18
Män hoüc: Váûn haình Hãû thäúng âiãûn Chæång 2 TÊNH TOAÏN PHÁN BÄÚ TÄÚI ÆU CÄNG SUÁÚT TRONG HÃÛ THÄÚNG ÂIÃÛN BÀÒNG PHÆÅNG PHAÏP LAGRANGE 2.1. MÅÍ ÂÁÖU Cáön phaíi xaïc âënh sæû phán bäú täúi æu cäng suáút giæîa caïc nhaì maïy âiãûn trong hãû thäúng âiãûn ( coï thãø chè coï caïc nhaì maïy nhiãût âiãûn , hoàûc coï caí nhæîng nhaì maïy thuíy âiãûn ) âuí âaïp æïng mäüt giaï trë phuû taè täøng cho træåïc (kãø caí caïc täøn tháút) nhàòm náng cao tênh váûn haình kinh tãú cuía hãû thäúng âiãûn . Âáy laì baìi toïan âa chè tiãu: - Chi phê nhiãn liãûu täøng trong toìan hãû thäúng laì nhoí nháút (min) - Âaím baío âäü tin cáûy håüp lyï - Cháút læåüng âiãûn nàng âaím baío... Giaíi quyãút baìi toïan âa chè tiãu nhæ váûy hiãûn nay chæa coï mäüt mä hçnh toïan hoüc chàût cheí, maì thæåìng chè giaíi quyãút caïc baìi toïan riãng biãût, sau âoï kãút håüp laûi. Vç váûy baìi toïan phán bäú täúi æu cäng suáút giæîa caïc nhaì maïy âiãûn thæåìng chè xeït âaût muûc tiãu quan troüng laì chi phê nhiãn liãûu täøng trong toìan hãû thäúng laì nhoí nháút. 2.2. BAÌI TOÏAN LAGRANGE: Baìi toïan âæåüc phaït biãøu nhæ sau: Cáön phaíi xaïc âënh caïc áøn säú x 1 , x 2 ,..., x i ,........ ,x n sao cho âaût cæûc trë haìm muûc tiãu : F(x 1 , x 2 ,..., x j ,........ ,x n )min (max) (2-1) vaì thoía maín m âiãöu kiãûn raìng buäüc: (m<n) g 1 (x 1 , x 2 ,..., x j ,........ ,x n ) 0 g 2 (x 1 , x 2 ,..., x j ,........ ,x n ) 0 (2-2) ........................................ g m (x 1 , x 2 ,..., x j ,........ ,x n ) 0 Trong træåìng håüp haìm muûc tiãu (2-1) laì giaíi têch, khaí vi, hãû raìng buäüc (2-2) gäöm toìan âàóng thæïc vaì säú nghiãûm khäng låïn ta coï thãø duìng phæång phaïp thãú træûc tiãúp âãø giaíi bçnh thæåìng. Khi caïc hãû (2-1) vaì (2-2) tuyãún tênh vaì x i 0 ta coï thãø duìng thuáût toïan qui hoüach tuyãn tênh âãø giaíi nhæ phæång phaïp hçnh hoüc, âån hçnh, váûn taíi.... Vê duû : Tçm cac ï giaï trë x1, x2 sao cho : min ) , ( 2 2 2 1 2 1 + = x x x x F thoía maîn : 1 3 2 2 1 = + x x Nhoïm Nhaì maïy âiãûn - Bäü män Hãû thäúng âiãûn - ÂHBK Âaì Nàông . 14

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  • Mn hoc: Vn hanh H thng in

    Chng 2

    TNH TOAN PHN B TI U CNG SUT TRONG H THNG IN BNG PHNG PHAP LAGRANGE

    2.1. M U Cn phai xac nh s phn b ti u cng sut gia cac nha may in trong h thng in ( co th ch co cac nha may nhit in , hoc co ca nhng nha may thuy in ) u ap ng mt gia tr phu ta tng cho trc (k ca cac tn tht) nhm nng cao tnh vn hanh kinh t cua h thng in . y la bai toan a ch tiu: - Chi ph nhin liu tng trong toan h thng la nho nht (min) - am bao tin cy hp ly - Cht lng in nng am bao... Giai quyt bai toan a ch tiu nh vy hin nay cha co mt m hnh toan hoc cht che, ma thng ch giai quyt cac bai toan ring bit, sau o kt hp lai. V vy bai toan phn b ti u cng sut gia cac nha may in thng ch xet at muc tiu quan trong la chi ph nhin liu tng trong toan h thng la nho nht. 2.2. BAI TOAN LAGRANGE: Bai toan c phat biu nh sau: Cn phai xac nh cac n s x1, x2,..., xi,........ ,xn sao cho at cc tr ham muc tiu :

    F(x1, x2,..., xj,........ ,xn) min (max) (2-1)

    va thoa man m iu kin rang buc: (m

  • Mn hoc: Vn hanh H thng in

    Bai giai :

    T 132

    21 =+xx suy ra

    236 1

    2xx =

    Thay vao ham muc tiu F :

    min236

    ),(2

    121

    22

    2121

    +=+=

    xxxxxxF

    iu kin cc tr :

    01

    =xF

    hoc la : 0)2(4

    182 111

    == xxxF

    giai ra c : x1 = 18/13 va x2 = 12/13 Xet ao ham cp 2 :

    04

    264

    18221

    2

    >=+=xF

    nn ham F at cc tr tai : 1318*

    1 =x va 1312*

    2 =x

    va khi o gia tr ham muc tiu la :

    1336* =optF

    Phng phap thay th trc tip trn y ch tin li khi h phng trnh rang buc la tuyn tnh va s lng m khng ln lm. Trong trng hp chung giai bai toan xac nh cc tr co rang buc la ng thc va tuyn tnh thng s dung rng rai phng phap nhn t Lagrange . Ni dung chu yu cua phng phap Lagrange nh sau: Cn phai xac nh cac n s x1, x2,..., xj,........ ,xn sao cho: F(x1, x2,..., xj,........ ,xn) min (max) (2-3) va thoa man

    g1(x1, x2,..., xj,........ ,xn) = 0 g2(x1, x2,..., xj,........ ,xn) = 0

    ........................................ (2-4) gm(x1, x2,..., xj,........ ,xn) = 0

    trong o m

  • Mn hoc: Vn hanh H thng in

    Nghim ti u X*opt cua ham muc tiu F cung chnh la nghim ti u cua ham Lagrange L(X) va ngc lai v gi(x1, x2,..., xi,........ ,xn) = 0 vi moi i=1..m. V vy ta cn tm li giai ti u cho ham L(x1, x2,..., xi,........ ,xn) Bai toan Larange phat biu nh sau: Hay xac nh (x1, x2,..., xi,........ ,xn) va (1, 2,.........., m ) sao cho :

    0)()()(1

    =+= =

    m

    i j

    ii

    jj xXg

    xXF

    xXL

    (2-6)

    vi j=1..n va thoa man cac ieu kin rang buc : vi 0),.....,,( 21 =ni xxxg mi ,1= (2-7)

    T (2-6) ta co n phng trnh va t (2-7) co m phng trnh nn se giai c (n+m) n s xj va i xac nh ham L(X) at cc tiu hay cc ai ta cn phai xet thm ao ham cp hai cua F(X) hay L(X) tai cac im dng a giai ra c trn: Nu d2L< 0 th ham F(X) ( hoc L(X) ) at cc ai va ngc lai nu d2L > 0 th ham muc tiu se at cc tiu. Ta se giai lai bai toan v du 1 theo phng phap Lagrange : Tm cac nghim s x1 , x2 sao cho : min),( 22

    2121 += xxxxF

    vi rang buc 132

    21 =+xx

    Thanh lp ham Lagrange :

    =

    =

    +=1

    1212121 ),(.),(),(

    m

    iii xxgxxFxxL

    )132

    (),( 21122

    2121 +++=

    xxxxxxL

    Xac nh cac im dng bng cach giai cac phng trnh :

    02

    2)( 111

    =+=

    x

    xXL

    03

    2)( 122

    =+=

    x

    xXL

    0132

    21 =+xx

    Giai h 3 phng trnh trn c :

    1318*

    1 =x va 1312*

    2 =x

    va khi o gia tr ham muc tiu la :

    1336* =optF

    ( nh kt qua a nhn c bng phng phap th )

    Nhom Nha may in - B mn H thng in - HBK a Nng . 16

  • Mn hoc: Vn hanh H thng in

    Xet cac ao ham bc hai tai im dng:

    02)(21

    2

    >=x

    XL

    02)(22

    2

    >=x

    XL

    nn ham L(X) va ham muc tiu F(X) at cc tiu tai im X* (18/13 ; 12/13). Trong trng hp ham muc tiu F(X) va cac rang buc g(X) la nhng phim ham ( tn tai tng quan gia nhng ham ) khi o tm cc tr cua cac phim ham phai s dung cac bai toan bin phn. V du nh trng hp tnh phn b ti u cng sut i vi cac nha may thuy in v khi o phai xet ti u trong ca chu ky iu tit. Bai toan c phat biu nh sau : Cn phai xac nh cac ham s x1, x2,..., xi,........ ,xn cua thi gian t sao cho ham muc tiu la phim ham at cc tr: (2-8) min(max).)',....,',',,....,,,(1

    02121 = dtxxxxxxtFV

    t

    t nn

    va thoa man m iu kin rang buc : g1(t,x1, x2,..., xj,........ ,xn) = 0 g2(t,x1, x2,..., xj,........ ,xn) = 0

    ............................................. (2-9) gm(t,x1, x2,..., xj,........ ,xn) = 0

    Trong o : dtdx

    x jj =' vi nj ,1= (2-10)

    Thanh lp ham Lagrange :

    (2-11) =

    +=m

    iii xtgtxtFxtL

    1

    )],().([),(),(

    sau o tm cc tr cua phim ham:

    (2-12) min(max).),(1

    0

    ** = dtxtFVt

    t

    vi (2-13) =

    +=m

    iii xtgtxtFxtF

    1

    * )],().(),(),(

    Cac gia tr xj(t) vi j = [1..n] va cac h s nhn i(t) vi i = [1..m] co th nhn c bng cach giai h phng trnh ao ham ring cua ham Lagrange va vit trong dang h phng trnh Euler nh sau :

    Nhom Nha may in - B mn H thng in - HBK a Nng . 17

  • Mn hoc: Vn hanh H thng in

    =

    =

    =

    0)'()(

    ......................................

    0)'()(

    0)'()(

    **

    2*

    2*

    1*

    1*

    nn xfdtdxf

    xfdtdxf

    xfdtdxf

    (2-14)

    Trong o :

    nj

    xFxf

    njxFxf

    jj

    jj

    ,1 ; '

    )'(

    ,1 ; )(

    **

    **

    ==

    ==

    (2-15)

    Kt hp n phng trnh cua h (2-14) va m phng trnh rang buc (2-9) ta se giai c (m+n) gia tr ham xj(t) va i(t) vi j = [1..n], i = [1..m]. Ngoai ra xac nh 2n hng s tch phn ta se s dung cac iu kin u :

    njxtxxtx jjjj ,1 )( ; )( 1100 === (2-16)

    2.3.- PHN B TI U CNG SUT GIA CAC NHA MAY NHIT IN: Xet bai toan : Co n nha may nhit in cung cp cho phu tai tng Ppt c nh. Bit nhng s liu v c tnh tiu hao nhin liu tng nha may. Cn phai xac nh cng sut phat ti u cua mi nha may Pj vi j = [1...n], sao cho chi ph nhin liu tng trong h thng at cc tiu, vi rang buc v iu kin cn bng cng sut. M ta dang toan hoc: Cn xac inh b nghim ti u P*(P*1,P*2,......,P*n) sao cho ham muc tiu v chi ph nhin liu tng at cc tiu :

    (2-17) min)(),...,,....,,(1

    21 == =

    n

    jjjnj PBPPPPfB

    thoa man iu kin rang buc v cn bng cng sut :

    (2-18) 0.......)(1

    21 ==+++++= =

    pt

    n

    jjptnj PPPPPPPPPPg

    vi const= P const;=P ; n1,=j 0 ptjP (2-19)

    Ta giai bng phong phap Lagrange : Thanh lp ham Lagrange : )()()( PgPBPL += (2-20)

    Nhom Nha may in - B mn H thng in - HBK a Nng . 18

  • Mn hoc: Vn hanh H thng in

    iu kin ham s L(P) at cc tr :

    =+=

    =+=

    =+=

    0)()()(.............................................

    0)()()(

    0)()()(

    222

    111

    nnn PPg

    PPB

    PPL

    PPg

    PPB

    PPL

    PPg

    PPB

    PPL

    (2-21)

    Gia thit : )(.........)()()( 21 PBPBPBPB n+++= (2-22) Khi o :

    jj

    j

    j

    n

    j

    j

    jjj PB

    PB

    PB

    PB

    PB

    PPB

    ==+++++= .............)( 21 (2-23)

    vi gia thit j k ; 0 =j

    k

    PB

    ngha la chi ph nhin liu nha may th k khng phu

    thuc vao cng sut phat ra cua nha may th j .

    Ta t jj

    j

    PB

    = va goi la sut tng tiu hao nhin liu cua nha may th j, noi ln

    nhp tng tiu hao nhin liu khi tng cng sut phat Pj , j phu thuc vao c tnh cua lo hi va turbin. T iu kin rang buc :

    (2-24) 0.......)(1

    21 ==+++++= =

    pt

    n

    jjptnj PPPPPPPPPPg

    ta tnh c :

    1)(

    .............)(

    1

    1

    111

    2

    1

    1

    1

    ==+

    +++=PP

    PPP

    PP

    PP

    PP

    PPg ptn

    (2-25)

    Tng quat :

    1)(

    .............)( 21 ==+

    +++++=j

    j

    j

    pt

    j

    n

    j

    j

    jjj PP

    PPP

    PP

    PP

    PP

    PP

    PPg

    (2-26)

    Thay vao iu kin cc tr (2-21 ) ta co h phng trnh :

    Nhom Nha may in - B mn H thng in - HBK a Nng . 19

  • Mn hoc: Vn hanh H thng in

    =+=+=

    =+=+=

    =+=+=

    0)()()(...........................................................

    0)()()(

    0)()()(

    2222

    1111

    nnnn PPg

    PPB

    PPL

    PPg

    PPB

    PPL

    PPg

    PPB

    PPL

    (2-27)

    Do o iu kin cc tr la:

    0...............21 =+==+==+=+ nn (2-28) hay : )( ...............21 ====== nn (2-29)

    y chnh la nguyn ly phn b ti u cng sut gia cac nha may nhit in trong HT. Khi xem Ppt = const , P = const th chi ph nhin liu tng trong h thng nho nht th cac nha may phai phat cng sut Pj* ti u khi thoa man nguyn ly cn bng sut tng tiu hao nhin liu j = const. Vi c tnh sut tng tiu hao nhin liu j cua cac t may phat la ham khng giam khi tng cng sut phat Pj (thc t nh vy) ta co th chng minh ham muc tiu B(P) at cc tiu bng cach xet thm cac ao ham cp hai va co c:

    0)(dhay 0)( 222

    PLP

    PL

    j (2-30)

    Nu xet tn tht cng sut phu thuc vao cng sut phat Pj ngha la: P = P(P1,P2,.....,Pn)

    iu kin cc tiu cua ham Lagrange co th vit :

    =

    +=+=

    =

    +=+=

    =

    +=+=

    0)1()()()(.........................................................................

    0)1()()()(

    0)1()()()(

    22

    222

    11

    111

    nn

    nnn PP

    PPg

    PPB

    PPL

    PP

    PPg

    PPB

    PPL

    PP

    PPg

    PPB

    PPL

    (2-31)

    Nhom Nha may in - B mn H thng in - HBK a Nng . 20

  • Mn hoc: Vn hanh H thng in

    Khi o, nguyn ly phn b cng sut ti u la :

    n

    n

    PP

    PP

    PP

    ==

    =

    1

    ..............11

    2

    2

    1

    1 (2-32)

    i

    i

    PP

    1 goi la sut tng tiu hao NL khi co xet n tn tht P

    Qua o cho thy khi P = const th cho ta kt qua iu kin phn b ti u cng sut nh a trnh bay trn. T nguyn ly cn bng sut tng tiu hao nhin liu nay, ta co th tm ra c nghim ti u P* = (P*1,P*2,.......,P*n). 4.4. THU TUC PHN PHI TI U CNG SUT : Vic phn phi ti u cng sut gia cac nha may nhit in c tun theo nguyn ly cn bng v sut tng tiu hao nhin liu . Sut tng th hin nhp tiu tn nhin liu khi tng cng sut P phat ra. V vy theo nguyn ly phn phi trn y at cc tiu nhin liu tiu hao trong toan h thng, nha may co nho se nhn phat nhiu cng sut va nha may co ln (ngha la lam vic khng kinh t) se phai phat t cng sut. Nguyn ly nay th hin tnh cng bng trong phn phi ti u. Cn quan tm nhng c im sau: 4.4.1. Sut tng tiu hao nhin liu va sut tiu hao nhin liu :

    Cn phai phn bit ro sut tng tiu hao nhin liu va sut tiu hao nhin liu .

    ng vi mi nha may nhit in co th xy dng c ng c tnh tiu hao nhin liu B phu thuc cng sut phat ra P nh hnh 2-1. Gia s t may phat ang lam vic im a :

    BP

    tgaa

    a= = (2-33)

    a: goi la sut tiu hao nhin liu cua nha may ng vi im a [kg n.lieu/KWh ]

    ]n.lieu/KWh [kg tgdPdB

    aa == (2-34)

    a: goi la sut tng tiu hao nhin liu.

    Nhom Nha may in - B mn H thng in - HBK a Nng . 21

  • Mn hoc: Vn hanh H thng in

    Hnh 2-1 T O ve tip tuyn Ob, im b goi la im lam vic kinh t , tai im lam vic nay cng sut phat la Pkt ng vi chi ph nhin liu la Bkt . Khi P > Pkt th theo c tnh ta thy sut tng tiu hao nhin liu tng nhanh, cang tiu hao nhin liu. V vy theo quan im kinh t tit kim nhin liu ch vn hanh vi P

  • Mn hoc: Vn hanh H thng in

    dPdQ

    L = - goi la sut tng tiu hao nhin liu cua tucbin [Kcalo/KWh]

    ng c tnh sut tng tiu hao nhin liu cua lo hi L thng co dang ng cong (hnh 2-3a) tuy thuc cac loai lo hi khac nhau.

    Hnh 2-3

    ng c tnh tiu hao nhit lng Q cua turbin trong nhiu trng hp co dang

    o nhit lng cua turbin T la gia tr ao ham cua

    ng phap gia cng toan hoc, chng han phng phap bnh phng cc tiu xy dng c quan h giai tch B = B(P). T o xac nh c c tnh s

    t trng hp tn tht cng sut la hng s, khng phu thuc vao cng sut phat

    i mi nha may ta xy dng c quan h sut tng tiu hao nhin liu phu

    ng cong j ta xy dng c ng cong (P) cua toan h ng g

    ,12 Ppt ), nh cach lam m ta trn hnh ve ta xac

    gn tuyn tnh (hnh 2-3b). ng c tnh co ch gay khuc ng vi gia tr Pkt, iu o giai thch khi van qua tai m, nhit lng tng nhanh va tnh kinh t giam t ngt. ng c tnh sut tng tiu hang Q theo P. T cac ng T va L xy dng c ng c tnh sut tng tiu hao nhin liu cua t may nh hnh 2-3c. Ngoai ra xy dng c tnh sut tng tiu hao nhin liu cua t may hoc nha may in co th thc hin bng cach thng k cac tp s liu B va P trong cac ch vn hanh khac nhau va nh cac ph

    ut tng tiu hao nhin liu. 4.4.3.Thu tuc phn phi ti u cng sut : Xecua cac nha may. Gia s ta cn phai phn phi cng sut Ppt cho n nha may, ta tin hanh nh sau: - Vthuc vao cng sut phat j = j(Pj) vi j = [1..n] bng dang giai tch hoc bng s cho theo bang . - Da trn cac th m n nha may, bng cach gi nguyn tr s trn truc tung, cng n gia tr cng sut P trn truc hoanh. - Cn c vao phu tai tng cng Ppt cn cung cp k ca tn tht cng sut P (trong tnh toan s b co th ly bng 0,07 - 0

    Nhom Nha may in - B mn H thng in - HBK a Nng . 23

  • Mn hoc: Vn hanh H thng in

    nh c cac g yia tr ti u cng sut phat ra t cac nha ma in Pj* thoa man iu kin cn bng sut tng tiu hao nhin liu: 1 2= = = = = = ....... ........ ( )n n

    tuc phn phi nh trn cn phai chu y: 1. Khi gia nhin liu nha may th i nao o khac gia nhin liu tiu chun th cn hiu chnh i thanh i theo :

    va thoa man iu kin cn bng cng sut. ptNJ PPPPPP +=+++++

    ***2

    *1 .......

    Ta nhn thy nha may nao co sut tng tiu hao nhin liu cang nho th nhn cang nhiu cng sut. Khi tin hanh thu

    0

    .'aai

    ii =

    Trong o : ai la gia nhin liu cua nha may th i va a0 la gia nhin liu tiu chun, t o ta thy rng nha may nao co gia nhin liu cang t th ch nn phat t cng sut. 2. Co th xay ra trng hp tm ra nho hn ng vi cng sut cc tiu Pmin

    y phn phi ti u ta se nha may co nho nhn thm cng sut trc, nhng ui cung cung phai am bao i bng nhau vi moi nha may th i va phai ap ng y u

    g sut trong h thng gm cac nha may thuy

    t la thi gian gia 2 ln thao nc va tr nc k tip nhau. Tuy

    y li, thi tit v.v.... V vy ch lam

    hoc ln hn ng vi cng sut cc ai cho phep Pmax th khi o ch cho nha may nhn cng sut Pmin hoc Pmax v o la gi han kha nng phat cng sut cua nha may. 3. Thng trong thc t vn hanh ngi ta ch cho bang sut tng tiu hao nhin liu va Pi thay cho ng c tnh d phn b hn. Khi phu tai tng ln th theo nguyn lcphu tai. 4.5. PHN B CNG SUT TI U GIA NHIT IN VA THUY IN: Trong vn hanh khng phai nha may thuy in lun lun phat ht cng sut la ti u mc du no co nhiu u im la gia thanh in nng re, khng tiu hao nhin liu... Ch tiu ti u cua s phn b cnin va nhit in la lam cc tiu chi ph nhin liu nhit in, ng thi phai thoa man iu kin thuy nng nha may thuy in. Ch ti u ch xet i vi nhng thuy in co h cha nc, ngha la co kha nng iu chnh dong chay vao tuc bin ( goi la kha nng iu tit ) Chu ky iu titheo dung tch h cha thng phn nha may thuy in iu tit theo ngay, tun, mua, nm hoc nhiu nm. Trong mt chu ky iu tit lng nc tiu ph cho nha may thuy in la khng i va c xac nh bi nhng iu kin v thuvic ti u cua thuy in phai xet trong toan b chu ky iu tit va iu kin rang buc y chnh la lng nc tiu hao a qui nh.

    Nhom Nha may in - B mn H thng in - HBK a Nng . 24

  • Mn hoc: Vn hanh H thng in

    Ngoai ra co nhng thi gian nha may thuy in buc phai lam vic theo ch gii han va vn phn b cng sut ti u khng cn t ra. Chng han i vi thuy in ch phat in khng co yu cu v giao thng, thuy li... thi im phu tai cao

    nh ( cn phai tit kim nc mua nc can ), hoc thuy

    p :

    a may nhit in ng tr theo iu kin cn bng sut tng tiu hao nhin liu .

    (2-35) V xet trong chu ky iu tit nn ta phai xet B con phu thuc vao t va xet ca s

    im phai am nhn phu tain khng co h cha, h cha nho phai tn dung ht thuy nng nn phai phat ht cng sut ngha la nhn phn phu tai nn (xem giao trnh Nha May in ). Ta xet trng h Co n nha may thuy in lam vic trong h thng cung vi mt s nha may nhit in ma ta xem nh mt nh

    Goi B la lng tiu hao nhin liu nha may nhit in ng tr trong mt n v thi gian. ( n v la tn/h )

    ),,( ,NDND PPtBB =

    thay i cua PN theo thi gian t :

    dtdP

    P NDND =,

    Goi Qi la lu lng nc tiu hao trong mt n v thi gian nha m3

    ay thuy in th i [ m /s ].

    n1,=i voi),,( ,TDiTDiii Lng nc qui nh i vi thuy in th

    PPtQQ = (2-36) u ti

    Khi o bai toan c phat biu nh sau : c nha may in liu:

    (2-37)

    thoa man cac rang buc v lng nc tiu hao i vi cac nha may thuy in:

    ,222 WdtPPtQ

    T

    TT = (2-38)

    i trong chu ky i t T:

    =T

    ii dtQW 0 .

    Xac nh cng sut phat cua nha may nhit in ng tr PN va cua cathuy in PT1, PT2,.........., PTn sao cho at cc tiu ham muc tiu v chi ph nh

    min).,,( ,0

    dtPPtB NT

    N

    .),,( 10,

    111 WdtPPtQT

    TT = .),,( 20

    .....................................

    .),,(0

    ,n

    T

    TnTnn WdtPPtQ = va thoa man rang buc v iu kin cn bng cng sut:

    0.....),( 21 =++++= PPptPPPPPtg TDnTDTDND (2-39)

    Nhom Nha may in - B mn H thng in - HBK a Nng . 25

  • Mn hoc: Vn hanh H thng in

    Ta giai bai toan ti u nay theo phng phap Lagrange nh a trnh bay muc t ta lp phim ham Lagrange:

    +++TT

    PtgdtPtQdtPtQ ),().,(........).,(

    1, 2,......, n : la nhng h s khng xac nh a vao cac phng trnh rang buc theo iu kin lu lng nc.

    s khng xac nh a vao phng trnh rang buc cn bng cng sut. T y tm cc tiu cua phim ham L(t,P) :

    01

    ++= =

    T

    i

    n

    ii PtQPtB

    ii

    =

    th

    tm nghim cua bai toan ta lp h phng trnh Euler di dang:

    2.2. Trc h

    +=T

    dtPtBPtL ).,(),( tnn 00 110 Trong o:

    t : h

    min)].,(,( t dtPtgPtL ),(),([)

    t ),(),(),(),(* PtgPtQPtBPtFn

    ++= ti1

    min).,(*),(0

    = (2-40)

    TdtPtFPtL

    0'** = PiPi fdf dt

    (2-41)

    o : Pi la cng sut cu ay nhit in n ,

    i N T1 T2 Tn

    Trong a nha m g tr PN va cac nha may thuy in PT1PT2,...,PTn. P la cac ao ham P ,P , P ,........,P

    i

    PiP

    PtFf

    ),(** = va i

    PiP

    PtFf'

    ),(*'

    *

    = (2-42)

    c h phng trnh Euler dang : Ta

    ..............................

    1TD

    =

    +

    =

    +

    =

    +

    0)1('

    (

    ......................................

    0)1('

    (

    0)1('

    11

    111

    tnn

    n

    TDt

    TD

    NDt

    NDND

    PP

    PQ

    dtd

    PQ

    PP

    PQ

    dtd

    PQ

    PP

    PB

    dtd

    PB

    (4-43)

    vi gia

    TDnTDnTDn

    thit : Ppt = hng s

    Nhom Nha may in - B mn H thng in - HBK a Nng . 26

  • Mn hoc: Vn hanh H thng in

    Ta k hiu :

    =NDPB - sut tn

    trong ch c lp.

    goi la g tiu hao nhin liu nha may nhit in

    xa

    11 qQ = , 2

    2

    2 qPQ

    TD

    = ,....... t tng tiu hao nc nha may thuy in

    1,2,.... trong ch xac lp. - la su

    1PTD

    Nhn thy cac thanh phn :

    '. '

    =

    Bd va iTD

    qQid '. =Pdt '

    NDPdtxut hin trong qua trnh bin i ch lam vic cua h i itc bin i theo thi gian cua cng sut nha may in.

    h phng trnh (4-43) kh t ta co :

    thng va , q phu thuc vao

    Thng ta gia thit i = 0, qi = 0 ; khi o t

    TDnTDND QP

    QP

    PP

    1111

    1

    1

    Nu xem tn th

    nq (4-44) q === ...........1

    t cng sut khng i th: nn qqq ............ 2211 ==== (4-45)

    y la nguyn ly cng bng cua vic phn b ti u cng sut gia cac nha may in theo sut tng tiu hao nhin liu, trong o i vi thuy in i co ai din la sut tng ng tr la i.qi. Nhng ga tr cua i la nhng hng s ng vi nha may thuy in i va c chon

    n ti u cua bai toan a nu. Sau y ta se x s va xy dng thu tuc phn phi cng sut ti u gia

    4.6. C IM VA THU TUC PHN PH4.6.1. Y ngha cua h s

    trong chu ky iu tit nhm thoa man iu kiet thm y ngha cua cac h i

    nhit in va thuy in.

    :

    Trong trng hp n gian khi khng xet n s thay i cua cng sut trong mang in, t biu thc (4-45) ta co :

    tdindi dPdQi

    dPdB

    qi :== (4-46)

    Gia thit rng s thay i cng sut phat r i cng sut phat ra nha may nhit in, chng han khi nhit in phat cng sut giam i th t

    a nha may thuy in th i la do thay

    huy in i phai phat cng sut tng ln. Mt cach gn ung v gia tr tuyt i ta xem nh : dPt = dPn. Nh vy tng quat ta co th vit :

    Nhom Nha may in - B mn H thng in - HBK a Nng . 27

  • Mn hoc: Vn hanh H thng in

    1,2...n=i voidQidBi = (4-47)

    Nh vy i c nh ngha la s bin i cua tiu hao nhin liu nha may

    i thuy in lam vic vi ln th nhin liu tit kim c nhit

    t cua thuy in i tng ln, thng gia tr cua sut tng tiu hao nc qi cua no se tng, khi o do

    c i cn phai

    va lai dn n gia tr khng i ban u.

    c (4-45).

    n liu, xy dng ng c tnh cho nha may nhit in ng tr (hnh 2-4).

    t la moi gia tr i la nhng hng s a cho, xy dng cac ng c tnh iqi cho cac nha may thuy in i=1,2,...,n (hnh 2-

    4 tn

    nhit in theo s thay i cua lu lng nc nha may thuy in i. Th nguyn cu i la [ tn nhin liu/m3 nc ] va chnh i la ch tiu phan anh hiu qua s dung nc nha may thuy in i. Khin trn 1m3 nc cang nhiu, do o goi la h s hiu qua s dung nng lng cua thuy in. Ngoai ra cn chu y rng co ch lam vic ti u ga tr i cua mi nha may thuy in sau khi xac nh cn gi khng i trong sut chu ky iu tit. iu o c giai thch nh sau : Gia thit thi im nao o ga tr i c chon tng ln. Khi o tit kim nhin liu nhit in cn tng cng sut phat thuy in i. Nhng v lng nc trong chu ky iu tit a xac nh nn khi tng cng sut thuy in se tng lng nc tiu hao va bt buc phai giam cng sut thi im khac. Mt khac, cng sut phang sut phat cua nhit in gam i nn gia tr cua giam, v vy = /q la

    chon giam i. Tom lai, khi tng i ta cn phai tng Pti, nhng khi Pti tng ( Pn gam ) se lam giam i va khi i giam tit kim nhin liu ta lai cn phai giam Ptitng i. Qua trnh tip tuc cho n khi i tr v 4.6.2. Thu tuc phn phi ti u cng sut gia nhit in va thuy in: Vic phn phi ti u cng sut gia nha may nhit in va thuy in trong HT da trn nguyn ly cn bng sut tng tiu hao nh trn biu th Thu tuc phn phi tin hanh nh sau: - i vi cac nha may nhit in cn c vao nguyn ly cn bng sut tng tiu hao nhi - i vi tng nha may thuy in, cn c vao lng tiu hao nc Qi va cng sut phat Pti ta xy dng ng c tnh sut tng tiu hao nc qi. - Trc ht khao sat trng hp n gian nh

    ).

    - T gia tr ph ng cua h th pt k ca tn tht trong mang trn th sut

    ng tiu hao nhin liu tng HT (hnh 2-4 ) ta xac nh cac gia tr ti u v cng sut cua hit in va cac thuy in P*n,P*t1,P*t2,.....,P*tn.

    u tai t ng P

    Nhom Nha may in - B mn H thng in - HBK a Nng . 28

  • Mn hoc: Vn hanh H thng in

    1q1 nqn

    P*N PN P*T1 PT1 P*Tn PTn

    Hnh 2-4 Tuy nhin trong thc t thng cac ga tr cua i cua thuy in phai xac nh theo iu kin ti u ma khng bit trc, v vy thu tuc phc tap hn. Nh a phn tch, ch lam vic ti u cua cac nha may thuy in phai am bao 2 muc tiu : - at cc tiu tiu hao nhin liu trong cac nha may nhit in. - at lng tiu hao nc Wi trong chu ky iu tit nh qui nh. T y thy rng phai chon cac gia tr i mt cach hp ly.

    Nhom Nha may in - B mn H thng in - HBK a Nng . 29

  • Mn hoc: Vn hanh H thng in

    Hnh 2-6

    T hnh 2- 4 ta thy rng nu nha may thuy in i nao o nu chon gia tr i ln th ng c tnh iqi nng cao ln do o cng sut phat cua thuy in th i se giam i va dn n lng nc trong chu ky iu tit nho hn qui nh. V vy trong trng hp tng quat thu tuc phn phi ti u cng sut gia nhit in va n nha may thuy in c tin hanh gn ung theo thut toan trn s hnh 2-5. Trong mt s trng hp do kho d bao chnh xac lng nc trong chu ky iu tit dai nn thng xac nh ch lam vic cua thuy in theo lng nc tiu hao trung bnh trong mt ngay m Qtb . Vi

    Hnh 2-5

    Nhom Nha may in - B mn H thng in - HBK a Nng . 30

  • Mn hoc: Vn hanh H thng in

    Nhom Nha may in - B mn H thng in - HBK a Nng . 31

    nhng gia tr chon khac nhau, gia tr cua QBtb B ta co th xy dng theo ng c tnh nh hnh 2-6, da theo th phu tai cua thuy in. T y cung thy rng khi chon ln, cng sut PBTB se nho, dn n QBtb B nho . Trong trng hp co mt nha may thuy in, vic xac nh gia tr co th n gan suy t gia tr QBtb B qui nh. Khi co nhiu thuy in vic xy dng cac ng QBtb B cung phc tap, luc o thng chon cac h s Bi B theo phng phap dn ung nh a nu . Cn chu y rng cac gia tr c chon co tuy thuc vao tnh thi tit. Chng han vao mua nc ln khi h khng cha ht toan b lng dong chay, cn chon nho, co th dn n Bq B nho hn ca gia tr cc tiu cua nhit in, nh vy QBTB se ln, thuy in se phat toan b cng sut, nhit in ch am bao phn phu tai con lai. Tng t khi nc can co th thc hin chon ln . Trn y khi xet ch lam vic ti u cua nhit in va thuy in ch nhm thoa man ch tiu cc tiu chi ph nhin liu va am bao cng sut phu tai h thng. Trong thc t vic chon cac tham s con phai thoa man nhng ch tiu khac nh mc nc qui nh ha lu phai am bao, cac ch tiu v cht lng in nng nh in ap v.v...

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