Solved Examples on the Power System Stability | ECE 504, Study notes of Electrical and Electronics Engineering

Material Type: Notes; Class: ST:Control Systems and Critical Infrastructures; Subject: Electrical & Computer Engr; University: University of Idaho; Term: Spring 2007;

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ECE 504 ST:
Power System Stability Example 12.3 University of Idaho
Session 38d
Rfd 0.0006:= LLfd 0.153:=
Given: P 0.9:= Q 0.3:= Vas 1.0 ej36deg
:=
Steady State
Small Signal
Ksdinc 1
1B
sat Asat
eBsat Ψat0 ΨTI
()
+
:= Ksdinc 0.4337=
Ksqinc Ksdinc
:=
RE0:=
RTRaRE
+:= RT310
3
×=
XE0.65:=
Lmdi Ksdinc Lmdu
:= Lmdi 0.7156=
Lmqi Ksqinc Lmqu
:= Lmqi 0.694=
Ldi Lmdi LL
+:= Ldi 0.8756=
Lqi Lmqi LL
+:= Lqi 0.854=
kVA kW:= MVA 106W:= rev 1:= j1:= m10 3:=
ORIGIN 1:=
Example 12.3 All values are in pu unless noted otherwise.
Xdu 1.81:= Xqu 1.76:= Xdp 0.3:= XL0.16:=
Ra0.003:= Tdop 8.0 sec:= H 3.5:= KD0.0:=
Asat 0.031:= Bsat 6.93:= ΨTI 0.8:= Ldp Xdp
:=
Lmdu 1.65:= Lmqu 1.60:= LLXL
:= Xs0.65:=
C:\JLAW\CLASSES\S07 ECE 504
\HANDOUTS\Small Signal
\s38d.mcd
Page 1 of 3 April 20, 2007
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Power System Stability Session 38d

R

fd

:= 0.0006 L

Lfd

Given: (^) P := 0.9 Q := 0.3 V as

1.0 e

j 36⋅ ⋅deg := ⋅

Steady State

Small Signal

K

sdinc

1 B

sat

A

sat

⋅ e

B sat

Ψ at

Ψ TI

K

sdinc

K

sqinc

K

sdinc

R
E
R
T
R

a

R
E
:= + R
T

− 3 = ×

X
E
L

mdi

K

sdinc

L

mdu

:= ⋅ L

mdi

L

mqi

K

sqinc

L

mqu

L

mqi

L

di

L

mdi

L
L
:= + L

di

L

qi

L

mqi

L
L
:= + L

qi

kVA := kW MVA 10

6 := W rev := 1 j := − 1 mΩ 10

− 3 := ⋅Ω

ORIGIN := 1

Example 12.3 All values are in pu unless noted otherwise.

X

du

:= 1.81 X

qu

:= 1.76 X

dp

:= 0.3 X
L
R

a

:= 0.003 T

dop

:= 8.0 sec⋅ H := 3.5 K D

A

sat

:= 0.031 B

sat

TI
:= 0.8 L

dp

X

dp

L

mdu

:= 1.65 L

mqu

:= 1.60 L
L
X
L
:= X

s

C:\JLAW\CLASSES\S07 ECE 504

\HANDOUTS\Small Signal

Page 1 of 3 April 20, 2007

Power System Stability Session 38d

a 3 3,

− 2 ⋅ 60 ⋅ πR fd

L

Lfd

L

mdpi

L

Lfd

− m 2

L

mdpi

a := ⋅ 3 2,

− 2 ⋅ 60 ⋅ πR fd

L

Lfd

m 1

⋅ L

mdpi

a := ⋅ 3 1,

a 2 3,

a := 0 2 2,

a := 0 2 1,

:=2 60⋅ ⋅π

a 1 3,

K
2 H⋅

a := 1 2,

K
2 H⋅

a := 1 1,

K
D
2 H⋅
K
K =0.

n 2

md

L

mqi

I

d

⋅ m 2

mq

L

mdpi

I

q

L

mdpi

L

Lfd

I

q

K
K =0.

n 1

md

L

mqi

I

d

⋅ m 1

mq

L

mdpi

I

q

n 2

n =0. 2

R
T
D
L

mdi

L

mdi

L

Lfd

m 2

m =0. 2

X

Tq

D
L

mdi

L

mdi

L

Lfd

n 1

n =0. 1

E
B
R
T

sin δ 0

⋅ X

Td

cos δ 0

D

m 1

m =1. 1

E
B
X

Tq

sin δ 0

⋅ R
T

cos δ 0

D
D R
T

2 X Tq

X

Td

X

Td

X =0.

Td

X
E
X

mdpi

+ X
L
X

mdpi

L

mdpi

X

Tq

X =1.

Tq

X
E
X

qi

L

mdpi

X

di

L

di

X :=

qi

L

qi

X

mdi

L

mdi

L

mdpi

L

mdi

L

Lfd

C:\JLAW\CLASSES\S07 ECE 504

\HANDOUTS\Small Signal

Page 2 of 3 April 20, 2007