang 3232Y Θang ) Kako se vidi gornji sustav jednadžbi je nelinearan i s kompleksnim varijablama Za rješavanje sustava jednadžbi (187) i (188) ili (189) i (190) odnosno izračunavanje nepoznatih veličina koristit će se Gauss-Seidel-ova iterativna metoda Prvo će se odrediti elementi matrice vlastitih i međusobnih admitancija čvorova Uvažavajući topolgiju mreže te pripadne uzdužne i poprečne admitancije grana (slike 1 2 i 3) slijedi da je matrica vlastitih i međusobnih admitancija čvorova jednaka ([1])

- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)

Sada će se krenuti u iterativni proces

- Iterativni proces

Budući da je čvor 1 čvor s kontrolom napona potrebno je odrediti da li elektrana može održavati željeni iznos napona Ako se izračunata reaktivna snaga koju elektrana daje u mrežu (Qg1) nalazi unutar granica moguće proizvodnje (Qg min 1 Qg max 1)

(193) le le

ova elektrana može održavati željeni iznos napona i ovaj čvor je i dalje čvor s kontrolom napona odnosno u daljnjem proračunu iznos ovog napona je poznata veličina koja je jednaka željenim iznosu napona

U slučaju da se izračunata snaga nalazi izvan granica moguće proizvodnje

Q 1ming1g Qlt (194)

tada se za proizvodnju reaktivne snage elektrane uzima pripadna granična vrijednost

1ming1g QQ = (195)

i u daljnjem postupku ovaj čvor postaje čvor snage To znači da mu više nije poznat iznos napona tj iznos (modul) napona postaje nepoznata veličina koju treba odrediti

Analogno je i za slučaj kada je

1g1maxg QQ lt (196)


1maxg1g QQ = (197)

i u daljnjem postupku ovaj čvor postaje čvor snage To znači da mu iznos (modul) napona postaje nepoznata veličina koju treba odrediti

- 16 -

Proizvodnja reaktivne snage elektrane u čvoru 1 odredit će se u skladu s jednadžbom (147) uz uvažavanje jednadžbe (167)

3132121111

1 VYVYVY

VS

sdot+sdot+sdot= (198)

Odavde je snaga čvora 1

31321211111 )( VYVYVYVS sdot+sdot+sdotsdot= (199)

Uvažavajući jednadžbu (154) iz ove jednadžbe slijedi da je prividna snaga koju elektrana daje u čvor 1 jednaka

1p

31321211111g )( SVYVYVYVS +sdot+sdot+sdotsdot=

[ ]1p

31321211111g1g )(Im)(Im SVYVYVYVSQ +sdot+sdot+sdotsdot==

[ ]1p(o)

313212(o)

111(o)

1)o(

1g(o)1g )(Im)(Im SVYVYVYVSQ +sdot+sdot+sdotsdot==

[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)

Odavde je u skladu s jednadžbo (157) reaktivna snaga elektrane

(1101)

Uvažavajući vrijednosti dane jednadžbama (118) (132) (134) (140) (142) (144) i (192) slijedi da je reaktivna snaga elektrane u čvoru 1 na početku iterativnog ciklusa ( o-ti iterativni korak ) jednaka

(1102)

(1103)

14180(o)

1g =Q (1104)

U skladu s nejednadžbom (193) i jednadžbama (120) i (122) može se napisati da je

15014180150 leleminus (1105) Dakle reaktivna snaga elektrane nalazi se unutar granica moguće proizvodnje To znači da se iznos napona u čvoru 1 može održati na željenom nivou Prema tome je iznos napon čvora 1 poznat i jednak je željenoj vrijednosti (V1=10) a njegov kut je jednak pretpostavljenoj vrijednosti (δ1=00o) kao što je navedeno u jednadžbi (140) Dakle u idući iterativni korak se ide

- 17 -

s vrijednošću napona čvora 1

o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)

Od prije su poznati naponi ostalih čvorova čvor 2 i čvor 3 (jednadžbe (142) i (144))

00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)

1 iterativni korak Uvažavajući jednadžbe (1107) jednadžbe (188) i (190) će biti u ovom koraku u skladu s Gauss-Seidel-ovom iterativnom metodom kod koje se izračunata vrijednost nepoznate varijable (u ovom slučaju napon čvora 1) čvora koristi odmah u slijedećim jednadžbama istog iterativnog koraka (u ovom slučaju kod izračuna napona čvora 2)

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)

Odnosno uvrštavajući vrijednosti iz jednadžbi (118) (132) (134) (136) (138) (192) (1107) (1108) i (1109) gornje jednadžbe dobiju se naponi čvorova Čvor 1 (Cv1)

- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus


minusminusminussdot=+ VV

(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)

Odnosno u polarnim koordinatama (eksponencijalnoj formi)

o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus

minussdot+minus++minus

sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)

Ispitat će se da li su ispunjeni uvjeti za završetak iterativnog procesa tj da li su zadovoljene slijedeće nejednadžbe

re)o(

1re)1(1re εleminusVV (1118)

im)o(1im

)1(1im εleminusVV (1119)

- 19 -

re)o(


im)o(3im


Uvrštavajući odgovarajuće vrijednosti iz jednadžbi (1107) (1109) (1113) i (1116) slijedi

00010003900000100391 le=minus (1122) Ovaj uvjet nije zadovoljen

00010008700000000870 le=minus (1123)

Ovaj uvjet nije zadovoljen


00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V

(1125) Ovaj uvjet nije zadovoljen

Da bi iterativni postupak bio završen potrebno je da su svi gornji uvjeti zadovoljeni Međutim kako isti nisu zadovoljeni potrebno je ići na idući iterativni korak

Pored toga što gornji uvjeti nisu zadovoljeni još se uočava iz jednadžbe (1114) da iznos napona u čvoru 1 nije jednak željenom iznosu (10039 ne 10 ) To znači da je potrebno napraviti korekciju proizvodnje reaktivne snage elektrane u ovom čvoru Sada će se uzeti da je napon čvora 1 jednak željenom iznosu (V1=10) a njegov kut je jednak izračunatoj vrijednosti u ovom iterativnom koraku ( ) Dakle u idući iterativni korak se ide s vrijednošću napona čvora 1 o)1(

1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)

Sada je potrebno provjeriti da li elektrana može s proizvodnjom odgovarajuće reaktivne snage zadovoljiti zahtjev za održavanjem iznosa napona na željenoj vrijednosti Reaktivna snaga koju elektrana daje u čvor je u skladu s jednadžbom (1101)

[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(

1g )(Im)(Im SVYVYVYVSQ +sdot+sdot+sdotsdot== (1128)

- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)


15010010150 leleminus (1131) Dakle reaktivna snaga elektrane nalazi se unutar granica moguće proizvodnje To znači da se iznos napona u čvoru 1 može održati na željenom nivou U idući iterativni korak ide se s vrijednošću napona čvora 1 danom jednadžbom (1126) odnosno (1127) Dakle naponi s kojima se ide u idući iterativni korak su

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)

te iznos reaktivne snage elektrane u čvoru 1 dan u jednadžbi (1130)

2 iterativni korak Slično kao kod 1 iterativnog koraka sada će jednadžbe za izračunavanje napona čvorova 1 (Cv1) i 3 (Cv3) biti Čvor 1 (Cv1)

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3

)2(3 3818197300V minusang=δang=V

(1140)

(1141)

(1142)


re)1(1re

)2(1re εleminusVV (1143)

im)1(1im


re)1(3re


- 22 -

im)1(3im


Uvrštavajući odgovarajuće vrijednost dobije se


00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)

Ovaj uvjet nije zadovoljen Budući da svi uvjeti isti nisu zadovoljeni potrebno je ići na idući iterativni korak


1 35560=δ

o)2(

1)2(

1)2(

1 3556001V ang=δang=V

00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)

3 iterativni korak Slično kao kod prethodnog iterativnog koraka će se izračunati naponi čvorova 1 (Cv1) i 3 (Cv3) Čvor 1 (Cv1)

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(

1re εleminusVV (1165)

im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus

Ovaj uvjet je zadovoljen

(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus


Pored toga što gornji uvjeti nisu zadovoljeni još se uočava iz jednadžbe (1160) da iznos napona u čvoru 1 nije jednak željenom iznosu (09992 ne 10 ) To znači da je potrebno napraviti korekciju proizvodnje reaktivne snage elektrane u ovom čvoru Sada će se uzeti da je napon čvora 1 jednak željenom iznosu (V1=10) a njegov kut je jednak izračunatoj vrijednosti u ovom iterativnom koraku ( δ ) Dakle u idući iterativni korak se ide s vrijednošću napona čvora 1 o)1(

1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(

1g )(Im)(Im SVYVYVYVSQ +sdot+sdot+sdotsdot==

[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)


00010000400241002450 le=+minus (1190) Ovaj uvjet nije zadovoljen

Budući da svi uvjeti isti nisu zadovoljeni potrebno je ići na idući iterativni korak

Pored toga što gornji uvjeti nisu zadovoljeni još se uočava iz jednadžbe (1182) da iznos napona u

- 27 -

čvoru 1 nije jednak željenom iznosu (09996 ne 10 ) To znači da je potrebno napraviti korekciju proizvodnje reaktivne snage elektrane u ovom čvoru Sada će se uzeti da je napon čvora 1 jednak željenom iznosu (V1=10) a njegov kut je jednak izračunatoj vrijednosti u ovom iterativnom koraku ( ) Dakle u idući iterativni korak se ide s vrijednošću napona čvora 1 o)1(

1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)

5 iterativni korak Naponi čvorova 1 (Cv1) i 3 (Cv3) u ovom koraku izračunavaju se pomoću slijedećih jednadžbi Čvor 1 (Cv1)

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(

3re minus=+ VV (1221)

o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)


00010000000246002460 le=+minus (1226) Ovaj uvjet je zadovoljen



1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -


00010000000000100001 le=minus (1241) Ovaj uvjet je zadovoljen

00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)

Ovaj uvjet je zadovoljen Budući da svi uvjeti isti nisu zadovoljeni potrebno je ići na idući iterativni korak

Ovdje se može konstatirati da je uvjet održavanja iznosa napona u čvoru 1 zadovoljen To znači da proizvodnja reaktivne snage elektrane ostaje nepromijenjena u odnosu na prethodnu iteraciju

11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus



Budući da svi uvjeti zadovoljeni iterativni proces je završen Dakle izračunate vrijednosti napona čvorova su

Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im

)8(3re3im3re3 minus=+=+= VV VVV (1260)

Odnosno o)8(

3)8(

3333 4507197330VV minusang=δang=δang=V (1261)

U slijedećoj tablici prikazani su naponi svih čvorova Tablica 1 Naponi čvorova

Napon čvora Broj

čvora Ime čvora Iznos

(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507

- Snaga regulacijske elektrane Regulacijska elektrane nalazi se u čvoru 2 (Cv2) Struja čvora 2 je prema jednadžbi (146)


)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2

+sdot+++sdot+=I + + sdot +

(1263)

12850j308402 minus=I (1264)

Snaga koja ulazi u čvor 2 je u skladu s jednadžbom (165)

222 IVS sdot= (1265)

- 36 -

Uvrštavajući odgovarajuće vrijednosti dobit će se

2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)

Općenito je snaga koja ulazi u čvor (snaga koja ide u mrežu) jednaka snazi koju daje elektrana umanjena za snagu koju uzima potrošač Budući da u ovom čvoru nema potrošača prema tome je snaga koja ulazi u čvor jednaka snazi elektrane Slijedi da je izračunata snaga regulacijske elektrane

22g SS = (1268)

12850j308402g +=S (1269) Radna snaga koju regulacijska elektrana daje u mrežu je

30840)(Re 2g2g == SP

12850)(Im 2g2g

(1270) Reaktiva snaga koju regulacijska elektrana daje u mrežu je

(1271) = SQ =

Sada će se provjeriti da li stvarna regulacijska elektrana s karakteristikama koje su definirane na početku zadatka može isporučiti ove snage U skladu s jednadžbama (124) (126) i (1270) vidi se da je

2maxg2g2ming PPP lele (1272) Odnosno

503084010 lele (1273) Analogno je i za reaktivnu snagu

2maxg2g2ming QQQ lele (1274)

- 37 -

Odnosno

201285020 leleminus (1275) Na temelju nejednadžbi (1273) i (1275) može se zaključiti da regulacijska elektrana sa svojim karakteristikama može zadovoljiti potrebe mreže tj njena proizvodnja (Pg2 i Qg2) se nalazi unutar dopuštenih granica

- Tokovi snaga koje teku vodovima Budući da su poznati naponi čvorova mogu se izračunati snage koje teku vodovima Vod između čvorova 1 i 3 (Cv1 ndash Cv3) Ekvivalentna shema ovog voda s pripadnim tokovima snaga prikazana je na slijedećoj slici

Slika 4 Tokovi snaga na vodu Cv1 ndash Cv3

Snaga koja ulazi u vod kod čvora 1 (Cv1) je

[ ]31u3131p

1131 )(2 minusminus

minus sdotminus+sdotsdot= yVVy

VVS (1276)

Uvrštavajući pripadne vrijednosti dobije se

- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(

minussdotminusminus++

++

sdot+sdot+=minusS (1277)

06580j2000031 +=minusS (1278) Snaga koja ulazi u vod kod čvora 3 (Cv3) je

[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(

minussdotminusminusminus+

++

sdotminussdotminus=minusS

07350j1966013

(1277)

(1278) =minusS minus minus Gubici snage na ovom vodu su

13311v minusminus +=Δ SSS (1279)

(1280) 00780j00340)07350j19660()06570j20000(1v +=ΔS + minus minus = minus

Slijedi da su gubici radne snage na ovom vodu

)(Re 1v1v SP Δ=Δ (1281)

003401v =ΔP (1282) Vod između čvorova 2 i 3 (Cv2 ndash Cv3)

- 39 -

Ekvivalentna shema ovog voda s pripadnim tokovima snaga prikazana je na slijedećoj slici



[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++


12850 + j3084032 =minusS (1285) Snaga koja ulazi u vod kod čvora 3 (Cv3) je

[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++

sdotminussdotminus=minusS (1287)

12650 - j30340-23 =minusS (1288) Gubici snage na ovom vodu su


(1290) 00200 + j00500)12650j30340()12850 + j30840(2v + minus minus=ΔS

)(Re 2v2v SP

=


(1291) Δ = Δ

(1292) 005002vΔP = Ukupni gubici radne snage u mreži su jednaki zbroju gubitaka radne snage po svim elementima mreže U konkretnom slučaju to je

2v1vu PPP Δ+Δ=Δ (1293)

008400050000340u =+=ΔP (1294) Ukupni gubici radne snage u mreži mogu se odrediti i na drugi način Naime oni su jednaki razlici sume radnih snaga elektrana i sume radnih snaga opterećenja potrošača (jednadžba (1295))

sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)

U skladu s tim je za analiziranu mrežu

sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)

- Fizikalne veličine Prethodno izračunate veličine će se prikazati u pripadnim fizikalnim jedinicama Općenito je neka veličina u fizikalnim jedinicama jednaka umnošku pripadne jedinične vrijednosti i pripadne bazne vrijednosti Naponi čvorova Općenito je fazni napon i-tog čvora u fizikalnim veličinama jednak

Vi = Vi VB i=1 2 3 (1298)

U slijedećoj tablici prikazani su fazni naponi svih čvorova Tablica 2 Fazni naponi čvorova

Fazni napon čvora Broj


(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -

Snage elektrana Općenito je trofazna radna snaga koju elektrana plasira u mrežu jednaka

Pgi = Pgi SB i=1 2 3 (1299)

Analogna je i trofazna reaktivna snaga koju elektrana plasira u mrežu

Qgi = Qgi SB i=1 2 3 (1300)

U slijedećoj tablici prikazani su trofazne snage koje elektrane daju u mrežu Tablica 3 Trofazne snage elektrana

Snaga elektrane Broj

čvora Ime čvora Radna

(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000

Opterećenje potrošača Općenito je trofazna radna snaga opterećenja potrošača jednaka

Ppi = Ppi SB i=1 2 3 (1301)

Analogna je i trofazna reaktivna snaga opterećenja potrošača

Qpi = Qpi SB i=1 2 3 (1302)

U slijedećoj tablici prikazani su trofazne snage koje potrošači uzimaju iz mreže

- 42 -

Tablica 4 Trofazne snage opterećenja

Opterećenje Broj

čvora Ime čvora Radno

(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000

3 Cv3 5000 2000 Snage koje teku vodovima Općenito je trofazna radna snaga koja teče vodom između čvora j i k

Pj-k = Pj-k SB i=1 2 3 (1303)

Analogna je i trofazna reaktivna snaga koja teče vodom između čvora j i k

Qj-k = Qj-k SB i=1 2 3 (1304)

U slijedećoj tablici prikazani su trofazne snage koje potrošači uzimaju iz mreže Tablica 5 Trofazne snage vodova

Vod Snaga Red br od do Radna

(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2

Cv3 Cv2 -3034 -1265 Ukupni gubici radne snage u mreži Ukupni gubici radne snage u sve tri faze su

- 43 -

- 44 -

ΔPu = ΔPu SB (1305)

ΔPu = 00084 100 = 084 MW (1306) Tokovi trofaznih snaga po elementima mreže i iznosi linijskih napona na sabirnicama prikazani su na slijedećoj slici

Slika 6 Tokovi snaga u elektroenergetskoj mreži

- 2 -

Podaci vodova

Vod od Cv1 do Cv3 (Cv1-Cv3) lv1 = 50 km Rd = 018 Ωkm Xd = 04 Ωkm Gd = 00 μSkm Bd = 26 μSkm

Vod od Cv2 do Cv3 (Cv2-Cv3) lv2 = 30 km

Rd = 018 Ωkm Xd = 04 Ωkm Gd = 00 μSkm Bd = 26 μSkm

Regulacijska elektrana je u čvoru 2 (Cv2)

Fazni napon na sabirnicama regulacijske elektrane kV03

110V o2 =

Željeni iznos faznog napona na sabirnicama elektrane u Cv1 kV3

110

Za početne vrijednosti faznih napona u iterativnom procesu uzeti

Cvor 1 (Cv1) kV03

110V o)o(1 =

Cvor 3 (Cv3) kV013

107V o)o(3 minus=

Dozvoljeno odstupanje vrijednosti napona između dvije iteracije je

realna komponenta napona 3

U10 n4re sdot= minusε

imaginarna komponenta napona 3

U10 n4im sdot== minusε

gdje je Un ndash nazivna vrijednost linijskog napona Rješenje Analiza će se provesti u metodi jediničnih vrijednosti U skladu s tim odabrat će se

- 3 -



110003

110V oB ==


100SBf =


00010110

11000010

3110

3U10

V

n4

B

rere =

sdot=

sdot

==ε

minus


00010110

11000010

3110

3U10

V

n4

B

imim =

sdot=

sdot

==ε

minus



Ω==B

2B

Bf

2B

B SU

SVZ (11)

( )

Ω=sdot

sdot= 121

1010010110Z 6

23

B (12)


SZ1Y

BB = (13)

S00083121

1YB == (14)


- 4 -

B

1vdd31u Z

)XjR(Z

lsdot+=minus (15)

01653j + 00744121

50)40j180(Z 31u =sdot+

=minus (16)


31u31u Z

1

minusminus =y (17)

03125 - j2640216530 + j07440

131u ==minusy (18)


B

1vdd31p Y


01570 +j000830

50)1062j00( 2

31p =sdotsdot+

=minus

minusy (110)



Vod Cv2 ndash Cv3

- 5 -


B

2vdd32u Z

)XjR(Z

lsdot+=minus (111)

00992j + 00446121

30)40j180(Z 32u =sdot+

=minus (112)


32u32u Z

1

minusminus =y (113)

38538 - j7734309920 + j04460

132u ==minusy (114)


B

2vdd32p Y


00940 +j000830

30)1062j00( 2

32p =sdotsdot+

=minus

minusy (116)


- 6 -


B

1g1g S

P=P (117)

4010040

1g ==P (118)

B

1ming1ming S

Q=Q (119)

150100

151ming minus=

minus=Q (120)

B

1maxg1maxg S

Q=Q (121)

15010015

1maxg ==Q (122)

Cv2

B

2ming2ming S

P=P (123)

100100

1002ming ==P (124)

B

2maxg2maxg S

P=P (125)

5010050

2maxg ==P (126)

B

2ming2ming S

Q=Q (127)

200100

202ming minus=

minus=Q (128)

- 7 -

B

2maxg2maxg S

Q=Q (129)

20010020

2maxg ==Q (130)


B

1p1p S

P=P (131)

2010020

1p ==P (132)

B

1p1p S

Q=Q (133)

050100

51p ==Q (134)

Cv3

B

3p3p S

P=P (135)

5010050

3p ==P (136)

B

3p3p S

Q=Q (137)

2010020

3p ==Q (138)


- 8 -

B

)o(1)o(

1im)o(

1re)o(

1(o)

1(o)

1 VV


00j01001

3110

03

110o

o

(o)1 +=ang=

ang=V (140)

Cv2

B

22im2re22 V


00j010001

3110

003

110o

o

+=ang=ang

=2V (142)

Cv3

B

)o(3)o(

3im)o(

3re)o(

3(o)3

(o)3 V


01700 - j972600197270

3110

013

107o

o

(o)3 =minusang=

minusang=V (144)




- 9 -


⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡sdot

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

3

2

1

VVV

YYYYYYYYY

III

(146)

Odnosno





2im2re222 jV VVV

(150)

(151) δang = +=

3im3re333 jV VVV

(152) δang = +=

1111111111 jY BGY

+=Θang=

1212121212 jY BGY

(153)

(154) = Θang = +




- 10 -














- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 3 -



110003

110V oB ==


100SBf =


00010110

11000010

3110

3U10

V

n4

B

rere =

sdot=

sdot

==ε

minus


00010110

11000010

3110

3U10

V

n4

B

imim =

sdot=

sdot

==ε

minus



Ω==B

2B

Bf

2B

B SU

SVZ (11)

( )

Ω=sdot

sdot= 121

1010010110Z 6

23

B (12)


SZ1Y

BB = (13)

S00083121

1YB == (14)


- 4 -

B

1vdd31u Z

)XjR(Z

lsdot+=minus (15)

01653j + 00744121

50)40j180(Z 31u =sdot+

=minus (16)


31u31u Z

1

minusminus =y (17)

03125 - j2640216530 + j07440

131u ==minusy (18)


B

1vdd31p Y


01570 +j000830

50)1062j00( 2

31p =sdotsdot+

=minus

minusy (110)



Vod Cv2 ndash Cv3

- 5 -


B

2vdd32u Z

)XjR(Z

lsdot+=minus (111)

00992j + 00446121

30)40j180(Z 32u =sdot+

=minus (112)


32u32u Z

1

minusminus =y (113)

38538 - j7734309920 + j04460

132u ==minusy (114)


B

2vdd32p Y


00940 +j000830

30)1062j00( 2

32p =sdotsdot+

=minus

minusy (116)


- 6 -


B

1g1g S

P=P (117)

4010040

1g ==P (118)

B

1ming1ming S

Q=Q (119)

150100

151ming minus=

minus=Q (120)

B

1maxg1maxg S

Q=Q (121)

15010015

1maxg ==Q (122)

Cv2

B

2ming2ming S

P=P (123)

100100

1002ming ==P (124)

B

2maxg2maxg S

P=P (125)

5010050

2maxg ==P (126)

B

2ming2ming S

Q=Q (127)

200100

202ming minus=

minus=Q (128)

- 7 -

B

2maxg2maxg S

Q=Q (129)

20010020

2maxg ==Q (130)


B

1p1p S

P=P (131)

2010020

1p ==P (132)

B

1p1p S

Q=Q (133)

050100

51p ==Q (134)

Cv3

B

3p3p S

P=P (135)

5010050

3p ==P (136)

B

3p3p S

Q=Q (137)

2010020

3p ==Q (138)


- 8 -

B

)o(1)o(

1im)o(

1re)o(

1(o)

1(o)

1 VV


00j01001

3110

03

110o

o

(o)1 +=ang=

ang=V (140)

Cv2

B

22im2re22 V


00j010001

3110

003

110o

o

+=ang=ang

=2V (142)

Cv3

B

)o(3)o(

3im)o(

3re)o(

3(o)3

(o)3 V


01700 - j972600197270

3110

013

107o

o

(o)3 =minusang=

minusang=V (144)




- 9 -


⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡sdot

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

3

2

1

VVV

YYYYYYYYY

III

(146)

Odnosno





2im2re222 jV VVV

(150)

(151) δang = +=

3im3re333 jV VVV

(152) δang = +=

1111111111 jY BGY

+=Θang=

1212121212 jY BGY

(153)

(154) = Θang = +




- 10 -














- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 4 -

B

1vdd31u Z

)XjR(Z

lsdot+=minus (15)

01653j + 00744121

50)40j180(Z 31u =sdot+

=minus (16)


31u31u Z

1

minusminus =y (17)

03125 - j2640216530 + j07440

131u ==minusy (18)


B

1vdd31p Y


01570 +j000830

50)1062j00( 2

31p =sdotsdot+

=minus

minusy (110)



Vod Cv2 ndash Cv3

- 5 -


B

2vdd32u Z

)XjR(Z

lsdot+=minus (111)

00992j + 00446121

30)40j180(Z 32u =sdot+

=minus (112)


32u32u Z

1

minusminus =y (113)

38538 - j7734309920 + j04460

132u ==minusy (114)


B

2vdd32p Y


00940 +j000830

30)1062j00( 2

32p =sdotsdot+

=minus

minusy (116)


- 6 -


B

1g1g S

P=P (117)

4010040

1g ==P (118)

B

1ming1ming S

Q=Q (119)

150100

151ming minus=

minus=Q (120)

B

1maxg1maxg S

Q=Q (121)

15010015

1maxg ==Q (122)

Cv2

B

2ming2ming S

P=P (123)

100100

1002ming ==P (124)

B

2maxg2maxg S

P=P (125)

5010050

2maxg ==P (126)

B

2ming2ming S

Q=Q (127)

200100

202ming minus=

minus=Q (128)

- 7 -

B

2maxg2maxg S

Q=Q (129)

20010020

2maxg ==Q (130)


B

1p1p S

P=P (131)

2010020

1p ==P (132)

B

1p1p S

Q=Q (133)

050100

51p ==Q (134)

Cv3

B

3p3p S

P=P (135)

5010050

3p ==P (136)

B

3p3p S

Q=Q (137)

2010020

3p ==Q (138)


- 8 -

B

)o(1)o(

1im)o(

1re)o(

1(o)

1(o)

1 VV


00j01001

3110

03

110o

o

(o)1 +=ang=

ang=V (140)

Cv2

B

22im2re22 V


00j010001

3110

003

110o

o

+=ang=ang

=2V (142)

Cv3

B

)o(3)o(

3im)o(

3re)o(

3(o)3

(o)3 V


01700 - j972600197270

3110

013

107o

o

(o)3 =minusang=

minusang=V (144)




- 9 -


⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡sdot

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

3

2

1

VVV

YYYYYYYYY

III

(146)

Odnosno





2im2re222 jV VVV

(150)

(151) δang = +=

3im3re333 jV VVV

(152) δang = +=

1111111111 jY BGY

+=Θang=

1212121212 jY BGY

(153)

(154) = Θang = +




- 10 -














- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 5 -


B

2vdd32u Z

)XjR(Z

lsdot+=minus (111)

00992j + 00446121

30)40j180(Z 32u =sdot+

=minus (112)


32u32u Z

1

minusminus =y (113)

38538 - j7734309920 + j04460

132u ==minusy (114)


B

2vdd32p Y


00940 +j000830

30)1062j00( 2

32p =sdotsdot+

=minus

minusy (116)


- 6 -


B

1g1g S

P=P (117)

4010040

1g ==P (118)

B

1ming1ming S

Q=Q (119)

150100

151ming minus=

minus=Q (120)

B

1maxg1maxg S

Q=Q (121)

15010015

1maxg ==Q (122)

Cv2

B

2ming2ming S

P=P (123)

100100

1002ming ==P (124)

B

2maxg2maxg S

P=P (125)

5010050

2maxg ==P (126)

B

2ming2ming S

Q=Q (127)

200100

202ming minus=

minus=Q (128)

- 7 -

B

2maxg2maxg S

Q=Q (129)

20010020

2maxg ==Q (130)


B

1p1p S

P=P (131)

2010020

1p ==P (132)

B

1p1p S

Q=Q (133)

050100

51p ==Q (134)

Cv3

B

3p3p S

P=P (135)

5010050

3p ==P (136)

B

3p3p S

Q=Q (137)

2010020

3p ==Q (138)


- 8 -

B

)o(1)o(

1im)o(

1re)o(

1(o)

1(o)

1 VV


00j01001

3110

03

110o

o

(o)1 +=ang=

ang=V (140)

Cv2

B

22im2re22 V


00j010001

3110

003

110o

o

+=ang=ang

=2V (142)

Cv3

B

)o(3)o(

3im)o(

3re)o(

3(o)3

(o)3 V


01700 - j972600197270

3110

013

107o

o

(o)3 =minusang=

minusang=V (144)




- 9 -


⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡sdot

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

3

2

1

VVV

YYYYYYYYY

III

(146)

Odnosno





2im2re222 jV VVV

(150)

(151) δang = +=

3im3re333 jV VVV

(152) δang = +=

1111111111 jY BGY

+=Θang=

1212121212 jY BGY

(153)

(154) = Θang = +




- 10 -














- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 6 -


B

1g1g S

P=P (117)

4010040

1g ==P (118)

B

1ming1ming S

Q=Q (119)

150100

151ming minus=

minus=Q (120)

B

1maxg1maxg S

Q=Q (121)

15010015

1maxg ==Q (122)

Cv2

B

2ming2ming S

P=P (123)

100100

1002ming ==P (124)

B

2maxg2maxg S

P=P (125)

5010050

2maxg ==P (126)

B

2ming2ming S

Q=Q (127)

200100

202ming minus=

minus=Q (128)

- 7 -

B

2maxg2maxg S

Q=Q (129)

20010020

2maxg ==Q (130)


B

1p1p S

P=P (131)

2010020

1p ==P (132)

B

1p1p S

Q=Q (133)

050100

51p ==Q (134)

Cv3

B

3p3p S

P=P (135)

5010050

3p ==P (136)

B

3p3p S

Q=Q (137)

2010020

3p ==Q (138)


- 8 -

B

)o(1)o(

1im)o(

1re)o(

1(o)

1(o)

1 VV


00j01001

3110

03

110o

o

(o)1 +=ang=

ang=V (140)

Cv2

B

22im2re22 V


00j010001

3110

003

110o

o

+=ang=ang

=2V (142)

Cv3

B

)o(3)o(

3im)o(

3re)o(

3(o)3

(o)3 V


01700 - j972600197270

3110

013

107o

o

(o)3 =minusang=

minusang=V (144)




- 9 -


⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡sdot

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

3

2

1

VVV

YYYYYYYYY

III

(146)

Odnosno





2im2re222 jV VVV

(150)

(151) δang = +=

3im3re333 jV VVV

(152) δang = +=

1111111111 jY BGY

+=Θang=

1212121212 jY BGY

(153)

(154) = Θang = +




- 10 -














- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 7 -

B

2maxg2maxg S

Q=Q (129)

20010020

2maxg ==Q (130)


B

1p1p S

P=P (131)

2010020

1p ==P (132)

B

1p1p S

Q=Q (133)

050100

51p ==Q (134)

Cv3

B

3p3p S

P=P (135)

5010050

3p ==P (136)

B

3p3p S

Q=Q (137)

2010020

3p ==Q (138)


- 8 -

B

)o(1)o(

1im)o(

1re)o(

1(o)

1(o)

1 VV


00j01001

3110

03

110o

o

(o)1 +=ang=

ang=V (140)

Cv2

B

22im2re22 V


00j010001

3110

003

110o

o

+=ang=ang

=2V (142)

Cv3

B

)o(3)o(

3im)o(

3re)o(

3(o)3

(o)3 V


01700 - j972600197270

3110

013

107o

o

(o)3 =minusang=

minusang=V (144)




- 9 -


⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡sdot

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

3

2

1

VVV

YYYYYYYYY

III

(146)

Odnosno





2im2re222 jV VVV

(150)

(151) δang = +=

3im3re333 jV VVV

(152) δang = +=

1111111111 jY BGY

+=Θang=

1212121212 jY BGY

(153)

(154) = Θang = +




- 10 -














- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 8 -

B

)o(1)o(

1im)o(

1re)o(

1(o)

1(o)

1 VV


00j01001

3110

03

110o

o

(o)1 +=ang=

ang=V (140)

Cv2

B

22im2re22 V


00j010001

3110

003

110o

o

+=ang=ang

=2V (142)

Cv3

B

)o(3)o(

3im)o(

3re)o(

3(o)3

(o)3 V


01700 - j972600197270

3110

013

107o

o

(o)3 =minusang=

minusang=V (144)




- 9 -


⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡sdot

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

3

2

1

VVV

YYYYYYYYY

III

(146)

Odnosno





2im2re222 jV VVV

(150)

(151) δang = +=

3im3re333 jV VVV

(152) δang = +=

1111111111 jY BGY

+=Θang=

1212121212 jY BGY

(153)

(154) = Θang = +




- 10 -














- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 9 -


⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡sdot

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

3

2

1

VVV

YYYYYYYYY

III

(146)

Odnosno





2im2re222 jV VVV

(150)

(151) δang = +=

3im3re333 jV VVV

(152) δang = +=

1111111111 jY BGY

+=Θang=

1212121212 jY BGY

(153)

(154) = Θang = +




- 10 -














- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 10 -














- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 11 -


111 IVS sdot= (164)

Odnosno za čvora 2

222 IVS sdot= (165)

te za čvor 3

333 IVS sdot= (166)


1

1

1 VSI = (167)

2

2

2 VSI = (168)

3

3

3 VSI = (169)


1

111

jV

QPI minus= (170)

2

222

jV

QPI minus= (171)

1

333

jV

QPI minus= (172)


- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 12 -

3132121111

11 j VYVYVYV

QPsdot+sdot+sdot=

minus (173)

3232221212

22 j VYVYVYV

QPsdot+sdot+sdot=

minus (174)

3332321313

33 j VYVYVYV

QPsdot+sdot+sdot=

minus (175)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (176)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 323121

2

22

222

j1 VYVYV

QPY

V (177)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (178)


( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (179)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

minussdot

Θang=δang 332323112121

22

2g2g

222222 VYVY

)(Vj

Y1V

QP (180)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (181)

- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 13 -

ili

[ ( ) ( )

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(182)

[

])j()j(

)j()j(jj

BjG1j

3im3re2323

1im1re21212im2re

3p2g

22222im2re

VVBG

VVBGVVQP

VV

+sdot+minus


minussdot

+=+

(183)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(184)


⎟⎟⎠

⎞⎜⎜⎝


minussdot= 313212

1

11

111

j1 VYVYV

QPY

V (185)

⎟⎟⎠

⎞⎜⎜⎝


minussdot= 232131

3

33

333

j1 VYVYV

QPY

V (186)

Odnosno

- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 14 -

( ) ( )⎟⎟⎠

⎞⎜⎜⎝


δminusang

minusminusminussdot

Θang=δang 331313221212

11

1p1g1p1g

111111 VYVY

)(Vj

Y1V

QQPP (187)

⎟⎟⎠

⎞⎜⎜⎝


δminusang

+minussdot

Θang=δang 223232113131

33

3p3p

333333 VYVY

)(Vj

Y1V

QP (188)

ili

( ) ( )[

])j()j(

)j()j(jj

BjG1j

3im3re1313

2im2re12121im1re

1p1g1p1g

11111im1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(189)

[

])j()j(

)j()j(jj

BjG1j

2im2re3232

1im1re31313im3re

3p3p

33333im3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(190)


- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 15 -

1maxg1g1ming QQQ

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+++++++++

=

333332323131

232322222121

131312121111

jjjj jjjjj

BGBGBGBGBGBGBGBGBG

Y (191)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

++++++

=403913 -j0374638538 j 77343-03125 j 26402-38538j 77343- 38068 - j7734300j0003125 j 26402-00j0002335 - j26402

Y (192)


- Iterativni proces


(193) le le



Q 1ming1g Qlt (194)


1ming1g QQ = (195)



1g1maxg QQ lt (196)


1maxg1g QQ = (197)


- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 16 -


3132121111

1 VYVYVY

VS





1p


[ ]1p


[ ]1p(o)

313212(o)

111(o)

1)o(


[])050j20())01700 - j97260()02335j26402(

)00j01()00 - j00()00j01()02335 - j26402(()00j01(Im

(o)1g

++sdot+minus+

++sdot++sdotsdot+=Q

(1100)


(1101)


(1102)

(1103)

14180(o)

1g =Q (1104)



- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 17 -


o)o(1

(o)1

(o)1 001V ang=δang=V (1106)

Odnosno

00j01j )o(1im

)o(1re

(o)1 +=+= VVV (1107)


00j01j 2im2re2 +=+= VVV (1108)

01700 - j97260j )o(

3im)o(

3re(o)

3 =+= VVV (1109)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

o)(3im

(o)3re1313

2im2re1212o)(1im

(o)1re

1p(o)1g1p1g

1111

)1(1im

)1(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1110)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)1(1im

)1(1re3131(o)

3im(o)

3re

3p3p

3333

)1(3im

)1(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1111)


- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 18 -

[ ( ) ( )

])01700 - j97260()03125 j 26402-(

)00j01()00j00(00j01

05014180j204002335 - j26402

1j )1(1im

)1(1re

sdot+minus



(1112)

00870 + j00391j )1(1im

)1(1re =+ VV (1113)


o)1(

1)1(

1)1(

1 4953000391V ang=δang=V (1114)

Čvor 3 (Cv3)

[

])00j01()38538 j 77343-(

)00870 + j00391()03125 j 26402-(01700 j 9726020j50

403913 -j037461j )1(

3im)1(3re

+sdot+minus


sdot=+ VV

02280 - j97470j )1(3im

)1(3re =+ VV

(1115)

(1116)


o)1(

3)1(

3)1(

3 3374197500V ang=δang=V (1117)


re)o(


im)o(1im


- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 19 -

re)o(


im)o(3im




00010008700000000870 le=minus (1123)



00010005800170002280 le=+minus

o)1(1

)1(1

)1(1 4953001V ang=δang=V




1 49530=δ

(1126)

Odnosno

00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+= (1127)


[ ]1p)1(

313212)1(

111)1(

1)1(

1g)1(


- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 20 -

[])050j20())02280 - j97470()02335j26402(

)00j01()00 - j00()00860 + j00001()02335 - j26402(()00860 + j00001(Im

)1(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1129)

10010)1(

1g =Q (1130)



00860 + j00001j )1(1im

)1(1re

)1(1 VVV =+=

00j01j 2im2re2 +=+= VVV

02280 - j97470j )1(3im

)1(3re

)1(3 =+= VVV

(1132)

(1133)

(1134)



[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)1(3im

)1(3re1313

2im2re1212)1(1im

)1(1re

1p)1(

1g1p1g

1111

)2(1im

)2(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1135)

- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 21 -

[ ( ) ( )

])02280 - j97470()03125 j 26402-(

)00j01()00j00(00860 j 00001

05010010j204002335 - j26402

1j )2(1im

)2(1re

sdot+minus



(1136)

00620 + j99890j )2(

1im)2(

1re VV =+ (1137)

o)2(

1)2(

1)2(

1 3556099890V ang=δang=V (1138)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)2(1im

)2(1re3131)1(

3im)1(3re

3p3p

3333

)2(3im

)2(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1139)

[

])00j01()38538 j 77343-()00620 j 99890()03125j

26402-(02280 j 9747020j50

403913 -j037461j )2(

3im)2(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02350 j 97270j )2(3im

)2(3re minus=+ VV

o)2(3

)2(3


(1140)

(1141)

(1142)


re)1(1re


im)1(1im


re)1(3re


- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 22 -

im)1(3im




00010002400086000620 le=minus (1148)



00010000700228002350 le=+minus (1150)



1 35560=δ

o)2(

1)2(

1)2(


00620 + j00001j )2(1im

)2(1re

)2(1 VVV =+=

(1151)

Odnosno

(1152)


[ ]1p)2(

313212)2(

111)2(

1)2(

1g)2(


[])050j20())02350 - j97270()02335j26402(

)00j01()00 - j00()00620 + j00001()02335 - j26402(()00620 + j00001(Im

)2(1g

++sdot+minus+

++sdot+sdotsdot=Q

(1154)

11350)2(

1g =Q (1155)

- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 23 -


15011350150 leleminus (1156)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)2(3im

)2(3re1313

2im2re1212)2(1im

)2(1re

1p)2(

1g1p1g

1111

)3(1im

)3(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1157)

[ ( ) ( )

])02350 - j97270()03125 j 26402-(

)00j01()00j00(00620 j 00001

05011350j204002335 - j26402

1j )3(1im

)3(1re

sdot+minus



00620 + j99920j )3(1im

)3(1re VV =+

o)3(1

)3(1

)3(1 2553099920V ang=δang=V

(1158)

(1159)

(1160)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)3(1im

)3(1re3131)2(

3im)2(

3re

3p3p

3333

)3(3im

)3(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1161)

[

])00j01()38538 j 77343-()00620 j 99920()03125j

26402-(02350 j 9727020j50

403913 -j037461j )3(

3im)3(3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1162)

- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 24 -

02410 j 97280j )3(3im

)3(3re minus=+ VV (1163)

o)3(

3)3(

3)3(

3 4221197310V minusang=δang=V (1164)


re)2(

1re)3(


im)2(1im


re)2(

3re)3(


im)2(3im



(1169) 00010000800000199920 le=minus


(1170) 00010000000062000620 le=minus


(1171) 00010000109727097280 le=minus


(1172) 00010000600235002410 le=+minus



1 25530=

o)3(1

)3(1

)3(1 2553001V ang=δang=V (1173)

- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 25 -

Odnosno

00450 + j00001j )3(1im

)3(1re

)3(1 VVV =+= (1174)


[ ]1p)3(

313212)3(

111)3(

1)2(

1g)3(


[])050j20())02410 - j97280()02335j26402(

)00j01()00 - j00()00450 + j00001()02335 - j26402(()00450 + j00001(Im

)3(1g

++sdot+minus+

++sdot+sdotsdot=Q

15011530150

(1175)

(1176)

11530)3(

1g =Q (1177)


(1178) minus le le


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)3(3im

)3(3re1313

2im2re1212)3(1im

)3(1re

1p)3(

1g1p1g

1111

)4(1im

)4(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1179)

[ ( ) ( )

])02410 - j97280()03125 j 26402-(

)00j01()00j00(00450 j 00001

05011530j204002335 - j26402

1j )4(1im

)4(1re

sdot+minus



(1180)

- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 26 -

00360 + j99960j )4(

1im)4(

1re VV =+ (1181)

o)4(

1)4(

1)4(

1 2055099960V ang=δang=V (1182)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)4(1im

)4(1re3131)3(

3im)3(

3re

3p3p

3333

)4(3im

)4(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1183)

[

])00j01()38538 j 77343-()00360 j 99960()03125j

26402-(02410 j 9728020j50

403913 -j037461j )4(

3im)4(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02450 j 97290j )4(3im

)4(3re minus=+ VV

o)4(3

)4(3


(1184)

(1185)

(1186)


(1187) 00010000400000199960 le=minus



00010000109728097290 le=minus (1189)





- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 27 -


1 20550=δ

o)4(1

)4(1

)4(1 2055001V ang=δang=V (1191)

Odnosno

00360 + j00001j )4(1im

)4(1re

)4(1 VVV =+= (1192)


[ ]1p)3(

313212)4(

111)4(

1)4(

1g)4(


[])050j20())02450 j 97290()02335j26402(

)00j01()00 - j00()00360 + j00001()02335 - j26402(()00360 + j00001(Im

)4(1g

++minussdot+minus+

++sdot+sdotsdot=Q

11570)4(1g =Q

(1193)

(1194)

(1195)


15011570150 leleminus (1196)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)4(3im

)4(3re1313

2im2re1212)4(1im

)4(1re

1p)4(

1g1p1g

1111

)5(1im

)5(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1197)

- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 28 -

[ ( ) ( )

])02450 j 97290()03125 j 26402-(

)00j01()00j00(00360 j 00001

05011570j204002335 - j26402

1j )5(1im

)5(1re

minussdot+minus



(1198)

00320 + j99980j )5(

1im)5(

1re VV =+ (1199)

o)5(

1)5(

1)5(

1 1849099980V ang=δang=V (1200)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)5(1im

)5(1re3131)4(

3im)4(

3re

3p3p

3333

)5(3im

)5(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1201)

[

])00j01()38538 j 77343-()00320 j 99980()03125j

26402-(02450 j 9729020j50

403913 -j037461j )5(

3im)5(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

02460 j 97300j )5(3im

)5(3re minus=+ VV

o)5(3

)5(3


(1202)

(1203)

(1204)



00010000400036000320 le=minus (1206)



- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 29 -




1 18490=δ

o)5(1

)5(1

)5(1 1849001V ang=δang=V (1209)

Odnosno

00320 + j00001j )5(1im

)5(1re

)5(1 VVV =+= (1210)


[ ]1p)3(

313212)5(

111)5(

1)5(

1g)5(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00320 + j00001()02335 - j26402(()00320 + j00001(Im

)5(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1211)

(1212)

11580)5(

1g =Q (1213)


15011580150 leleminus (1214)


- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 30 -

[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)5(3im

)5(3re1313

2im2re1212)5(1im

)5(1re

1p)5(

1g1p1g

1111

)6(1im

)6(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1215)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00320 j 00001

05011580j204002335 - j26402

1j )6(1im

)6(1re

minussdot+minus



(1216)

00310 + j99990j )6(

1im)6(

1re VV =+ (1217)

o)6(

1)6(

1)6(

1 1771099990V ang=δang=V (1218)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)6(1im

)6(1re3131)5(

3im)5(

3re

3p3p

3333

)6(3im

)6(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1219)

[

])00j01()38538 j 77343-()00310 j 99990()03125j

26402-(02460 j 9730020j50

403913 -j037461j )6(

3im)6(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1220)

02460 j 97300j )6(

3im)6(


o)6(

3)6(

3)6(

3 4495197330V minusang=δang=V (1222)



- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 31 -


00010000009730097300 le=minus (1225)





1 17710=δ

o)6(1

)6(1

)6(1 1771001V ang=δang=V (1227)

Odnosno

00310 + j00001j )6(1im

)6(1re

)6(1 VVV =+= (1228)


[ ]1p)3(

313212)6(

111)6(

1)6(

1g)6(


[])050j20())02460 j 97300()02335j26402(

)00j01()00 - j00()00310 + j00001()02335 - j26402(()00310 + j00001(Im

)6(1g

++minussdot+minus+

++sdot+sdotsdot=Q

(1229)

(1230)

11580)6(

1g =Q (1231)


15011580150 leleminus (1232)

- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 32 -


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)6(3im

)6(3re1313

2im2re1212)6(1im

)6(1re

1p)6(

1g1p1g

1111

)7(1im

)7(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1233)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00310 j 00001

05011580j204002335 - j26402

1j )7(1im

)7(1re

minussdot+minus



0030 + j00001 j )7(1im

)7(1re =+ VV

o)7(1

)7(1

)7(1 1743000001V ang=δang=V

(1234)

(1235)

(1236)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)7(1im

)7(1re3131)6(

3im)6(

3re

3p3p

3333

)7(3im

)7(3re

VVBG

VVBGVV

QPVV

+sdot+minus


minus +sdot

+=+

(1237)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )7(

3im)7(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

(1238)

02460 j 97300j )7(

3im)7(


o)7(

3)7(

3)7(

3 4404197330V minusang=δang=V (1240)

- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 33 -



00010000100031000300 le=minus (1242)



00010000000246002460 le=+minus (1244)



11580)6(1g

)7(1g ==QQ (1245)


[ ( ) ( )

])j()j(

)j()j(j

jBjG

1j

)7(3im

)7(3re1313

2im2re1212)7(1im

)7(1re

1p)7(

1g1p1g

1111

)8(1im

)8(1re

VVBG

VVBGVV

QQPPVV

+sdot+minus


minusminusminussdot

+=+

(1246)

[ ( ) ( )

])02460 j 97300()03125 j 26402-(

)00j01()00j00(00300 j 00001

05011580j204002335 - j26402

1j )8(1im

)8(1re

minussdot+minus



(1247)

00300 + j00001 j )8(

1im)8(

1re =+ VV (1248)

- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 34 -

o)8(1

)7(1

)8(1 1733000001V ang=δang=V (1249)

Čvor 3 (Cv3)

[

])j()j(

)j()j(j

jBjG

1j

2im2re3232

)8(1im

)8(1re3131)7(

3im)7(

3re

3p3p

3333

)8(3im

)8(3re

VVBG

VVBGVV

QPVV

+sdot+minus


+minussdot

+=+

(1250)

[

])00j01()38538 j 77343-()00300 j 00001()03125j

26402-(02460 j 9730020j50

403913 -j037461j )8(

3im)8(

3re

+sdot+minus+sdot+

+minus++minus

sdot=+ VV

o)8(3

)8(3


(1251)

02460 j 97300j )8(

3im)8(


(1253)


(1254) 00010000000000100001 le=minus


(1255) 00010000000030000300 le=minus


(1256) 00010000009730097300 le=minus




Čvor 1 (Cv1)

00300 + j00001 jj )8(1im

)8(1re1im1re1 =+=+= VVVVV (1258)

Odnosno

- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 35 -

o)8(1

)8(1111 1733000001VV ang=δang=δang=V (1259)

Čvor 3 (Cv3)

02460 j 97300jj )8(3im


Odnosno o)8(

3)8(



Napon čvora Broj


(pu)

Kut

(o)

1 Cv1 10000 01733

2 Cv2 10000 00000

3 Cv3 09733 -14507



)02460j97300()38538j 77343(-)00j01()38068 - j77343()00300j00001()00j00(2


(1263)

12850j308402 minus=I (1264)


222 IVS sdot= (1265)

- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 36 -


2 )12850j30840()00j01( minussdot+=S (1266)

12850j308402 +=S (1267)


22g SS = (1268)


30840)(Re 2g2g == SP

12850)(Im 2g2g


(1271) = SQ =





- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 37 -

Odnosno





[ ]31u3131p

1131 )(2 minusminus


VVS (1276)


- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 38 -

[ ] 31

)03125j26402()02460j97300()00300j00001(2

01570j00)00300j00001()00300j00001(


++



[ ]31u1331p

3313 )(2 minusminus


VVS (1276)


[ ] 13

)03125j26402()00300j00001()02460j97300(2

01570j00)02460j97300()02460j97300(


++


07350j1966013

(1277)





)(Re 1v1v SP Δ=Δ (1281)


- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 39 -




[ ]32u3232p

2232 )(2 minusminus


VVS

(1283)


[ ] 32

)38538j77343()02460j97300()00000j00001(2

00940j00)00000j00001()00000j00001(


++



[ ]32u2332p

3323 )(2 minusminus


VVS (1286)

- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 40 -


[ ] 23

)38538j77343()00000j00001()02460j97300(2

00940j00)02460j97300()02460j97300(


++





)(Re 2v2v SP

=


(1291) Δ = Δ




sumsum==

minus=ΔN

1jjp

N

1jjgu PPP (1295)


sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -





sumsum==

minus=Δ3

1jjp

3

1jjgu PPP (1296)

Odnosno

00840)500000000020000()000003084040000(u =++minus++=ΔP (1297)


Vi = Vi VB i=1 2 3 (1298)




(kV)

Kut

(o)

1 Cv1 3110 01733

2 Cv2 3110 00000

3 Cv3 31107 -14507

- 41 -


Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -





Pgi = Pgi SB i=1 2 3 (1299)


Qgi = Qgi SB i=1 2 3 (1300)




(MW)

Reaktivna

(Mvar)

1 Cv1 4000 1158

2 Cv2 3084 1285

3 Cv3 000 000


Ppi = Ppi SB i=1 2 3 (1301)


Qpi = Qpi SB i=1 2 3 (1302)


- 42 -


Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -





Opterećenje Broj


(MW)

Reaktivno

(Mvar)

1 Cv1 2000 500

2 Cv2 000 000


Pj-k = Pj-k SB i=1 2 3 (1303)


Qj-k = Qj-k SB i=1 2 3 (1304)



(MW) Reaktivna

(Mvar)

Cv1 Cv3 2000 658 1

Cv3 Cv1 -1966 -735

Cv2 Cv3 3084 1285 2


- 43 -

- 44 -




- 44 -




Documents

ELEKTROENERGETSKE MREŽE - eihp.hrmmajstro/Elektroenergetske_mreze-Radni_materijal_1.pdf · - 1 - ELEKTROENERGETSKE MREŽE PRORAČUN NAPONA ČVOROVA I TOKOVA SNAGA . vježbe s pripadnim