IEEE Transactions on Power Delivery, Vol. 20, No. 1, 2005, pp.

286-291

The Effect of the Design Method

on Efficiency of Resonant Harmonic Filters
Leszek S. Czarnecki, Fellow, IEEE and Herbert L. Ginn III, Member, IEEE

Abstract—Distribution voltage harmonics and load current nes is referred to as an optimized filter. Such a procedure
harmonics other than harmonics to which a resonant harmonic requires that conditions of the filter operation with respect to
filter (RHF) is tuned, deteriorate the filter efficiency in reducing the load and the system parameters as well as the distribution
harmonic distortion. The paper presents results of a study on voltage and load current harmonics are specified. Therefore,
dependence of this deterioration on the method of the filter
design. The study was confined to four-branch RHFs of the 5th,
the filter can be considered as an optimized filter only for
7th, 11th and 13th order harmonics, installed on buses that those conditions.
predominantly supply six-pulse ac/dc converters or rectifiers. The most common RHFs in distribution systems are those
The filters under investigation were designed according to used for reduction of harmonic distortion caused by six-pulse
two different approaches: a traditional approach and an ac/dc converters and rectifiers. Characteristic harmonics of
approach based on an optimization procedure. In the traditional such devices are of the order n = 6k ± 1, while their asym-
approach, the reactive power allocated to particular branches of metry, asymmetry of the thyristors’ firing angle and other
the filter and their tuning frequencies are selected at the loads contribute [1-4, 7] to the presence of other current
designer’s discretion, according to recommended practices. In harmonics. Investigations of the filter effectiveness in this
the optimization based approach, the reactive power allocated to
particular branches and tuning frequencies are resultants of an
paper are confined to just such RHFs, composed of four
optimization procedure that minimizes the bus voltage and the resonant LC branches for reduction of the 5th, 7th, 11th and 13th
supply current THD in the system with the filter under design. order harmonics. Filters with high-pass branches are beyond
Index terms--Resonant harmonic filters, harmonic distortion, the scope of this study.
harmonic filter design, nonsinusoidal systems Resonant harmonic filters are often superseded by swit-
ching compensators, commonly known as “active harmonic
I. INTRODUCTION filters”(AHFs). Such devices have a number of advantages
over RHFs. First of all, they have an adaptive capability.
The efficiency of resonant harmonic filters in reduction of However, the power rating of AHFs is limited by their transis-
harmonic distortion is reduced by distribution voltage harmo- tors’ switching power. Moreover, high frequency switching,
nics and the load current harmonics other than harmonics to necessary for operation of these devices, is a source of elec-
which the filter is tuned. Harmonic amplification due to filter tromagnetic interference. Therefore, RHFs, might still be an
resonance with the distribution system inductance is the main important alternative, in particular, if an optimization proce-
cause of this efficiency deterioration. dure could elevate their efficiency.
Harmonic amplification caused by the filter resonance This paper does not present results of a “case study” for a
with the distribution system inductance depends on frequen- particular field situation. The results are based on computer
cies of this resonance and can be reduced by appropriate se- modeling of different filters operating in different conditions
lection of the filter parameters. Harmful effects of the filter’s with respect to the short circuit power and waveform dis-
low impedance at tuning frequencies can be reduced [1-6] by tortion. This makes it possible to draw more general conclu-
detuning the filter from frequencies of characteristic harmo- sions on the effect of the method of the filter design on the
nics. Unfortunately, this detuning reduces the attenuation of filter efficiency.
the load current characteristic harmonics. Thus, to improve In order to present, in the limited space of this paper, the
the filter efficiency, a trade off between attenuation and effect of some important parameters and distortion on the
amplification of particular harmonics is needed. This trade off filter efficiency, less important parameters are neglected or
is a core of some recommended practices, commonly applied kept constant at the level that can be expected in field
during RHF design. Also, it can be achieved by a “cut and situations. Consequently, the results presented in this paper do
trial” approach or by an optimization procedure. not have the accuracy common for “a case study”. However,
Although the “cut and trial” approach may improve the at the cost of lower accuracy, these conclusions are not
filter performance, optimization is a better approach to such a confined to a specific field situation, thus they are more
trade off problem. A filter designed using optimization routi- general.

II. MEASURES OF FILTER EFFICIENCY

L.S. Czarnecki is with the ECE Department of the Louisiana State
University, czarneck@ece.lsu.edu and H.L. Ginn is with ECE Dept. of the Installation of a RHF at a supply bus, as shown in Fig. 1,
Mississippi State University, ginn@ece.msstate.edu. changes the bus voltage and the supply current distortion. The
reduction of this distortion owing to the presence of a filter
provides a quantitative measure for the filter efficiency.
1
 without the filter be denoted by δi0. Then, the filter efficiency
in reducing the supply current distortion can be defined as
δ −δ
εi = i 0 i . (5)
δi0
The RHF efficiency does not depend only on the filter
itself but also on equivalent parameters of the system at the
bus where it is installed as well as on the harmonics of the
distribution voltage, e, and the load generated current, j.
Fig. 1. Distribution system bus with harmonic generating load
and resonant harmonic filter III. TRADITIONAL DESIGN OF RHFs
A one phase equivalent circuit of the system in Fig. 1 is Resonant harmonic filters for the 5th, 7th, 11th and 13th
shown in Fig. 2. order harmonics, i.e., of the structure shown in Fig. 3,

Fig. 2. One phase equivalent circuit of the system in Fig. 1. Fig. 3. Four branch RHF structure
The efficiency of RHFs in reduction of the voltage are designed traditionally by calculating the capacitance Ck
distortion differs from their efficiency in reduction of the and inductance Lk, k = 5, 7, 11, 13, in such a way, that the
current distortion. Therefore, the filter efficiency is specified branch has a resonance at the frequency
by two different measures. One for the voltage, and one for 1
the current. zk = , (6)
LkCk
Let u1 denote the fundamental harmonic of the bus voltage
equal to or in a vicinity of harmonic frequency, ωk = kω1. The
and U1 is its rms value. Let ud denote the distorting compo-
reactive power of the fundamental harmonic, Qk, compensated
nent of this voltage, i.e., the sum of harmonics
by such a branch is
∞
ω1 Ck
ud = ∑ un (1) Qk = ak Q = B1k U12 = U12 (7)
n=2 1 − ω12 Lk Ck
and ||ud|| is its rms value [8, 9]. The Total Harmonic Distor- where Q is the load reactive power per phase, ak is the coef-
tion (THD) of the bus voltage in the system with a filter is ficient of the reactive power allocation to the branch LkCk and
|| u ||
δu = d . (2) B1k is the branch susceptance for the fundamental harmonic.
U1 Combining (6) and (7) gives
Let us denote by δu0 the THD of the bus voltage in the same ω a Q
system but without the filter. Thus, the filter efficiency in Ck = [1 - ( 1 ) 2] k 2 . (8)
zk ωU
reduction of the bus voltage distortion, εu, can be expressed in 1 1

terms of the this voltage THD value before and after the filter 1
Lk = 2 . (9)
is installed: zk Ck
δ −δ The resistance Rk depends on the inductors’ Q-factor, q,
ε u = u0 u . (3)
δ u0 defined as
The filter efficiency is positive when it reduces the voltage ω L
q= 1 . (10)
distortion and it is negative when this distortion, due to a filter R
resonance, increases. A filter that entirely reduces the bus According to Ref. [6], for high voltage applications where air-
voltage distortion has εu = 1; a filter that does not affect THD core inductors are used, the Q-factors of 50 < q < 150 are
has efficiency εu = 0. typical, while for low voltage applications iron-core inductors
Similarly, a measure of the filter efficiency in reduction of are needed with 10 < q < 50.
The opinions with respect to the reactive power allocation
the supply current distortion, εi, can be defined as follows.
to particular branches are divided. According to Ref. [10], this
Let i1 denote the fundamental harmonic of the supply
allocation is irrelevant for the filter properties. Consequently,
current and I1 denote its rms value. Let id be the distorting
it could be assumed that each branch compensates the same
component of this current and ||id|| is its rms value. Then the
reactive power, i.e., allocation coefficients have the same
THD of the supply current in the system with the installed
value. Such filters will be referred to as Type A filters in this
filter is
paper. However, there are also other practices or recommen-
|| i ||
δi = d . (4) dations. The reactive power allocation for a two branch filter
I1 of the 5th and 7th order harmonics assumed in Ref [5] is in
Let the THD of the supply current in the same system but proportion of Q5/Q7 = 2:1, while in Ref. [4] this proportion is
2
Q5/Q7 = 8:3. According to Ref. [11], the reactive power 13th order harmonics is installed, δu and δi, are compiled in
allocation should be “...proportional to total harmonic current Tables 2 and 3. The filter branches were detuned by -12 Hz.
each filter will carry”. Filters designed according to this The filter inductors’ q-factor was assumed to be q = 40.
recommendation will be referred to as Type B filters.
In the presence of distribution voltage harmonics, the filter Table 2. Bus voltage and supply current THD with Type A filter
branches are tuned traditionally to a frequency below the Ssc/P - 20 25 30 35 40 45 50
harmonic frequency. It increases the branch reactance at the δu % 2.0 1.8 1.7 1.6 1.5 1.4 1.3
harmonic frequency and keeps it inductive, even if the capa- δι % 7.8 9.0 9.7 10.8 11.5 12.2 12.8
citance of the capacitor bank declines in time. However, there
are substantial differences in opinions on how much the The following coefficients of the reactive power
branches should be detuned. Reference [5] assumes that filters allocation, proportional to harmonic content, were chosen,
are detuned by 5% below harmonic frequencies, while Ref. according to Ref. [11], for the Type B filter
[1] suggests that detuning should be in the range of 3 to 10% a5 = 0.39, a7 = 0.28, a11 = 0.18, a13 = 0.15.
below these frequencies. Indeed, detuning assumed in Ref. [7]
Table 3. Bus voltage and supply current THD with Type B filter
amounts to 8% for all branches, i.e., the relative detuning is
the same for all branches. According to Ref. [4] the branches Ssc/P - 20 25 30 35 40 45 50
are detuned by 18 Hz, i.e., the absolute detuning is the same. δu % 1.3 1.2 1.2 1.1 1.1 1.0 1.0
Branches are tuned to frequencies 4.7 ω1 and 6.7 ω1, respec- δι % 5.0 6.0 6.8 7.5 8.2 8.9 9.5
tively. It means that there is the lack of a clear recommen-
dation with respect to the filter detuning. Even the degree of The filter efficiency, εu and εi, in reducing the bus voltage
detuning is not related to the level of these harmonics. and the supply current distortion, calculated according to
When a harmonic filter is under design, the attenuation of formulae (3) and (5) for the data compiled in Tables 2 and 3,
dominating, characteristic harmonics is the subject of main are tabulated in Table 4. Since this is efficiency of filters in
concern. The ac/dc converters and other nonlinear loads sup- the lack of other harmonics than the 5th, 7th, 11th and 13th
plied from the same bus, also generate other, non-characteris- order, therefore, this efficiency could be considered as an
tic harmonics. Their level is reported in numerous papers [1-5, upper limit of the efficiency of the analyzed filters.
7, 12]. The traditional approach to filter design essentially Table 4. Upper limit of efficiency of Type A and B filters
neglects the presence of non-characteristic harmonics in the
load current and the distribution voltage harmonics in the Filter Ssc/P 20 25 30 35 40 45
filter design process, considering them as kind of “minor” [8] A εu 0.76 0.74 0.71 0.69 0.67 0.66
harmonics. Tuning the filter branches to a frequency below ει 0.61 0.55 0.52 0.48 0.45 0.42
harmonic frequencies is a common counter-measure to the B εu 0.85 0.83 0.80 0.78 0.76 0.74
degrading effect of distribution voltage harmonics.
ει 0.75 0.70 0.67 0.64 0.61 0.57
IV. UPPER LIMIT OF FILTERS EFFICIENCY
The results compiled in this table show that the filter
The filter efficiency in the lack of harmonics other than
efficiency declines by a few percent with the short circuit po-
harmonics to which the filter is tuned, could be considered as
wer increase. Moreover, the Type B filters are more efficient
a reference for an investigation on how other harmonics affect
than the Type A filters. Also, the filters are more efficient in
the filter performance.
suppressing the bus voltage harmonics than the supply current
Let us consider a filter for reducing harmonic distortion
harmonics.
caused by a load that generates current harmonics of the
relative content Jn/I1 = 0.8 x I1/n, i.e., V. EFFECT OF NON-CHARACTERISTIC CURRENT
J5/I1 = 16%, J7/I1 = 11.4%, J11/I1= 7.3%, J13/I1= 6.1%. HARMONICS
AND DISTRIBUTION VOLTAGE DISTORTION
and the power factor λ = 0.8. Such a situation could be
considered as typical for buses loaded with six-pulse ac/dc The load current harmonics other than those to which the
converters, rectifiers and some amount of linear loads. The filter is tuned, i.e., non-characteristic harmonics, are attenu-
ated or amplified depending on the frequency of the filter
bus voltage and the supply current THD, δu0 and δi0, before
resonances with the distribution system.
the filter was installed, for a few different short circuit powers
Their rough effect on the filter efficiency, without going
and the reactance to resistance ratio of the supply, Xs/Rs = 5,
into detail with respect to harmonic spectrum, can be obtained
are tabulated in Table 1.
assuming that non-characteristic harmonics form a uniformly
Table 1. Bus voltage and supply current THD distributed harmonic noise, i.e., they have the same rms value.
before any filter is installed, δu0 and δi0 To calculate this effect more accurately, information on a true
spectrum of non-characteristic harmonics is needed, but this
Ssc/P - 20 25 30 35 40 45 50
changes from case to case.
δu0 % 8.4. 6.9 5.9 5.1 4.5 4.1 3.7 The filters’ efficiency, assuming that non-characteristic
δι0 % 19.8 20.2 20.4 20.6 20.8 20.9 21.0 current harmonics in the range from the 2nd to the 12th order
have the same rms value and their total rms value is of 1% of
The THD of the bus voltage and the supply current after a the fundamental harmonic, i.e., each of them amounts to Jn =
four-branch Type A or Type B filter of the 5th, 7th, 11th and 0.35% of I1, is shown in Table 5.
3
Table 5. Efficiency of Type A and Type B filters at 1% of distortion worst case scenario, than statistically the most probable rms
by non-characteristic current harmonics value of the distorting current can be calculated as
Filter Ssc/P 20 25 30 35 40 45
|| id || = || id(e)||2+|| id( j)||2 (12)
A εu 0.75 0.72 0.69 0.63 0.64 0.61
The same applies to the distorting component of the bus
ει 0.56 0.54 0.49 0.39 0.42 0.39 voltage, i.e.,
B εu 0.57 0.65 0.71 0.67 0.73 0.73
|| ud || = || ud(e)||2+|| ud( j)||2 (13)
ει 0.51 0.53 0.61 0.61 0.59 0.56
where ud(e) denotes the voltage distorting component caused
The results compiled in Table 5 show that the load current by distribution voltage harmonics and ud(j) denotes the distor-
distortion by non-characteristic harmonics of only 1% causes ting component caused by the load generated current harmo-
a substantial reduction of the filter efficiency. nics. However, when a worst case scenario is a matter of
To compare the reduction of the filter efficiency by the concern, the rms values of distorting components should be
distribution voltage harmonics with this reduction by non- added arithmetically.
characteristic current harmonics, it was assumed that the THD Assuming that the THD of the supply current and the load
of the distribution voltage amounts to 1%. Moreover, it was voltage are calculated according to (12) and (13), the filter
assumed that the distribution voltage harmonics decline as 1/n efficiency in the conditions specified in Sections V and VI are
and, according to IEEE 519 Standard, the even order compiled in Table 8.
harmonics contribute only to 25% to the voltage distortion. Table 8. Efficiency of Type A and B filters at 1 % of distribution
Thus, they have the values shown in Table 6. The filter effi- voltage THD and 1 % of current distortion by non-characteristic
ciency is shown in Table 7. harmonics
Table 6. Distribution voltage harmonics at THD δe = 1% Filter Ssc/P 20 25 30 35 40 45
Odd: E3 E5 E7 E9 E11 E13 A εu 0.69 0.68 0.64 0.53 0.53 0.37
% 0.72 0.44 0.31 0.24 0.20 0.17
ει 0.46 0.50 0.44 0.29 0.34 0.19
Even: E2 E4 E6 E8 E10 E12
% 0.20 0.13 0.07 0.05 0.04 0.03
B εu 0.33 0.55 0.63 0.65 0.64 0.63

ει 0.25 0.41 0.54 0.56 0.54 0.52

Table 7. Efficiency of Type A and Type B filters at 1% of
distribution voltage distortion The comparison of the filter efficiency compiled in Table
4 with this efficiency in the presence relatively low distortion
Filter Ssc/P 20 25 30 35 40 45
of the distribution voltage and the presence of non-
A εu 0.70 0.70 0.66 0.57 0.56 0.39 characteristic harmonics in the load current, compiled above,
ει 0.50 0.51 0.46 0.36 0.36 0.21 show how strongly these harmonics degrade the filter
performance. This efficiency declines drastically with the
B εu 0.46 0.67 0.69 0.69 0.67 0.63
increase of the distribution voltage distortion. Tables 9 and 10
ει 0.38 0.53 0.59 0.58 0.56 0.53 show this efficiency for the distribution voltage THD 2.5%
and 4%, respectively.
The results tabulated above show how the distribution
voltage harmonics, of an almost negligible value, can sub- Table 9. Efficiency of Type A and B filters at 2.5 % of distribution
stantially degrade the efficiency of resonant harmonic filters. voltage THD and 1 % of current distortion by non-characteristic
Their harmful effect is much stronger than the effect of non- harmonics
characteristic current harmonics. Filter Ssc/P 20 25 30 35 40 45
The measures of the filter efficiency, defined by formulae
(3) and (5), in the presence of both load current non-charac-
A εu 0.46 0.51 0.37 0.16 0.16 -0.32
teristic harmonics and distribution voltage harmonics are no ει 0.11 0.33 0.23 -0.10 0.02 -0.47
longer unique. It is for the following reason. The distorting B εu -0.26 0.20 0.36 0.37 0.33 0.32
component of the supply current is composed of two ει -0.50 -0.03 0.29 0.36 0.36 0.34
components
id = id(e) + id( j) (11) Table 10. Efficiency of Type A and B filters at 4 % of distribution
voltage THD and 1 % of current distortion by non-characteristic
where id(e) denotes the distorting component caused by distri- harmonics
bution voltage harmonics and id(j) denotes the distorting com-
ponent caused by the load generated current harmonics. Filter Ssc/P 20 25 30 35 40 45
Harmonics of the same order of these two components, A εu 0.21 0.28 0.15 -0.24 -0.27 -1.07
depending on their phase, may add up or subtract. In general, ει -0.30 0.09 -0.05 -0.56 -0.39 -1.23
they may have any value between their sum and their
B εu -1.08 -0.19 0.03 0.08 0 -0.05
difference. If the phases of harmonics of e and j are random
and mutually independent and we are not looking for the ει -1.31 -0.53 -0.01 0.10 0.12 0.11

4
 At 4% and in some cases at 2.5% of the distribution optimization procedures and the authors of this paper are not
voltage THD, the filter efficiency declines to such a degree sufficiently experienced in this area to suggest that the method
that the filter is almost not capable of reducing the bus voltage we applied should be recommended. Optimization procedures
and the supply current distortion or even, when εu or ει usually result in a number of local minima and there is no
becomes negative, the filter increases harmonic distortion. proof that a lowest local minimum is a global minimum. A
Thus, installation of such a filter might be useless or even better solution can be found. Nonetheless, even if better
harmful with respect to the waveform distortion. parameters of the filter might be found using another
optimization procedure, the filters obtained in this study have
VI. OPTIMIZATION OF FILTER EFFICIENCY much higher efficiency than the Type A and Type B filters.
The filter efficiency might be improved if the fixed rules The filter efficiency compiled in Table 11 was calculated
with respect to the reactive power allocation, i.e., selection of with the assumptions, as discussed in Section V, that non-
allocation coefficients, ak, to the filter branches and their characteristic harmonics of the load current have the same
tuning frequencies, ωk, are abandoned for a selection of these value and the distribution voltage harmonics decline as 1/n.
parameters that minimizes the voltage and current distortion. While the first assumption is justified in the case when non-
However, a difficulty occurs when using such an characteristic harmonics occur because of rectifier or ac/dc
approach. The set of ak, and zk, parameters that minimizes the six-pulse converter asymmetry, the second assumption is
THD of the supply current is different from the set of these more artificial. However, there is no general rule with respect
parameters that minimizes the THD of the bus voltage. Only to harmonic spectrum of the distribution voltage, valid in all
one of them could be minimized at the cost of another. field situations. Therefore, a specific spectrum was selected to
Another option is to minimize a weighted THD, defined for a compare efficiency of filters designed using different
four-branch filter that should suppress the 5th, 7th, 11th and 13th methods. Numerical results will be different for a different
order harmonics as spectrum and filter detuning.
δ = Wi δi + Wu δu = f(a5,…a13, z5,…z13) (14) The values of the reactive power allocation coefficients,
ak, and tuning frequencies, zk, found in optimization procedure
where Wi is the weighting factor of the supply current THD
for conditions specified previously, are compiled in Table 12.
and Wu is the weighting factor of the bus voltage THD. It is up
to the filter designer to decide which distortion is more Table 12. Allocation coefficients and tuning frequencies for an
crucial, the bus voltage distortion or the supply current optimized filter (2.5% of distribution voltage THD and 1% of non-
distortion. If the HGL is the only high power load supplied characteristic current harmonics)
from the bus, then the reduction of harmonics injected by such Ssc/P 20 25 30 35 40 45
a load is the primary objective of the filter. However, when
voltage quality sensitive loads are supplied from the same bus a5 0.09 0.11 0.11 0.12 0.15 0.09

then, keeping a low THD of the bus voltage might be more a7 0.11 0.30 0.61 0.55 0.73 0.69
crucial. a11 0.60 0.46 0.21 0.14 0.08 0.10
A filter with a set of parameters ak, and zk, and cones- a13 0.20 0.14 0.07 0.20 0.04 0.13
quently, Ck,and Lk, that minimizes the weighted THD is z5/ω1 5.0 4.99 4.99 4.99 4.99 4.99
referred to as an optimized filter. Such a filter is optimized, of z7/ω1 6.99 7.00 7.02 6.95 6.88 6.86
course, for fixed parameters of the load and the supply source z11/ω1 11.3 10.8 10.9 10.9 11.0 11.0
and fixed spectra of distribution voltage and the load current z13/ω1 13.00 13.0 13.0 12.7 13.0 13.0
as well as for fixed weighted factors.
The filter efficiency of an optimized filter is calculated for The values of design parameters, i.e., ak, and zk, compiled
its comparison with the efficiency of the Type A and Type B in Table 12 for the optimized filter show that there is no
filters. It is assumed that the supply current contains 1 % of general rule with respect to their selection. They strongly
harmonics other than the 5th, 7th, 11th and 13th order and 2.5 % depend on the short circuit power of the bus where the filter is
of distribution voltage harmonics. The results for an optimi- to be installed. It is easy to predict that they also depend on
zed filters are compiled in Table 11. Comparison of these the voltage and current harmonic spectra.
results with those compiled in Table 9 for Type A and Type B Unfortunately, a strong dependence of the filter efficiency
filters installed in similar situations, shows that the filter on the distribution voltage harmonics is also visible even
optimization enables a substantial improvement of the filter when a filter is optimized. This is illustrated with the filter
efficiency. efficiency compiled in Table 13, of optimized filters operating
at 4% the distribution voltage THD. As it is shown in Table
Table 11. Optimized filter efficiency
for 2.5% of distribution voltage THD and 1% of non-characteristic 11 and 13, this efficiency declines with an increase of the
current harmonics short circuit power of the bus.
Table 13. Optimized filter efficiency
Ssc/P - 20 25 30 35 40 45 for 4 % of distribution voltage THD and 1% of non-characteristic
εu % 0.67 0.62 0.58 0.53 0.49 0.44 current harmonics

εi % 0.57 0.54 0.52 0.48 0.44 0.39 Ssc/P - 20 25 30 35 40 45

Details of the optimization procedure applied for this study εu % 0.46 0.39 0.34 0.25 0.18 0.10
are not discussed here because there is a great variety of opti- εi % 0.32 0.30 0.25 0.20 0.16 0.10

5
 VII. CONCLUSIONS [7] C.-J. Wu, J.-C. Chiang, S.-S. Jen, C.-J. Liao, J.-S. Jang and T.-Y.
Guo, (1998) “Investigation and mitigation of harmonic
The results of this study show that when a filter is amplification problems caused by single-tuned filters”, IEEE
designed according to traditional methods, as are the Type A Trans. on Power Delivery, Vol. 13, No. 3, pp. 800-806.
or Type B filter, then there is a substantial margin for [8] L.S. Czarnecki (1995) “Effect of minor harmonics on the
improving its efficiency. Recommended practices with respect performance of resonant harmonic filters in distribution
to the reactive power allocation and detuning do not provide systems,” Proc. IEE, Electr. Pow. Appl., Vol. 144, No. 5, pp.
reliable grounds for the design of effective filters. 349-356.
At low distortion, on the level of approximately 1%, the [9] L.S. Czarnecki (2000) “Harmonics and power phenomena,”
filer effectiveness is more degraded by distribution voltage Wiley Encyclopedia of Electrical and Electronics Engineering,
John Wiley & Sons, Inc., Supplement 1, pp. 195-218.
harmonics than by non-characteristic current harmonics.
[10] D.E. Steeper and R.P. Stratford (1976) “Reactive compensation
There is no clear regularity as to the effect of the short circuit
and harmonic suppression for industrial power systems using
power on the filter effectiveness and which type of filter, A or thyristor converters”, IEEE Trans. on IA, Vol. 12, No. 3, pp.
B, is more preferable. This irregularity increases with the 232-254.
voltage distortion. Moreover, this effectiveness approaches [11] J.A. Bonner and others, (1995) “Selecting ratings for capacitors
zero or can be even negative, i.e., the filter can increase the and reactors in applications involving multiple single-tuned
harmonic distortion. It may happen even if the voltage dis- filters,” IEEE Trans. on Power Del., Vol.10, January, pp.547-
tortion is within limits recommended by Standard 519. 555.
It is rather unlikely, though possible, that the filter effi- [12] C.-J. Chou, C.-W. Liu, J.-Y. Lee, K.-D. Lee (2000) “Optimal
ciency could be elevated to an upper limit by a ‘cut and trial’ planning of large passive harmonic filters set at high voltage
method. Optimization methods are much more appropriate. level”, IEEE Trans. on PS, Vol. 15, No. 1, pp. 433-441.
However, the Reader should be aware that even an optimized [13] K-P. Lin, M-H Lin and T-P Lin, (1998) “An advanced computer
code for single-tuned harmonic filter design,” IEEE Trans. on
filter, after it is built and installed, does not operate with a
IA, Vol. 34, No.4, July/August, pp. 640-648.
maximum efficiency. This is because of the tolerance of
filter’s elements and change of their parameters with tempe-
BIOGRAPHIES
rature and time. Also, the distribution and the load parameters
as well as voltage and current harmonic spectra are known Leszek S. Czarnecki received the M.Sc. and
with limited accuracy and they change with time. Ph.D. degrees in electrical engineering and
Habil. Ph.D. degree from the Silesian Technical
The efficiency obtained from the optimization procedure University, Poland, in 1963, 1969 and 1984,
is only the upper limit that can be achieved for the assumed respectively, where he was employed as an
values of the distribution voltage and load current harmonics. Assistant Professor. Beginning in 1984 he
The question of how a change in the system parameters and worked for two years at the Power Engineering
Section, Division of Electrical Engineering,
limited accuracy of the filter LC parameters degrade the filter National Research Council of Canada as a
efficiency cannot be answered without a separate study. Research Officer. In 1987 he joined the Elec-
However, this question also applies to filters that are not trical Engineering Dept. at Zielona Gora Tech-
opimized. nical University, Poland. In 1989 Dr. Czarnecki
joined the Electrical and Computer Engineering
VIII. REFERENCES Dept. at Louisiana State University, Baton
Rouge, where he is a Professor of Electrical Engineering now. For developing
[1] D.A. Gonzales and J.C. McCall (1980) “Design of filters to a power theory of three-phase nonsinusoidal unbalanced systems and methods
reduce harmonic distortion in industrial power systems,” Proc. of compensation of such systems, he was elected to the grade of Fellow IEEE
of IEEE Ann. Meeting, Toronto, Canada, pp. 361-365. in 1996. His research interests include network analysis and synthesis, power
phenomena in nonsinusoidal systems, compensation and supply quality
[2] M.M. Cameron (1993) “Trends in power factor correction with improvement in such systems. (ECE Dept., LSU, Baton Rouge, LA 70803,
harmonic filtering”, IEEE Trans. on IA, IA-29, No. 1, pp. 60-65. Phone: 225 767 6528), czarneck@ece.lsu.edu).
[3] S.J. Merhej and W.H. Nichols (1994) “Harmonic filtering for the
offshore industry”, IEEE Trans. on IA, IA-30, No. 3, pp. 533- Herbert L. Ginn (M’ 96) received the M.S.
and Ph.D. degrees in electrical engineering
542. from Louisiana State University in 1998 and
[4] R.L. Almonte and A.W. Ashley (1995) “Harmonics at the utility 2002 respectively. He is employed as an
industrial interface: a real world example,” IEEE Trans. on Ind. Assistant Professor in the Department of
Appl., Vol. 31, No. 6, pp. 1419-1426. Electrical and Computer Engineering at
[5] S.M. Peeran and C.W.P. Cascadden (1995) “Application, design, Mississippi State University. His current
and specification of harmonic filters for variable frequency research interests include optimization of
resonant harmonic filters and design of power
drives”, IEEE Trans. on IA, Vol. 31, No. 4, pp. 841-847.
electronic devices. (ECE Dept., Mississippi
[6] J.K. Phipps (1997) “A transfer function approach to harmonic State University, MS 39762, Phone: 662 325
filter design,” IEEE Industry Appl. Magazine, pp. 68-82. 3530, ginn@ece.msstate.edu).