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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003 587

Analysis of the Neutral Conductor Currentin 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 , andRonnie J. M. Belmans , Senior Member, IEEE

Abstract—This paper describes what factors (i.e., load andsupply) 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 conditionsincreases the neutral conductor current. Harmonics in the powersupply voltage highly affect the rms value of the neutral conductorcurrent.

Index Terms—Current measurement, harmonic distortion, neu-

tral conductor, nonlinear loads, power quality.

I. INTRODUCTION

NOWADAYS, 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 cur-

rents [1], [2]. In this paper, the influence of power supply asym-

metry and unbalance and load unbalance on the neutral con-

ductor 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.

II. THEORETICAL CONSIDERATIONS

A. Assumptions

A three-phase supplied network with neutral conductor is

considered. The load phase currents are assumed to be steady-

state periodic signals only containing odd harmonics.

Paper ICPSD 01–101, presented at the 2001 IEEE International Electric Ma-

chines and Drives Conference, Cambridge, MA, June 17–20, and approved forpublication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by thePower Systems Engineering Committee of the IEEE Industry Applications So-ciety. Manuscript submitted for review July 23, 2001 and released for publi-cation January 28, 2003. This work was supported by the Flemish Governmentunder 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 arewith the Department P.I.H., Hogeschool West-Vlaanderen, B-8500 Kortrijk,Belgium (e-mail: [email protected]; [email protected];[email protected]; [email protected]).

R. J. M. Belmans is with the Division ELEN, Department of Electrical En-gineering (ESAT), Katholieke Universiteit Leuven, B-3001 Leuven, Belgium(e-mail: [email protected]).

Digital Object Identifier 10.1109/TIA.2003.810638

B. Derivation of the Harmonics in the Neutral Conductor

Current From the Phase Currents

Symmetric and Balanced Network: Using the Fourier trans-

form, 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

(1)

(2)

(3)

(4)

Notice that the first-order harmonics ( , with the

order of the harmonic and ) in the phase cur-

rents areforming a direct system, thethird-orderharmonics

are forming a homopolar system, and the fifth-order har-

monics an inverse system. Consequently, the neu-

tral conductor current only consists of third-order harmonics.

Arbitrary Network: Using the Fortescue transform [3],an ar-

bitrary (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 (5.b)

0093-9994/03$17.00 © 2003 IEEE

Authorized licensed use limited to: Belgium Hogeschools Consortium. Downloaded on March 20, 2009 at 11:11 from IEEE Xplore. Restrictions apply.

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DESMET et al.: NEUTRAL CONDUCTOR CURRENT IN A THREE-PHASE SUPPLIED NETWORK 589

(a)

(b)

Fig. 2. (a) Phase and (b) neutral conductor currents in case of a symmetricand balanced power supply and a symmetric and balanced load (five compactfluorescent lamps in each phase).

load conditions, the phase and neutral conductor currents

are measured and analyzed. Measurements are done using ahigh-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

phase and are leading with, respectively, 120 and 240 .

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 con-

ductor 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 har-

monics in the neutral conductor current are three times as high

as the corresponding harmonics in the phase currents, as the-

oretically 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 per-

fectly symmetric and balanced. The small unbalance in the load

can be seen in the small differences between the phase currents

[Fig. 2(a)].

TABLE IPOWER SOURCE PARAMETERS

TABLE IITOTAL CURRENT AND THIRD HARMONIC IN THE NEUTRAL CONDUCTOR

FOR DIFFERENT POWER SUPPLY PROPERTIES

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

andphaseangles of thepower supplyvoltages is given in Table I.


of 15 W/220–240 V.

Results of Measurement: In Table II, a summary of the

measured rms values of the total neutral conductor currentand the third harmonic in the neutral conductor current

is given for the different power source setups according toTable 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




590 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003

(a)

(b)

Fig. 3. (a) Phase and (b) neutral conductor currents in case of a symmetricand unbalanced power supply and a symmetric and balanced load (five compactfluorescent 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 inthe 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 neu-

tral 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 cur-

rent. Finally, it is concludedthat the rms valueof the total neutral

conductor current is only slightly affected by an asymmetry or

unbalance in the power supply (Table II).

Fig. 4. Neutral conductor current in case of a balanced and (a) symmetricpower supply and a symmetric and balanced load (five compact fluorescentlamps in each phase).

D. Influence of Load Unbalance on the Neutral Conductor

Current

Setup Parameters—Power Source: A sinusoidal voltage isgenerated in each phase, with rms value and phase angle as in

Table I.

Load : Each phase is loaded by a number of compact fluo-

rescent lamps of 15 W/220–240 V. Measurements were done

for the following load conditions, considering a constant three-

phase power:

• six lamps in phase , six lamps in phase , and no lamps

in phase (unbalanced load);

• six, four, and two lamps in phases , , and , respec-

tively (unbalanced load);

• four lamps in each phase (balanced load).

Results of Measurement: Table III(a) summarizes the mea-sured 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 in-

fluence 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 de-

pending 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 in-

creasing 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





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)

(b)

Fig. 5. Neutral conductor current in case of a balanced and symmetric powersupply 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 funda-

mental.


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 cur-

rents and the neutral conductor current. In the phase currents

(a)

(b)

Fig. 6. (a) Phase and (b) neutral conductor currents for different harmoniccontents of the power supply voltage. The power supply and load are symmetricand balanced.

[Fig. 6(a)] the fifth harmonic is more influenced than the third

harmonic (changes of respectively 10% and 2.5%). The changeof 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 fifth-

order harmonics are zero in the neutral conductor. Only the

changes of the third-order harmonics are determining the neu-

tral conductor current.

Table IV gives, for different harmonic contents of the power

supply voltage, the deviations (%) of the rms value of the neu-

tral conductor current from the reference value in case of a si-

nusoidal 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 increasingamplitude of the harmonic. The rms value of the neutral con-

ductor 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.




592 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003

TABLE IVSENSITIVITY OF THE rms VALUE OF THE NEUTRAL CONDUCTOR CURRENT TO

THE HARMONICS IN THE POWER SUPPLY VOLTAGE

These conclusions can be drawn for all equipment with sim-

ilar current signatures as those of the tested compact fluorescent

lamps (e.g., computers).

REFERENCES

[1] A.-C. Liew, “Excessive neutral currents in three-phase fluorescentlighting circuits,” IEEE Trans. Ind. Applicat., vol. 25, pp. 776–782,July/Aug. 1989.

[2] T. M. Gruzs, “A survey of neutral currents in three-phase computerpower systems,” IIEEE Trans. Ind. Applicat., vol. 26, pp. 719–725,July/Aug. 1990.

[3] C. L.Fortescue,“Methodof symmetricalcoordinatesappliedto thesolu-tion 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 theEur. Copper Institute Workshop Economic Cost of Poor Power Quality,Brussels, Belgium, June 8, 2000.

Jan J.M. Desmet (M’00) received the PolytechnicalEngineer degree from the Polytechnic, Kortrijk, Bel-gium, in 1983, and the M.S. degree in electrical en-gineering 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-Vlaan-deren, Kortrijk, Belgium, where he is currently aProfessor. His areas of teaching are variable-speeddrives and industrial electric measurement tech-niques. 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 Scienceand Technology for Development (IASTED), SC77A (IEC), and TC210(CENELEC)

Isabel Sweertvaegher graduated in electronicsfrom the Vrij Hoger Technisch Instituut, Kortrijk,Belgium, in 1996, and received the PolytechnicalEngineer degree from the Department P.I.H.,Hogeschool West-Vlaanderen, Kortrijk, Belgium, in1998.

Currently, she is a Research Assistant in theDepartment P.I.H., Hogeschool West-Vlaanderen,teaching in the areas of control technique andelectronics. Her research interests include powerquality and control technique.

Greet Vanalmereceivedthe M.S.degree in electricalengineering and the Ph.D. degree in sciences fromtheUniversityof Ghent,Ghent, Belgium, in 1994 and2000, respectively.

Currently, she is a Researcher in the field of powerquality in the Department P.I.H., Hogeschool West-Vlaanderen, Kortrijk, Belgium.

Kurt Stockman (S’02) received the degree of Industrial Engineer in Electrical Engineering fromthe Provinciale Industriële Hogeschool, Kortrijk,Belgium, in 1994. He is currently working towardthe Ph.D. degree at the Katholieke UniversiteitLeuven, Leuven, Belgium.

Since 1995, he has been with the DepartmentP.I.H., Hogeschool West-Vlaanderen, Kortrijk,Belgium. His research interests are adjustable-speeddrives, voltage sags, and control engineering.





Ronnie J. M. Belmans (S’77–M’84–SM’89) re-ceived the M.S. degree in electrical engineering andthe Ph.D. degree from the Katholieke UniversiteitLeuven (KULeuven), Leuven, Belgium, in 1979 and1984, respectively, and the special Doctorate degreeand 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. Heis Director of several basic and industrial researchprojects. Currently, he is Head of the Department of Electrical Engineeringand Vice President of the KULeuven Energy Institute. Since June 2002, he hasbeen the Chairman of the Board of Elia, the Belgian grid operator. His researchinterests include variable-speed drives, distributed power, power quality, andrenewable energy in the grid. He is also performing research on the systemaspect of the liberalization of the electricity market. He was with the Laboratoryfor Electrical Machines, RWTH Aachen, as a Von Humboldt Fellow fromOctober 1988 to September 1989. From October 1989 to September 1990, hewas a Visiting Professor at McMaster University, Hamilton, ON, Canada. Heobtained the Chair of the Anglo–Belgian Society at London University forthe year 1995–1996. Since 1997, he has been a Visiting Pofessor at RWTHAachen, and since 1999, at Imperial College, London, U.K.

Dr. Belmans is a Fellow of the Institution of Electrical Engineers, U.K., and aMember of the Koninklijke Vlaamse Ingenieursvereniging (KVIV). Since1997,he has been President of the International Organization on Electricity Use (UIE,

based in Paris, France).

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