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אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
١٥٣١٥٣
א١٥٣אא
א
،،אא،אW
אאאאאאאאאאא א א א א א א ،א
אאאאאאאאאא؛אא
אאאK
אאאאאאא א ،א אא
א ، א א א אא אא،אאאאאאאאאאאאאאאאא
א א ،א אא،אאK
אא?אא??א?
אאאאאאאK
אאאאאאא،א،אאאא
אאאאאK
אאא،אאK
אאאא
א١٥٣אא
א
אאא
אאאאאאWאאאאאאKא
אאאאאאאאאאKאאאאאאK
אאאאאאK
אאאאאK
א١٥٣אא
א
אאאאאאא
אאאאאאאאK
אאאאאאאאאאאאאאK
אאאאאאאאאK
אאאW١JאאWאאאא
אאאאאK
٢JאאאWאאאאאאאK
٣JאWאאאאאאאאאאאK
אאאאאKאאKאאאא
אKא١א٣
N S
١Wאא
א١٥٣אא
א
التيار خارج
التيار داخل
٢Wא
I
٣Wאאאאאאאאא
אאאאאאאKאאאאאאאא
אא
I
٤Wא
א١٥٣אא
א
٤JאאWאאאאאא)(WaberK
אאאאאאאאK
٥JאאHWאאאאאאאאא Hאאא
אאK 1) E∑∫ = IdlH .
אאאאHאא
∫: إلى ∑= IdlH .אאאאא
אאW∑ ∑= IlH .
Hθ
dlI1 I2 I3
٥אW
א١٥٣אא
א
١:אאW
Hr
I
٦אWאIlH =.
lאאrrl π2=אW (A/m)
rIHπ2
=HאאlאFאE2WNאאא
אאאאאאאK
r
A
Nلفة
I٧אWא
אNI
אrאאאאH W∑ ∑= IlH .
א١٥٣אא
א
אאאאאNIאאאrrl π2=אאאW
NIHl =r
NIHπ2
=
אאNI אאאא אKא
lNIH =אאאא
אNאIאאאאאאK٦JאאFאאEBWאאΦא
AאאW
F٢EAB Φ
=mWb
2Tesla
אאHאBאאאאא
אאאWF٣EHB µ=
אאאאאאFאKEµאאK
BHאאאאאWHB µ 0=m
H10 7
04 −Π= xµ
אאאאאא)(HfB =KאאאאאW
F٤EHBr µµ 0
=µ r
אאK1=µ r
אאFאאEאאKµ r
אאK٧JאFאEאRmWאאאאאNI
אאΦW
F٥EΦ=
NIRm
א١٥٣אא
א
אאאlאאW
Al
µ=
HANI
µ=
BHNI
=Φ
=NIRm
F٦EAlRm µ
=
אאאlAµµµ0r
=
WbtA.)( 1henry −Rm
AlR
σ=אאאW
• lאA• אσµ • אא W
JאאאאאאWF٧E⋅⋅⋅⋅⋅+++= RRRR mmmmeq 321
JאאאאאWF٨E⋅⋅⋅⋅⋅+++=
RRRR mmmmeq 321
1111
∑ ∑= NIlH .אאΦW
ΦΦ ⋅=⋅== 11111
11
1
111 RA
llBlH mµµ
אאWF٩E∑∑ =Φ⋅ NIRm
RmאאאאאK الدائرة المغناطيسية المكافئة -٨
אאאאאאאאאאאאKאאאאא
אKאאאאNIΦRmW
RmNI Φ=אאאK
א١٥٣אא
א
אאאאאWאאאאאאאאא
אF٨WE
If
٨אWאא
אאאFאאאאאEאאאKאאאאאאNIW
- אA
lRcr
cc µµ 0
=אאאA
lRg
gg µ 0
=
אאWRR gc
NI+
=ΦlHlH ggccNI +=אlc
אאאאאl gאאאK
אאאWAB
cc
Φ=אאאאW
ABg
g
Φ=
WAA gc ≅אWABB
ccg
Φ==
א١٥٣אא
א
٩- אאאאאאאאא
אאא
• אאאאE אFVoltE
• אאRVI =
אFAE• אא
AlR
σ=
אFΩE• א
AIJ =
אFmA
2E
• אאאאFNIF =EאFtA ⋅E
• אאRm
NI=Φ
אFWaber(
• אאAlRm µ
=
אFhenry 1−E• א
AB Φ
=
אFTeslaE
١٠J אW
A
N=250لفة
I
٩אWא
٩אאאNK
א١٥٣אא
א
B
H
مقاومة مغناطيسية عالبة
مقاومة مغناطبيبة منخفضة
التشبع
µ0B= H
B= µ rµ0
عالقة خطية
عالقة غير خطية
١٠אא
אאאאHאIאאאאBאאW
אאBאאאאאHאאאא
א)(HfB =אKאאRmאאאB
אאKאאאאK
١١J المفاقيد الحديديةWאאW
FEאאFאאאאKE
FEאאאאאK١١١JאאW
אאאאאF٩Eאא0=B0=HF0=IKEאאאאאIא
א١٥٣אא
א
א1א–2אF١١KE
1
3
5
24
BBmax
rB
cH
rB-
- cH
Bmax-
H=Nil
Hs
Hs-
67
١١אW2אאH 1FאI 1אEאא
אאH sאא3KאאאאBmWאאאFHE
אBKאאHאאא3-4
0=HאאאאBrאאאאאKאאאאאא
אאKאאאFH−EBאאF0=BE
אאH c−אא4-5אH c−אאאאאK
אאאאאאא5א-6-7 אאאאאאFH+Eא
א7-3Kא3-4-5-6-7-3אאאאאאKאBאHא
א١٥٣אא
א
אאW0=H0≠BאאHH c−BאאK
JאאWאאאאאKא
אאאאאאאאאאאאא
אKאאאIFHEאאאאKאאא
KאאאאאאKאאאאאא
אאאאKאאאKאאאאאאFאא
EאאאKאאאאאאאאאא
אאאKאאאאאאK
١١٢JאאאאאאאאאK
אאאאאאאאאאאie
אאRאאie
אRie
2RאאאאאK
אאאאאאאאאאאאKאא
WJאאאאאF0
04EאאK
א١٥٣אא
א
JאאאאאאאאK
Wאאאאאאא
אאאאאאאאאאאאא
PcאWppP ehc += : أسئلةمحلولة في الدوائر المغناطيسية -١٢
אאאWאאאcm48
cm212220Kא200אאאאmH /10 7
04 −= XπµK
لفة220
i
cl =48cm
A = 12 cm2
١٢Wא
١JאW١١JאאאRc١٢JאאI 1T1.1
٢Jאאאאcm1אאאW
1.2אאאאאאRmtotal2.2אאI 2אאאאK
א١٥٣אא
א
אW
1.1אאאWA
lRcr
cc µµ 0
11 =
1010 47 124200
48.0−−=
xxxx πWbtA /.1591549=
١٢אאאאTBc 1.1=אאאW
N
N RIRI cc
1111
⋅Φ=⇒⋅Φ=
NRAB ccc 1⋅⋅
=
2201591549121.1 10 4 xxx −
= A55.9=
2.1אאאאW
WbtA /1558392 ⋅= 1010 472 124200
47.0−−=
xxxxRc π ,
AlR
cr
cc ⋅⋅
=µµ 0
22
lc2אאאאmlc
47.001.048.02
=−=אWאאאאאW
AA cg =אאאאאl g
אאאm01.0אW
WbtA /6631456 ⋅=1010 47 124
01.0−−=
xxxRg π
AlRA
lRc
gg
g
gg ⋅
=⇒⋅
=µµ 00
JאאאאאאWWbtA /8189848 ⋅=66314561558392 +=RRR gctotal += 2
2.2אאאאאאW
A14.49=220
8189848121.1 10 4 xxx −
=N
RAB totalcc ⋅⋅=
NRI total⋅Φ
=2 W
JאאאאאאWtA ⋅= 210155.92201 xN I =JאאאאאאWtA ⋅= 1081114.492202 xN I =
א١٥٣אא
א
אאאאאאאאK
אאאW
r m
ri =20cm
ro=25cmA
N=250لفة
١٣WK
250אאא١١٣
אאאcmri 20=אאcmro 25=Kאאא2204אאאmH /10 7
04 −= XπµK
אאאאA5.2W-1אאאאאK-2אאאאא
אKאW
-1אאHאאrmאW
lNIH =
Nא250=Nlאאאאrmrml π2=mrrr oim 225.0)20.025.0(
21)(
21
=+=+=
אmtAx
xH /3.442225.02
5.2250⋅==
πאאBאאW
THB r 225.13.4421042204 70 =×××== −πµµ
א١٥٣אא
א
-2אI
NL Φ=AcB ⋅=ΦrAc
2π=אאאאr
אmr rr io 025.0)20.025.0(21)(
21
=−=−=m210)025.0( 62625 −== xxAc ππ
Wbxxx 1010 46 04.24625225.1 −− ==Φ π
אאWmHHxx
L 4.2402404.05.2
04.24250 10 4
===−
١٣JאאאאeW
lBאאθאאאW
F١٠FEVEθsinBlue =θאאאאאאK
א90o=θBlue =אאאK
ظم منت
ي يساطمغن
ل جام
uθ
ض لفيه اجاات
سي طيغناالم
اتجاه القوة الدافعة الكهربائية
اتجاه الحرآة
١٤WאאאאK
אאאאאאאא
אאאאאאWאאאאאאאאאא
אאאאאאאאאK
א١٥٣אא
א
١٤JאאFאאTW١٤١JאאאKאאאאF١١٥אE
אFאאאWF١١FENEθsinBilF =θאאאאאא
א( ) 90, o== Blθ1sin =θFNEBilF =
N S
F
0θ=90
I
lموصل طوله
θ
N S
F
I
lموصل طوله
١٥Wאאאא
אאFאאWאאאאאאאאאאאאא
אאאאאK١٤٢JאאאK
F
Fa
bc
d
d
x
x'
N SI(A)
א١٥٣אא
א
١٦WאאאאKאFabEFcdEאאאKאFadEFbcEאK
١٤٣Jالعزم
אאאFabEFcdEאF١٦אKEFאאFTEאאאאאא
אdאKאK(Nm) אF١٢E(Nm)BIldFdT ==
א)(θאאאאאאWθcosFBIlT =١٥J تحويل الطاقة:
אאאאאאFEאאא
FEאאKאאאא
אאKאאאאא( )eא( )iא( )Tא( )n
אK
محركمولد
تدفقالطاقة
تدفقالطاقة
nT
+
-
V
الجزءالكهربائي
الجزءالميكانيكي
المجالالمغناطيسي
(e,i)
المجالالمغناطيسي
نظامميكانيكي( T,wm )
نظامآهربائي
א١٥٣אא
א
١٦אWאא
אאאאאW
GאאאאGאא
FKEאאאאאאאאאK
אאאאאאא אאא
אאאאאאאא
אאאאאKאאאאאאא
FEאאא
אאאKאאאא
אאאאא
אאאא
אאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
א
١
א١٥٣אאאאאא
- ١ -
אאWאא-1אאW
אא אאאאאאאF١١EK
الثابت
N
S
العضو الدوار
خطوط المجالالرئيسي
الفكملفات المجال
القطب
الثغرة الهوائية
مجاري يوزع فيهاملف المنتج
١١אWאא
١١Jא( stator )WאאאאאאאאKאאK
אאאאאאאאK
١٢Jאאאא) ( rotor or armatureWאאאאאאאאאאא
אאאאאאאאאKאאאאא
אאאאאKאאאאאאאאאאאא
אאF١١E١٣Jאא) ( commutatorWאאאאא
אאאאאא
א١٥٣אאאאאא
- ٢ -
אאאKאאאאאאKאאא
אאאאאK١٤JאאFbrushesEWאאא
אאאאאאK
١٥JFEאאאא
אאאאאאאאאאאאאא
אאאאאאאאK
٢JאWאF١٢E
a
b
2BB1
Sa
bS
θ
+ -1 2
e
l
a
b
+
-eab
اتجاه الدوران
N S
١٢אWא
אF١٣EאאאאאאKאablא
אאאKאאsasbKאאB1 B2אאאאKאא
אאאא( )luBe θ=Kא
א١٥٣אאאאאא
- ٣ -
אאאאאW( )luBeabθ2=Kאא
אeabאאא
אאאאאאF N SKE
θ
e12eab
=2B(θ)lv
=B(θ)
θ
N
S
N
א١٣Wאא١٤Wאאאא
אאאאאאא
אאאאאCaCbB1B2אF١٥KE
אCaאaאbאCbKאאאאאאאאאאאאN
אאאאאSאB1אאאFEאB2אFKEא
אWאאאeabאאe12
אאF١٦Eא
bN S
a
f
f
B 1 2B
1 2
b
(أ)
bN Saf
f
B 1 2B
1 2
b
(ج)
N S
b
a
B1 2B
21(ب)
א١٥٣אאאאאא
- ٤ -
١٥אWאאאא אFrippleKEאא
אאאאאאאאאאאFאEא
אאאF١٦KE
θ0
eab
e12
θ0
E12(avg)
(أ)
e12
θ
et1 et2 et3 et4
0
(ب)١٦WאאK
EאKEאK
٣JאאאאFelectromotive force (e.m.f ) equationEEאאאאאא
אאאW-1אאΦ-2אאאwm
-3kaא
א١٥٣אאאאאא
- ٥ -
אאאאאEaאאאKKאאאאאאא( )AK
אאאאאאאאW
F١١EwkE maa ⋅Φ⋅=אאאW( )VoltEa( )waberΦ⎟
⎠⎞
⎜⎝⎛
ondsradianswm sec
ka
AZP
ANPka ππ 2
==א
NאאאAאאאאאNZ 2=אאאPאΦאאאFwbE
srdnwm/
602π=אאאnאא
٤JאאFequation electromagnetic torqueE T eWאאא א
א א א א אא א Kאאאאא
אאאאWF١٢EIkT aae ⋅Φ⋅=אאאאאK
אא א א א FIE aa ⋅ E א א א אאאאאFwT me ⋅Eא
אא א א אאא א FshaftK EאאאW (3.1)wTIwkIE meamaaa =Φ=
٥JW
אאWאcm25cm5.12K
0א075אKאא33
733KאאאאT75.0K
א١٥٣אאאאאא
- ٦ -
١Jאאאאאא4אWFEאka
FEאאאEaאא1000אFEאאאI cאאא
אAI a 400=FEאאPaא٢Jאאאאאא2אאFKEא
אאאאK אW
-1אאאא4=AWFEא
AZPka π2
=4=Pא4=AאאאאZ
אאcאtאאאא
46273322 =××== ctZאא53.73424462
=××
=πka
FEאאאwkE maa ⋅Φ⋅=wm
אאאΦאא
srdnwm
72.10460
1000260
2 =×=×= ππBAp ×=ΦApאאא
אאWmA Prl
p
2322
101010 8.3675.04
255.1220752 −
−−
×=×××××
=×=ππ
אאWWb0276.0=75.08.36 10 3 ××=Φ −אאאאWVolt5.212=72.1040276.053.73 ××=Ea
FEאאאWAAII a
c 1004
400===
אאWmN ⋅= 8.8114000276.053.73 ××=IkT aae ⋅Φ⋅=FEאאאWKw85=W850004005.212 =×=IEP aaa ⋅=
אWKw85=W8500072.1048.811 =×=wTP mea ⋅=-2אאאאא2=AWFEאW06.147
224462
=××
=πA
ZPka π2=
FEאאאWVolt425=72.1040276.006.147 ××=wkE maa ⋅Φ⋅=FEאאאWAI c 100=
א١٥٣אאאאאא
- ٧ -
אאאאאאWAAII ca 2001002 =×==אאWmN ⋅=××= 8.8112000276.006.147IkT aae ⋅Φ⋅=
FEאאאWKw85=W85000200425 =×=IEP aaa ⋅=אאW12אאאאא٢א
144א 10K0.011 Ωאא0.05 Wbא200אK
FEאאאאKFEאאאKFEאא1 KΩאאא
אאאאאFאאאאKEאW
FEאW2880=1014422 ××== ctZאW2750≈22122880
2 ××
==ππA
ZPka
אאאWsec94.20 rds=602002
602 ×== ππ nwm
אאאWVolt2880≈94.2005.02750 ××=wkE maa ⋅Φ⋅=
FEאאאא722
144=
10אאאאאW7201072 =×=NאאאאW
אWΩ=×== 92.7011.072021 RR
Ω= 96.3 292.7
21
11
11 ==+
×= R
RRRRRa
FEאΩ= 1000RLאאא
אאRaאאWAREI
L
aa 88.2
10002880
===
אאאWmN ⋅= 39688.205.02750 ××=IkT aae ⋅Φ⋅=
٦Jאאאאאאאא
אW
א١٥٣אאאאאא
- ٨ -
FEאאאKFEאאאאאKK
אאאאאאאאאאאאK
אאאאאאאאאאא
אאאאאאאאאאאאאI f
אאאאאאאאK
אאI fW٦١JאאאאאFseparate excitationEאאF١٧KEאאא
Vt
I f
Ra
Ea
Ia
Rfw
+
-
+
-+ -
١٧W٦٢JאאאאאאKFself-excitationKEאאאΦresאא
אאאאאאאאאאאאאK
אאאאאאאFאEW
א١٥٣אאאאאא
- ٩ -
٦٢١JאFWshunt-excitationEאאאאאא
אאF١٨אKE
I f
Rfw
Vt
Ra
Ea
Ia
+
-
+
-
Rfc
IL
١٨Wאא
٦٢٢JאFWseries excitationE
אאאאK
VtRsr
-
+
Ea
+
-
Ia
Ra
١٩אא
WאאאאF
5%אאEאאאK٦٢٣JFWcompound excitationE
אא א Fאאאא EאאKאאאא Kאאא
אאאאאאאאאאאאאאאאאאK
אKאאאאאאאאא
א١٥٣אאאאאא
- ١٠ -
אאאFcummulatively compounded excitationEKא
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
١١٠Wאא١١١Wא
אאאאאא
Fdifferentially compounded excitationEKא
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
١W١٣א١W١٢א
אאאאK
٧JאאאWאאאאאא
אא( prime mover )KאאאאאאאFEאאK
א١٥٣אאאאאא
- ١١ -
אאאIE aaאאאRI 2Kאאא
אאאאKאאאאאאאאאאא
אאאאאK٧١JאאאW
אאאאאאGFRI 2GEאGאאG
אאאאאאאאאאא
אאאאFEאK
٧١١Jאא(copper losses ) WאאאFאאEאאאFאE
אאFאEKאאאאאא
אRIP aaA2=אאRIP fwfF
2=I aRaאI fR fwאאK
אאאאאאKאאאאK
٧١٢J א ( brush losses )WאאאאאאK
٧١٣J אא ( core losses ) Wאאאאאאאאאא
אאאאאאאKאאאאK
א١٥٣אאאאאא
- ١٢ -
٧١٤Jאא( mechanical losses )WאאאאWאאאK
אאאאאאK٧٢JאFאEefficiency ) E
אאFW١٤E10000 ×=
PP
in
outη
אאאאאא
אFW١٥E10000 ×
−= ∑
PPP
in
lossesinη
FW١٦E10000 ×
+=
∑PPP
lossesout
outη
אאאאאאאK٧٣Jא power -flow giagram ) E
אאאאאאאאKאF١١٤EאאאאF١١٥E
אאאK
قدرة آهربائبة
Pinقدرة ميكانيكية
على عمود اإلدارة
+PironPmech
المفاقيد الميكانيكيةو الحديدية
مفاقيد المنتجالنحاسية2
RaIa
مفاقيد ملفاتالتوازيالنحاسية
مفاقيد ملفاتالتواليالنحاسية
aE aI‘‘قدرة الدخلقدرة الخرج
2RI fwf rs
2RIL
Pout = tV IL
١١٤אWא
א١٥٣אאאאאא
- ١٣ -
אאאאF١١٥E
قدرة آهربائبة قدرة ميكانيكيةعلى عمود اإلدارة
+PironPmech
المفاقيد الميكانيكيةو الحديدية
مفاقيد المنتجالنحاسية2
RaIa
مفاقيد ملفاتالتوازيالنحاسية
مفاقيد ملفاتالتواليالنحاسية
aE aIقدرة الدخلقدرة الخرج
2RI fwfrs
2RIL
PoutPin = tV IL
١١٥אאK
א١٥٣אאאאאא
- ١٤ -
١٢JאאאאאאFEאKאאאא
אאאאאאא
١JאאאאאאWאאאאFE
אKאאאאK
אF١١٦EאאאאאאאאK
Ra
Ea
Ia
+
-
I f
Rfw
+ -
Rfc
Vf
Vt
+
-
١١٦אWא
R fcאאאא R fwאRRR fwfcf +=אאאאRLאI fאI aאI LאV f
אV LV t
אאא ١١JאאאאאאW
F١٧EwkE maa ⋅Φ⋅=F١٩EII La =F١٨ERIEV aaat −=F١١٠ERIV fff
=
א١٥٣אאאאאא
- ١٥ -
١٢JאאאאW
Ra
Ea
+
-
I f
Rfw
+ -
Rfc
Vf
+
-
Vt
Εa
I f
Ε rs
١١٧אWאא١١٨Wא
١٢١Jא( )IEV faL f== 0,0,WEaIאא fאI fאא
אאאאאאאאKKאאKKאאאK
אKKאאאwkE maa ⋅Φ⋅=0,
sec602 rdsnwmπ=אאאnאLKא
אאFKאF١١٩E
I f
Εa
n1
n2
n2n1>
א١٥٣אאאאאא
- ١٦ -
١١٩אWאא١٢٢Jאא( )IV LL
f=אאtconsn tan=אI fאאא
אאאV LאI LאאאI aK
אאWRIEV aaaL −= 0,
I f
Ra
Ea
Ia
Rfw
+
-
+
-+ -
Vt
V t
RLI L=
ΕaVt
IL
نقطةالتشغيل
IaRa
א١٢٠Wא١٢١Wאא
אאאאאאאאאאRI aa
אאאאאאRaKאאאאאK
אאאאא١٣JאאאאW
אאאאאאאאEaאKאRIEV aaaL −=אאEaV L
אEaV LKאאwkE maa ⋅Φ⋅=
אאK١٣١Jאאwm
אאאwm
EaאאV L
א١٥٣אאאאאא
- ١٧ -
١٣٢JאI f
Rאאאא fאRVI
f
ff =V f
אΦKאאאאEaאאV L
אאKאאאאאא
אאאאאאK١٤JW
אא1200Lא200 A125 Vא0.04 Ω K
١JאWאאאאאK٢Jאאאא1000LאאW
אאאאאאאאאאK : الحل ١J אאאW
VEa 13304.0200125 =×+=RIVE aaLa +=אRLRIV LLL
=אIVR
L
LL =Ω== 625.0
200125RL
٢Jאא1000LאW
אאwkE maa 11 ⋅Φ⋅=60
2 11
nwm×= πאאאn1א
אאwkE maa 22 ⋅Φ⋅=60
2 22
nwm×= πn2
אא
אאnn
nk
nkEE
a
a
a
a
1
2
1
2
1
2
602
602
=×
Φ
×Φ
=π
π
אkaΦK
אאKKאVVnnEE aa 1118.110
12001000133
1
212 ≅=×=×=
אאWARR
EILa
aa 1679.166
625.004.01112
2 ≅=+
=+
=
א١٥٣אאאאאא
- ١٨ -
٢JאאאאWאאאא
אאאΦresאKאאאאא
אאאKאאאאאאאאאK
אאWאאאאאאאK
אאאאאאאW٢١JאאW
אאאאאאאאאאאאאI f
٢١٢JאאאאאאאאF١٢٢EאאאאאאKאאאאאאאאW
F١١١ERIEV aaaL −=F١١٢EIII Lfa += F١١٣E( ) RIRRIV fffcfwfL =+=
٢١٢Jאא( )IV LLf=אא
I f
Rfw
Ra
Ea
Ia
+
-
+
-
Rfc
IL
RLVt
0
Vt
Ian Iaא١٢٢אא١٢٣אא
א١٥٣אאאאאא
- ١٩ -
אאאאאאאאאא
אאאאFאEV LKאא
אאאאאWRIEV aaaL −=
אאאV LאאEaK
אF١٢٣EאאאKKאEa 0,אאאאאK
אאאאאאאאאאאאאאא
אאאאאאאאK
٢١٣Jאאאאאא
אאW٢١٣١Jאאwm
٢١٣٢JאאR fWR fcאאא
אאאKאאאאאאאV LKא
Rאאא f( )RRR fcfwf +=R fwאR fcאא
א↓
=↑RVI
f
LfאאאאΦא
אאאאwkE maa ↑Φ=↑אאEaאאאRIEV aaaL −=↑↑אK
٢١٤JאאאאWJאאאאKJאאKJאאאאאK
א١٥٣אאאאאא
- ٢٠ -
JאאK٢١٥JW
אאA100200500Lא0.025 Wb
4אאאאאA=2Kא0.1 Ωא80 ΩKאאא
1660א WאאW١Jאאאאא٢Jאאאא٣Jא٤Jא٥JאאאFאE٦Jאא٧Jא
אW١JאאאאEawkE maa ⋅Φ⋅=
א03.84
224264
2=
××
==ππA
ZPka
אאאsec/36.52
605002
602 rdnwm
=×=×= ππ
אאKKאא36.52025.003.84 ××=EaVEa 110=٢JאאאאאאV L
RIEV aaaL −= , 1.0100110 ×−=V LVV أو L 100=
٣JאI fRVI
fw
Lf =
80100
=I fAI f 25.1=
٤JאI LWIII faL −=25.1100 −=I LAI L 75.98=٥JאאאWIVP LLout ×=75.98100×=PoutWPout 9875=
٦JאאWRIRIP aaffcu
22 +=( ) ( ) 1.080 10025.1 22
×+×=PcuWPcu 1125=
٧JאW10000 ×
+=
∑PPP
lossesout
outηPPPP cumechironlosses ++=∑
100112516609875
98750
0 ×++
=η 0 أو0
00 78=η
א١٥٣אאאאאא
- ٢١ -
٢٢JאאWאאאאאאKא
אאאאאאאאאאK
אאאאNIF =אאKKאאKאאאאא
אאKאF١٢٤Eאאאאא
Rsr
-
+
Ea
+
-
Ia
Ra
Vt
א١٢٤א
אאאאאאאאFאI aאI fאI LEא( )III Lfa ==
אאFאאEאאאK ٢٢١JאאאאאאW
F١١٤E( )RRIEV saaaL+−=אF١١٥EIII Lfa ==
٢٢٢JאFאE( )IE fa f=WאאאאKא
אאאV L( )E resa .אא
אΦresKאאאאא
אFKE
א١٥٣אאאאאא
- ٢٢ -
٢٢٣Jאא( )IV LLf=W
Vt RL
-
+
RsrEa
+
-
Ia
Ra
0
خاصيةالحمل
الخاصيةالخارجية
خاصيةالالحمل
Ra Rsr+( )Ia Vt
Ea
Ia
Vt
Ea
P
Ian א١٢٥אאא١٢٦אאאא
אאRLאRIV LLL =RLKאPF١٢٦אEאאא
אאKאאאRLאאאאאאK
٢٢٤JאאאאWאאאאאאא
אאאאאאK٢٣JאאאאW
אאאאאאאאאאאאאא( )RI aa
אFאאאKEאאאאאא
אאאאאKאאאאאאאא
F١٢٧א١٢٨EאאF١٥٩א١٦٠EKאאאΦserא
אΦshאאאאאא( cumulative compound machine )
א١٥٣אאאאאא
- ٢٣ -
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
ترآيب طويل (ب)(أ) ترآيب قصير١٢٧אא
אאאא(differential compound machine )
(ب) ترآيب طويل(أ) ترآيب قصير
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
١٢٨א
אאאאאאאאאK
אאאאאאKאא
אאאK
٢٣١Jאא( short shunt connection )אF١٢٩Eאאאאא
אאאK
א١٥٣אאאאאא
- ٢٤ -
אאאאאאאאWF١١٦ERIRIEV srLaaaL
−−=F١١٧EIII fLa +=
F١١٨ER
RIEIf
aaaf
−=RRR fwfcf +=
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt RL
١٢٩אא
٢٣٢Jאא( long shunt connection )
אאאאאאאאF١٣٠EאאאאאאאאאאאK
אאאאאאאאאאא
FW١١٩E( )RRIEV sraaaL +−=F١٢٠ERVI
f
Lf =F١٢١EIII Lfa +=
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt RL
١٣٠אא
א١٥٣אאאאאא
- ٢٥ -
٢٣٣Jאאאאאאאאאאאאא
אאW( )wkE msrshaa Φ±Φ=Φshאאאאא
ΦsrאאאאאHאאאאאאאאא–אאאאאאאאK
٢٣٤Jאאאאא( )IV LL
f=WאאאאאאF١٣١KE
אאאאאאאאאאאאא( overcompound )אא
א( undercompound )אאא( flat compounding )KאאאאK
Vt
IL0
FLI
Ea,0ترآيبمستويترآيبناقص
توازي
ترآيبزائد
١٣١אאאאאא
א١٥٣אאאאאא
- ٢٦ -
אאאאאאאאאאF١٣٢EאאאאאK
Vt
IL0
Ea,0
توازي
ترآيبتفاضلي
١٣٢אאאאא
א١٥٣אאאאאא
- ٢٧ -
٢٣٥JWאאא476101.3 A
1800Lא0.015WbאאאאאA=2א0.1 Ωאא 150 Ω
אא0.04 ΩKאאאא1827 WאW
١JאKKאא٢Jאאאא٣Jאא٤Jא٥Jאאאאא٦Jאא٧Jאא
אW
١JאKKwkE maa ⋅Φ⋅=60
2 nwm×= π
ππ 22Z
APZka
==
א75.752476
==πka
אאאsec/5.18860
18002 rdwm =×= π5.188015.075.75 ××=EaVEa 2.214=٢Jא( )RRIEV sraaaL +−=( )04.01.03.1012.214 +×−=V L
VV L 200=
٣JאאRVI
fw
Lf =AI f 3.1
150200
==
٤JאIII faL −=AI L 1003.13.101 =−=٥JאIVP LLout ×=KwWPout 2020000100200 ==×=٦JאאPPPP cumechironlosses ++=∑
אאאWPP mechiron 1827=+אא( )RRIRIP sraaffcu +×+= 22( ) ( ) ( )04.01.0150 3.1013.1 22
+×+×=PcuWPcu 1703=K
אאא∑ =+= WPlosses 353017031827
٧Jא10000 ×
+=
∑PPP
lossesout
outη00
00 85100
35302000020000
=×+
=η
א١٥٣אאאאאא
- ٢٨ -
١٣אא
١JאאאאאF١٣٣KE
אאאK
آلة التيارالمستمر
א(If)אא
آلة التيارالمستمر
א(If)אא
١٣٣אאא
אאאאW١JאאאאאאאאאאאאאאאאאאאאK٢JאאאאKאאאאא
KאאאאאאK
אאאאW١Jאאאא٢Jאאאא٣Jאאאא٤Jאאאא٥Jאאאאא
אאFEאKאאWwkE maa ⋅Φ⋅=IkT aae ⋅Φ⋅=
אKאאאאאא
W
א١٥٣אאאאאא
- ٢٩ -
٢JאאאאאאWאאאאא
אאאאא
KאאאאאאאאאאאאK
אאאKאאאאאא١٣٤
Vt
Ra
Ea
Ia+
-
+
-
I f
Rfw
+ -
Rfc
Vf
I f
Rfw
Vt
Ra
Ea
Ia
+
-
+
-
Rfc
IL
١٣٤אאאא١٣٥א
אאאאא١٣٥אאאאאV t
K ٢١JאאאאאאW
F١٢٢ERIEV aaat +=F١٢٣ERVI
f
tf =F١٢٤EIII faL +=F١٢٥E
IkT aam ⋅⋅= Φ0אאאאאwPT
m
mm =
IEwTP aLammm ,==F١٢٦Eאאאא: אI aאwm
אאאאK٢٢JאאאFאאE
אאאאאאאאWאאאאאKאאאK
• אאאאאאK• אאאאK
א١٥٣אאאאאא
- ٣٠ -
אאאא אאאאאK
٢٢٢JאאW( )I afn =V tFI fΦ0E
אאΦ
−=
0kRIVw
a
aatmF١٢٧E
Φ−
=01kRIV aatnאא
אאאאא( )RI aaאאRI aaאא
אV tFKא١٣٦אE
אאאאאKאאאK
0
nU1
U2 U1<
Ia١٣٦אWאאא
٢٢٣JאW( )IT am f=אאFאאEWIkT aam ⋅⋅= Φ0א
Ww
IETm
aLam
,=KאאאΦ0אא
אאFW١٢٨EIKIkT aaam =Φ= 0אI aאאאΦ0אK
GאFאאEwIV
wPPT
m
at
m
ironmechf
0,≅+
=I a 0,
KאאאאGאאאT 2אאWTTT fm −=2FTT m⟨2KE
א١٥٣אאאאאא
- ٣١ -
0
T
Tm
Ia١٣٧אWאאא
٢٣JאאאאWאאאאאאאא
אאאאאKאא١KEF٢٧אאאאאאא
٢٣١JאV t
٢٣٢JאאאΦ0R fcאאאאK٢٣٣JאאאאKאא
אI fאאאK٢٤JאאאאW
אאאאאאאאאאאאאא
אאאאאאאאKאאאאאא
אKאאאאאאK٢٥JאאאW
אאאאאאFאאEאאK
٢٦JאאאאW
א١٥٣אאאאאא
- ٣٢ -
אאאאאאאא
אFΦ
−=
01kRIV aatnKEאאאאא
אאאΦresאאאאאwkE mresaa Φ=אאאאאאאא
אT rאאK ٢٧JW
אאW אאאאא63 A120 V אא
0.12א Ω ٣٣٨ א Ω٤٠ אא0.02 WbK
אאאW١JאI f 1٢KJאI a1K٣JאאאאאEa1٤Jאn1
K٥JאT 1
אWאאאW
١JΑ=== 340
1201 R
VIfw
tf٢KJΑ=−=−= 606063111 III fLa
٣KJVRIVE aata 8.11212.06012011 =×−=−=٤KJא79.53
424338
2=
××
==ππA
ZPk a
אאאsec/85.10402.079.53
8.11211 rd
kEw
a
am =
×=
Φ=
אL10002
6085.1042
601
1=
×=
×=
ππwn m
אאWא12 Kw 100 VK
א0.1Ω א80ΩKאא١٠٠٠L6 AאK אאאא١٠٠٠
LאאW
א١٥٣אאאאאא
- ٣٣ -
1.4 1.32 1.20.99 0.860.83 0.60.4 0.20 ( )AI f
114.2110108.599.494.4 93.577.1 6531.4 8.5( )VEa
١JאאFR fcE٢JאאאFאאאE א١٠٠٠L٣JאאאאFאאEאאאא
אאאFאאEאא
אאאאאK٤Jאאאאאא150%א
אW١JאFNo-Load EאΑ= 6,I oa
אאאאאWVRIVE aata 4.991.061000,0, =×−=−=אKKVEa 4.990, =א١٠٠٠L
Α= 99.0I fK
אאאWΩ===+= 10199.0
100
IVRRR
f
tfwfcf
אאאWΩ=−=−= 2180101101 RR fwfc٢JאאאאFEאW
WIEPP aaironmech 4.59664.990,0, =×==+٣JאWVEa 4.990, =
אאWFull-Load )EΦΦ = LF .0
אאWΑ==== 120100
12000
VPII
ratedt
rateda
ratedaa
אאWVRIVE aLFatLFa 881.0120100.. =×−=−=
אWmprE
Enn
a
LFaLF ..3.885
4.99881000
0,
.0. =×=×=
nknk
EE LFLF
a
LFa
00
..
0,
.
ΦΦ=
אאאWsec/71.9260
3.885260
2 .., rdnw LFLFm =×=×= ππ
א١٥٣אאאאאא
- ٣٤ -
אאmNw
IEIkTLFm
LFaLFa
LFaLFam .9.11371.9212088
.,
..
.. =×
=== Φ
אאאmNw
PPTLFm
ironmechf .43.6
71.924.596
.,
==+
=
אאאאWTTT fm −=2mNT .47.10743.69.1132 =−=אאאW( ) WPPIEP ironmechLFaLFa 6.99634.59612088..2 =−×=+−=
WWwTP LFm 6.996347.9247.107.,22 =×==אFאאאאWE
( ) ( ) WIIVIVP fLFatLt1209999.0120100.1 =+=+==
אW00
00
00
1
2 35.8210012099
6.9963100 =×=×=PPη
٤Jאאאאא150%אI LFa .אאאאK
72.1044.99 00,00, ×=== ΦΦ kwkE amaaאsec//949.00. radVkk aLFa == ΦΦאאאWΑ=×=×= 1801205.15.1 .II LFastarta
אWmNIkT startaLFastartm .82.170180949.0. =×== Φ٣Jאאאא
٣١JWאאאאאאאאאאאW
VtRsr
-
+
Ea
+
-
Ia
Ra
١٣٨אWאא
אאאI aאI fאI LאאאFIII Lfa ==Eאאאאאאאא
אאFאאKEאאא
א١٥٣אאאאאא
- ٣٥ -
אאFאKE
אאאאאאאאK
٣٢Jאאאא אwkE maa Φ=IkT aam Φ=אאΦא
אאKאאאFW١٢٩E( )RRIEV sraaat ++=
אאאאאאאאאאאWIkk asra =Φ
אאאIkT aam Φ=Ikk asra=Φ
אאFW١٣٠EIkT asrm2=ksr
אאKאאאאF١٣١EIII Lfa ==
אF١٣١E( )
Φ+−
=k
RRIVwa
sraatm( )
IkRRIVn
asr
sraat +−=
٣٣JאאאW٣٣١Jא( )I afn =V t
0
n
Ia١٣٩אWאאא تج
אאL( )Ik
RRIVnasr
sraat +−=א
אאאI aאאאא
א١٥٣אאאאאא
- ٣٦ -
אאאאאאאאאF١٣٩אKEאאאא
FEאKאאאאאא
K
٣٣٢Jא( )IT am f=( )IT af=2
0
Tm
Ia١٤٠אWאאא
אאאאאאKאאאאWIkT asrm
2=אאאאאאאK
אאאאאאK
٣٤JאאאאאאW٣٤١R1אאאאFאV tE
אאאא אאאאאאאא
אאK٣٤٢JאV t
FאאE
א١٥٣אאאאאא
- ٣٧ -
٣٤٣JאאאFאV tE
אאאRhאאאאאRsrאאI a
'
WRR
RIhsr
ha +
Rh0א=ΦאK
אאאאאאאאאK٣٥Jאא
אאאאאאאאאK
٣٦Jאאאאאאאאאאאאא
אאאאאאאאאאאאאאאK
٣٧JWאאאא٢א:المسألة األولى
٢א500 VKאא60 AאאאKא0.15 Ωא٤٠٠א0.1Ωא0.0255א WbK
אאאW١JאאאאאEa1٢Jאn1
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אW١JאKKאW( ) ( ) VRRIVE sraata 48515.01.06050011 =+×−=+−=
٢JאאW66.63222400
2=
××
==ππA
ZPkaאאאאA=2
אאאWsec/77.2980255.066.63
48511 rad
kEw
a
am =
×=
Φ=
אWmprwn m ..28532
77.298602
601
1=
×==
ππ
א١٥٣אאאאאא
- ٣٨ -
٣JאאWmNIkT aam .4.97600255.066.6311 =××=Φ=
٤JאאאK٤١JW
אאאאFאאאEאאאאאKאאא
FאאEאאאאאאאאאKאא
א١٤١١٤٢KאאאאW
JאאאאΦnetאאאΦsrאאאאΦ fF١٤١אKE
JאאאאאאאF١٤١אKE
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
١٤١אWאאאאF٩
א١٥٣אאאאאא
- ٣٩ -
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
ILI f
Rfw
Ra
Ea
Ia
-
+
-
Rfc
Rsr
+
Vt
١٤٢אWאאאFE
WאאאאאK
٤٢JאאW٤٢١Jאא
F١٣٢E( )RRIEV sraaat++=F١٣٣E
RVI
f
tf =
٤٢٢אאF١٣٤ERIRIEV srLaaat ++=F١٣٥ERIVRIERIV srLtaaafff
−=+==אאאW
wkE mnetaa ⋅⋅= ΦFΦ±Φ=Φ srfnetEIII faL +=IkT anetam ⋅⋅= ΦTTT fm −=2II asr =אאII Lsr =אא
אHאאאJא خواص محرك الترآيب الطويل التراآمي-٣٫٤
אאאאאאΦnetΦ fΦsrאאΦΦΦ += srfnetאא
K٤٣١J( )I afn =V t
אאΦnetI fFV t
Eאאאא( )I afn =אn0אI a
אאF١٤٣אE
א١٥٣אאאאאא
- ٤٠ -
0
0n
IaaFLI
n
مرآب تراآمي
توازي
١٤٣אWאאאאא
٤٣٢JאW( )IT am f=אאא( )IT am f=
אאF١٤٤אEאאאאאאאאFאאEא
אאFאאאKEאאאאאאאאאאאאאא
אאT2
توازي
0IaaFLI
مرآب تراآمي
I a,0١٤٤אWאאאא
א١٥٣אאאאאא
- ٤١ -
אFאKEאאאאאאאאא
אאKאאאאאאאאאאאאאאK
٤٤JאאאאWאאאאאאאאאאאRHאאRh
אאK٤٥JאאאאאאW
אאאאאאאאאאאאK
٤٦JאאאWאאאאאΦsrאאΦ f
אאΦnetאאKאאאאאא
אKאאאאאאאאאאKאאא
אאאאאK
٥JאWאאאאאא
אאI startaאאאאאאI LFa .אK
אאאאאWR
EVIa
ata
−=K
אאאאאאאאא( )wkE maa ⋅Φ⋅=אK
א١٥٣אאאאאא
- ٤٢ -
אאאFW١٣٦ERVI
a
tstarta =אא
אאאKאאאאW
١JRaeאאאאאא
אאF١٣٧ERR
VIaea
tstarta +
=K
٢Jאא( )V tאאK
אאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
א
٢
א١٥٣אאאאאא
- ٤٣ -
אאWאאTRANSFORMERS
WאאFאEאאאאאאK،אאאאאא
אאKאאאאאאאאאK
٢J١ :א
٢J١ א TRANSFORMER CONSTRUCTION אאאאאאאאאאא
אא KאאאאאאF٢-٢KE
א١٥٣אאאאאא
- ٤٤ -
٢J٢אא
،אאWאאאאאאF٢J٣EK
F٢J٣Eאאא
אאא،א،אא
אאאאא،אאאKאאאא٣٪א
٩٧٪אKK
א١٥٣אאאאאא
- ٤٥ -
٢J١J١אCOREאא
KאאאG ،אאאא
٥٣٪אאאKאאאאאאא،א
אאאאאאK• אאWאא،
אאאאאF٣-٢E،KאאאאאאאK
אאאאא٩٦K٪ • אW،אאאא
א،אאאאF٢J٤EKאאאF٢J٤EK
F٢J٤Eאא
א١٥٣אאאאאא
- ٤٦ -
אאאאאאאאאF٢J٤EKאאאא
אא،אאF KE אאאא א K
אאאKאFEאאאא
א،אאאאאK
אאאאאאאאKאאאאא
אFKEאאא א אא ،
א אא אא א א K אאאאאK
٢J١J٢ אWindings אF٢J٥E،K
א א א ، א א אאאK
F٢J٥EFאאאE
א١٥٣אאאאאא
- ٤٧ -
אאא ،א אאאאאאK
אאאאאאאאאF٢J٦Eאא،K
אאאאאאאאאF٢J٦E،،Kאאא
אאאאאאאאאאא،אF٢J٦Eאאא،
F٢J٦Eאאאא
F٢J٦Eא
٢J٢אאאSingle- Phase TransformersF٢J٧Eאאאא،
אאאאK
א١٥٣אאאאאא
- ٤٨ -
F٢J٧Eאאאא אאאKאאא
אאאאאK א א אא א א א K
אאאאאאא א SאאאאאאאאאK
אאאא אאא א א אW
F٢–١E2211 IVIVS ≈=
אאאאאFאEאאK
אאאאFאKKEKאאא،א
אKאאאאאW
F٢–١EdtdV Φ
=ΦאאK
אאNאאΦאאWF٢–٣E
dtdNV Φ
=
א١٥٣אאאאאא
- ٤٩ -
אאFאEאF٢J٨E
٢J٨ אאאאאFא
אKEF٢J٣EW
F٢–٤EdtdNV Φ
−=אאאאאאK
אאאאאאאאWF٢J٥EmNfV Φ= 44.4
VאאאFrmsEfאmΦאאאK
אאאאאאאKאאאאאא٢אJ٥K
אאאאF٢J٢EW
F٢–٦EdtdNv Φ
= 11
F٢J٧EdtdNv Φ
= 22
F٢J٨EaNN
vv
==2
1
2
1
i
v
اجتاه الفيض املغناطيسي املعاكس
اجتاه الفيض املغناطيسي األصلي
א١٥٣אאאאאא
- ٥٠ -
aאאKאF٢J٨Erms W
F٢J٩EaNN
VV
==2
1
2
1
٢J٤אאThe Ideal Transformer
אאאאאאאKאאאאאא
אFEKF٢J٩EאאאאW
F٢J٩Eאא
F٢J١٠EdtdNv Φ
−= 11
F٢J١١E dtdNv Φ
−= 22אF٢J١٠EF٢J١١E2vW
F٢J١٢E1
212 N
Nvv =
א11 Vv =22 Vv =
W
N1 N2V1
I1
I2
V2 Zv2v1
א١٥٣אאאאאא
- ٥١ -
F٢J١٣E1
212 N
NVV =
אF٢J١٤E
2
112 N
NII =
F٢J١٥E1
11 I
VZ =
F٢J١٦E2
22 I
VZ =
1Z2ZאאאאאאאאאK
אF٢J١٣EF٢J١٤EאאW
F٢J١٧E2
2
121 ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
NNZZ
WאF٢J١٢EF٢J١٤EF٢J١٧EאאKאאאאF٢J١٠KE
F٢J١٠Eאאאא
٢J١W
א5KVA-480-120 v F٢J١١E120 vKאא؟אאא
N1 N2
I1 I2
V2V1
א١٥٣אאאאאא
- ٥٢ -
F٢J١١E
אW
אאאF2IE
AVS
I 67.411205000
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אאאW
4120480
2
1
2
1 ===VV
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אאאאאא٢J١٤WAI 42.10)67.41(
41
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Load
V = 120
א١٥٣אאאאאא
- ٥٣ -
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א6 m wb؟אW
א٢J٥אאאאW
180)105)(60)(44.4(
24044.4 3
11 =
×=
Φ= −Hz
Vf
VNm
א2N90
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44.4 32
2 =×
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= −HzV
fVN
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902
18012 ===
aNN
2120240
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1 ===VVa
אאא א א אא א א אא א
אאKאF٢J١٢EאZLאאאא
אאK
א١٥٣אאאאאא
- ٥٤ -
I1 I2
V1 ZL
+
-
V2
+
-
N2N1
I1 I2
V1
+
-N2N1
Z'L
( أ )
( ب )
F٢J١٢EאZL אאאאאא
אאאאאFPhasorsEאא،ZL
WF٢J١٨E
2
2
IVZL =
א٢J١٢FEאאאאWF٢J١٩E
1
1'IVZ
L=
F٢J٢٠E 21 aVV =
א١٥٣אאאאאא
- ٥٥ -
F٢J١٢EaII 2
1 =
אF٢J٢٠EF٢J٢١EאF٢J١٩EאאאאאW
F٢J٢٢E
2
22
2
2
1
1'IVa
aIaV
IVZ
L===
F٢J٢٣ELL ZNNZaZ
L
2
2
12'⎟⎟⎠
⎞⎜⎜⎝
⎛==
אF٢J١٣EאאאאK
Z'LV1
+
-
LL ZaZ 2' =
F٢J١٣Eאאא
אאאאאאאW
F٢J٢٤E1
2
1
221'
1 ZNN
aZZ ⎟⎟
⎠
⎞⎜⎜⎝
⎛==
٢J٣W
אאW24000/240 v , 250 KVA , 60 Hz WאJ אFאEa KJ אאאKJ אאאא1I
א١٥٣אאאאאא
- ٥٦ -
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K10
2402400
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1
2
1 ====VV
NNa
KאאW
2211 IVIVS ==A
VSI 67.1041
240250000
22 ===
KאאאאWA
aII 167.104
1067.10412
1 ===
AVSI 167.104
2400250000
11 ===
KאאאאW
Ω=== 2304.067.1041
240
2
2
AV
IVZL
Ω=×==⎟⎟⎠
⎞⎜⎜⎝
⎛= 04.232304.01022
2
2
1'LLL ZaZ
NNZ
אאFא (The Real Transformer
אאאאא K א אF٢J١٤EK
• אאאא1R 2RK • אאא
1Lφ2LφאאאאאאK
• אאK• אmφאK
אF٢J١٤EאאK
1LX2LXאאאאאאאאאK
א١٥٣אאאאאא
- ٥٧ -
V1
I1I2
v2
N1 N2V1
+
-
R2R2
+
-
mΦ
1lΦ
2lΦ
-
+V2
-
+
mΦ1R
1lX 2l
X2R
( أ )
( ب )F٢J١٤Eאא
אF٢J١٥Eא1I W
F٢J٢٥EeIII += '21
WF٢J٢٦E
aII
NNI 2
21
2'2 ==
אאאאKeIאWאCIא1VאmI
אאmφאאCIא،אmIאKאאCImIאאאF٢J١٥Eאא
אאאאCRאאFאEmX אFאKE
א١٥٣אאאאאא
- ٥٨ -
I1 I2
V1
+
-
V2
+
-
N2N1
1R1l
X 1R1l
X
1R1l
X
I'2
Ie
ImIc
E1E2
+
--
+
+ j + j
F٢J١٥Eאאאאאא
א א א F٢J١٥ Eאא א א
אF٢J١٦E
I1
V1
+
-
+
-
1R1X
cR mX
Ie
ImIc
+ j
LL ZaZ 2' =
22
22 XjaRa + a
II 2'2 =
2'
2 aVV ='221 EaEE ==
+
-
F٢J١٦EאאאאאאאאW
2'
2 aVV =אאא2
'2 aEE =אאאאא
aII 2'
2 =אאא
א١٥٣אאאאאא
- ٥٩ -
22
22 XjaRa +אאא
אאאאאאאF٢J١٧KE
I1
+
-
+
-
21
aR
21
aXj
2aRc
2aX m
LZ
22 jXR + aII 2'
2 =
2VaEE 1
2 =
+
-
aVV 1'
1 =
CaI maI
eaI
F٢J١٧Eאאאאא
W
aVV 1'
1 =אאא
21
21
aXj
aR
+אאא
1'1 aII =אאא
mCe aIaIaI += א
٢J٧אאאא(The Equivalent Circuit of A Real Transformer )
אאאאאאF٢אJ٦EאF٢J١٦EאF٢J١٧Eאאא،א
אeIא،אאאאאאF11 jXR +EKאאאאeI
אאאF٢J١٨EאאאF٢J١٨EK
א١٥٣אאאאאא
- ٦٠ -
+
-
CR mX
22
22 XjaRa +
21 aEE =
+
-
1V
CI mI
eI
11 jXR +1I a
I2
+
-
2aV
+
-
CR mX
22
11XaXX eq +=
1V
CI mI
eI
1I aI2
+
-
2aV
22
11RaRReq +=
( أ )
( ب )
+
-
1V
1I aI2
+
-
2aV
111 eqeqeq jXRZ +=
+
-
1V
1I aI2
+
-
2aV
11 eqeq jXZ =
( ج )
( د )
F٢J١٨Eאאאא
אאאאF٢J١٨EW
F٢J٢٧Eeqeqeq jXRZ +=11
א١٥٣אאאאאא
- ٦١ -
F٢J٢٨E2
211
RaRReq +=
F٢J٢٩E22
11XaXX eq +=
אאאאF٢J١٩EW
F٢J٣٠E222
eqeqeq jXRZ += F٢J٣١E22
12
RaRReq +=
F٢J٣٢E22
12
XaXX eq +=
אאאאאאאeI
אאF٢J١٨EF٢J١٩EKאאeqRאeqXא
eqXeqRאF٢J١٨EאF٢J١٩EאאW
F٢J٣٣E11
eqeq jXZ =
F٢J٣٤E22
eqeq jXZ =
א١٥٣אאאאאא
- ٦٢ -
+
-
2aRC
2aX m
22 jXR +
aEE 1
2 =
+
-
aV1
CaI maI
eaI
21
21
aXj
aR
+1aI 2I
+
-
2V
+
-
221
1X
aXXeq +=
aV1
1aI 2I
+
-
2V
221
1R
aRReq +=
2aRC
2aX m
CaI maI
eaI
+
-
aV1
1aI 2I
+
-
2V
222 eqeqeq jXRZ +=
+
-
aV1
1aI 2I
+
-
2V
22 eqeq jXZ =
F٢J١٩Eאאאאאאא
א١٥٣אאאאאא
- ٦٣ -
אאאא אאאאא K
אאאאאKאאאאאאאאאאK
٢J٨J١אאאאThe Open-Circuit Test א א א 1(א(
mee jXR
Y−
، ، א
א אFא E א א،א א אאאאאאאKאא
אאאF٢J٢٠EK
CR mX
Ie
ImIc
A
V
+
-
OCI
OCVV =1
OCp
OCV
W
الدائرة املكافئة. ب
دائرة توضح اختبار الدائرة املفتوحة. أ
F٢J٢٠Eאאאא
א١٥٣אאאאאא
- ٦٤ -
אאW
F٢J٣٥EOCOC
OCOCOC IV
PPF ==θcos
WOCPFאאאאOCθאא
F٢J٣٦EmC
OCOC
OCOCe X
jRV
IYY 11−=−∠== θ
eYאאאאא
F٢J٣٧E
CC G
R 1=
F٢J٣٨Em
m BX 1
=
WF٢J٣٩E2
OC
OCOCC V
PGG =≅א
F٢J٤٠E2122 )( OCOCOCm GYBB −=≅
٢J٨J٢אאאאThe Short Circuit Test אאאאא
،אאאאאא٢٪١٢٪אאKאאאאא
אאאאF٢J٢١EK
א١٥٣אאאאאא
- ٦٥ -
A
Vجهد امللفاالبتدائي بعدخفضه
+
-
SCI
SCVدائرة مغلقة
Close Circuit
SCp
W
الدائرة املكافئة. ب
دائرة توضح اختبار الدائرة املقصورة. أ
+
-
SCV
SCI22 eqeq jXR +
F٢J٢١Eאאאא
אאאאאאW
F٢J٤١E
SC
SCeqSC I
VZZ ==1
F٢J٤٢ESCSC
SCSC IV
PPF =
WF٢J٤٣E111 eqeqSC
SC
SCeq jXR
IVZ +=∠= θ
F٢J٤٤E2
211
RaRReq +=F٢J٤٥E2
211
XaXX eq +=
א١٥٣אאאאאא
- ٦٦ -
W
F٢J٤٦E21SC
SCSCeq I
PRR =≅
F٢J٤٧E( ) 21221 eqeqSCeq RZXX −=≅
אאאאאאאW
F٢J٤٨E2
12
21
eqRRaR ==
F٢J٤٩E2
12
21
eqXXaX ==
٢J٤W15 KVA , 7500/480V- 60 HzKאאאאא(O.C.T)
אאאא(S.C.T)אאאאאאאW
אאאא אאאאאאא
VVSC 366= VVOC 7500= Voltmeter AISC 2= AIOC 2006.0= Ammeter
WPSC 300= WPOC 180= Wattmeter
אאאאאאKאאאאאW
1196.02006.07500
180cos =×
===OCOC
OCOCOC IV
PPF θ
אא٢J٣٦W
OCOC
OCOCe PF
VIYY 1cos−−∠==
( )1196.0cos75002006.0 1−−∠=eY
S129.380000267.0 −∠= Sj 0000265.00000032.0 −=
א١٥٣אאאאאא
- ٦٧ -
mC Xj
R11
−=
W
Ω≅Ω== kRC 5.3123125000000032.0
1
Ω≅Ω== kX m 736.3785.377350000265.0
1אאאאאW
SCSC
SCSC IV
PscPF == θcos
41.02366
300=
×=
∴אאאF٢J٤٣EWPF
IVZZ
SC
SCSCeq
1cos1
−∠==
Ω∠=∠= − 81.6518341.0cos2
366 1Ω+= 93.16675 j
א Transformer Efficiency
אאאאאW
in
out
PP
=ζ
F٢J٥٠Elossin
out
PPP+
=
W• outPאאא• inPאאא• lossPאא
א١٥٣אאאאאא
- ٦٨ -
אF٢J٥٠EW
in
lossin
PPP −
=ζ
F٢J٥١Ein
loss
PP
−=1
אאאאאאאinP
F٢J٥٢ECucoreoutin PPPP ++=W
• corePאאא• CuPאא
F٢J٥٣Eθθ coscos22 outout SIVP ==
θcosאאW
F٢J٥٤E
Cucore PPIVIV
++=
θθζ
coscos
22
22
W 2
221
21 RIRIPCu +=
F٢J٥٥E1
21 eqRI=
SCeq PRI ==2
22
F٢J٥٦EOCcore PP =
אOCcore PP =
א١٥٣אאאאאא
- ٦٩ -
٢J١٠אVoltage Regulation of a Transformer
אאאאאאאאאאאא،אאK
אאאK
F٢J٥٧E( ) ( )( ) 100Re%
2
22 ×−
=loadfullV
loadfullVloadnoVgulationVoltage
א( )aVloadnoV 1
2 =א
F٢J٥٨E( )
( ) 100Re%2
21
×−
=loadfullV
loadfullVaV
gulationVoltage
אאאאאאאאאאאאW
F٢J٥٩E1121 eqZIaVV +=
F٢J٦٠E11 1121 eqeq XjIRIaVV ++=
אאאאאאאאאאW
F٢J٦١E222
1eqZIV
aV
+=
F٢J٦٢E22 222
1eqeq XjIRIV
aV
++=Wאאאאאאא
אאK٢J٥W
100KVA ,200/240V-60Hz KאאאאאאאאW
א١٥٣אאאאאא
- ٧٠ -
אאאאFאאE
אאאאאאא
VVSC 250= VVOC 7500= Voltmeter AI SC 889.13= AIOC 65.0= Ammeter
WPSC 1420= WPOC 425= Wattmeter אאאא٩٠،אW
J אאאאאKJ אאאאKJ אKJ אK
אWKΩ=== 18
889.13250
1SC
SCeq I
VZ
( ) Ω=== 36.72889.13
14201
SC
SCeq I
PR
( ) ( ) Ω=−=−= 43.1636.718 212221221 SCSCeq RZX
KאאWA
VVA
VSI 89.13
7200100000
11 ===
אF٢J٥٢EאWWRIP eqCu 98.141936.789.13 22
1 1=×==
אF٢J٥٦EWWPP OCcore 425==
∴אאW coreCuloss PPP +=
W98.184442598.1419 =+=KאF٢J٥٣EאoutPאאW
kWKVASPout 909.0100cos =×== θאF٢J٥٢EW
WPin 98.9184495.184490000 =+=
א١٥٣אאאאאא
- ٧١ -
אאאF٢J٥١WE9799.0
98.9184498.184411 =−=−=
in
loss
PPζ
KאאF٢J٦٠EאאאאאW ( )
11121 eqeq jXRIaVV ++=( )( )43.1636.784.2589.1307200 00 j+−∠+∠=
V025.119.7393 ∠=
68.21007200
720019.7393
100Re%2
21
=×−
=
×−
=∴aV
aVVqV
%68.2Re =qVאא
אאאאא،K
٢J١١J١אFאאאWEאאאא،אאאא
אאאאא،אאאאאF٢J٢٢E،אאא
FFEE٢J٢٢אאא
אאאאאאאא
Zاحلمل
א١٥٣אאאאאא
- ٧٢ -
א٢J٢٢FEא،אאאאא٢J٢٢FEאאא
אאאK
٢J١١J٢אאאWאאאא
،אאאאאW١K אאK٢K אאK٣K אאאXRאK٤K אא
אאאא،
אKאאאאאK٢١١٣JאאW
אאאאאא،אאאאאא
،אא،אאF∆EFΥKE
F٢J٢٣EW
Υ−ΥאF٢J٢٣FEaE∆−∆אF٢J٢٣FEbE∆−ΥאF٢J٢٣FEcEΥ−∆אF٢J٢٣FEdE
א١٥٣אאאאאא
- ٧٣ -
F٢J٢٣Eא
אFΥEאFNEאאK
• JFΥ−ΥE
א١٥٣אאאאאא
- ٧٤ -
Υ−ΥΥאאאKאאאאאאאא،
א،אאאאאאΥ−Υאאאאא؛
،אאאאΥ−ΥאאאאK
• J∆−∆
∆−∆؛אאא،אאא60KVK
• –∆−Υ
Υאא∆אאF٢٣-٢EKKאאאאFאKE
∆−ΥאאאאK
• –Υ−∆
Υ−∆א–Kאאאאא°30KאאK
• א
אאאאא°30אK
F٢J٦٣EPPLL VV −− =F٢J٦٤E
303 −∠= PL IIא،PאL אK
א١٥٣אאאאאא
- ٧٥ -
• אאאאא
°30אF٢J٦٥EPL II =F٢J٦٦E°∠= −− 303 NLLL VV
• אאאWאאאאאW
θcos3 LLL IVP −=אאθsin3 LLL IVQ −=אא
*3 LLL IVS −=אאW
)(rmsV LL−א)(rmsILא
θאאאLI Is the conjugate of *
LI JJ
F١WEא5KVA , 240-120 V 120 V K
אאאא؟F٢WE
א13.8 KV 2.4 KVא100א KVAK
אWJ אKJ אאאאאKJ אאאK J אאK
א١٥٣אאאאאא
- ٧٦ -
F٣WE75KVA ,2400/240 –60Hz אא
Ω+= 058462.0009318.01
jZeqWאאאא
J 0.85 J אאKJ 0.85 KK
א500KVA , 2300-208 V , 60 Hz אאאאW
אאאא אאאא
V95 V208 Voltmeter A4.217 A85 Ammeter
W8200 W1800 Wattmeter
אWJ אאאאאKJ אאאאאא
0.8 208V KJ אאK
F٤WE75KVA ,2400/240 –60Hz אא
Ω+= 058462.0009318.01
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J 0.85 J אאKJ 0.85 K
א١٥٣אאאאאא
- ٧٧ -
F٥WEא15 MVA 138/13.8 KV K
אאFאEאאW١J –٢J J
אאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
א
٣
١٥٣אאאאאאאא
- ٧٨ -
אאWאאThree Phase Induction Motors
٣J١אאאא
אKאאא،אא،אאאא
אאאאא٥٪אKאא٣J٢אW
אאאאאאאאאאK
אאאא١٢٠،
אאאא،אאאאאאאא
אאאאאאאאאאFאEאאאאK
אאאאאאאאאאאא
אאאאאאאאאא
אאאאאאאא
،F١JEאאKאאאאאאאK
١٥٣אאאאאאאא
- ٧٩ -
אאאאאאאאאאא
אKF٣J١JEאאאאאא
אאאאאאK
אאאאF٣JEאא
F٣JE٣J١
אאאאאאאאאאאאא
אאאK
٣Jא٣אאאRotating Magnetic Field אאאא١٢٠
א?Three Phase Supply?א١٢٠אאא
אאW
١٥٣אאאאאאאא
- ٨٠ -
אאאאאאאאאאKאא
אאWtm ωφφ cos1 =
( )120cos2 −= tm ωφφ ( )240cos3 −= tm ωφφ
אאא١٢٠אאאאאאθאאא
WJ
θωφφ coscos tmt =( ) ( )120cos120cos −−+ θωφ tm( ) ( )120cos120cos +++ θωφ tm
אאאא( ) ( )BABABA ++−= cos
21cos
21coscos
אאאW( )θωφφ −= tmt cos
23
אאאאאא 0=−θωt
θω =t
١٥٣אאאאאאאא
- ٨١ -
tω،אθאאאאאtωK
אאאאאאאאאאאSn
Synchronous SpeedKאאאW
FW٣J١Escn
Pf s /60
=
אf
אאP אאSn
F٣J٢E rpmP
fns60
=
אאאאאאאא
Kאאאאאאאאאאאאא?אא?אא
אאאאאאאאאאאאאא
F٣J٣E) poleturnAmperKIP
TAT wph
ph /35.1=
אאאאאאאאאאאאKאאאאאא
F٣J٢KE
١٥٣אאאאאאאא
- ٨٢ -
٣J٤אWJאא?א?
אאאאאאאאאא
אאאאאKאאאאאאאא
א א אא א א א א אאאאK
אאאאאא
אאאSnLKאאאאאאאאאאmφ
אאאאאאKאאאKKF٣JאE1E
אW
F٣J٤EVoltsNfE m 111 44.4 φ=
אאא1f
אא1Nאאאאאאאאאא
אKKא20Eא
F٣J٥EVoltsNfE m 2120 44.4 φ=
אאאאאאאאא 2N
אאאאאא
١٥٣אאאאאאאא
- ٨٣ -
F٣J٦E220
22
20
20
2020
XR
EZE
I+
==
אאאאאאאאא
אאאאאאאאאאאאאאאאאאא
אאKאF٣J٥E،F٣J٦Eאאאאאא
אא
F٣J٧E2
1
20
1
NN
EE
=
JאאאWאאאאאאאאאאאאאאאאאאאא
אאאn א?Slip Speed K?F٣J٨EnnspeedSlip s −=
אאאאS ?Slip ?א
s
s
nnn
S−
=
F٣J٩E100% ×
−=
s
s
nnn
S
אאאאאאKאאאאאאKKא
אאKKאא2EF٣J١٠E222 44.4 NfE mφ=
אא
١٥٣אאאאאאאא
- ٨٤ -
F٣J١١ESn
nnff
s
s =−
=1
2
F٣J١٢E12 Sff =∴KKאW
F٣J١٣ESn
nnEE
s
s =−
=20
2
F٣J١٤E202 SEE =∴
אאאאאאאא
אKKאאאאאאאאF١٠٪،٢٠٪אא
٠٥٠KE٪אאאאא٣٪٥K٪
אאאאאאאF٣J٢EאאאאאאK
אאאאאאאאאKF٣J٣EאאאאFאKE
W
אאאאאאאאאאאאKKאא،אאאKאאא،אא
KKאאאאאאא،אאאSK
F٣J٢Eא
١٥٣אאאאאאאא
- ٨٥ -
F٣J٣Eא
nאS KK 202 SEE =אאאאF٣J٣Eא02 ≠Iאא
F٣J٤KEאאאSF٣J٤E
F٣J٤Eאא
אאאאאאאWF٣J١٥E
1
2
2
12
NN
II
=
F٣J١٦E2
1
20
1
NN
EE
=
F٣J١٧EoIII += 121
F٣J١٨Emo III += µF٣J١٩EooII φµ cos=F٣J٢٠EooII φµ sin=
oR،oXאאאאאF٣J٢١E
mo I
VR 1=
١٥٣אאאאאאאא
- ٨٦ -
F٣J٢٢Em
mo IVXX 1==
אאאאאאא2
1
NNa =א
F٣J٢٣E22
12 .aRR =
F٣J٢٤E22
12 .aXX =
F٣J٢٥Ea
II 1.212 =
F٣J٢٦E1120 EE =
אאאא
SR1
2SR1
2
12
12
12
12 RR
SR
SR
−+=
⎟⎠⎞
⎜⎝⎛ −+= 111
212 S
RR
F٣J٢٧E⎟⎠⎞
⎜⎝⎛ −
+=S
SRRSR 11
212
12
אאא٥Fאאאא
אאE
F٣J٥Eאאאאאאאאאא٦
F٣J٢٨E( ) ( )21
221
2
12011
2
/ XsR
EEI
+
==
F٣J٢٩EoIII += 121
1111 ZIEV +=F٣J٣٠E22
mo III += µ
١٥٣אאאאאאאא
- ٨٧ -
2
2
I1
I1
I1
2I
2I
2I
2I
1X
1R
V
1E
1E
1
= E2X
Rs
o
oI
II
I
I
I
I
I
F
F
F
1
2
F٣J٦E אאS
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- ٨٨ -
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אאאאF٣J٣١E1111 cos3 φIVP =
1V،1IאאאאאK
אאאאאאאאאאא?1R?אאא
F٣J٣٢E12
11 3 RIPcu =אאאאאא
אאאoRאiPאאאאאאא?stP?
F٣J٣٣Eicust PPP += 1אא1Pאאאאאא
אאאאאאאאאאא
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א2אcuPאF٣J٣٥E2
222 3 RIPcu =
אאאmPF٣J٣٦E212 cum PPP −=אmPאאאאא
אאאאא2Pא
F٣J٣٧EFm PPP −=2FPאאא
١٥٣אאאאאאאא
- ٨٩ -
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W12אPאאאF٣J٥EWP
P
P
P
1
2
12
m
st
cu2
fP
P
P
F٣J٧Eא
F٣J٣٨E21
1212 cos3 φEIP =
F٣J٣٩E
1
12
12
2/cos
EsRI
=φ
אF٣J٣٨E
F٣J٤٠ESR
IP 22212 3=
אF٣J٣٥E،F٣J٣٦EW2
22
222 33 RI
SR
IPm −=
F٣J٤١ESSRIPm
)1(3 222
−=
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- ٩٠ -
א٤٠،٣٥،٤١א،W
F٣J٤٢E( )
SS
RISSR
ISR
I
PPP cum
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3:13:3
::
222
222
222
212
−
−
אSאאאאאאאא
אאאאS١٪אאאK
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אאא?Total Torque?אאאאאאאאא
F٣J٤٣E mN.
602 n
PPT mm
πω==
Or F٣J٤٤E mN.
602
1212
nsPPT
s πω==
א12PאF٣J٣٨E
F٣J٤٥EmN.60
2
cos3 221
snIETπ
φ=
١٥٣אאאאאאאא
- ٩١ -
F٣J٤٦E( ) ( )21
221
2
112
/ XsR
EI+
=
F٣J٤٧E
( ) ( )212
212
2
/
/cosXsR
sR
+=φ
F٣J٤٦E،F٣J٤٧EאF٣J٤٥E
F٣J٤٨EmN.
( )⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛
⋅=
212
212
12
21
602
/3
Xs
Rns
sRET
π
1
2
12
XR
∝=
אF٣J٤٨Eא F٣J٤٩EMN.22
12
21
602
3∝+
∝×
⋅=
SS
XnsET
π
F٣J٥٠E22 ∝+
∝×=
SSKT T
TKאF٣J٥١E
12
21
602
3
XnsEKT
⋅=
π
אאאS11 EV ≅אאאאK
אאאאאTK،∝٨K
١٥٣אאאאאאאא
- ٩٢ -
٨شكل
א∝1
2R1
2
12
XR
∝=
אאאאאאאאאאאאאאK
אא٨W١J אאstTא1=SאF٣J٥٠E
F٣J٥٢E21 ∝+
∝×= Tst KT
٢J אאאאאmaxTKא
אF٣J٥٠E
F٣J٥١E( )( )2
22
22 25.00∝+
∝−∝∝+==
S
sSKdSdT
T
אא
F٣J٥٢E22 =∝mSF٣J٥٣E∝±=∴ mS
אF٣J٥٠E
١٥٣אאאאאאאא
- ٩٣ -
22
2
22max ∝+∝∝
×=∝+∝
= Tm
mT K
SS
KT
F٣J٥٤E21
max ×= TKT
אאאאsnn =אmS،mT FS−1 Esnn =אאאא?Stable Operation?אאFS−1Esnn =א1=S،0=nאאאאא?KUnstable
Operation K?אאאאאא
max21 TT LF =⋅
אאאאאאאאא
אאאאאאF٣J٩Eא1
2RK
F٣J٩E
١٥٣אאאאאאאא
- ٩٤ -
Wאאא∝אאאא
אאאאאF٣J٥٤Eא1א
2RK
٣J٧אאאאאW
٥אאאאאKאאאאאאאאאאV
F٣J١٠EאאK
F٣J١٠Eאאאא
אאF٣J١١E
F٣J١١E
1
21 RRReq +=
F٣J٥٥E 2
2
121 ⎟⎟
⎠
⎞⎜⎜⎝
⎛+=
NN
RR
١٥٣אאאאאאאא
- ٩٥ -
1
21 XXX eq +=
F٣J٥٦E2
2
121 ⎟⎟
⎠
⎞⎜⎜⎝
⎛+=
NNXX
אאאאאא
אא( )s
sR −112אאאא
אאK
٣J٨אאאאא
אאאאאאאאאאK
JאNo-load Test
אאאאאF٣J١١EאאאאZK
א0=SאאאZאאאאאאאאאK
אאאאאאא–א–אאאאאאאאאאאאאאאW
21 WWPo +=אאאאא
אאKF٣J٥٧Eoooo IVP φcos3=
١٥٣אאאאאאאא
- ٩٦ -
F٣J٥٨Eoo
oo IV
P3
cos =∴ φ
F٣J٥٩EooII φη cos=F٣J٦٠Eoom II φsin=F٣J٦١E
µIV
R oo =∴
F٣J٦٢Em
oo I
VX =
F٣J١٢EW
אאאאאאאאאאאאאאK
אאאאאאאאאא
אאאאאK
١٥٣אאאאאאאא
- ٩٧ -
Jא Short Circuit Test
אאאאאאאאא?Blocked Rotor Test ?אאאאF٣J١١Eא
א( ) 011
2 =−S
SR
אא1=Sאאאאאא0=nK
אאאKאאאאאאK
אאאאאKא–אאאא
KאאF٣J١٢EאאאeqR،eqX
F٣J٦٣Eeqcphscs RIP ⋅= ⋅⋅
23אאא
F٣J٦٤Ephcs
cseq I
PR 23 ⋅
⋅=∴
F٣J٦٥E
cs
cseq I
VZ
⋅
⋅=
22
eqeqeq XRZ +=F٣J٦٦E22
eqeqeq RZX −=∴
١٥٣אאאאאאאא
- ٩٨ -
אאאאאאאאאאאoP،csP .
אא100%
1
2 ×=PP
η
F٣J٦٧E100%
2
2 ×++
=⋅cso PPP
Pη
אאאאא
אאK
Jא
אאאאאאאאKאאאאאא
אאאאאאאאFPא
K
١٥٣אאאאאאאא
- ٩٩ -
٣J٩W
١WFE٦٠c /s אא١٧٤٠
r.p.mאאאאאK
אW
rpmP
fns 18002
606060=
×==
rpmn 1740=
nnn s −=∆א
rpm6017401800 =−=
s
s
nnn
S−
=
033.01800
60==
%3.3=٢
٦٥٠c/sאאאאאאא٥٢ c/s אאאאאK
אW05.050
5.2
1
2 ===ffS
( )Snn s −= 1rpmns 1000
35060
=×
=
( )05.011000 −×=nrpm950=
١٥٣אאאאאאאא
- ١٠٠ -
٣א٦٤٤٠v،٥٠c/sאאאאאאKw٨٠
אא١٠٠אc /m FLEאWJאJאאJאאאJאאאאאFאאE
Jאאאאאאא٦٥KאW
033.05060
100
1
2 =×
==ffS
rpmP
fns 10003
506060=
×==
( )Snn −= 12( ) rpm967033.011000 =−×=
80033.0122 ×== sPPcuKw67.2=
KwPm 33.7767.280 =−=
2222 3 RIPcu =
( )
Ω≅×
×==∴ 2.0
6531067.2
3 2
3
22
22 I
PR cu
٤
אא١٠٠٠r.p.m א٥hpFE٩٣٥r.p.m
אאאאאאא٤٠٠אw K
١٥٣אאאאאאאא
- ١٠١ -
אW
WPm 37307465 =×=
065.01000
9351000=
−=
−=
s
s
nnn
S
( )SPPm −= 112
935.0
3730065.01
3730112 =
−=
−=∴
sP
P m
W3990=
stPPP +=∴ 121W43904003990 =+=
85.043903730
1
===PPmη
٥W
א٥٠٠v٥٠c/s ٦٢٠hp٩٥٠r.p.mא٨٦٠אא
١אhpאאאW
JאJאאאאא–אאאאא١٥٠٠wJאאאK
אW
rpmP
fns 10003
506060=
×==
05.01000
50==
−=
s
s
nnn
S
WP 14920746202 =×=
١٥٣אאאאאאאא
- ١٠٢ -
WPPP fm 15666746212 =×=+=
Ws
PP m 16500
95.015666
112 ==−
=
stPPP +=∴ 121W18000150016500 =+=
WsPPcu 8251650005.0122 =×==
φcos3VIP =A
VPI 15.24
86.0500318000
cos3=
××==∴
φ
83.0
1800014920
1
2 ===PP
η
٦W
אא٤٠Kwא٩٧٥r.p.m٥٠٠vc/s٥٠אא٦אאא١Kw
אאא٢KwאאאJאJאאאJאאאאאJאFאE
א
rpmP
fns 10003
506060=
×==
J%5.2025.01000
9751000=
−=
−=
s
s
nnn
S
stPPP −= 112
Kw39140 =−=
J975.039025.0122 =×== sPPcu
١٥٣אאאאאאאא
- ١٠٣ -
212 cum PPP −=
Kw025.38975.039 =−=
fm PPP −=2
025.362025.38 =−=
J( ) hPhpP 50746
360252 ≅=
J%9090.040025.36
==η
٧Wאא٢٤pole٣٠٠٠v٥٠ c/s
Kאאאא٠١٦٠א٢٦٥٠Kאאאאאא٢٤٧r.p.m
אאאאאאאאאאאאאmaxTK
אW
scf /50=PolesP 242 =
247=nΩ= 265.02XΩ= 016.02R
rpmP
fns 25012
506060=
×==
012.0250
247250=
−=
−=
s
s
nnn
S
%2.1=⋅lfS22
lf
lfTlf S
SKT
⋅
⋅⋅ +∝
∝=
21
max ⋅= TKT
١٥٣אאאאאאאא
- ١٠٤ -
lf
lf
lf
lfT
T
lf SS
SS
K
K
TT
⋅
⋅
⋅
⋅⋅ ∝
+∝=
+∝
∝⋅
⋅=
221
22
22
max
06.0
265.0016.0
2
2 ==∝=XR
( ) ( ) 5.2012.006.02
012.006.0 22
≅××
+=
( )msm Snn −= 1אאא( )06.01250 −×=
rpm235=
אאאאא؟max1 S=∝=
22 XRR ext =+12
2 =+
∴X
RR ext
22 RXRext −=016.0265.0 −=
249.0=
٨Wא٦٠٠hp ،٥٠c/sאאאW
אW٢٠٠٠٠w،١٤A،٦٠٠٠vאW٣٠٥٠٠w،٧٠A،١٠٠٠v
אא121 RR =א4
2
1 =NNKאאאאא
א1א201 XX =אK
١٥٣אאאאאאאא
- ١٠٥ -
אWאoo IVP φcos3 11=
138.01460003
20000cos =××
=∴ oφ
99.0sin =∴ oφ07.82=∴ oφAmpII oo 12.1138.0
314cos =×== φµ
AmpII oom 899.03
14sin =×== φ
Ω=== 535712.1
6000
µIVRo
Ω=== 7508
6000
µIVX o
אΩ=== 7.24
370
1000
2IVZ
Ω=
⎟⎟⎠
⎞⎜⎜⎝
⎛×
= 22.6
3703
305002eqR
( ) ( ) Ω=−=−=∴ 94.2322.67.24 2222eqeqeq RZX
Ω===∴ 11.32
121
eqRRR
Ω==== 97.11294.23
2121
eqXXX
( )
Ω=== 748.04
97.1122
12
2 aX
X
( )
Ω=== 194.0411.3
22
12
2 aR
R
١٥٣אאאאאאאא
- ١٠٦ -
٣J١٠אאW אאאאאאאא
אאKאאאאאאאאא
א1=S222 JXRZ += אאאא
אWאאאאאאאאאאאא
אאאאאאאאF٣J١٣KEאא
F٣J٦٨E
( ) ( )2121
2121
1
XXRRR
VIst
st
++++=
אאאאאא
F٣J١٣E
F٣J٦٩E20
2
XRR st+
∝=
١٥٣אאאאאאאא
- ١٠٧ -
∝אאאאאאאאא
F٣J٧٠E120
121X
RRS st
m+
=∝==
אאאF٣J٧١E1
212 RXRst −=
א=∝= 1mSאאאאאאK
אאאאאאאאאא
אKאאאFאאWE
אאאFאאאאEאאW
١Jאאאאאאאאאא،א
אאאאK١٤א
F٣J١٤E
١٥٣אאאאאאאא
- ١٠٨ -
٢JאאאאאAuto Transformer אאFאEאאאאא
אאאKאאאאאאאאאאK
٣JאאאLStar/ Delta Switch
אאאאאא
31א
31אאאאאא
אK
٣J١١אאאWאאאאא،
אאא אא אאאאאאאאאאא
אאW٣J١١J١ אאאאאאא
אWאאאאא
א،אאאאאKאא12אPאאKא
אאא2cuPאS
S−1
אאK
אא١٠٪J١٥٪אאאאאאאאאאאא
K
٣J١١J٢אאאאאW
١٥٣אאאאאאאא
- ١٠٩ -
JאW
אW
אאKאאאאאאK
אאאKאאאFאאKE
C B אאאאאאK
אאאאFHarmonicsEאאא،אאאאאא،אא
אאKאאאא
אא،אאאAKJא
אא
Pfns
60=
snאאאJfאLJPאאK
١٥٣אאאאאאאא
- ١١٠ -
אאאsnn ≅אאKאא
אאאאאאאאFאE
?Dahalander Connection K?אאKא
אK–א
אאאאKאא
FConverter InverterE،אאאא
אאאTאTf 1
=
אאאאאאfV
K
אאאDsnK
T
n
V=100%
V=80%
V=60%
V=40%
لا مزعةحورم
مزعلا
ةعرسلا1234 snnnnn
אאאא
אאאאK
٣J١٢אאאאW
١٥٣אאאאאאאא
- ١١١ -
אאאאאאא٥٠L،٦٠LKאאאאאאK
א٦٠٥٠אא111 44.4 NfE mφ=
אאא11 VE =אא٥٠٦٠אאאא١٠٠١١٥אK
אאFאEאאK٥٠٦٠א
אאאאאאאK
אPns
5060×=
P6060×
א
אאאאאωPT =
K
אאאאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
א
א
٤
א١٥٣אאאאאאאא
- ١١٢ -
אאאWאאא Synchronous Machines
٤J١א אW אאאאאאאאא
אאאKאאאאKאאאאאאSynchronous
Speed אאאאאאאא
F٤J١E 60
spnf =
snאאLPאאf אL
٥٠L K ٣٠٠٠א،١٥٠٠،١٠٠٠
א٢،٤،٦אKא א א א א א
אאאאאאאאא K אאאאאאFStator E
אאאאאאKאאFSEאאאtNF٤J٢E
2ZNt =
Z אאאC Wאא
F٤J٣ENZ
NN
C t
2==
Nאאא
א١٥٣אאאאאאאא
- ١١٣ -
אאאK
אאאאאאאW١JWSalient Pole
אאאאאאאאאK٢JFאWENon Salient Pole
אאאאאאאאאKאאאאאאאא
אאK٤J٢אאאW
אאFאאEFPhase٣Eאאאאאא
א?P2?אאq F٤J٤E
PSq23×
=phTF٤J٥E
332t
phNZT =
×=
א א א אא אאאאאאאא
K א א א אאאאאK
א א א ١٨٠ אKאאא١٢٠K
אאאWJאאWConcentric Coils
אאא א אא אאאא א
אF٤J١E
א١٥٣אאאאאאאא
- ١١٤ -
F٤J٢EF٤J١E
JאאWאאאאאאאא
٢Kאא א
אKאF∆EאFγEא K א א א אא א א Kאא א א
אאאאאאCIK
aI
I ac 2
=a2אאאKאאאאא
K W ٢٤ א א א א
Concentric WindingKאאKא6
424
2===
psy
243
2423
=×
=×
=P
sqKאא
א٢٠،١٩،١٤،١٣،٨،٧،٢،١אF٤J٣E אאאאאK
א١٥٣אאאאאאאא
- ١١٥ -
F٤J٣Eא
٤Jא٣אאאאאW
אאאאאאאאאאאא
אאא אאאא א אאא
F٤J٦Eφ60nPec 2.22=
F٤J٧E
60pnf =
turnVolt /φfec 44.4=
א א א אא א א אא א א א א
אאF٤J٦EאאאאאFWinding FactorEWKאאא
אאאאF٤J٨EturnVoltfE ph /44.4 φ=
אW
א١٥٣אאאאאאאא
- ١١٦ -
אdKאאאאא
F٤J٩E( )( )2sin
2sin∝∝
=q
qK d
qאSא∝אאא
s
p 1802 ×∝=
אCKאאאאא
א١٨٠אאאאאאאCKא
F٤J١٠E⎟⎠⎞
⎜⎝⎛
=2
cos θCK
θאאאאאאאK1א=CKאאZאKאWKא
F٤J١١EdCW KKK ⋅=
١אאאא١٦،١٤٤١٠Kא
٠٣٠אא٣٧٥LKאאאe.m.fאאאאאאא
KאאKSC50
603758
60=
×==
pnf
3316
144=
×=q
א١٥٣אאאאאאאא
- ١١٧ -
°=×
=∝= 20144
8360360S
Pאא
2
20sin3
2203sin
2sin
2sin
°
°×
=∝
∝
=∴q
q
Kd
96.010sin330sin
=°°
=∴ dK
١J١٠א916
1442144
===P
y
10cos =0.1=CK
ddcw KKKK ===∴ 96.0אאא
32×=
ZTphZאא
144010144 =×=×= slotZSZ FE turn240
321440
=×
=phTwphph KTFE φ44.4=
96.024003.05044.4 ××××=voltE ph 1534=
153433 ×== phline EEvolt2655=
٤J٤אאאW
אאאאאאאאאאא
א١٥٣אאאאאאאא
- ١١٨ -
א١٢٠אאKאאאאאאאK
אאאאP2אאאאאאאאאאאאאK
אאאאאאאאאאאאאאאאאK
אאאאאאאאא،אאאאאאאFRotating FieldE
אאאאאאF٤J١٢Ew
phav KI
pT
fmm .35.1.. =
٤J٥אאאFאאWE
אאFaIEאאאאאאאאphT
KKKKF٤J١٣Ewa
pha KI
pT
fmm .35.1.. =
אאאPfmm ..
אffP INfmm ... =
Patotal fmmfmmfmm ...... +=
אאאאאאאאאאאRφאאאאאאא
א phEK
א١٥٣אאאאאאאא
- ١١٩ -
אאVאאאFEaR אlXFPhase Leakage ReactanceEaI
F٤J١٤E( )laaphph jXRIVE ++=
אאאKאאאאא
אאאאאאאoEא
F٤J١٥EWpho KfTE ..44.4 φ=
אאVoE אאאאא
VVEo −אאאאξ
F٤J١٦EV
VEo −=ξא
אאאאאאאאאאאאאאאW
١J אאאאאK٢J אFאKE٣J אאאאאאK٤J אאאאאK
אאאWאF٤J١Eאאאאאא
אZ١אאאאאF٤J١٧Eat EEE +=
אאFφtφאאאאאאאaφ K
א١٥٣אאאאאאאא
- ١٢٠ -
ϕ
ϕϕ
F٤J٤Eאאא
אF٤J٤EאאאאאאאאאאאאאאאאאaEא
aIaIא٩٠K Ea α Ia (4-18)
אאaEאFEאאאאאאא
אאאא٩٠אאaXK
F٤J٢EאaRaXאאאאאאK
( )aaas XxjrZ ++=F٤J١٩Esa jXr +=
F٤J٢٠Eaas XxX +=δ
ϕ
F٤J٥EאF٤J٦Eאאא
א١٥٣אאאאאאאא
- ١٢١ -
F٤J٥EאאאאF٤J٦EאאtEאV،E sXא
אאKF٤J٢١Eaas xXX +=
אאא)٢٢ -٤ ( 100% ×
−=
VVEξ
٤J٦אאאFאאE–אNo Load Test
אאאאאאאאFאאאEאאאאאאF٧-٤E
)الالحمل(الدائرة المفتوحة ) ٧-٤ (شكل אאאאאא
אאאאאKF٤J٨Eאא
"Open Circuit Charact ) " O.C.C(
F٤J٨Eאאא
א١٥٣אאאאאאאא
- ١٢٢ -
JאShort Cir. Test אאאאאאא
אאאF٤J٩KEאאK
F٤J٩Eא
אאאאאSZaI
E
FIאאSZF٤J٨Eאאאאאא
אאאאאF٤J١٠KE
P
P
x
x
x
x
x
xx
Ia
iron
F٤J١٠E
אWאHאאFא٪١SZE
אSS ZX =אאא٩٠KאאאK
א١٥٣אאאאאאאא
- ١٢٣ -
אVoltage Regulatim אאאאאאאאא
אאאא?Protection?אאFParallel OperationEאK
אאאאאאאאאאאאK
א אא א א א אKאאא
F٤J٢٣E100% ×−
=V
VEoξאoEאאאא
Vאאאאאאאאאאא
אאKאאאאאאK
אאאאאאאW
١JאאאSyn.Impedence Methodאאאאאאאאאאא
SZ،aR22
ass RZX −=אF٤J١EאאאEאI
אאא F٤J٢٤E100
sincos% ×
+=
VIXIR sa φφ
ξ• אAmpere-turn Method
אאאאאאאKאK
א١٥٣אאאאאאאא
- ١٢٤ -
٤J٧אאאאאWאIאאאאF٤J٢٦Eφcos30 VIP =
I،VאאKI،EFδφאאאאאאאEא +E
אאאאF٤J٢٧E)cos(31 δφ += EIPאאאאaRF٤J٢٨E)cos(3)cos(31 aIRVIEIP +=+= φδφ
]cos[3 2aRIVI += ϕ
אאaRI 2אFאEF٤J٢٩EoPP ≅1
א
F٤J٣٠Eos
PXEVP ≅= δsin3
1אאאאאאאא
א
F٤J٣١EωPT =
ωאאFsωE
F٤J٣٢Ess wXEVT 1.sin3 δ=∴
אאδאאאאאאא
אאKאF٤J٣٠E،F٤J٣٢EEאא
אP ،T δsin אאK
א١٥٣אאאאאאאא
- ١٢٥ -
אאאאאאParallel Operation of S.M.
٤J٨אאאאאאParallel Operation of S.M. אאZ1Z،1Eאאא
،אאאא2אZ ،2Eאאאאאאאא1I،2IאאI
F٤J١١KE
2
ZI
E
ZI
E1
11
2
22
sI
Z
I
F٤J١١Eאא
אאאא21 Zz =،21 EE =
אא
21 II =א،אא1E،2Eא1Z
1Z
EEE == 21222111 ZIEZIEV −=−=2211 ZIEZIEV −=−=∴
21 III +=2211 ZIZI =
F٤J٣٣E21
21 ZZ
ZII+
=∴
F٤J٣٤E21
12 ZZ
ZII+
=
אאאאאאאאאאW
א١٥٣אאאאאאאא
- ١٢٦ -
JאאאאאאKJאKJאאאFאאאA1A،B 1B،C 1CKEJאFPhase Shift KEאאאאא
אאאאאאאאאא
SIאאאאאאKאאאאאאFSynch. powerEא
אאאאKF٤J٣٥E221 IEIEP ss ≅≅
אאאאאKאאאKKSXF٤J١١E21 III +=
אאאKאאאSIא
21
21
ZZEFI s +
−=
א١،٢W Z1،Z2
٤J٩אאאW
A Synchronous Machine On Infinite Bus-Bars אאאאאא
אאאאKאאאאאW
١JאK٢JאK
א١٥٣אאאאאאאא
- ١٢٧ -
٣JאK٤JאאK
F٤J١٢Eא
W
١JאאאאF٤-١٢Eאאא١א١א١א٢
א٢א٣٣א٣א٢Kאאאאא٢،٣א
אאאאbm VV =0=SV
אKK
אאאאאאאאאאK
אאאKאאאאאא
אאאאאאא١א٢،٣אKאא
אאאאS K
א١٥٣אאאאאאאא
- ١٢٨ -
٢JאאאSynchroscopeאאאאאאאאאK
אאאאאאאאאאאאא
אאאאאאאאK
F٤J١٣EאאאאSynchroscopeאא
אאאאאK
F٤J١٣Eאאאא
٤J١٠אאאFאאESynchronous Motors
אאאאאאאאאאאאא
F٤J٣٨EPfns
60=
אאאאאאאאאK
אא( )δsinאF٤J٣٢E
ss wXEVT 1.sin3 δ=
אאאאKאאאאK
א١٥٣אאאאאאאא
- ١٢٩ -
אאאאאאKאאאאאK
٤J١٠J١אאאW١-אאאא
אאאאאאאאאאאאאאK
٢-אDamping Coilsאאאאא
אK אאאא
אאאאאאאאאKאאאא
אאאאK٤J١٠J٢V?The V-Curves?אאW
אאאאאאK
F٤J١٤EאאV-CurvesאKאאאאאאאא½،¼،F.LאV-Curves
אVאאKאF٤J١٥KELeadLag א
אאאאא אאאאאUnity P.F. line
א١٥٣אאאאאאאא
- ١٣٠ -
F٤J١٥EVF٤J١٤Eאא
٤J١٠J٣אFאEEfficiency
אאאאאאKאאאאW
אאאאאאK
אאK אK
אאאא
φcos3VIPo =φcos3VIPi =
א
F٤J٣٩E100% ×
+=
lossesPP
o
oξ
F٤J٤٠E100% ×
−=
o
o
PlossesP
ξ
٤J١٠J٤אאאאאW
אאאאW١JאאאThe Syn.Capacitor ( compensator )
אאאאאKאאאאאאא
א١٥٣אאאאאאאא
- ١٣١ -
אאא١٠٠אאאK
٢JאPower-Factor Correction אאאא
אאאאאאאאאאא
אאאאאאאאאאא
KאאאאאאאKאאאאא
K٤J١٠J٥אאאW
١א٧٢،٦
٢٠א،65
אאKא6108.4א ×( )048.0אא١٢٠٠LKאWJא dKJא CK
JאאאאאKאW
scpnF 6060
1200360
=×==
180
65180 ×−=θ
،2cosθ
=cK
°=−= 30150180
967.02
30cos ==∴ cK
4
6372
=×
=×
=عدداألوجةعدداألقطاب
qعددالمجاري
א١٥٣אאאאאאאא
- ١٣٢ -
°=
×∝= 15
721806
( )
( )( )
( )215sin42154sin
2sin2sin ×
=∝∝
=q
qK d
cdw KKK .=،95.0=∴ dK
TurnNTph 480
3272202
=×
××=
Turn4803
7220=
×=
wphph KTfE φ44.4= 917.095.0480048.06044.4 ×××××=
VoltE ph 5347=
٢Wא١٦٣٧٥L١٤٤٧
אאאאאא٠٣٨٩٠אאאא١٦٠אKאא
אKאW
3
163144
=×
=q
scnpf 50
603758
60=×==
°=−= 20160180θאא
985.0220cos
2cos ===
θcK
°=
×∝= 20
33180
( ) ( )
⎟⎠⎞
⎜⎝⎛×
=⎟⎠⎞
⎜⎝⎛ ∝∝
=
220sin3
2203sin
2sin
2sin
q
qK d
96.0=dK
א١٥٣אאאאאאאא
- ١٣٣ -
אא
10087144 =×=Z
TurnZN 84
121008
232==
××=
dcph KNKfE φ44.4=
96.0985.0840389.05044.4 ×××××=6859=
1188068593 =×=∴ lineE
٣אא٥٠LK١٠٠٠א٢٥٪אאאא٣٣٠٠א٣٧٥LK
א3=qאF٩٦٠Eאא٠٥٨١٠K
אאאKאW
δ=
×=∴
3755060P
60pnf =
VV 1905
33300
==
VVEo −
== 25%ξ
VoltEo 25.2381=∴،19051905
25.0−
=∴ oE
96.00581.05044.425.2381 ××××= phN،wNKfE φ44.4=
turnN ph 192=
condcond 8
1632192
=×
×=
א١٥٣אאאאאאאא
- ١٣٤ -
٤Wא٢٣٠٠٢٠אא٢٢
٥٠אא٢٠٠KKאאאאWא
אWאאphI ،phV
1328
32300
==phV
AI ph 200=א5.0cos 1−°60אאא°60
אא
IX s
ϕ
א
( ) ( )22 sincos IXVIRVE ph ++−= φφ( ) ( )22 2.2200868.013282.02005.01328 ×+×+×−×=phE
voltE ph 1708≅א phEאאאאאאא
אאK
٥אא٢٥٠٤٠٤אאא
אא٤٠٠٠אאאKאWאאאKאאאאאK
א١٥٣אאאאאאאא
- ١٣٥ -
אW
0.1cos =φRIVIP 2cos −= φ
24.02504000 II −=040002504.0 2 =+− II
( )
4.0240004.04250250 2
×××−±
=I
AmpI 5.16=∴( ) ( )22 sincos IXVIRVE ++−= φφ
( ) ( )22 45.164.05.16250 ×+×−=VE 2.252=∴
א١٥٣אא
א
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٣Jאאאא) electromotive force (e.m.f ) equation ( E.............................................٤ ٦Jאאא...........................................................................................................................٧ ٧Jאאא: ......................................................................................١٠
١٢Jאאא.................................................................................................................................١٤ ١JאאאאאW................................................................................................١٤
١٢JאאאאW....................................................................................١٥ ٢Jאאאא: ...........................................................................................................................١٩
٢١Jאא: ...................................................................................................................................١٩ ٢٢JאאW...................................................................................................................................٢٢
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١J................................................................................................................................................٢٩ ٢JאאאאW..........................................................................٢٩ ٣Jאאאא....................................................................................................................٣٥ ٤Jאאא.............................................................................................................٣٩
אאWא٤٣............................................................................................................................א א TRANSFORMER CONSTRUCTION....................................................................٤٣
٢J٢אאאSingle- Phase Transformers............................................................................٤٧ א.......................................................................................................................................٤٨
٢J٤אאThe Ideal Transformer........................................................................................٥٠ אא................................................................................................................................٥٣
אאFא (The Real Transformer.....................................................................................٥٦ ٢J٧אאאא(The Equivalent Circuit of A Real Transformer )............................٥٩
אאא....................................................................................................................٦٣ ٢J٨J١אאאאThe Open-Circuit Test...........................................................................٦٣ ٢J٨J٢אאאאThe Short Circuit Test...........................................................................٦٤
א Transformer Efficiency...................................................................................................٦٧ ٢J١٠אVoltage Regulation of a Transformer...............................................٦٩
א٧١..................................................................................................................................א ٢J١١J١אFאאאWE.................................................................................٧١ ٢J١١J٢אאאW.........................................................................................................٧٢
א١٥٣אא
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٣٫١١٫٢JאאW.......................................................................................................٧٢
אאWא٧٨.............................................................................................................................א ٣J١א...............................................................................................................................................٧٨ ٣J٢אW...........................................................................................................................................٧٨
٣J٣אאאאRotating Magnetic Field...........................................................................٧٩ ٣J٤אW...........................................................................................................................٨٢
٣J٥אאWPower Relations For I.M.....................................................................٨٨ ٣J٦אאTorque..........................................................................................................- ٩٠ - ٣J٩W..............................................................................................................................- ٩٩ -
٣J١٠אאW.....................................................................................................- ١٠٥ - ٣J١١J١ אאאאאאאאW...........................................................- ١٠٨ - ٣J١١J٢אאאאאW.......................................................................- ١٠٨ - ٣J١٢אאאאW.............................................................- ١١٠ -
אאאWאאא.........................................................................................................................- ١١٢ - ٤J١א אW.........................................................................................................................- ١١٢ - ٤J٢אאאW.......................................................................................................- ١١٣ - ٤J٣אאאאאא..................................................................................- ١١٥ -
٤J٥אאאFאאWE.........................................................................................- ١١٨ - ٤J٦אאאFאאE..................................................................................................- ١٢١ -
אVoltage Regulatim....................................................................................................- ١٢٣ - ٤J٧אאאאאW...................................................................................................- ١٢٤ - ٤J٨אאאאאאParallel Operation of S.M..................................................- ١٢٥ -
٤J٩אאאW...................................................................................- ١٢٦ - ٤J١٠J٢V?The V-Curves?אאW..................................................................- ١٢٩ - ٤J١٠J٣אFאEEfficiency.........................................................................................- ١٣٠ - ٤J١٠J٤אאאאאW................................................................................- ١٣٠ - ٤J١٠J٥אאאW...................................................................................- ١٣١ -
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