Space Vector PWM Technique with Minimum Switching ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 2, APRIL 1997

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Space Vector PWM Technique with Minimum Switching Losses and a Variable Pulse Rate Andrzej M. Trzynadlowski, Senior Member, IEEE, R. Lynn Kirlin, Senior Member, IEEE, and Stanislaw F. Legowski, Senior Member, IEEE

Abstract—A novel randomized control strategy for three-phase voltage source inverters, based on the voltage space vectors, is described. An implicit asymmetrical modulating function results in switching losses in the inverter being reduced by about half in comparison with those using the classic space vector pulsewidth modulation (PWM) method. The pulse rate is varied within individual 60 sectors of the vector plane, so that the power spectra of the output voltage are spread over a wide frequency range and acquire a continuous part. The relevant theoretical analysis, computer simulations, and experimental results are presented. Index Terms—Inverters, random PWM, space vectors, switching losses.

I. INTRODUCTION

A

LL THE regular-sampling pulsewidth modulation (PWM) techniques for power electronic converters utilize, directly or indirectly, linear transformation of a given modulating function into duty ratios of switching signals of the converter. Considering a three-phase inverter, duty ratio of the phase A switching signal within th switching interval can be expressed as (1) where modulating function; modulating index; center angle of the interval. The modulating function does not have to be sinusoidal, but it must be contained within the 1 to 1 range. Then, the duty ratios of inverter switches can be varied between zero and unity, allowing full magnitude control of the inverter voltage. Clearly, (1) also applies to the other two phases of the inverter, with replaced with 120 for phase B and 240 for phase C. A variety of modulating functions have been presented in [1]. The classic space-vector PWM (SVPWM) strategy, first proposed in [2] and [3], and very popular nowadays because of its simplicity and good operating characteristics, consists of the generation of a specific sequence of states of the inverter.

In essence, the modulator represents a timed ring counter. Durations of the individual states are determined from simple formulas that are easy to implement in a microprocessor. The complex plane of the voltage space vectors of the inverter is divided into six 60 wide sectors (0 –60 , 60 –120 , etc.) corresponding to 60 long subcycles of the cycle of the output voltage of the inverter. In turn, each subcycle is divided into equal switching intervals. Three states, and of the inverter are imposed within each switching interval. A given of an inverter is defined by values of the phase A, state, B, and C switching signals, and as For example, if and then the inverter is said to be in state 5, since The duty ratios, and of the individual states in th switching interval are calculated as (2) (3) (4) where is the center angle of th switching interval, measured with respect to the beginning of the subcycle, while and in subcycles 1–6, respectively. State occurs when all three output terminals of the inverter are clamped to the same dc supply bus, either the negative or positive one. In the SVPWM technique, the sequence of states in the consecutive switching intervals is States and are, complementarily, 0 and 7, and so selected that the transition from one state to another involves switching of one inverter leg only. Denoting by the per-cycle per-phase number of switching pulses, i.e., the ratio of the average switching frequency to the output frequency, this number in the SVPWM strategy is (5) The implicit modulating function, obtained by averaging over two consecutive switching intervals, is given by

Manuscript received February 27, 1996; revised June 24, 1996. A. M. Trzynadlowski is with the Department of Electrical Engineering, University of Nevada, Reno, NV 89557-0153 USA. R. L. Kirlin is with the Department of Electrical and Computer Engineering, University of Victoria, B.C., V8W 3P6 Canada. S. F. Legowski is with the Department of Electrical Engineering, University of Wyoming, Laramie, WY 82071 USA. Publisher Item Identifier S 0278-0046(97)01814-5. 0278–0046/97$10.00  1997 IEEE

for for for

and and and (6)

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and shown in Fig. 1 for It is a continuous function, linearly dependent on the modulation index and symmetrical with respect to the center of the cycle. The continuity of the modulating function implies that, in each leg of the inverter, switchings occur within all six subcycles of the output voltage. The fixed pulse rate, defined here as the number of switching intervals per subcycle and specific for the SVPWM technique, results in clusters of prominent harmonics in the fully discrete power spectrum of the inverter output voltage. This is illustrated in Fig. 2, that shows an example spectrum of the line-to-neutral voltage of a space-vector pulsewidth modulated inverter. The modulation index, is 1, the output frequency, is 50 Hz, and the pulse rate, is 8 switching intervals per subcycle. That, according to (5), yields 24 switching pulses per cycle, a value typical for mediumpower inverters. Two distinct harmonic clusters can easily be discerned: one centered about the frequency of 2.4 kHz and the other about 4.8 kHz, i.e., about even multiples of the switching frequency of 1.2 kHz (24 50 Hz). If the inverter is used in an adjustable-speed ac drive system, these harmonics cause annoying tonal noise in the motor [4]. In certain circumstances, the periodic harmonic torque developed in the motor due to the harmonic component of the supply voltage may also lead to resonant vibration in the drive system [5], [6]. This paper describes a novel approach to the control of three-phase voltage source inverters, based on the same idea of voltage space vectors as the SVPWM strategy, but significantly enhanced in two aspects. First, switching losses in the inverter are greatly reduced by employing a different implicit modulating function. Second, power spectra of the inverter output voltages are improved by using a randomly varied pulse rate, changed from subcycle to subcycle. Because of these changes, switching patterns differ from cycle to cycle of the output voltage, yielding spread partly continuous spectra. As reported in many papers, notably in [7]–[11], such spectra result in significant attenuation of the tonal noise and vibration in inverter-fed drive systems. II. MINIMUM-LOSS MODULATING FUNCTION Apart from several versions of the basic SVPWM technique [12]–[15], there exist many strategies using various modulating functions in an explicit manner, which means that duty ratios of the switching signals are computed directly from (1). Discontinuous modulating functions have gained special attention for their reduced-switching properties [1], [15]. In particular, a modulating function given by for for for for for for (7) and presented in Fig. 3 for and has been utilized in several PWM techniques proposed in papers spanning a period of 16 years, e.g., in [17]–[19], always with

Fig. 1. Implicit modulating function for the SVPWM strategy (M = 1):

Fig. 2. Power spectrum of the line-to-neutral voltage of an inverter with the SVPWM technique (M = 1; N = 8; fo = 50 Hz).

good results. It can be seen that within the total of one-third of the cycle of output voltage, the modulating function assumes the values of either 1 or 1, independently of the value of the modulation index. Consequently, in a given leg of the inverter, switchings occur within the total of only two-thirds of the cycle. As a result, switching losses are significantly reduced in comparison with those in an inverter controlled by using a continuous modulating function. Inspection of the discontinuous modulating function of Fig. 3 reveals that the most efficient operation of the inverter corresponds to the load angle of 0 , i.e., a purely resistive load. Then, individual phase currents are not switched when passing through their peaks, and the highest switching losses, which are roughly proportional to the second power of current, are avoided. However, in practice, the currents are usually lagging the fundamental voltage due to the inductive component of a typical load, such as an ac motor. On full load, the motors draw currents with the phase lag of order of 30 . Therefore, a modulating function with the “inactive” intervals at 0 –60 and 180 –240 seems to represent a better solution.

TRZYNADLOWSKI et al.: SPACE VECTOR PWM TECHNIQUE

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(a)

(a)

(b) Fig. 3. Discontinuous modulating function. (a)

(b) M

= 1: (b)

M

= 0:5:

Shifting by 30 the validity intervals of the discontinuous modulating function given by (7), a new modulating function is obtained as for for for for for for (8) Although (7) and (8) appear similar, the function expressed by (8), and subsequently called a minimum-loss modulating function, significantly differs from that given by (7), as illustrated in Fig. 4, again for and The minimum-loss modulating function imposes such switching pattern of that no switching occurs in phase A within the 0 –60 and 180 –240 intervals. In contrast to the modulating functions utilized in the existing PWM methods, the minimum-loss function is asymmetrical with respect to the center of the cycle, yet it still maintains the desirable half-wave symmetry. It can be shown that the minimum-loss modulating function is implicit for a space-vector PWM strategy in which the state sequence is where

Fig. 4. Minimum-loss modulating function. (a)

in even subcycles and switching frequency ratio,

M

= 1: (b)

M

= 0 :5 :

in odd subcycles. Then, the is (9)

i.e., significantly lower than that for the classic SVPWM strategy given by (5). To illustrate the superiority of the space-vector method employing the minimum-loss modulating function over the classic SVPWM technique, computer simulations have been performed. A unity dc supply voltage and a unity resistive–inductive load impedance with the load angle of 30 were assumed. Since switching losses depend on the type of power switches, the so-called switching loss indicator (SLI) was introduced as a comparative measure of these losses. The SLI was calculated as a sum of squared values of the phase A output current at the instants of switching the corresponding switches of the inverter. Such approach to comparative evaluation of switching losses has been proposed in [1]. Also, the total harmonic distortion (THD) of the output current was determined. The inverter was simulated with a constant pulse rate of 8 pulses per subcycle for the SVPWM method and 16 pulses per subcycle for the minimum-loss PWM strategy. The modulation index, was varied from 0.05–1.

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currents in practical loads has been stressed in [21] by the co-authors of this paper, and the minimum-loss space-vector, deterministic PWM technique has been thoroughly evaluated by computer simulations and laboratory experiments. The novel control method proposed here, and subsequently called a minimum-loss variable pulse rate (MLVPR) strategy, is based on the same state sequence as that yielding the minimum-loss modulating function, but realized with a ranof switching intervals per subcycle domly varied number, of the output voltage. The effect of the variable pulse rate on power spectra of the output voltage of the inverter is analyzed below. III. SPECTRAL ANALYSIS OF THE MLVPR PWM STRATEGY

Fig. 5. Switching loss indicator versus modulation index using the classic = 8) and minimum-loss (continuous line, space-vector (dashed line, = 16) PWM strategies.

N

N

Switching signals and for the three legs of an inverter are trains of pulses of unity amplitude and variable width. Considering for instance phase A, pulses of appear in these subcycles where at least one of the and states, when expressed in the binary notation, contains a 1 as the most significant bit. For example, in the first, 0 –60 , subcycle, hence during the whole subcycle. In the second, 60 –120 , subcycle, therefore is 1 only during the fraction of the given, th switching interval. Length of this interval is where denotes the period of the output frequency, Consequently, the width of the pulse of within the interval in question is The Fourier transform of the contribution of a given state, to within th switching interval of th subcycle is

(10)

Fig. 6. Current THD versus modulation index using the classic space-vector (dahed line, = 8) and minimum-loss (continuous line, = 16) PWM strategies.

N

N

The SLI versus and THD versus curves for the strategies under comparison are shown in Figs. 5 and 6, respectively. It can be seen that the minimum-loss modulating function results in lower switching losses in spite of the twice as high pulse rate than that in the SVPWM technique. In turn, this high pulse rate yields currents of significantly higher quality than those produced by an SVPWM inverter. It must be mentioned that the space-vector PWM strategy with minimum-loss modulating function first appeared in a theoretical paper [20] devoted to comparative analysis of PWM techniques for three-phase voltage-source inverters. With regard to space-vector PWM techniques, the authors considered all practical state sequences, listing the strategy in question as, simply, “No. 7 discontinuous modulation method.” The method has not been distinguished as an optimal one, probably because other criteria than those used here were employed in the analysis. The absence of switching at peak

where denotes a general frequency (the variable of the Fourier transform) and is the delay of state in the interval. The sum of such transforms over all states, switching intervals, and subcycles constitutes the Fourier transform, of the phase A switching signal. Transforms and of the and signals can be determined in a similar way. If is a random variable changing from subcycle to subcycle, then the expected value of is (11) where the scaling factor in front of the summation indicates that equally likely integer values of between and are assumed. Note that if takes on selected integer values such as, for instance, only even values, then the scaling factor still reflects the correct number of equally likely values of If the possible values of were unequally weighted, then each term in the sum would carry its corresponding weight. In the subsequent considerations, equal weighting and even values of are employed.


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Fig. 7. Theoretical power spectra of the line-to-neutral voltage with the MLVPR modulation (M = 1; N = 8; 16; 24; fo = 50 Hz).

Fig. 8. Experimental power spectrum of the line-to-neutral voltage with the minimum-loss modulation and fixed pulse rate (M = 1; N = 8; fo = 50 Hz).

The power, in watts, carried by given by

th harmonic of

is

(12) and the continuous power spectrum, in watts/hertz, for

voltages of an MLVPR PWM inverter. The dc supply voltage of the inverter is taken as the base voltage. 1) Line-to-Line Voltage (A to B) Discrete part:

is

(14)

(13) where Equations (12) and (13) can be used for computation of the discrete and continuous parts of power spectra of the output

(15)

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Fig. 9. Experimental power spectrum of the line-to-neutral voltage with the MLVPR modulation (M = 1; N = 8; 16; 24; fo = 50 Hz).

Fig. 10.

Oscillogram of the output current with the MLVPR modulation (M = 1; N = 8; 16; 24; fo = 50 Hz).

Continuous part: (16) 2) Line-to-Neutral Voltage (A to Neutral) Discrete part: (17) where (18) Continuous part: (19)

An example theoretical spectrum of the line-to-neutral voltage at is shown in Fig. 7. Three values, 8, 16, and 24, of the number of switching intervals were randomly assigned to consecutive subcycles. Comparing this spectrum with that in Fig. 2 for the SVPWM strategy, significant differences can be observed. The number of prominent harmonics has been greatly reduced and a continuous spectrum has appeared. The acoustic noise and vibration in electric drive systems result primarily from the coincidence of harmonic torques with frequencies of mechanical resonance of the system. Therefore, the reduced discrete spectra of an inverter with the MLVPR modulation are likely to have a beneficial impact on the noise and vibration characteristics of the supplied drive system. As mentioned before, such impact has already been proven for other PWM techniques with the randomly varied pulse rate [7]–[11].


Fig. 11.

179

Inverter loss measurement scheme. TABLE I EXPERIMENTAL RESULTS OF LOSS MEASUREMENTS

IV. EXPERIMENTAL RESULTS Experimental investigation of the proposed PWM technique was conducted using an IGBT-based inverter with a resistive–inductive load. Fuji’s 2MBI150L-120 (1200 V, 150 A) transistors with internal freewheeling diodes were used in the power circuit of the inverter. The inverter was supplied, via a six-pulse diode rectifier with a capacitive dc link, from a 208-V ac line. The average dc supply voltage of the 3 inverter was 271 V, and the load, consisting of three 8resistors in series with 11-mH inductors, was drawing currents The switching patterns were of roughly 12.5 A/ph at generated in a personal computer and stored in a lookup table of the Motorola’s MC68332 Integrated Microcontroller that generated switching pulses for the inverter switches. The goal of the experiments was to verify the theoretical characteristics of the MLVPR PWM strategy. The power spectrum of line-to-neutral voltage of the inverter Hz, and a fixed pulse rate of is at

shown in Fig. 8 (see Fig. 2 for comparison). An experimental power spectrum measured under the same conditions as those used for the theoretical spectrum of Fig. 7, i.e., with a varied pulse rate, is depicted in Fig. 9, and the respective output current in Fig. 10. Comparing Fig. 9 with Fig. 7, good agreement between the theoretical and actual power spectra can be observed, particularly with respect to the continuous spectrum. The discrete spectrum is even less pronounced than expected. This can be credited to the differences between the analytical model and the real system with its finite switching times. To evaluate the reduction in switching losses, the SVPWM technique was used as a benchmark. With eight switching intervals per subcycle, the SVPWM strategy resulted in a 5% THD of the currents in the employed load. The same level of current distortion was obtained when the MLVPR modulator operated with the pulse rate varied between 6–10, i.e., with the same average rate as that for the reference SVPWM method.

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However, in agreement with (6) and (11), each switch of the inverter was turned on and off 24 times per cycle when the SVPWM was used and, on average, 17 times with the MLVPR modulation. This alone would mean a 30% improvement. Taking into account the additional reduction in switching losses due to the absence of switching when the output currents are at their peak values, it can be estimated that, depending on the load angle (here 23.4 ), the MLVPR technique results in the switching losses reduced by 40%–50% in comparison with those in an inverter employing the SVPWM strategy. The conclusion above has been verified by direct measurement of the input and output power of the inverter. Because of the nonideal dc and ac quantities involved, instead of standard wattmeters, three analog multipliers combined with low-pass filters were used, as shown in Fig. 11. The total power losses in the inverter were obtained by subtracting the output power from the input power. To separate the switching losses from the conduction losses, the conduction losses in transistors and diodes were calculated using the method described in [22] and increased by 10% to account for losses caused by ripple currents and losses in other elements of the inverter. The results are summarized in Table I. There, denotes the input power, the otput power, the total power loss in the inverter, the conduction losses, and the switching losses. To accentuate the switching losses, higher pulse ratios than those in the previous simulations and experiments were used. Even allowing for the possible inaccuracy of computation of the conduction losses, the smaller extent of total losses associated with the MLVPR strategy in comparison with the SVPWM method indicate the predicted reduction of switching losses, since the conduction losses do not depend on the PWM technique. Generally, IGBT’s have relatively high conduction losses, due to the high voltage drop across the conducting transistor and low switching losses due to the short switching times. Should other, slower switches, such as power BJT’s, or higher switching frequencies be used, the reduction of total losses would certainly be greater.

V. CONCLUSION The MLVPR PWM technique, characterized by an asymmetrical modulating function and randomly varied pulse rate within consecutive subcycles of the inverter output voltage, results in an improved power spectrum of this voltage and significantly reduced switching losses in comparison with the existing PWM strategies. The technique, belonging in the class of PWM methods based on the voltage space vectors, shares the technical advantages of that class, such as good operating characteristics and simplicity of implementation, but it is superior with respect to the efficiency of the inverter and effects on the supplied drive systems. It is worth noting that the idea of combining the random pulsewidth modulation with a discontinuous modulating function has already been proposed in [23] as the so-called random dead-band PWM (RDBPWM) method. However, the RDBPWM technique, based on the concept of a random carrier, similar to that described in [24] and [25], do not

seem to yield as good overall operating characteristics as does the MLVPR strategy. The modulating function employed in the RDBPWM method does not prevent the inverter switches from switching the currents within their positive-peak areas, and the use of the random carrier for generation of switching signals requires higher switching frequencies than those with the MLVPR technique to maintain comparable quality of the output current. REFERENCES [1] H. Van der Broeck, “Analysis of the harmonics in voltage fed inverter drives caused by PWM schemes with discontinuous switching operation,” in Proc. EPE’91, Florence, Italy, 1991, vol. 3, pp. 261–266. [2] H. W. Van Der Broeck, H .C. Skudelny, and G. Stanke, “Analysis and realization of a pulse width modulator based on voltage space vectors,” in Conf. Rec. 1986 IEEE-IAS Annu. Meeting, Denver, CO, 1986, pp. 244–251. [3] J. Holtz, P. Lammert, and W. Lotzkat, “High-speed drive system with ultrasonic MOSFET PWM inverter and single-chip microprocessor control,” IEEE Trans. Ind. Applicat., vol. IA-23, pp. 1010–1015, Nov./Dec. 1987. [4] R. J. M. Belmans, D. Verdyck, W. Geysen, and R. D. Findlay, “Electromechanical analysis of the audible noise of an inverter-fed squirrel-cage induction motor,” IEEE Trans. Ind. Applicat., vol. 27, pp. 539–544, May/June 1991. [5] D. J. Sheppard, “Torsional vibration resulting from adjustable-frequency AC drives,” IEEE Trans. Ind. Applicat., vol. 24, pp. 812–817, Sept./Oct. 1988. [6] C. O. Hong and S. K. Sul, “Analysis of shaft torsional vibration in inverter-fed induction motor drive systems,” in Conf. Rec. 1993 IEEEIAS Annu. Meeting, Toronto, Canada, 1993, pp. 588–594. [7] T. G. Habetler and D. M. Divan, “Acoustic noise reduction in sinusoidal PWM drives using a randomly modulated carrier,” IEEE Trans. Power Electron., vol. 6, pp. 356–363, Nov. 1991. [8] J. T. Boys and P. G. Handley, “Spread spectrum switching: low noise modulation technique for PWM inverter drives,” Proc. Inst. Elect. Eng., vol. 139, part B, no. 3, pp. 252–260, 1992. [9] J. K. Pedersen and F. Blaabjerg, “Digital quasirandom modulated SFAVM PWM in AC drive system,” IEEE Trans. Ind. Electron., vol. 41, pp. 518–525, Oct. 1994. [10] H. Stemmler and T. Eilinger, “Spectral analysis of the sinusoidal PWM with variable switching frequency for noise reduction in inverter-fed induction motors,” in Proc. PESC’94, Taipei, Taiwan, R.O.C., 1994, pp. 269–277. [11] A. M. Trzynadlowski, F. Blaabjerg, J. K. Pedersen, R. L. Kirlin, and S. Legowski, “Random pulse width modulation techniques for converterfed drive systems—A review,” IEEE Trans. Ind. Applicat., vol. 30, pp. 1166–1175, Sept./Oct. 1994. [12] S. Ogasawara, H. Akagi, and A. Nabae, “A novel PWM scheme of voltage source inverter based on space vector theory,” in Proc. EPE’89, Aachen, Germany, 1989, pp. 1197–1202. [13] S. Fukuda, H. Hasegawa, and Y. Iwaiji, “PWM technique for inverter with sinusoidal output current,” IEEE Trans. Power Electron., vol. 5, pp. 54–61, Jan. 1990. [14] P. Enjeti and B. Xie, “A new real time space vector PWM strategy for high performance converters,” in Conf. Rec. 1992 IEEE-IAS Annu. Meeting, pp. 1018–1024. [15] V. R. Stefanovic and S. N. Vukosavic, “Space-vector PWM voltage control with optimized switching strategy,” in Conf. Rec. 1992 IEEE-IAS Annu. Meeting, Houston, TX, 1992, pp. 1025–1033. [16] J. W. Kolar, H. Ertl, and F. C. Zach, “Calculation of the passive and active stresses of three phase PWM converter,” in Proc. EPE’89, Aachen, Germany, 1989, pp. 1303–1311. [17] M. Depenbrock, “Pulse width control of a 3-phase inverter with nonsinusoidal phase voltages,” in Proc. 1977 IEEE-IAS Int. Semiconductor Power Converter Conf., 1977, pp. 399–403. [18] T. H. Chin, M. Nakano, and Y. Fuwa, “New PWM technique using triangular carrier wave of saturable amplitude,” IEEE Trans. Ind. Applicat., vol. IA-20, pp. 643–650, May/June 1984. [19] D. R. Alexander and S. M. Williams, “An optimal PWM algorithm implementation in a high performance 125 kVA inverter,” in Proc. IEEE APEC’93, San Diego, CA, 1993, pp. 771–777. [20] J. W. Kollar, H. Ertl, and F. C. Zach, “Influence of the modulation method on the conduction and switching losses of a PWM converter


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system,” IEEE Trans. Ind. Applicat., vol. 27, pp. 1063–1075, Nov./Dec. 1991. A. M. Trzynadlowski and S. Legowski, “Minimum-loss vector PWM strategy for three-phase inverters,” IEEE Trans. Power Electron., vol. 6, pp. 26–34, Jan. 1994. R. C. Thurston and S. F. Legowski, “A simple and accurate method of computing average and rms currents in a three-phase inverter,” IEEE Trans. Power Electron., vol. 8, pp. 192–199, Mar. 1993. V. G. Agelidis and D. Vincenti, “Optimum nondeterministic pulse-width modulation for three-phase inverters,” in Proc. IEEE IECON’93, Maui, HI, 1993, pp. 1234–1239. A. M. Trzynadlowski, S. Legowski, and R. L. Kirlin, “Random pulse width modulation technique for voltage-controlled power inverters,” in Conf. Rec. 1987 IEEE-IAS Annu. Meeting, 1987, pp. 863–868. S. Legowski and A. M. Trzynadlowski, “Advanced random pulse width modulation technique for voltage-controlled inverter drive systems,” in Proc. IEEE APEC’91, Dallas, TX, 1991, pp. 100–106.

Andrzej M. Trzynadlowski (M’83–SM’86) received the M.S. degree in electrical engineering in 1964, the M.S. degree in electronics in 1969, and the Ph.D. degree in electrical engineering in 1974, all from the Technical University of Wroclaw, Poland. From 1966 to 1979, he was a faculty member at the Technical University of Wroclaw. In the following years, he was at the University of Salahuddin, Iraq, the University of Texas, Arlington, and the University of Wyoming, Laramie. Since 1987, he has been with the University of Nevada, Reno, where he is currently Professor of Electrical Engineering and Assistant Director of the Industrial Assessment Center. He has authored or co-authored over 80 publications in the areas of power electronics and electric drive systems and has been granted eleven patents. He is the author of The Field Orientation Principle in Control of Induction Motors (Norwell, MA: Kluwer, 1994). Dr. Trzynadlowski is a member of the IEEE Industry Applications Society Industrial Drives and Industrial Power Converters Committees. He was the recipient of the 1992 IEEE-IAS Myron Zucker Student-Faculty Grant.

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R. Lynn Kirlin (S’66–M’68–SM’82) received the B.S. and M.S. degrees from the University of Wyoming, Laramie, in 1962 and 1963, respectively, and the Ph.D. degree from Utah State University, Logan, in 1968, all in electrical engineering. He analyzed data transmission circuitry and an EMP pulse simulation system at Martin-Marietta, Denver, during 1963–1964. At Boeing, from 1965 to 1966, he performed analysis and design tasks for various space communication projects. From 1968 to 1969, Datel in Riverton, Wyoming, afforded him experience in computer peripheral design and analysis. At Floating Point Systems, Beaverton, Oregon, during 1978–1979, he specified and developed a basic image processing library and a signal processing library addition for the array processor AP-120B. From 1969 through 1986, he was with the Electrical Engineering Department, University of Wyoming, where he became a Professor in 1978. During that time he taught nearly 30 different courses in electrical engineering, establishing several in communication theory and signal processing. Since 1987, he has been a Professor of Electrical and Computer Engineering at the University of Victoria, British Columbia, Canada. He has published considerably in control theory applications, signal demodulation and detection, pseudonoise applications, and speech, image, sonar, and seismic signal processing.

Stanislaw F. Legowski (SM’84) received the M.S. and Ph.D. degrees in electronic engineering from the Technical University of Gdansk, Poland in 1962 and 1971, respectively. From 1958 to 1962, he was a Research Assistant in the Oceanographic Institute, Polish Academy of Sciences, Sopot, Poland, where he conducted research in instrumentation and measurement methods used in hydrography. From 1962 to 1983, he was with the Technical University of Gdansk as a Teaching Assistant, Lecturer, and Assistant Professor. His main research areas were electrical measurement of nonelectrical quantities and automated measurement methods for analog integrated circuits. In 1983, he joined the faculty of the University of Wyoming, Laramie, where he is currently a Professor of Electrical Engineering. His research interests include analog and digital system design and power electronics. Dr. Legowski was elected the Best Teacher for the 1979–1980 academic year in the Electronics Department, Technical University of Gdansk, and the Outstanding Faculty Member of the College of Engineering, University of Wyoming, for the 1983–1984 academic year. He is a member of the IEEE Industry Applications Society Industrial Drives Committee.