Electrical Power Systems

Assuming q ik – d i + d k » d ik, eqn. (7.60) can be written as:
Load low Analysis 183
Qi
| V | = –|Vi|Bik ...(7.72)
k
Therefore, eqns. (7.55) and (7.56) take the following form:
DP
= –B¢ Dd
| Vi|
...(7.73)
DQ
= –B¢¢ Dd
| Vi|
...(7.74)
B¢ and B¢¢ are the imaginary part of the bus admittance matrix Y BUS. B¢ and B¢¢ are constantmatrices
and they need to be inverted once. The decoupled and fast decoupled power flow
solutions requires more interations than the coupled NR method but requires less computing
time per iteration.
7.16 TAP CHANGING TRANSORMERS
When the tap ratio is at the nominal value (a = 1), the transformer is represented by a series
admittance y pq . When tap ratio is off-nominal, the admittance is different from both sides of the
transformer.
igure 7.9 shows a transformer with admittance y pq in series with an ideal transformer
representing the off-nominal tap ratio 1 : a. t is a fictitious bus between the ratio and admittance
of the transformer.
rom ig. 7.9,
Vt = Vq
ig. 7.9: Equivalent circuit.
...(7.75)
a
Ip = –aIq ...(7.76)
The current Ip is given by
Ip = ypq(Vp – Vt) ...(7.77)
Using eqns. (7.77) and (7.75), we get,
rom eqn. (7.76),
Ip = ypqVp – ypq
Vq ...(7.78)
Iq = -Ip
a
rom eqns. (7.79) and (7.78), we have
I q = -
1
a
HG
y V
pq p
a
y
-
a V
pq
q
I KJ
...(7.79)