IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003
587
Analysis of the Neutral Conductor Current
in a Three-Phase Supplied Network
With Nonlinear Single-Phase Loads
Jan J. M. Desmet, Member, IEEE, Isabel Sweertvaegher, Greet Vanalme, Kurt Stockman, Student Member, IEEE, and
Ronnie J. M. Belmans, Senior Member, IEEE
Abstract—This paper describes what factors (i.e., load and
supply) have an important effect on the neutral conductor current.
It is shown that an asymmetry up to 10 or an unbalance of 10%
in the power supply has only a minor effect on the rms value of
the neutral conductor current. An unbalance in load conditions
increases the neutral conductor current. Harmonics in the power
supply voltage highly affect the rms value of the neutral conductor
current.
B. Derivation of the Harmonics in the Neutral Conductor
Current From the Phase Currents
Symmetric and Balanced Network: Using the Fourier transform, the phase currents in a symmetric and balanced network
can be written. The neutral conductor current is given by the
summation of the three phase currents. The same reference is
used for the phase angles in these equations
Index Terms—Current measurement, harmonic distortion, neutral conductor, nonlinear loads, power quality.
(1)
I. INTRODUCTION
N
OWADAYS, nonlinear loads (compact fluorescent lamps,
computers, variable-speed drives, etc.), mostly used with
the aim of rational energy use, are very common. These loads,
producing harmonic currents, yield high neutral conductor currents [1], [2]. In this paper, the influence of power supply asymmetry and unbalance and load unbalance on the neutral conductor current is investigated. Also, the sensitivity of the neutral
conductor current to harmonics in the power supply voltage is
studied. In order to have a better insight into the experimental
results, some theoretical considerations are supplied first.
(2)
(3)
II. THEORETICAL CONSIDERATIONS
(4)
A. Assumptions
A three-phase supplied network with neutral conductor is
considered. The load phase currents are assumed to be steadystate periodic signals only containing odd harmonics.
Paper ICPSD 01–101, presented at the 2001 IEEE International Electric Machines and Drives Conference, Cambridge, MA, June 17–20, and approved for
publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the
Power Systems Engineering Committee of the IEEE Industry Applications Society. Manuscript submitted for review July 23, 2001 and released for publication January 28, 2003. This work was supported by the Flemish Government
under the project “Studie van de nadelige gevolgen van het grootschalig gebruik
van verlichting en office-equipment in nutsgebouwen” (IWT-HOBU).
J. J. M. Desmet, I. Sweertvaegher, G. Vanalme, and K. Stockman are
with the Department P.I.H., Hogeschool West-Vlaanderen, B-8500 Kortrijk,
Belgium (e-mail: jan.desmet@ieee.org; isabel.sweertvaegher@howest.be;
greet.vanalme@howest.be; kurt.stockman@howest.be).
R. J. M. Belmans is with the Division ELEN, Department of Electrical Engineering (ESAT), Katholieke Universiteit Leuven, B-3001 Leuven, Belgium
(e-mail: ronnie.belmans@esat.kuleuven.ac.be).
Digital Object Identifier 10.1109/TIA.2003.810638
, with the
Notice that the first-order harmonics (
) in the phase curorder of the harmonic and
rents are forming a direct system, the third-order harmonics
are forming a homopolar system, and the fifth-order haran inverse system. Consequently, the neumonics
tral conductor current only consists of third-order harmonics.
Arbitrary Network: Using the Fortescue transform [3], an arbitrary (asymmetric and unbalanced) system can be written as
the summation of a direct, an inverse, and a homopolar system.
In (5), the Fortescue transform is applied to the harmonics of
order in the phase currents
(5.a)
with
0093-9994/03$17.00 © 2003 IEEE
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(5.b)
588
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003
As the sum of the direct components and also the sum of the
, only the
inverse components equals zero
sum of the homopolar components results in a neutral conductor
current
(6)
The neutral conductor current only consists of the homopolar
components of the phase currents. In case of a symmetric and
balanced network, these homopolar components correspond to
the third-order harmonics.
Working out (6), Kirchoff’s law yields
Fig. 1. Measurement setup.
(7)
Assuming
, then
,
is given by
, and
(8)
and the phase
From the above equation, the amplitude
of the th harmonic in the neutral conductor current
angle
of the th harmonic in
can be calculated. The amplitude
the neutral conductor current is shown by (9), at the bottom of
is the amplitude of the th harmonic in the
the page, where
,
,
is the amplitude of the
neutral conductor current,
th current harmonic in, respectively, phases , , and , and
,
,
is the phase angle of the th current harmonic
of
in, respectively, phases , , and . The phase angle
the th harmonic in the neutral conductor current is
where
is the rms value of the total neutral conductor current,
is the rms value of the total phase current, and
,
,
is the rms value of, respectively, a first-, third-,
and fifth-order harmonic in the phase current with order, respec,
, and
.
tively,
Consider the particular case in which the phase currents are
with
(
consisting of odd harmonics
,
) or
,
,
,
.
The rms value of the phase current is
(12)
The rms value of the neutral conductor current equals
(13)
(10)
The rms ratio of the neutral conductor current and the phase
current is
If the harmonics (amplitudes and phase angles) in the phase
currents are known, the harmonic content of the neutral conductor current can be calculated using (9) and (10).
(14)
C. rms Ratio of Neutral Conductor and Phase Currents for a
Symmetric and Balanced Network
For a symmetric and balanced network, the rms ratio of
neutral conductor and phase current increases with increasing
third-order harmonics and with decreasing first- and fifth-order
harmonics in the phase current (11). The neutral conductor
current never can be more than three times the phase current.
The maximum ratio is hypothetically possible if the third-order
harmonics in the phase current are infinite in comparison to
the part of first- and fifth-order harmonics in the phase current
(e.g., with a third-order load)
(11)
The maximum rms ratio of the neutral conductor current and the
(all the harmonics in the
phase current is obtained when
.
phase current have the same weight) and equals
In [4], it is mentioned that the neutral conductor current can
reach 1.73 times the phase current.
III. EXPERIMENTS
A. Test Configuration
The test configuration is shown in Fig. 1. Using a programmable power source, an arbitrary voltage waveform is
generated, independently for each phase. Each phase is loaded
by a variable number of compact fluorescent lamps of 15
W/220–240 V. For different setups of the power source and
(9)
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DESMET et al.: NEUTRAL CONDUCTOR CURRENT IN A THREE-PHASE SUPPLIED NETWORK
589
TABLE I
POWER SOURCE PARAMETERS
(a)
TABLE II
TOTAL CURRENT AND THIRD HARMONIC IN THE NEUTRAL CONDUCTOR
FOR DIFFERENT POWER SUPPLY PROPERTIES
(b)
Fig. 2. (a) Phase and (b) neutral conductor currents in case of a symmetric
and balanced power supply and a symmetric and balanced load (five compact
fluorescent lamps in each phase).
load conditions, the phase and neutral conductor currents
are measured and analyzed. Measurements are done using a
high-performance power analyzer.
B. Neutral Conductor Current for a Symmetric and Balanced
Network and Sinusoidal Power Supply Voltages
Setup Parameters: Power source: A sinusoidal voltage with
rms value of 220 V is generated on each phase. The voltage
signal on phase is taken as reference, the voltage signals on
are leading with, respectively, 120 and 240 .
phase and
Load: Each phase is loaded by five compact fluorescent lamps
of 15 W/220–240 V.
Results of Measurement: In Fig. 2, two graphs are given,
representing the harmonic contents of phase and neutral conductor currents. The phase currents contain harmonics of first,
third, and fifth order, while the neutral conductor current mainly
contains third order harmonics. Notice that the third-order harmonics in the neutral conductor current are three times as high
as the corresponding harmonics in the phase currents, as theoretically expected (4). The small part of first- and fifth-order
harmonics in the neutral conductor current is caused by the fact
that the lamps are not completely identical. The load is not perfectly symmetric and balanced. The small unbalance in the load
can be seen in the small differences between the phase currents
[Fig. 2(a)].
The rms ratio of the neutral conductor current and the phase
currents is 1.7.
C. Influence of Asymmetry or Unbalance in the Power Supply
on the Neutral Conductor Current
Setup Parameters—Power Source: A sinusoidal voltage is
generated on each phase. An overview of the used rms values
and phase angles of the power supply voltages is given in Table I.
Load: Each phase is loaded by five compact fluorescent lamps
of 15 W/220–240 V.
Results of Measurement: In Table II, a summary of the
measured rms values of the total neutral conductor current
and the third harmonic
in the neutral conductor current
is given for the different power source setups according to
Table I and for a load consisting of five compact fluorescent
lamps in each phase. The deviations of the rms values for an
asymmetric and/or unbalanced power supply from the values
for a symmetric and balanced supply are also mentioned in the
table.
Notice that the neutral conductor current, mainly consisting
of the third harmonic, has the highest rms value for a symmetric
and balanced power supply. Only in this case, the phase angles
of the third harmonics in the phase currents are the same and
the amplitude of the third harmonic in the neutral conductor
current is the sum of the amplitudes of the third harmonics in the
phase currents (9). In the other cases, the amplitude of the third
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590
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003
(a)
Fig. 4. Neutral conductor current in case of a balanced and (a) symmetric
power supply and a symmetric and balanced load (five compact fluorescent
lamps in each phase).
D. Influence of Load Unbalance on the Neutral Conductor
Current
(b)
Fig. 3. (a) Phase and (b) neutral conductor currents in case of a symmetric
and unbalanced power supply and a symmetric and balanced load (five compact
fluorescent lamps in each phase).
harmonic in the neutral conductor current is less than the sum
of the amplitudes of the third harmonics in the phase currents.
Fig. 3 shows two graphs representing the harmonics in the
phase and the neutral conductor currents for a symmetric and
unbalanced power supply. As a result of the unbalance in the
power supply, the harmonic contents of the phase currents are
different [Fig. 3(a)] and the first- and fifth-order harmonics
show the highest differences, so the neutral conductor current
contains more first-order and fifth-order harmonics than in the
case of a balanced power supply [Figs. 2(b) and 3(b)]. The
third-order harmonics in the neutral conductor have slightly
decreased in comparison with a balanced power supply. This
can be attributed to the differences (caused by the power supply
unbalance) in the phase angles of the third-order harmonics in
the phase currents. The rms value of a harmonic in the neutral
conductor current is not only dependent on the rms values of
the corresponding harmonics in the phase currents, but also on
their phase angles (9).
Fig. 4 shows clearly that an asymmetry in the power supply
increases the first-order and fifth-order harmonics in the neutral conductor current and decreases the third-order harmonics.
However, the change is the smallest for the third harmonic,
while it is the determining factor in the neutral conductor current. Finally, it is concluded that the rms value of the total neutral
conductor current is only slightly affected by an asymmetry or
unbalance in the power supply (Table II).
Setup Parameters—Power Source: A sinusoidal voltage is
generated in each phase, with rms value and phase angle as in
Table I.
Load: Each phase is loaded by a number of compact fluorescent lamps of 15 W/220–240 V. Measurements were done
for the following load conditions, considering a constant threephase power:
• six lamps in phase , six lamps in phase , and no lamps
(unbalanced load);
in phase
• six, four, and two lamps in phases , , and , respectively (unbalanced load);
• four lamps in each phase (balanced load).
Results of Measurement: Table III(a) summarizes the measured rms values of the neutral conductor current for different
power supply (Table I) and load conditions. Table III(b) gives
the ratio of the neutral conductor current to the average of the
phase currents.
Again, an asymmetry or unbalance in the power supply has
only a minor effect on the rms value of the neutral conductor
current. The load conditions, on the other hand, have a high influence on the neutral conductor current. The neutral conductor
current increases with increasing load unbalance. Consequently,
the lowest neutral conductor current is obtained for a balanced
load.
Fig. 5 shows the harmonic content of the neutral conductor
current for different load conditions in case of a symmetric and
balanced power supply. The third-order harmonics are not depending on the load conditions considering the constraint of the
constant three-phase power. The first- and fifth-order harmonics
are nearly zero for a balanced load and they increase with increasing load unbalance.
E. Sensitivity of the Neutral Conductor Current to Harmonics
in the Power Supply Voltage
Setup Parameters—Power Source: The power supply is
symmetric and balanced (with setup parameters as in Table I),
but the power supply voltage contains only one odd harmonic
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DESMET et al.: NEUTRAL CONDUCTOR CURRENT IN A THREE-PHASE SUPPLIED NETWORK
591
TABLE III
(a) rms VALUES OF THE NEUTRAL CONDUCTOR CURRENT FOR DIFFERENT
POWER SUPPLY AND LOAD CONDITIONS. (b) RATIO OF THE NEUTRAL
CONDUCTOR CURRENT TO THE AVERAGE OF THE PHASE CURRENTS FOR
DIFFERENT POWER SUPPLY AND LOAD CONDITIONS
(a)
(a)
(b)
(b)
Fig. 5. Neutral conductor current in case of a balanced and symmetric power
supply and for different load conditions.
(with order 3, 5, , 21) in addition to the fundamental. The
amplitude of the voltage harmonic (relative to the fundamental)
varies from 1% to 5%; the phase angle is 0 , 90 , or 180
(values seen from the harmonic) referred to the voltage fundamental.
Load: Each phase is loaded by five compact fluorescent lamps
of 15 W/220–240 V.
Measurement Results: Fig. 6 shows the influence of a third
harmonic (2%) in the power supply voltage on the phase currents and the neutral conductor current. In the phase currents
Fig. 6. (a) Phase and (b) neutral conductor currents for different harmonic
contents of the power supply voltage. The power supply and load are symmetric
and balanced.
[Fig. 6(a)] the fifth harmonic is more influenced than the third
harmonic (changes of respectively 10% and 2.5%). The change
of the fifth harmonic in the phase currents has no effect on the
neutral conductor current [Fig. 6(b)]. Consequently, the same
conclusions can be drawn as for the setup of a symmetric and
balanced network considered in , where the first- and fifthorder harmonics are zero in the neutral conductor. Only the
changes of the third-order harmonics are determining the neutral conductor current.
Table IV gives, for different harmonic contents of the power
supply voltage, the deviations (%) of the rms value of the neutral conductor current from the reference value in case of a sinusoidal voltage. From this table, it is seen that in general the
changes of the rms values of the neutral conductor current are
higher for voltage harmonics of higher order and for increasing
amplitude of the harmonic. The rms value of the neutral conductor current is very sensitive to the presence of harmonics
with high order in the power supply voltage.
IV. CONCLUSIONS
It is shown that an asymmetry up to 10 or an unbalance of
10% in the power supply has only a minor effect on the rms
value of the neutral conductor current. An unbalance in load
conditions increases the neutral conductor current. Harmonics
in the power supply voltage highly affects the rms value of the
neutral conductor current.
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003
TABLE IV
SENSITIVITY OF THE rms VALUE OF THE NEUTRAL CONDUCTOR CURRENT TO
THE HARMONICS IN THE POWER SUPPLY VOLTAGE
[2] T. M. Gruzs, “A survey of neutral currents in three-phase computer
power systems,” IIEEE Trans. Ind. Applicat., vol. 26, pp. 719–725,
July/Aug. 1990.
[3] C. L. Fortescue, “Method of symmetrical coordinates applied to the solution of polyphase networks,” Trans. AIEE, pt. II, vol. 37, pp. 1027–1140,
June 1918.
[4] L. Van der Veken, “Safety and Inspection Perspective,” presented at the
Eur. Copper Institute Workshop Economic Cost of Poor Power Quality,
Brussels, Belgium, June 8, 2000.
Jan J. M. Desmet (M’00) received the Polytechnical
Engineer degree from the Polytechnic, Kortrijk, Belgium, in 1983, and the M.S. degree in electrical engineering from the University of Brussels, Brussels,
Belgium, in 1993.
Since 1984, he has been a member of the staff
of the Department P.I.H., Hogeschool West-Vlaanderen, Kortrijk, Belgium, where he is currently a
Professor. His areas of teaching are variable-speed
drives and industrial electric measurement techniques. His research interests include variable-speed
drives, rational use of electrical energy, and power quality.
Prof. Desmet is a Member of the International Association of Science
and Technology for Development (IASTED), SC77A (IEC), and TC210
(CENELEC)
Isabel Sweertvaegher graduated in electronics
from the Vrij Hoger Technisch Instituut, Kortrijk,
Belgium, in 1996, and received the Polytechnical
Engineer degree from the Department P.I.H.,
Hogeschool West-Vlaanderen, Kortrijk, Belgium, in
1998.
Currently, she is a Research Assistant in the
Department P.I.H., Hogeschool West-Vlaanderen,
teaching in the areas of control technique and
electronics. Her research interests include power
quality and control technique.
Greet Vanalme received the M.S. degree in electrical
engineering and the Ph.D. degree in sciences from
the University of Ghent, Ghent, Belgium, in 1994 and
2000, respectively.
Currently, she is a Researcher in the field of power
quality in the Department P.I.H., Hogeschool WestVlaanderen, Kortrijk, Belgium.
These conclusions can be drawn for all equipment with similar current signatures as those of the tested compact fluorescent
lamps (e.g., computers).
REFERENCES
[1] A.-C. Liew, “Excessive neutral currents in three-phase fluorescent
lighting circuits,” IEEE Trans. Ind. Applicat., vol. 25, pp. 776–782,
July/Aug. 1989.
Kurt Stockman (S’02) received the degree of
Industrial Engineer in Electrical Engineering from
the Provinciale Industriële Hogeschool, Kortrijk,
Belgium, in 1994. He is currently working toward
the Ph.D. degree at the Katholieke Universiteit
Leuven, Leuven, Belgium.
Since 1995, he has been with the Department
P.I.H., Hogeschool West-Vlaanderen, Kortrijk,
Belgium. His research interests are adjustable-speed
drives, voltage sags, and control engineering.
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DESMET et al.: NEUTRAL CONDUCTOR CURRENT IN A THREE-PHASE SUPPLIED NETWORK
Ronnie J. M. Belmans (S’77–M’84–SM’89) received the M.S. degree in electrical engineering and
the Ph.D. degree from the Katholieke Universiteit
Leuven (KULeuven), Leuven, Belgium, in 1979 and
1984, respectively, and the special Doctorate degree
and the Habilitierung from RWTH Aachen, Aachen,
Germany, in 1989 and 1993, respectively.
He is currently a Full Professor at KULeuven,
where he teaches courses on electrical machines,
variable-speed drives, and CAD in magnetics. He
is Director of several basic and industrial research
projects. Currently, he is Head of the Department of Electrical Engineering
and Vice President of the KULeuven Energy Institute. Since June 2002, he has
been the Chairman of the Board of Elia, the Belgian grid operator. His research
interests include variable-speed drives, distributed power, power quality, and
renewable energy in the grid. He is also performing research on the system
aspect of the liberalization of the electricity market. He was with the Laboratory
for Electrical Machines, RWTH Aachen, as a Von Humboldt Fellow from
October 1988 to September 1989. From October 1989 to September 1990, he
was a Visiting Professor at McMaster University, Hamilton, ON, Canada. He
obtained the Chair of the Anglo–Belgian Society at London University for
the year 1995–1996. Since 1997, he has been a Visiting Pofessor at RWTH
Aachen, and since 1999, at Imperial College, London, U.K.
Dr. Belmans is a Fellow of the Institution of Electrical Engineers, U.K., and a
Member of the Koninklijke Vlaamse Ingenieursvereniging (KVIV). Since 1997,
he has been President of the International Organization on Electricity Use (UIE,
based in Paris, France).
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