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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
Analysis of Zig-Zag Transformer Applying in the
Three-Phase Four-Wire Distribution Power System
Hurng-Liahng Jou, Member, IEEE, Jinn-Chang Wu, Kuen-Der Wu, Wen-Jung Chiang, and Yi-Hsun Chen
Abstract—The load unbalance and the nonlinear loads result
in a significant neutral current in the three-phase four-wire
distribution power system. The Zig-Zag transformer has been
proposed to attenuate the neutral current of the three-phase
four-wire distribution power system. In this paper, an analysis
is carried out and computer simulation is used to evaluate the
performance of the Zig-Zag transformer under ideal and nonideal
power conditions. The simulation results show that (a) the Zig-Zag
transformer can effectively attenuate the neutral current and
zero-sequence harmonic currents on the utility side under the
balanced utility voltage, (b) the utility side neutral current becomes
larger under the unbalanced utility voltage or the distorted utility
voltage with zero sequence harmonic components after applying
the Zig-Zag transformer, (c) the insertion of an inductor in the
utility side of the neutral conductor can alleviate overloading
of the neutral current caused by the unbalanced utility voltages
and the distorted utility voltages with zero sequence harmonic
components.
Index Terms—Neutral current, three-phase four-wire, Zig-Zag.
I. INTRODUCTION
T
HREE-PHASE four-wire distribution power system has
been widely used for supplying low-level voltage to office
buildings, commercial complexes, manufacturing facilities,
etc [1]. The loads connected to the three-phase four-wire
distribution power system may be either the single-phase
or the three-phase loads. The typical loads connected to the
three-phase four-wire distribution power systems may be computer related equipment, automatic office machines, adjustable
speed drives, lighting ballasts and other power electronic related equipment. Most of these loads have the nonlinear input
characteristic, which creates a problem of high input current
harmonics. The harmonic current will pollute the power system
and result in the problems such as transformer overheats, rotary
machine vibration, degrading voltage quality, damaging electric
power components, medical facilities malfunction, etc. The
third harmonic is most serious for the single-phase nonlinear
loads. The current of the integer multiples 3rd are regarded as
the zero-sequence current. The zero-sequence current flowing in
Manuscript received December 9, 2003; revsied July 12, 2004. Paper no.
TPWRD-00621-2003.
H.-L. Jou is with the Department of Electrical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan, R.O.C. (e-mail:
hljou@mail.e.kuas.edu.tw).
J.-C. Wu is with the Department of Electrical Engineering, Kun
Shan University of Technology, Tainan 710, Taiwan, R.O.C. (e-mail:
jinnwu@mail.ksut.edu.tw)
K.-D. Wu, W.-J. Chiang, and Y.-H. Chen are with the Department of Electrical
Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung
807, Taiwan, R.O.C.
Digital Object Identifier 10.1109/TPWRD.2005.844281
the neutral conductor of the three-phase four-wire distribution
power system is three times of the zero-sequence components
of each phase current. Furthermore, the single-phase loads may
result in serious load unbalance. The unbalanced load currents
contain zero-sequence components and also flow in the neutral
conductor. Survey results across computer sites in U.S. show
that 22.6% of the sites have neutral currents exceeding the
full-load phase currents [2], which may result in an overload
accident of the neutral conductor. Additionally, a large neutral
current may also result in the saturation problem in the distribution power transformer. Thus, the three-phase four-wire
distribution power systems have the problems of harmonic
pollution, load unbalance and over-load of neutral conductor
[3]–[6].
The Zig-Zag transformer has been used to attenuate the neutral current and zero-sequence harmonic currents on the utility
sites [7]–[9] in recent years due to the advantages of low cost,
high reliability and simplified circuit connection. The Zig-Zag
transformer has also another application for avoiding DC magnetization and iron losses caused by the three-phase single-way
rectifier [10]. In order to understand the performance of the
Zig-Zag transformer, the analysis and computer simulation are
made under ideal and nonideal power conditions in this paper.
The simulation results can be used as the reference in the application of the Zig-Zag transformer.
II. BASIC THEORY
Zig-Zag transformer is a special connection of three
single-phase transformer’s windings or a three-phase transformer’s windings [8], [9]. The circuit connection is as shown
in Fig. 1(a). In the three-phase four-wire distribution power
,
system, the three-phase zero-sequence currents (
and
) have the same amplitude and the same phase, and
they can be represented as
(1)
The neutral current
is the sum of three-phase zero-sequence currents, and it is represented as
(2)
Because the turn ratio of the transformer’s windings is 1:1 in
Fig. 1, the input current flowing into the dot point of the primary
winding is equal to the output current flowing out from the dot
point of the secondary winding. Then, we can obtain
0885-8977/$20.00 © 2005 IEEE
(3)
(4)
(5)
JOU et al.: ANALYSIS OF ZIG-ZAG TRANSFORMER APPLYING IN THE THREE-PHASE FOUR-WIRE DISTRIBUTION POWER SYSTEM
1169
Fig. 2. The system configuration of three-phase four-wire distribution power
system with the Zig-Zag transformer.
Fig. 1.
Zig-Zag transformer: (a) circuit connection and (b) phasor diagram.
Fig. 3. The zero-sequence equivalent circuit.
Equations (3)–(5) indicate that three-phase currents flowing
into three transformers must be equal. This means that the
Zig-Zag transformer can supply the path for the zero-sequence
current. Fig. 1(b) shows the phasor diagram [10] of Fig. 1(a).
From Fig. 1(b), it can be found that the voltage across the
transformer’s winding is
of the phase voltage of the
three-phase four-wire distribution power system.
III. ANALYSIS OF ZIG-ZAG TRANSFORMER IN THE
THREE-PHASE FOUR-WIRE SYSTEM
From (6), the zero-sequence voltage can be expressed as
(7)
is the zero-sequence current source, and it contains the
unbalanced fundamental load currents and zero-sequence of
harmonic load currents , and it can be derived as
(8)
Fig. 2 shows the system configuration of the Zig-Zag transformer applied in the three-phase four-wire distribution power
systems. In Fig. 2,
is the impedance of the neutral conductor between the load and the Zig-Zag transformer, and
is
the impedance between the utility and the Zig-Zag transformer.
consists of
and
, where
is the impedance of
the neutral conductor and
is the impedance of the inserted
inductor.
The current flowing through the Zig-Zag transformer is only
the zero-sequence component, and the zero-sequence equivalent
circuit of Fig. 2 is shown in Fig. 3. This consists of two zero-sequence sources,
and
. In the practical three-phase
four-wire industry distribution power system, the unbalanced
utility voltages may occur frequently due to the unequal load
distribution of the upstream in each phase or the abnormal phase
change even when the loads are balanced. The
is a zero
sequence voltage source caused by the unbalanced utility voltages. Assuming the thee-phase voltages (
,
,
)
are unbalanced, the zero-sequence, the positive-sequence and
the negative-sequence components (
,
,
) can
be represented as
(6)
is the zero-sequence impedance of the Zig-Zag
In Fig. 3,
transformer. The effects of the
and
to the neutral
current of the utility side after using the Zig-Zag transformer can
be analyzed by using the superposition theory. For considering
the effect of the
, the
should be assumed to be a
short circuit in Fig. 3. Then, the utility side neutral current
caused by
can be expressed as
(9)
Equation (9) indicates that the magnitude of the utility side neutral current caused by
will be reduced after applying the
Zig-Zag transformer. If
is reduced or
is increased,
in the utility side can be further attenuated.
For considering the effect of
,
should be assumed
to be an open circuit in Fig. 3. From Fig. 3, it can be found that
the Zig-Zag transformer supplies a low impedance path for the
zero-sequence voltage
. This implies that the utility neutral current becomes larger under the unbalanced utility voltage
after applying the Zig-Zag transformer. The neutral current of
the utility side
caused by
can be expressed as
(10)
JOU et al.: ANALYSIS OF ZIG-ZAG TRANSFORMER APPLYING IN THE THREE-PHASE FOUR-WIRE DISTRIBUTION POWER SYSTEM
three-phase four-wire active power filter is limited due to its
high cost. The Zig-Zag transformer is still a popular solution
for this problem due to its low cost, easy installation and free
maintenance. The analysis and simulation results in this paper
show that:
(1) the Zig-Zag transformer can effectively attenuate the
neutral current and zero-sequence harmonic currents
on the utility side under the balanced utility voltages;
(2) the utility side neutral current becomes larger under the
unbalanced utility voltages after applying the Zig-Zag
transformer;
(3) the utility side neutral current becomes larger under the
distorted utility voltages with zero sequence harmonic
components after applying the Zig-Zag transformer;
(4) the insertion of an inductor in the utility side can increase the attenuated rate of the utility side neutral current, however, it may cause abnormal operation of the
electric facilities in the load side and even electrical
accidents;
(5) the insertion of an inductor in the utility side neutral conductor can improve the undesired increasing
of the neutral current and the zero-sequence harmonic
currents of the utility side after applying the Zig-Zag
transformer under the unbalanced utility voltages and
the distorted utility voltages with zero-sequence harmonic components;
(6) the performance of the Zig-Zag will be better if the
Zig-Zag transformer is installed near to the load.
REFERENCES
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scheme for three-phase four-wire distribution systems,” in Proc. IEEE
APEC, vol. 2, 2001, pp. 1287–1293.
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design of a new active power filter to cancel neutral current harmonics
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[4] C. A. Quinn, N. Mohan, and H. Mehta, “A four-wire, current-controlled
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[7] Z. J. Wang, “A Study of the Harmonics for the Taiwan Electrified
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Hurng-Liahng Jou (M’98) was born in Taiwan, R.O.C., in 1959. He received
the B.S.E.E. degree from Chung Yuan University, Jonglih, Taiwan, in 1982,
and the M.S.E.E and Ph.D.E.E. degrees from National Cheng Kung University,
Tainan, Taiwan, in 1984 and 1991, respectively.
Currently, he is a Professor in the Department of Electrical Engineering of
National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan. His
research interests include power electronics applications and power quality improvement technique.
Jinn-Chang Wu was born in Tainan, Taiwan, in 1968. He received the M.S.E.E.
and Ph.D.E.E. degrees from National Cheng Kung University, Tainan, Taiwan,
in 1992 and 2000.
Currently he is an Associate Professor at the Department of Electrical Engineering, Kun Shan University of Technology. His research interests are power
quality and power electronic applications.
Kuen-Der Wu was born in Tainan, Taiwan, R.O.C., in 1954. He received the
B.S.E.E. degree from Tamkang University, Taipei, Taiwan, in 1977, and the
M.S.E.E. degree from National Cheng Kung University, Tainan, Taiwan, in
1980.
He is currently an Associate Professor in the Department of Electrical Engineering of National Kaohsiung University of Applied Sciences, Kaohsiung,
Taiwan. His research interests are power electronics applications and power
quality improvement technique.
Wen-Jung Chiang was born in Changhua, Taiwan, R.O.C., in 1980. He received the B.S.E.E. degree from National Kaohsiung University of Technology,
Taiwan, in 2003. He is currently pursuing the M.S. degree in the Electrical Engineering Department of National Kaohsiung University of Applied Sciences,
Kaohsiung Taiwan.
His research interests are power electronics applications and DSP control.
Yi-Hsun Chen was born in Kaohsiung, Taiwan, R.O.C., on April 16, 1984. He is
currently pursuing the B.S. degree in electrical engineering, National Kaohsiung
University of Applied Sciences, Kaohsiung Taiwan.