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Lecture Notes on Power System Stability II | ECE 504, Study notes of Electrical and Electronics Engineering

University of Idaho (U of I)Electrical and Electronics Engineering

Material Type: Notes; Class: ST:Control Systems and Critical Infrastructures; Subject: Electrical & Computer Engr; University: University of Idaho; Term: Spring 2005;

Typology: Study notes

Pre 2010

Uploaded on 08/19/2009

koofers-user-c8h
koofers-user-c8h 🇺🇸

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ECE 504 Power System Stability II Session 28b
Phasor Diagrams
n01,Nmax Nmax2
+..:=
In
PjQ
n
⋅−
VRn
:=VRnVRnej−β
n
⋅
⋅:=
VRn
βn
Find VRnβn
,
:=
Qn
EV
Rn
⋅
Xcos βn
()
⋅
VRn
2
X
−=P
EV
Rn
⋅
Xsin βn
()
⋅=
Given
Qn
nN
max
−
()
Nmax
Qlead Qlag
−
()
⋅Qlag
+:= βn120 deg⋅:=VRn0.3:=
Qlead 0.2−:=Qlag 0.20:=nN
max 1+Nmax Nmax2
+..:=Nmax2 20:=
In
PjQ
n
⋅−
VRn
:=VRnVRnej−β
n
⋅
⋅:=
VRn
βn
Find VRnβn
,
:=
Qn
EV
Rn
⋅
Xcos βn
()
⋅
VRn
2
X
−=P
EV
Rn
⋅
Xsin βn
()
⋅=
Given
Qn
n
Nmax
Qlag Qlead
−
()
⋅Qlead
+:= βn20 deg⋅:=VRn0.9:=
Qlag 0.21:=Qlead 0.2−:=n01,Nmax
..:=Nmax 20:=
j1−:=X 1.0:=E 1.0:=P 0.2:=
C:\JLAW\CLASSES\S05PSSII
\HANDOUTS\s28b.mcd
Page 1 of 2 March 28, 2005
pf2

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ECE 504 Power System Stability II Session 28b

Phasor Diagrams

n 0 1, N max

N

max

I

n

P j Q n

V

R

n

V :=

R

n

V

R

n

e

− jβ n ⋅

:= ⋅

V

R

n

β n

Find V R n

β n

Q

n

E V

R

n

X

cos β

( n)

V

R

n

2

X

P = −

E V

R

n

X

sin β

( n)

Given

Q

n

n N max

N

max

Q

lead

Q

lag

⋅ Q

lag

β n V :=120 deg⋅ R n

Q

lead

Q :=−0.

lag

n N :=0. max

+ 1 N

max

N

max

N := .. +

max

I

n

P j Q n

V

R

n

V :=

R

n

V

R

n

e

− jβ n ⋅

:= ⋅

V

R

n

β n

Find V R n

β n

Q

n

E V

R

n

X

cos β

( n)

V

R

n

2

X

P = −

E V

R

n

X

sin β

( n)

Given

Q

n

n

N

max

Q

lag

Q

lead

⋅ Q

lead

β n V :=20 deg⋅ R n

Q

lag

Q :=0.

lead

n 0 1, N :=−0. max

N := ..

max

P :=0.2 E :=1.0 X :=1.0 j := − 1

C:\JLAW\CLASSES\S05PSSII

\HANDOUTS\s28b.mcd

Page 1 of 2 March 28, 2005

ECE 504 Power System Stability II Session 28b

Phasor Diagrams

0

30

60

90

120

150

180

210

240

270

300

330

1

0

V R n

I n

arg V R n

arg I

( n)

,

0 0.2 0.4 0.6 0.8 1 1.

0

Q-V Curves

Magnitude of Receiving Voltage (pu)

Reactive Power (pu)

Q n −

V R n

C:\JLAW\CLASSES\S05PSSII

\HANDOUTS\s28b.mcd

Page 2 of 2 March 28, 2005