Electrical Power Systems

\ V i = 1
Y ii
L
NM
P - jQ
i i
*
Vi
7.5 GAUSS-SEIDEL ITERATIVE METHOD
-
n
å
Y V
ik k
k = 1
k¹ i
O
QP
Load low Analysis 153
...(7.12)
or the purpose of explanation consider a 4-bus sample power system as shown in igure 7.5.
BUS 1 is considered as slack bus, where voltage magnitude and its angle are known.
ig. 7.5: 4-bus power system.
In this case n = 4 and slack bus s = 1. rom eqn 7.12 we can write
V i = 1
Y ii
\ V 2 = 1
Y 22
\ V 2 = 1
Y 22
Similarly,
V 3 = 1
Y 33
L
NM
P - jQ
*
V
L
NM
L
NM
L
NM
i i
i
P - jQ
*
V
2 2
2
P - jQ
V
-
4
å
Y V
ik k
k = 1
k¹ i
-
4
å
Y V
O
QP
2k k
k = 1
k ¹ 2
i = 1, 2, 3, 4
i ¹ s, i.e., i ¹ 1
O
QP
2
*
2
2 - Y21V1-Y23V3-Y24V4 P - jQ
- Y V -Y V -Y
V
3 3
* 31 1 32 2 34 4
V3
O
QP
O
QP