Electrical Power Systems

154 Electrical Power Systems
V 4 = 1
Y 44
L
NM
P - jQ
4 4 - Y V -Y V -Y
V
* 41 1 42 2 43 3
V4
In the Gauss-Seidel method, the new calculated voltage at (p + 1) i.e. V i (p + 1) immediately
replaces V i (p) and is used in the solution of the subsequent equations. Therefore, above set of
equations can be written in iterative form, i.e.,
V 2 (p + 1) = 1
Y 22
V 3 (p + 1) = 1
Y 33
V 4 (p + 1) = 1
Y 44
L
NM
L
NM
L
NM
P2 - jQ2
- Y V -Y V -Y
V
( p)
V
*
e j
2
O
QP
( p) ( p)
21 1 23 3 24 4
P3-jQ3 p+1
- Y V -Y V -Y
V
( p)
V3
*
e j
O
QP
( ) ( p)
31 1 32 2 34 4
P4-jQ4 p+1
- Y V - Y V - Y V
( p)
V4
*
e j
O
QP
O
QP
( ) ( p+1)
41 1 42 2 43 3
Note that bus 1 is slack bus. Under normal operating conditions, the voltage magnitude of
buses are in the neighbourhood of 1.0 per unit or close to the voltage magnitude of slack bus.
Therefore, an initial starting voltage of (1.0 + j 0.0) for unknown voltages is satisfactory, and the
converged solution corelates with the actual operating states.
7.6 CALCULATION O NET INJECTED POWER
rom eqn. (7.11), we get,
P - jQ
*
V
i i
i
= Y V
ii i
n
åYikVk +
k =¹ 1
k i
\ Pi – jQi = V Y V + Y V
i *
L
NM
ii i
n
å
k = 1
k¹ i
ik k
Let Yii = | Yii| q , Y
ii ik = | Yik| q , V
ik i = | Vi| i d
*
\ Vi = | Vi| – i d , Vk = | | Vk k d
O
QP
...(7.13)