Electrical Power Systems

156 Electrical Power Systems
p + 1 \ ei = | V| - f
Where
7.8 CONVERGENCE PROCEDURE
RST
UVW
1
2
2 p+1 2
i e i j ...(7.19)
e i p + 1 = real part of Vi p+1
f i p + 1 = imagining part of Vi p+1
The updated voltages immediately replace the previous values in the solution of the subsequent
equations. This process is continued until changes of bus voltages between successive iterations
are unithin a specified accuracy, Define
( p+
1)
( p)
i - i
DV = max V V , i = 1, 2, ..., n ...(7.20)
if DV £ Î, then the solution has converged. Î is prespecified. Usually Î = 0.0001 or 0.00001
may be considered.
Another convergence criteria is the maximum difference of mismatch of real and reactive
power between successive iterations. Define
DP = max P - P
...(7.21)
i calculated
i scheduled
D Q = max Q - Q
...(7.22)
i calculated
i scheduled
if DP £ Î and DQ £ Î, the solution has converged. In this case Î may be taken as 0.0001 or
0.00001.
Acceleration actor
In practice, the process of convergence of GS method is slow and it requires a large number of
iterations before a solution is obtained. The process of convergence can be speeded up if the
voltage correction during iterative process is modified to
(p+1)
Vi (acceleration)
(p+1) (p) e i i j
= Vi + a V - V
where a is known as acceleration factor and is a real number. 1.4 < a < 1.6, recommended range
of a for most of the power system problem.
7.9 COMPUTATION O LINE LOWS AND LINE LOSSES
Consider the line connecting busses i and k. The line and transformer at each end can be
represented by a circuit with series admittance y ik and two shunt admittances y o ik and y o ki as
shown in ig. 7.6.