Page 413 - Decision Making Applications in Modern Power Systems

374 Decision Making Applications in Modern Power Systems

FIGURE 14.5 Three-phase equivalent circuit of a delta-connected STF at the fundamental fre-
quency. STF, Single-tuned harmonic filter.
X CFab X CFbc X CFca
X LFab 5 ; X LFbc 5 andX LFca 5 ð14:26Þ
h 2 h 2 h 2
tab tbc tca
The three capacitive reactances ðX CFab ; X CFbc ; andX CFca Þ are able to
adjust DPF to its desired interval. In addition, to mitigate the total harmonic
distortion values of the phase voltages (THDV a , THDV b , and THDV c ) and
their mean value (THDV Mean ) expressed as follows:
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P
P 2
V mh m 5 a;b;c THDV m
h $ 2
THDV m 5 100 and THDV Mean 5 ð14:27Þ
V m1 3
the values of the tuning harmonic orders ðh tab ; h tbc ; andh tca Þ should be decided.
Thus regarding Eq. (14.26), three inductive reactance values of the STF branches
ðX LFab ; X LFbc ; andX LFca Þ are found. In practice the STFs have a better harmonic
mitigation capability than other types of passive filters. However, they may result
in parallel resonance in the system. Therefore during their design stage, it should
be checked whether resonance risks are safely avoided or not [47].

14.3 Problem formulation and solution algorithm
In the system, SC may amplify the harmonic distortion level, and STF may
increase the unbalance level. Due to this, the design of the proposed compen-
sator consisting of SC and STF is an optimal design problem. Regarding the
harmonic distortion and unbalance levels of the grid voltages, desired funda-
mental frequency reactive power compensation level, and the PPL of the sys-
tem, for the problem formulation of the proposed optimal compensator, the
objective and constraints are presented in this section.

14.3.1 Objective function
For the optimal sizing of the proposed compensator, the objective function
(OF) is considered as minimization of VUF, and THDV Mean of the phase