Reducing losses in distribution transformers - IEEE Xplore

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Abstract—This paper examines three methods of reducing distribution transformer losses. The first method analyzes the effects of using aluminum ...
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 3, JULY 2003

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Reducing Losses in Distribution Transformers Juan Carlos Olivares, Member, IEEE, Yilu Liu, Senior Member, IEEE, Jose M. Cañedo, Member, IEEE, Rafael Escarela-Pérez, Member, IEEE, Johan Driesen, Member, IEEE, and Pablo Moreno, Member, IEEE

Abstract—This paper examines three methods of reducing distribution transformer losses. The first method analyzes the effects of using aluminum electromagnetic shields in a distribution transformer. The goal of placing electromagnetic shields in the distribution-transformer tank walls is to reduce the stray losses. A 500-kVA shell-type transformer was used in the experiments. The overall results presented indicate that stray losses can be considerably reduced when electromagnetic shielding is applied in the transformer tank. In the experiment, the tank walls were lined with aluminum foil. The possibility of reducing the dielectric losses was shown through experiments in the second method. And the third method of this work analyzes the behavior of wound-cores losses in distribution transformers, as a function of joint configuration design parameters. The joint configuration used in this paper is called step-lap joint. Index Terms—Dielectric losses, loss measurements, shielding, transformer, transformer cores.

I. INTRODUCTION UE to environmental considerations and rising energy costs, customers have been putting high requirements on transformer efficiency [1]. Although the efficiency of a modern transformer lies above 99%, the loss cost is still significant [2]. The present study is part of such effort to further increase the efficiency. The loss topic continues to be a topic of huge interest. In 1990, only about 92.5% of the energy generated at U.S. power plants was actually distributed to the consumer. The other 7.5% of the energy (approximately 229 billion kilowatt-hours annually) was dissipated as losses in the transmission and distribution system [3]. The distribution transformer efficiencies steadily increased with the introduction of improved materials and manufacturing methods [4]. Even so, 26.6% of the average transmission and distribution losses are still associated with distribution transformers [3]. The previous figures of losses are a consequence of the large number of transformers installed among other factors. It is estimated that there are 50 million distribution transformers [3] in use in the U.S. The objective of this research is to find ways to reduce the distribution transformer losses. In order to reduce these losses,

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Manuscript received July 18, 2001; revised May 9, 2002. This work was supported in part by CONACYT. J. C. Olivares and Y. Liu are with Virginia Polytechnic Institute and State University, Bradley Department of Electrical and Computer Engineering, Blacksburg, VA 24061 USA (e-mail: [email protected]). J. M. Cañedo and P. Moreno are with CINVESTAV, Jalisco 45090, México (e-mail: [email protected]; [email protected]). R. Escarela-Pérez is with Universidad Autónoma Metropolitana-Azcapotzalco, México, D.F. (e-mail: [email protected]). J. Driesen is with Katholieke Universiteit Leuven, Research Group Electrical Energy ESAT-ELEN Kasteelpark Arenber, Heverlee 10B-3001, Belgium (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRD.2003.813851

TABLE I COMPARATIVE ANALYSIS OF TRANSFORMER COSTS

we are using three methods. The first method investigates the effects of electromagnetic shields upon distribution transformer tank losses. In today’s competitive market, accurate estimation and subsequent reduction of the stray loss by shielding techniques could give a competitive advantage [5]. The second method is related with an experiment, in which 12 measurements of four transformers were made in order to show how the transformer losses could vary during its manufacturing process. The dielectric losses can be reduced if the transformer manufacturer carries out an adequate drying process. The third method deals with the core joints. Core joints play an important role in the performance of transformer cores. Due to the importance of improved electrical core performance, transformer manufacturers [6]–[8] and research institutions [9]–[11] are very active in the development of better electrical steel and the optimization of the core design parameters. Of the various materials required to build a transformer, the electrical steel comprises the largest investment. Table I shows a comparative analysis of transformer costs by component [12]. Table I was made taking into account six transformers, from 15 to 1000 kVA and the voltage considered was 13 200 V–220 Y/127 V. In this study, the effect of the following two factors is considered: (a) overlap length and (b) number of laminations per step or group. The experimental data presented in this work will be helpful for a practicing engineer in the transformer industry. II. EXPERIMENTAL STUDY TO REDUCE DISTRIBUTION-TRANSFORMERS STRAY LOSSES USING ELECTROMAGNETIC SHIELDS A 500-kVA experimental transformer on loan from a factory was used to investigate in detail the stray losses and to examine how these losses can be described physically. This transformer (see Fig. 1) is a shell-type, which means the windings are surrounded by the core. In the transformer, the leakage flux is high in the tank walls, which causes high-power losses [13]. The main effort to reduce

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 3, JULY 2003

Fig. 1. Shell-type transformer picture taken during manufacturing; the right side core is not assembled yet.

load losses has concentrated in the area of stray losses [2]. A reduction of the magnetic flux is required to reduce these losses. Placing a physical barrier, called a shield, between the electromagnetic field source and the region of interest can accomplish this purpose. Shielding materials include magnetic and electric conducting materials [14]. Magnetic materials are high permeability material and shield by a mechanism called “flux shunting.” In this case, the flux from a source is diverted into the magnetic material and away from the region to be shielded. Electric materials are high-conductivity materials and shield by a phenomenon known as “eddy-current cancellation.” In this case, currents are induced in the conductor, which create magnetic fields that partially cancel those from the source [15]. losses. The stray losses The main load-losses are the arise from eddy currents induced in metallic parts of the transformer; for instance, in clamps and in tank walls. Therefore, good understanding of stray losses and their reduction mechanisms are necessary for improving the transformer design [16], [17]. The stray losses are a function of many factors including physical geometry of the cores and windings, voltage class, and the material used in the tank construction [18]. According to Fig. 2, the stray losses increase with the growing of transformer rating [19]–[21]. Hence, the application of shielding in very small transformers is not attractive to reduce stray losses. Using the least square fitting method, the stray losses that could be reduced by placing shielding are expressed as a function of the transformer rating as follows [12]: kVA

kVA

The ratio of stray losses to load losses using regression analysis as given below [12] kVA

(1) was estimated (2)

versus transformer rating. Fig. 3 shows the behavior of A magnetic shield comprises a large number of packets of aluminum laminations mounted on the vertical sides of the steel tank. The height of the aluminum shield is equal to the height of the steel tank and the separation between the laminations is of the order of 0.3 mm. The process of lining the steel tank wall of the transformer with aluminum foil is rather time-consuming.

Fig. 2.

Stray losses versus the transformer rating at temperature 85 C.

Fig. 3. Stray loss load loss ratio versus the transformer rating (kilovolt amperes).

The total aluminum cost was about U.S.$ 311.70, which represents 10% of the total transformer material cost. See Table II. The load loss and stray loss are measured under three conditions: (a) without shield, (b) with aluminum shield of 1.2 mm of thickness, (c) with aluminum shield thickness of 10 mm. Table III shows the measurement values of stray losses and the efficiency for cases (b) and (c) of the previous paragraph. The load losses without shield were 504.12 W at ambient temperature. This base-case efficiency was of 99.09%. It is observed that stray losses are increased by 20.9% when the 10-mm aluminum shield is not used. On the other hand, there was little change in the losses between the 1.2-mm shield and the unshielded case, since the depth of penetration is larger than the aluminum shield thickness so the magnetic flux density reaches the carbon steel. For the case of steel tank when the depth of penetration is less than the steel-wall thickness, the half thickness of the plate, the inner part of the plate remains unmagnetized, and the magnetic flux as well as the eddy currents are confined to a layer of depth on the plate surface [22]. Placing aluminum shielding in the internal tank wall reduces the stray losses because induced currents of considerable magnitude in the shielding produce a magnetic field that partially cancels the incident field. In other words, the magnetic flux density

OLIVARES et al.: REDUCING LOSSES IN DISTRIBUTION TRANSFORMERS

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TABLE II MASS OF THE ALUMINUM SHIELD, THICKNESS OF 10 MM

TABLE III MEASUREMENT VALUES OF STRAY LOSSES

Fig. 4. No-load test with a test coil of 12 turns.

TABLE IV NO-LOAD LOSSES DURING THREE STAGES MANUFACTURING

OF

TRANSFORMER

induced is opposed to the magnetic flux density incident. The superposition of induced field and incident field gives a total field, which is repelled from the tank superficies. It is important to recognize that the previous phenomenon occurs regardless of the application of aluminum shielding. Then, the difference is based on the material properties; for the carbon steel, the product is in the order of 2 10 , while for the aluminum shield this value is 500 times less, that is, 3.8 10 , which is reflected in the losses. III. IMPORTANCE OF DIELECTRIC LOSSES THE NO-LOAD TEST

IN

The no-load losses include the eddy-current , the hysteresis losses , and the dielectric losses losses . Since the no-load current will be very small compared losses in the windings will be to the full load value, the negligible. Thus [23], [24] (3) Table IV shows the no-load losses measured for a sample of four 37.5-kVA transformers during three stages of the manufacturing process. Column 1 shows the no-load losses when a test coil of 12 turns is used (see Fig. 4). Column 2 indicates the no-load losses when the cores are assembled with their design windings but without the tank (The high-voltage winding has 1066 turns and the low-voltage winding has 16 turns). Column 3 indicates the no-load losses when the transformer is completed, that is, when the transformer has a tank and it is filled with oil. In Table IV, two main observations can be made. First, the no-load losses of the active-element (set core winding) are higher than the no-load losses of the completed transformer because when the active-element is tested, its insulation contains a high content of moisture, which causes high dielectric losses. The dielectric losses are determined by the expression [25], [26] (4)

where is voltage (V), is angular frequency (rad/s), is Delta tangent, is capacitance of the configuration. Second, column 2 losses are higher than the column 1 losses because undesirable stresses are created in the electric steel for manufacturing operations introduced during the core-coil assembly. The stresses due to the slitting of the core steel as well as the stresses due to the core winding and forming operations are relieved by the heat treatment process (or stress relief annealing). Normally, stresses create a harmful effect by causing a degradation of magnetic properties. These changes occur because the metal crystals are distorted. All of the measurements in this paper were carried out on a new transformer and before the impulse test. This is important because when the test transformers are old [27] or have received the impulse test, the no-load losses can be higher. This difference exists because there are local breakdowns between individual laminations, which would result in higher loss [2]. IV. IMPACT OF THE JOINTS DESIGN PARAMETERS OF THE WOUND CORE IN DISTRIBUTION TRANSFORMER LOSSES The following core manufacturing-parameter definitions are related to Fig. 5. These definitions are exclusive for the wound-core distribution-transformer family. • Step or book. Set of laminations, which can vary between four and 25 and this set of laminations form a cycle. In Fig. 5, the first four laminations (from top to bottom) form a step.

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 3, JULY 2003

TABLE V NO-LOAD LOSSES

FOR A 15-KVA TRANSFORMER LAMINATIONS PER STEP

WITH DIFFERENT

TABLE VI NO-LOAD LOSSES WITH DIFFERENT OVERLAP LENGTH Fig. 5. Core with step-lap joint.

• Air gap (g). The air gap is the separation between lamination and lamination in the direction of rolling. In the practice, this value is less than 3 mm. • Overlap (L). The overlap is the length between the half points of the air gaps of two laminations contiguous in the rolling direction. The typical range of this parameter is 1 to 2 cm. • Lamination thickness (T). Grain oriented silicon steel is graded according to the American iron and steel institute (AISI) designations. . Grain oriented electrical steels • Insulation thickness are coated with C-2 coating or C-5 over C-2 coating. Typical C-2 coating thickness is 0.0001 cm per surface. Whenever C-5 is applied over C-2 coating, the thickness of C-5 coating is approximately 0.0001 cm per surface for wound-core distribution transformer [28]. A safe value of interlamination resistance must be maintained to prevent stray losses in the core [29]–[31]. In Fig. 5, the laminations are in succession in order to obtain a higher mechanical stability. If the joints are rigid and strong, it prevents them from coming apart under severe operation conditions, and also diminishes the noise, from vibrations during the operation of the transformer [32]. Most of the technical papers have analyzed the stacked transformer cores. Until now, little attention has been paid to wound transformer cores. The objective of these measurements is to investigate experimentally the effects of core-parameter changes on wound-core losses in a distribution transformer. This goal was carried out by two experiments. In these experiments, the number of laminations per step or book and the overlap length were varied. The transformers were excited with a 60-Hz generator and the measurements were made under design flux density. The following experiments were performed using a 15-kVA transformer. The cores were assembled using six and 25 laminations per step. The grain-oriented electrical steel laminations (0.23 mm thick) produced a nominal core loss at 1.5 T and 60 Hz of 0.98 W/kg. The overlap and the air gap length were mm and mm, respectively. Table V shows that laminations per step do not have an important effect on the core losses. This experiment only tested one core for each measurement. In order to comply with manufacturing limitations, the number of laminations per step is increased. Conversely,

the overlap lengths are decreased and the net result of these opposing factors results in no change. These results agree with the conclusion of [33] where it was stated that “when the number of laminations per one group is increased core losses are slightly increased.” A separate experiment examined a sample of nine 37.5-kVA transformer cores, in which six cores were manufactured with an overlap length of 1 cm and three cores were manufactured with an overlap length of 2 cm. The results are shown in Table VI. In this experiment, only one core was tested in each measurement. Table VI shows that the sample with higher losses was the transformer with an overlap length of 2 cm. This is most likely due to the increased area, where the flux is forced to pass perpendicularly to the laminations, since the core steel is anisotropic [34]. The results of the no-load test vary with the temperature of the transformer core [35]. For this reason, the measurements in Tables V and VI were carried out at the same temperature. Sixty cores were manufactured to test the repeatability of the loss measurements. V. CONCLUSIONS This paper presented results of experimental investigations regarding reduction of distribution-transformer losses. The work contains experimental data that will be helpful for practicing engineers in the transformer industry. Experiments were carried out in well-controlled conditions. First, a load loss test was carried out under three different conditions: (a) tank walls without shield, (b) tank walls with aluminum shield of 1.2 mm of thickness, and (c) tank walls with aluminum shield of 10-mm thickness. The electromagnetic shields of the transformer in this experiment prevented the penetration of the magnetic stray flux in the magnetic materials, where high losses would be

OLIVARES et al.: REDUCING LOSSES IN DISTRIBUTION TRANSFORMERS

induced. In this case, an increase of the stray losses by 20.9% was observed when the aluminum shield of 10 mm was not used. On the other hand, there were not significant changes in the losses when the 1.2-mm shield was used with respect to unshielded case, since the depth of penetration was larger than the shield thickness and the magnetic flux could reach the carbon steel. The study also demonstrated that the dielectric losses are important in no-load loss in the transformer when the transformer insulations have a high water content. Until now, little attention has been given to the design of wound transformer cores. In the paper, results for the wound-core distribution-transformer family were presented. It is known that minimum losses occur when the rolling direction coincides with flux magnetic lines, but this condition is not satisfied in the core joints since the joints air gaps cause local disturbances of magnetic flux. Two experiments were carried out, varying: (a) the overlap length and (b) the number of laminations per step. It is observed that the number of laminations per step does not have much effect on the core losses. This is because as the number of laminations was increased, the overlap length was decreased in order to comply with manufacturing limitations. The test showed that transformers had higher losses when an overlap length of 2 cm is used. ACKNOWLEDGMENT The authors want to thank Mr. A. L. Von Holle and F. Gaudino (Ak Steel, USA), Mr. A. Trujillo (EMSA, Mexico), Mr. P. Subbaraman (GE, India), Mr. J. Avila and Mr. D. Posadas (Prolec-GE, Mexico), Mr. M. Alley and Mr. N. Clark, (Virginia Tech), and Mr. E. Melgoza (Ph.D. Student, University of Bath) for their helpful discussion. REFERENCES [1] T. H. Harrison and B. Richardson, “Transformer Loss Reduction,” Session, Cigre 12-04, 1988. [2] R. Beaumont, “Losses in Transformer and Reactors,” Session, Cigre 12-10, 1988. [3] P. R. Barnes, “The Feasibility of Replacing or Upgrading Utility Distribution Transformers During Routine Maintenance,” Rep., ORLN-6804/R1, Apr. 1995. [4] D. J. Allan, “Power transformers- the second century,” Power Eng. J., pp. 5–14, Jan. 1991. [5] B. Szabados, “A new approach to determine eddy current losses in the tank walls of a power transformer,” IEEE Trans. Power Delivery, vol. PWRD-2, pp. 810–816, July 1987. [6] R. S. Girgis, K. Gramm, E. G. teNijenhuis, and J. E. Wrethag, “Experimental investigations on effect of core production attributes on transformer core loss performance,” IEEE Trans. Power Delivery, vol. 13, pp. 526–531, Apr. 1998. [7] G. F. Mechler and R. S. Girgis, “Magnetics flux distributions in transformer core joints,” IEEE Trans. Power Delivery, vol. 15, pp. 198–203, Jan. 2000. [8] E. G. teNyenhuis, G. F. Mechler, and R. S. Girgis, “Flux distribution and core loss calculation for single phase and five limb three phase transformer core designs,” IEEE Trans. Power Delivery, vol. 15, pp. 204–209, Jan. 2000. [9] M. A. Jones, A. L. Moses, and J. E. Thompson, “Flux distribution and power loss in the mitered overlap joint in power transformer cores,” IEEE Trans. Magn., vol. MAG-9, pp. 114–122, June 1973. [10] F. Loffler, H. Pfützner, T. Booth, C. Bengtsson, and K. Gramm, “Influence of air gaps in stacked transformer cores consisting of several packages,” IEEE Trans. Magn., vol. 30, pp. 913–915, Mar. 1994. [11] Z. Valkovic and A. Rezic, “Improvement of transformer core magnetic properties using the step-lap design,” J. Magn. Magn. Mater., vol. 112, pp. 413–415, 1992.

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[12] J. C. Olivares, Distribution Transformer Design Course (in Spanish). Guadalajara, Jalisco, Mexico: EMSA, 1998. [13] F. J. Vogel and E. J. Adolphson, “A stray loss problem in transformer tanks,” in Amer. Inst. Elect. Eng. Trans., Aug. 1954, pp. 760–764. [14] P. Moreno, “Extra Low Frequency Magnetic Fields Shielding With Finite Width Planar Shields,” Ph.D., Univ. Washington, 1997. [15] K. V. Namjoshi and P. P. Biringer, “Power efficiency of eddy current shielding of structural steel in transverse magnetic field,” IEEE Trans. Magn., vol. 25, pp. 2829–2831, Sept. 1992. [16] S. V. Kulkarni and S. A. Khaparde, “Stray loss evaluation in power transformer—a review,” in IEEE Power Eng. Soc. Winter Meeting, Paper no. 0.7803-5938-0/00, Singapore, Jan. 2000, pp. 2269–2274. [17] Y. Inui, S. Saito, K. Okuyama, and K. Hiraishi, “Effects of tank shields on magnetic fields and stray losses in transformer windings,” in IEEE Power Eng. Soc. Summer Meeting Conf., Vancouver, Canada, 1973. [18] K. Kazmierski, M. Kozlowski, J. Lasocinski, I. Pinkiewicz, and J. Turowski, “Hot Spot Identification and Overheating Hazard Preventing When Designing a Large Transformer,”, Cigre 12-12, 1984. [19] C. Yongbin, Y. Junyou, Y. Hainian, and T. Renyuan, “Study on eddy current losses and shielding measures in large power transformer,” IEEE Trans. Magn., vol. 30, pp. 3068–3071, Sept. 1994. [20] D. A. Koppiker, S. V. Kulkarni, P. N. Srinivas, S. A. Khaparde, and R. Jain, “Evaluation of flitch plate losses in power transformer,” IEEE Trans. Power Delivery, vol. 14, pp. 996–1001, July 1999. [21] A. A. Berezovskii, “Calculation of stray losses in transformer tanks,” Elektrichestvo, no. 9, pp. 421–448, 1966. [22] P. D. Agarwal, “Eddy-current losses in solid and laminated iron,” in Amer. Inst. Elect. Eng. Trans., May 1959, pp. 169–181. [23] R. Feinber, Ed., Modern Power Transformer Practice. New York: Macmillan, 1979, pp. 128–129. [24] P. Georgilakis, N. Hatziargyriou, and D. Paparigas, “Al helps reduce transformer iron losses,” IEEE Comput. Applicat. Power, vol. 12, pp. 41–46, Oct. 1999. [25] E. Wasilenko and M. Olesz, “On-site loss tangent measurements of high voltage insulation,” in Proc. Dielectric Materials, Measurements and Applicat., 1992, Sixth Int. Conf., 1992, pp. 170–173. [26] H. Kurita, T. Hasegawa, and K. Kimura, “Dielectric loss of high voltage/high frequency transformers used in switching power supply for space,” in Proc. 19th Annu. IEEE Power Electron. Specialists Conf. Rec., vol. 2, 1988, pp. 1120–1126. [27] D. J. Ward, “An analysis of loss measurements on older distribution transformers,” IEEE Trans. Power Apparat. Syst., vol. PAS-103, pp. 2254–2261, Aug. 1984. [28] F. Gaudino, Letter (Private Communication), July 6, 1999. [29] J. P. Barton, “Interlamination resistance,” in Amer. Inst. Elect. Eng. Trans., Sept. 1944, pp. 670–672. [30] A. C. Beiler and P. L. Schmidt, “Interlaminar eddy current loss in laminated cores,” Amer. Inst. Elect. Eng. Trans., vol. 66, pp. 872–878, 1947. [31] N. S. Sheth, “Development in core plate varnishes for the electrical industry,” Elect. India, pp. 3–6, Nov. 1991. [32] A. J. Pansini, Electrical Transformer and Power Equipment. Englewood Cliffs, NJ: Prentice-Hall, p. 25. [33] T. Nakata, N. Takahashi, and Y. Kawase, “Magnetic performance of step-lap in distribution transformer cores,” IEEE Trans. Magn., vol. MAG-18, pp. 1055–1057, Nov. 1982. [34] C. Lee and H. K. Jung, “Two-Dimensional analysis of three-phase transformer with load variation considering anisotropy and overlapped stacking,” IEEE Trans. Magn., vol. 36, pp. 693–696, July 2000. [35] R. M. Bozorth, Ferromagnetism: IEEE Press, IEEE Magne. Soc., 1978, pp. 11–12.

Juan Carlos Olivares (M’02) was born in Zamora, Michoacan, Mexico, on March 26, 1969. He received the Bachelor’s and Master’s degrees from the Instituto Tecnologico de Morelia, Mexico, in 1995 and 1997, respectively. He is currently pursuing the Ph.D. degree in electrical engineering at Centro de Investigación y de Estudios Avanzados (CINVESTAV), Guadalajara Campus, Mexico. Currently, he is a Visiting Scholar at Virginia Tech., Blacksburg, VA. He worked in Electromanufacturas, Mexico, from 1997 to 1999. His main interests are related to transformers.

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Yilu Liu (SM’99) received the Ph.D. degree from The Ohio State University, Columbus, in 1989. Currently, she is a Professor of Electrical Engineering at Virginia Tech., Blacksburg, VA. She also has 17 years of experience in transformer modeling and diagnosis.

José M. Cañedo (M’91) received the Ph.D. in 1985 from the Moscow Power Institute, Russia. Currently, he is a Professor at Centro de Investigación y de Estudios Avanzados (CINVESTAV), where he has been since 1997. His main areas of interest are control of power systems and electrical machines.

Rafael Escarela-Pérez (M’97) was born in Mexico City, Mexico, in 1969. He received the B.Sc. degree in electrical engineering from Universidad Autonoma Metropolitana, Mexico City, in 1992, and the Ph.D. degree from Imperial College, London, U.K., in 1996. His research interest includes the modeling of electrical machines.

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 3, JULY 2003

Johan Driesen (S’93–M’97) received the Ph.D. degree in electrical engineering from K.U. Leuven in 2000 on the finite element solution of coupled thermalelectromagnetic problems and related applications in electrical machines and drives, microsystems, and power quality issues. Currently, he is a postdoctoral research fellow of the Belgian “Fonds voor Wetenschappelijk Onderzoek—Vlaanderen.” Dr. Driesen received the 1996 R&D-award of the Belgian Royal Society of Electrotechnical Engineers (KBVE) for his Master Thesis on power quality problems.

Pablo Moreno (M’00) received the Ph.D. degree in electrical engineering from Washington State University, Pullman. Currently, he is Research Professor in Centro de Investigación y de Estudios Avanzados (CINVESTAV), Guadalajara Campus, Mexico. His main interests are related to electromagnetic wave propagation and electromagnetic compatibility.