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Power System Stability II Session 15d
Ignore amortisseur windings.
L
mdp
L
mdu
L
Lfd
Given: (^) P := 0.9 Q := 0.3 V
as
1.0 e
j 36⋅ ⋅deg
:= ⋅
L
mdp
S := P +j Q⋅ S =0.9 +0.3i
X
mdp
L
mdp
φ := arg S( ) φ =18.4349 deg
I
as
S
V
as
:= I
as
= 0.9487 arg I as
( )
=17.5651 deg
α arg V as
( )
:= α =36 deg
at
V
as
I
as
R
a
j X L
( )
I
A
sat
e
B sat
Ψ at
Ψ TI
− ( )
⋅
I
K
sd
at
at
I
:= K
sd
K
sq
K
sd
:= K
sq
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
R
fd
:= 0.0006 L
Lfd
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Power System Stability II Session 15d
arg i
( fdphasor0)
=−10.8745 deg
i fdphasor
i =1. fdphasor
E
as
j X md
arg E
( as0)
E =79.1255 deg as
E =2.
as
E
qas
j X d
X
q
⋅ I
ad
arg I
( aq0)
I =79.1255 deg aq
I =0.
aq
I
as
cos δ i
+φ
⋅ e
j θ r
π
2
⋅
arg I
( ad0)
I =−10.8745 deg ad
I =0.
ad
I
as
sin δ i
+φ
⋅ e
j θ r
⋅
θ r
θ =−10.8745 deg r
arg E
( qas)
π
δ i
δ =43.13 deg i
arg E
( qas)
:= −α
L
md
K
sd
L
mdu
:= ⋅ L
md
L
mq
K
sq
L
mqu
L
mq
L
d
L
md
L
L
:= + L
d
L
q
L
mq
L
L
:= + L
q
X
md
L
md
X
q
L
q
:= X
d
L
d
E
B
V
as
j 0.65⋅ I as
:= − ⋅ E
B
= 0.9951 arg E
( B)
=− 0 deg
E
qas
V
as
R
a
j X q
I
as
E
qas
= 1.998 arg E
( qas)
=79.1255 deg
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Power System Stability II Session 15d
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
L
qi
L =0.
qi
L
mqi
L
L
L
di
L =0.
di
L
mdi
L
L
L
mqi
md
L
md
I
fd
I
d
( )
md
mq
L
mq
− I
q
mq
δ 0
δ i
:= +α
δ 0
=79.13 deg
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
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Power System Stability II Session 15d
a
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
⋅ X
Td
cos δ
D
m 1
m =1. 1
E
B
X
Tq
sin δ
⋅ R
T
cos δ
D
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