Page 414 - Decision Making Applications in Modern Power Systems

Integration of fixed-speed wind Chapter | 14 375

voltages and maximization of PPL and DPF using the weight factors (k 1 , k 2 ,
k 3 , and k 4 ). OF can be written as follows:

ð
Min f STF P ; SC P ; P Gmax Þ 5 k 1 3 VUFð Þ 1 k 2 3 THDV Mean Þ
ð

1 1
1 k 3 3 1 k 4 3 ð14:28Þ
PPL DPF
Because the sensitivity of PPL to voltage imbalance and harmonic distor-
tion is case dependent; therefore the first two subobjectives were included in
the OF to ensure maximization of the PPL at any level.
14.3.2 Nonequality constraints

For the problem formulation of the proposed optimal compensator sizing,
nonequality constraints are detailed as follows:

Rms voltage limits
The rms values of the positive-sequence component of the fundamen-
1
tal bus voltage (V ) should be within a desired range as 6 10% of the
1
per unit (p.u.) nominal voltage value. Thus the rms voltage constraint is
given as
1
0:9 , V , 1:1p:u: ð14:29Þ
1
Harmonic distortion limits
The individual and total harmonic distortions of the phase voltages
measured at the PCC are taken into considerations as per the IEEE
Standard 519 [48]. Accordingly, the harmonic distortion limits can be
expressed regarding the voltage rms level as

V mh
IHDV m ð%Þ 5 3 100 # IHDV max ð14:30Þ
V m1
THDV m ð%Þ # THDV max ð14:31Þ
where V mh and V m1 denote the hth harmonic and fundamental har-
monic voltages for m 5 a, b,and c phases, respectively. IHDV m is the
individual harmonic distortion of voltages for the a, b,and c phases.
IHDV max and THDV max are the maximum permissible individual and
total harmonic voltage distortion reported in the IEEE Standard 519,
respectively.
VUF limit
According to the standard IEC 61000-2-4: 2002 [49], VUF in a DN
should not exceed 2%. As a result, the VUF limit is expressed as
VUF %ðÞ # 2 ð14:32Þ