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. Index Terms Current measurement, harmonic distortion, neutral 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 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. II. THEORETICAL CONSIDERATIONS 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 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 (4) Notice that the first-order harmonics (, with the order of the harmonic and ) in the phase currents are forming a direct system, the third-order harmonics are forming a homopolar system, and the fifth-order harmonics an inverse system. Consequently, the neutral 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 with (1) (2) (3) (5.a) (5.b) 0093-9994/03$17.00 2003 IEEE
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 inverse components equals zero, only the 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. Assuming,, and, then is given by From the above equation, the amplitude and the phase angle of the th harmonic in the neutral conductor current can be calculated. The amplitude of the th harmonic in the neutral conductor current is shown by (9), at the bottom of the page, where is the amplitude of the th harmonic in the neutral conductor current,,, is the amplitude of the th current harmonic in, respectively, phases,, and, and,, is the phase angle of the th current harmonic in, respectively, phases,, and. The phase angle of the th harmonic in the neutral conductor current is (7) (8) (10) 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). 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) 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, respectively,,, and. Consider the particular case in which the phase currents are consisting of odd harmonics with (, )or,,,. The rms value of the phase current is The rms value of the neutral conductor current equals (12) (13) The rms ratio of the neutral conductor current and the phase current is (14) The maximum rms ratio of the neutral conductor current and the phase current is obtained when (all the harmonics in the 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)
DESMET et al.: NEUTRAL CONDUCTOR CURRENT IN A THREE-PHASE SUPPLIED NETWORK 589 TABLE I POWER SOURCE PARAMETERS TABLE II TOTAL CURRENT AND THIRD HARMONIC IN THE NEUTRAL CONDUCTOR FOR DIFFERENT POWER SUPPLY PROPERTIES Fig. 2. Phase and 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 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 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]. 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
590 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 3, MAY/JUNE 2003 Fig. 4. Neutral conductor current in case of a balanced and symmetric power supply and a symmetric and balanced load (five compact fluorescent lamps in each phase). Fig. 3. Phase and 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] 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 and 3]. 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). D. Influence of Load Unbalance on the Neutral Conductor Current 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 in phase (unbalanced load); six, four, and two lamps in phases,, and, respectively (unbalanced load); four lamps in each phase (balanced load). Results of Measurement: Table III summarizes the measured rms values of the neutral conductor current for different power supply (Table I) and load conditions. Table III 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
DESMET et al.: NEUTRAL CONDUCTOR CURRENT IN A THREE-PHASE SUPPLIED NETWORK 591 TABLE III rms VALUES OF THE NEUTRAL CONDUCTOR CURRENT FOR DIFFERENT POWER SUPPLY AND LOAD CONDITIONS. RATIO OF THE NEUTRAL CONDUCTOR CURRENT TO THE AVERAGE OF THE PHASE CURRENTS FOR DIFFERENT POWER SUPPLY AND LOAD CONDITIONS Fig. 6. Phase and neutral conductor currents for different harmonic contents of the power supply voltage. The power supply and load are symmetric and balanced. 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] 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]. 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.
592 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 West- Vlaanderen, 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.
DESMET et al.: NEUTRAL CONDUCTOR CURRENT IN A THREE-PHASE SUPPLIED NETWORK 593 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).