Abstract-- This paper presents a study of passive harmonic
filter planning in the power system. The purpose is to find the
optimal locations for harmonic filters among existent capacitor
busses in the power network based on the sensitivity analysis.
The planning problem is formulated as an unconstrained
optimization problem. The inductor size of each shunt filter is
then determined while IEEE-519 recommended harmonic
voltage and voltage distortion limits are maintained at each
network bus. Simulation results obtained by testing a
distribution system show that the proposed approach is robust,
computationally efficient, and suitable for siting and sizing
passive harmonic filters.
Index Terms-- Passive harmonic filters, Harmonic voltage,
Voltage distortion, Sensitivity, Harmonic impedance
I. INTRODUCTION
For most conventional analyses, the power system is
essentially modeled as a linear system with passive elements
excited by constant-magnitude and constant-frequency
sinusoidal voltage sources. However, with the widespread
proliferation of nonlinear loads nowadays, significant
amounts of harmonic currents are being injected into power
systems. Harmonic currents not only disturb loads that are
sensitive to waveform distortion, but also cause many
undesirable effects on power system elements. As a result,
system-wide solutions to harmonics become a growing
concern [1]-[3].
Among various solutions to harmonics, passive harmonic
filters are the most popular and effective mitigation method
for harmonic problems. The passive filter is generally
designed to provide a path to divert the troublesome harmonic
current in the power system. For electric utility practices, the
most commonly seen filters are shunt passive filters. The
shunt filter is characterized as a series-resonant and trap type
branch that has low impedance at its tuned frequency. The
single tuned LC filter is the most common design in power
systems.
In the past most passive filters are designed for individual
bus application only. System-wide design and planning of
passive harmonic filters to effectively control harmonic
problems in the power network are rarely discussed. This
paper intends to investigate the problem for optimally siting
the passive filters by converting existent capacitor banks at
candidate busses in a power system while IEEE-519 harmonic
The authors are with the Department of Electrical Engineering, National
Chung Cheng University, Min-Hsiung, Chia-Yi 621 TAIWAN (e-mail:
wchang@ee.ccu.edu.tw).
voltage and voltage distortion limits as well as filter
component rms constraints are maintained.
II. PROPOSED SOLUTION METHOD
A. Network Analysis
Fig. 1 shows a typical M-bus power network with an h-th
order of harmonic current source,
h
k
I at bus k. The harmonic
voltage at each bus is given in (1).
Fig. 1. Schematic diagram for the h-th order of harmonic current at bus k
injected into the power system.
=
0
0
0
2
1
2
1
2
2
22
12
1
1
21
11
2
1
M
M
M
M
L
O
L
O
L
L
M
M
L
O
L
O
L
L
M
M
M
M
M
M
h
k
h
MM
h
kM
h
M
h
M
h
Mk
h
kk
h
k
h
k
h
M
h
k
h
h
h
M
h
k
h
h
h
M
h
k
h
h
I
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
V
V
V
V
, (1)
where the h-th order of harmonic voltage at bus i is
h
k
h
ik
h
i
I Z V =
, i = 1, 2, …, M, and where
h
ik
Z
is the h-th order
of harmonic transfer impedance between busses i and k.
The conventional approach for mitigating harmonic
problem is to install single-tuned passive filters at selected
busses, as shown in Fig. 2. The passive filter is typically
composed of a capacitor in series with an inductor. Assume
that the internal resistance of the inductor is R and the quality
factor is Q. Then, the filter impedance at the any harmonic
order h can be expressed as
C
C
L
h
filter
X
h
n
h
j
n
h
h
X
hX j R Z
- + =
- + =
1
Q
) (
2 2
, (2)
where n is the harmonic order of the tuned frequency, Q =
X
L
/R and n
2
= X
L
/X
C
.
Gary W. Chang Shou-Yung Chu Hung-Lu Wang
Sensitivity-Based Approach for Passive Harmonic
Filter Planning in a Power System
937
0-7803-7322-7/02/$17.00 © 2002 IEEE