Piyadanai Pachanapan, 303427 Power System Analysis, EE

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?????????????????????????? ???????????????????????
????????
Piyadanai Pachanapan, 303427 Power System
Analysis, EECPE, NU
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??????????????????????????????????????????????? Sy
nchronous Generator Modeling in Steady State
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??????????????????????????? (Synchronous
Generator)
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??????????????
Cylindrical Rotor / Round Rotor
Salient - Pole Rotor
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Rotation produced flux linkage variation.
(a) Flux is perpendicular to phase A (b) Flux is
parallel to phase A
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Flux Linkage ( )
N
- ???????????????????????????
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• ?????????? Flux Linkage ???????????????????
  ???????

• ????????????????????? (Voltage Induce) ????????
  ???????

8

• ??? RMS ????????????????????? (Internal
  Generate Voltage) ???????

• ????????????? emf ??????????????????????? (Slot
  ????????) ?????

?????? ??????? 3 ??? ???
??????????? 0.85 0.95
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????????????? (No Load)

• ????????????????????????????????????? (Vt)
  ??????? ????????????????????????????? (E)

• ??????????????????????? ???? 90o

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• ??????? (Frequency) ?????????????????????????????
  ?

???????????????????????????????????????????????
??????????????????
f
- Electrical Frequency (Hz)
??????
- Speed of Roter (r/min)
n
P
- Number of poles
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??????????????????????????
Field Current
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????????????????? (ON Load)

• ???????????????????????????

• ????????????????????????????????????? (Vt)
  ?????????? ????????????????????????????? (E)
  ?????????????????

1. ????????????????????????????????????
   ???????????????????????????????????? (Armature
   Reaction)

2. ??????? self inductance ?????????????????????
3. ???????????????????????????????????????
4. ?????????????????????????????(???????)
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• ???????????????? 3 ??? ??????????? ????????????

?????
?????????????????????? ????????
????????????????????? (e)

• ?????????????????????????????????????????????????
  ?????????? ?????????? ????????????????????????????
  ??????

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• ???? (Amplitude) ??? mmf ???????????
  ????????????? (proportional) ?????????????????????
  ?????????

??????????????
K
?????
???????????????????????????????????????? ???
????????????
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Field mmf

• ???? Round Rotor (On load)

Fr ???? mmf ???????? no load generated emf E
?????????? ???? ??????????
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• ?????? armature mmf ?????????????????????????
  mmf ?????????????????????????

• ?????????????? ?????????????????????
  ???????????????? mn ??????????????????? mn

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????????????????????????????? mn
???????????????????? ?????
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??????????????????????????????? mn
???????????????????? ?????
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• Amplitude of the resultant armature mmf / Stator
  mmf

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Phase / vector Diagram for Round Rotor
Synchronous Machine
Fsr The Resultant mmf
??????? armature reaction
Fsr Fr Fs
Esr On load induced generated emf
Ear the amature reaction voltage
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Xar reactance of the armature reactance
Ra armature resistance
Xl leakage reactance
Xs synchronous reactance
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????????? Xl ????????????
- Power Angle
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• Synchronous Machine Equivalent circuit (Round
  Rotor)

V Terminal Voltage

• Synchronous Machine Connect to an infinite bus
  (Round Rotor)

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• Synchronous Generator Phase Diagram

?????????????????????????????????????????
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• ???????????? XS ???????????? Ra ??? ? ?????? Ra
  ???

E ????????????
??????????????????????????
Eg
Em
????????????????????
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????????????
??????????????????
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• ???? Salient-Pole Rotor (On load)

• air gap ??????????? ? Magnetic Reluctance
  ???????????

• ??? ???????????????????????????????????
  ??? ???????????????????????????

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d
??? d - direct axis
??? q - quadrature axis
q
??????
- ???????? ,
- ?????????
??????????????????????? Id ??? Iq
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• Phasor Diagram for a salient pole generator

The Excitation Voltage Magnitude ???????
?????
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• ????????????????

?????
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• ???????????????????????????????? Id ??? Iq
  ???????

• ?????????????? 3 ??? ?????????????????????????
  ???????

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• ?????? Id ??? Iq ??????????????????? 3 ???
  ???????

• ?????????????????????????????? Reluctance Power

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???? ???????????????????????? ?????????????????

• ????????? X/R ??????????? (X gtgt R)

• ??????????????????? (Power Factor) ??????????????

• ????? Iq ????????????????

• ?????????????????? ??????????????????????????????
  ???????????????

• ??????????? Xd ??? Salient Pole ?????? Xs ???
  round rotor ???

• ??? Xd ???????????????????????????????????????

• ??? Xd ?????????????????????????
  ?????????????????????

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• Synchronous Machine Equivalent circuit (Salient
  Pole)

V Terminal Voltage

• Synchronous Machine Connect to an infinite bus
  (Salient Pole)

Short Circuit Case
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??????????????????????????????? Fault Current at
Generator Terminal
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???????????????????????????????

• ???????????????????????????????????
  ???????????????????????????? (e.m.f, Eg)
  ???????????????????????

• ????????????? ???????????

- ?????????????????????
- ??????????????????????????? (AVR, Governor)
- ?????????????????????????????????????????
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?????????????????????????? RL
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• ???? ??????????????????????????????? ?????

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???????????????????? 1 ????????????
- sinusoid - a.c. component
- exponential - d.c. component / d.c. offset
?????????
??????
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• ???????????? ???????????

????
????????? ????????? Z
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• ???????????? ???????????

????
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????????????????????????????
?????
(???????????)

• ?????

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??????????
????????????????? (D.C. Component)
??????????????????
- D.C. Component ??????????? ????? ????????????
????????????
- D.C. Component ???????????? ????? ????????????
???????????? ?????
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????????????? 3 ??? ????? ??????? 120O
?????????????????????????????????????????????
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??????????? 1
???????????? ????? ???
???????????????????????????
???????????????????????????????????
??????????? ??????

1. ????? DC Offset
2. ????? DC Offset ?????????

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???

• ?????

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• ??????????????????????

1. ????? DC Offset

?????
2. ?? DC Offset ??????
?????
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????????????????????? matlab
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??????? 1
??????? 2
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?????????????????????????????????
???? Symmetrical Fault
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????????????????????? a.c. component (t 0, e
Vmax)
0
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????????? Sub - transient

• ????????????????????????????????????????????
  (Air Gap) ??????? ????????????????????????????? R
  ltlt L ????????????????????????

????????? Transient

• ?????????????????????? Damper ????????????
  ????????????????? ??? ???????????????????????

????????? Steady

• ??????????????????????????????? ????????????????

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??? rms ???????????????

• Sub Transient

• Transient

• Steady

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??????????????????????????????????

• ?????????????????????????????????????????????????
  ???????? (direct axis reactance)

• ???????????????????????????????????????

- ???? oc ??? Subtransient direct axis reactance
- ???? ob ??? Transient direct axis reactance
- ???? oa ??? Direct axis reactance
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??? rms ???????????????
???????? IC

• Sub Transient

• Transient

• Steady

?????
??? rms ??????????????????????????????????????????
???? (rms, e.m.f.)
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???????????????????????????????????????
????? Xd
- ??????????????????????????????????????????
- ?????????????????????????????? (manufactorys
data)
????? Xd, Xd
- ???????????????????????? ?????? Oscilloscope
- ???????????????????? semi-log ???????????? ?????
- ????? ??????? Xd, Xd
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???????? Oscilloscope
??????? Semilog
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??????????????
???
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????? Xd, Xd
???
???????????????? d ?????????????? q
???????????????????????????? Iq ????????????
????????????? Id
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???????? ?????????????????????????????????????????
???
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Effect of Load Current

• ???????????????????????????????????????????????

V
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??????????? 2
?????????????????? 2 ??????? ?????????????????????
????????????????? ??? ??????? 75,000
kVA, kV ??????????????? 8
????????????????????????????????????????????
G1 50,000 kVA, 12 kV, X 20
G2 25,000 kVA, 12 kV, X 20
????????????? ????????????????????? 66 kV
???????????????????? ??????????????????
?????????????????????????????????????????????????
???????????????? 3 ??? ?????????????????????
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?????? MVAbase 75,000 kVA
??????base 12 kV
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??? p.u. ?????????????
G1
G2
????????
?????????????????????
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????????? 2 ???????????? ? ???????????????????????
????

• ??????????????????????? p.u.

p.u.
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VLV
p.u.
??????????????????????????? (???? )
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????? sub transient ?????????????????????????????
G1
p.u.
????????
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????? sub transient ?????????????????????????????
G2
p.u.
????????