Induction Motor Drive System For Low-Power Applications - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 35, NO. 1, JANUARY/FEBRUARY 1999

Induction Motor Drive System for Low-Power Applications Cursino Brandão Jacobina, Member, IEEE, Maur´ıcio Beltrão de Rossiter Correa, Edison Roberto Cabral da Silva, Senior Member, IEEE, and Antonio Marcus Nogueira Lima, Member, IEEE

Abstract— This paper investigates the utilization of three different configurations of induction motor drives to implement low-cost systems for low-power applications. The static power converter side is implemented by a single-phase rectifier cascaded with a four-switch inverter. Three different types of induction machines are supplied with the static power converter. In the first configuration, a standard three-phase induction machine is employed. The second configuration also employs a standard three-phase induction machine, but only two of three windings are used. In the third configuration, a standard two-phase induction machine is employed. Simulation and experimental results are provided to illustrate the operation of the systems. Index Terms—Induction motor drive, low-power applications.

I. INTRODUCTION

T

HE development of low-cost motor drive systems is a relevant topic, particularly when the power demanded by the target application is within the low-power range. For this reason, the three-phase component-minimized voltage-source inverter has been proposed and its performance compared to the conventional three-phase inverter for driving an induction machine [1]. Also, the idea of reduced switch count has been extended for a rectifier–inverter system with active input current shaping [2]. The rectifier–inverter system was then analyzed in [3] and compared to a three-phase standard converter in terms of space-vector and scalar modulation techniques [4], [5]. An alternative application is found in [6], in which the main and auxiliary windings of a single-phase motor are driven by such a system. Moreover, if one leg of a six-switch voltage-source inverter (SSI) fails, it becomes a component-minimized voltage-source inverter, which can still supply the three-phase induction motor, avoiding loss of functionality of the drive and increasing its reliability [7]. This paper investigates the utilization of three different configurations of induction motor drives for the implementation of low-cost systems for low-power applications, as shown in Fig. 1. Each one of the configurations mentioned above is the combination of the power converter given in Fig. 1(a) together with one of the machines of Fig. 1(b)–(d), respectively. The Paper IPCSD 98–56, presented at the 1997 Industry Applications Society Annual Meeting, New Orleans, LA, October 5–9, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Drives Committee of the IEEE Industry Applications Society. Manuscript released for publication July 27, 1998. The authors are with the Departamento de Engenharia Elétrica, Universidade Federal da Para´ıba, 58109-970 Campina Grande, PB, Brazil. Publisher Item Identifier S 0093-9994(99)00449-1.

Fig. 1. AC drive system configurations.

three different types of induction machines are as follows: 1) a standard three-phase machine [Fig. 1(b)]; 2) a three-phase machine with two windings [Fig. 1(c)]; and 3) a standard two-phase machine [Fig. 1(d)]. In all three configurations, the static power converter side is implemented by a single-phase rectifier cascaded with a split capacitor bank and a threephase component-minimized voltage-source inverter, namely, a four-switch inverter (FSI). The main contributions of this paper in relation to previous work are as follows: 1) a detailed study of the configuration that employs a three-phase machine operating with only two

0093–9994/99$10.00  1999 IEEE

JACOBINA et al.: INDUCTION MOTOR DRIVE SYSTEM FOR LOW-POWER APPLICATIONS

windings [Fig. 1(c)] and the configuration that uses a twophase machine [Fig. 1(d)] (this study includes the analysis of the vector and scalar pulsewidth modulation (PWM) techniques utilized to control the power converter output voltage in both configurations); 2) the introduction of fully digital drive control strategy, which includes the stator current control; and 3) an overall comparison of the three configurations being investigated. II. THREE-PHASE MACHINE Considering the scheme of Fig. 1(a), let us assume that the conduction state of the power switches is associated to the binary variables – Therefore, from now on, the binary “1” will indicate a closed switch and the “0” an open one. The pairs – and – are complementary and, as a consequence, and The space-vector analysis of the static converter is done stationary reference frame. The variables using the are determined by the transforming equation (1) with

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found that (5) (6) is neglected, In this case, the homopolar component and the machine is assumed to be symmetbecause ric. The combination of the conducting states of the power plane switches originate four different vectors in the

(7) away from each other. Using the above These vectors are plane can be split into four (I–IV) vector definitions, the and are opposite sectors [see Fig. 2(a)] [5]. The vectors and their amplitude is times in direction and Also, the smaller than the amplitude of the pair and are opposite in direction vectors It is possible to define either a vector or a scalar PWM technique to control the FSI [5]. In this paper, only the scalar PWM is discussed, as the formulation in [5] was modified for making the study of the two other configurations easier. B. Scalar Modulation

where the vector can be either the stator voltage vector or the stator current vector and The first configuration being studied in this paper is composed of Fig. 1(a) plus Fig. 1(b). This configuration employs a three-phase machine where the phase 3 is connected to dc-bus midpoint, point 0. The basic equations of the PWM technique, as well as the steady-state analysis of this configuration, are based on the definitions given above. A. Space-Vector Analysis The voltages measured at the machine terminals, i.e., and depend on the states of the power switches and may be expressed in terms of the previously defined and as follows: binary variables (2) (3) (4) is the voltage between the dc-bus midpoint, point where as indicated in Fig. 1(a) and (b). Also, 0, and the point and are the machine voltages referred to the dc, it can be bus midpoint. By using (2)–(4) and matrix

In the scalar modulation technique, the pulsewidths are calculated directly from the three-phase reference voltages. In this case, the reference voltages of the PWM technique are and with If the desired stator voltage components and then, by using the is given in with the desired machine transformation matrix and can be calculated. The threevoltages, i.e., phase reference voltages may be expressed in terms of the desired machine voltages by and with so Thus, and are the expressions for (8) (9) Fig. 3 shows typical waveforms observed at the output of an during which the switches FSI. The pulsewidths and and must be kept conducting in order to obtain the desired reference voltage at the output of the FSI, are (10) (11)

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Fig. 2. Vectors and sectors in the


plane to a same dc-bus voltage. (a) Three-phase machine. (b) Two-windings machine. (c) Two-phase machine. components of the three-phase voltages and currents can be obtained by (14) (15) 1, 2, and 3. where In this case, the dc-bus voltage must be increased by a factor of two to generate the same maximum output voltage that would be obtained with an SSI. Moreover, there is an ac current component flowing through the capacitor bank that is half of the phase current [3], [8].

Fig. 3. FSI voltage waveforms.

III. THREE-PHASE MACHINE WITH TWO WINDINGS

C. Steady-State Analysis In the steady-state analysis of the configurations being investigated, it is assumed that the nominal specification of coordinates is the same. That the equivalent machine in is, the fundamental voltages and currents of the equivalent machine, in steady state, are given by

The second configuration being studied in this paper is composed of Fig. 1(a) plus Fig. 1(c). This configuration employs a three-phase machine where only two of the three phases are used, i.e., phase 3 is open. A. Space-Vector Analysis

(12) (13) and are voltage and current amplitudes, the where pulsation of the stator variables, and the angle of the machine power factor, respectively. The fundamental components of the three-phase voltages and currents determine the dc-bus voltage and the ratings of the power converter. From (12), (13), and (1), the fundamental

and are also given In this case, the machine voltages and by (2) and (3). However, the homopolar components are different from zero. Using the transformation matrix with and given by (2) and (3), with and the expression of the space vector components becomes (16)


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TABLE I INDIVIDUAL SECTORS

(17) Thus, the space vectors that depend on

are given by

(18) These vectors are also away where As an example, Fig. 2(b) from each other when shows the space-vector plot obtained for Note that vectors and are identical and and are three times greater when compared to those obtained for the three-phase machine presented in the previous section. B. Space-Vector Modulation represent the reference voltage to be synthesized by Let According to the the FSI within one cycle time of length space-vector technique,

TABLE II GROUPED SECTORS BY THE COMMON TEST CONDITION t13

(19) with the time weights

and

restricted to (20)

The problem now is to find out the values of the time and In order to simplify the algebraic weights given manipulation, let us introduce and Replacing the vectors and into (19) results in

TABLE III GROUPED SECTORS BY THE COMMON TEST CONDITION t24

(21) and with Rewriting (21) in terms of the

components gives (22) (23)

Now, given that and

and

are

given by (24) (25) The computation of the values of the time weights is an underdetermined problem. To overcome this problem, let us assume that only three of four vectors will be employed. In this case, one of the four time weights must be set equal to zero. This choice not only solves the underdetermined problem, but reduces the switching frequency of the FSI. For each one of the sectors of Fig. 2(b), there exist two groups of three vectors which may be sequenced to compose the reference voltage, as shown in Table I. The test conditions

employed to determine the sectors of Fig. 2(b) may be grouped by pairs. The adjacent sectors are grouped together to create two double sectors. Tables II and III show the double sectors, as well as the corresponding vectors. The last columns of Tables I–III present the test conditions employed to identify the sectors. This test is also employed to compute the time weights, as will be illustrated by the following example. Considering the use of Table II, the following steps must be executed. and by using (24) and (25). 1) Compute is positive, then a) use the vectors 2) If the sign of and b) set and . is negative, then a) use the vectors 3) If the sign of and b) set and . and by using (20) and (25). 4) Compute C. Scalar Modulation and In this configuration, and can be determined directly from using (1)

Thus, and by

(26)

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(27) and during which the switches and The pulsewidths must be kept conducting, are obtained by placing (26) and (27) into (10) and (11)

where and are the resistance and homopolar inductance. is equal to the stator resistance and Also, the resistance is the stator leakage inductance. Hence, in steady state, the is voltage (36) where

(28) (29) and computed from (28) and (29), the average With are equal output voltages during the switching period to the reference voltages (see Fig. 3). Depending upon the and the same vector switching sequence of switches sequences discussed in the previous section can be obtained. and are flushed to the beginning of If the pulsewidths the switching period, this is equivalent to the use of vector when and when sequences this corresponds to Table III. On the other hand, if starts while remains blocked for this conducting for when and is equivalent to using when this corresponds to Table II. and In both cases, the relations are observed. Based on these relations and using (20), (24), and (25), a general relationship between the vector and scalar PWM techniques is established as

Using (1), it can be found that, in steady state, the threephase voltages are (37) 1, 2, and 3. where the dc-bus voltage must be In this case, for to generate the same maximum increased by a factor of output voltage as that which would be necessary with an SSI. IV. TWO-PHASE MACHINE The third configuration is composed of Fig. 1(a) plus Fig. 1(d). This configuration employs a standard two-phase machine. A. Space-Vector Analysis

(30) (31)

Using the two-phase machine with the converter of voltages are given by Fig. 1(a), the

Conversely, (28) and (29) are obtained if (24) and (25) are introduced in (30) and (31), respectively. Therefore, the same results are obtained for both vector and scalar modulation techniques.

(38) (39) The combination of the states of the switches originates four different vectors in the plane

D. Steady-State Analysis The fundamental voltages and currents of the equivalent machine are given by (12) and (13). From (13) and (1) with it follows that

(32) (33) and are times Thus, the amplitudes of the currents the current that would be obtained with a three-phase machine [Fig. 1(b)]. Also, it can be shown that the ac current in the of the amplitude of the phase current. capacitor bank is The homopolar current is (34)

(40) away from These vectors have the same amplitude and are plane each other. Using the above vector definitions, the can be split into four (I–IV) sectors, as presented in Fig. 2(c). B. Space-Vector Modulation Using (19) and (20), and introducing and and and in this case, are that

where , it can be found

and the current–voltage model for the homopolar terms is given by

(41)

(35)

(42)


For each one of the sectors of Fig. 2(c) there exist two groups of three vectors that can be employed to compose the reference voltage, as shown in Table I. The test conditions employed to determine the sectors of Fig. 2(c) are grouped by pairs. Also, the adjacent sectors are grouped to create two double sectors. Tables II and III show the double sectors and the corresponding vectors. As the vectors have the same amplitude, the utilization of Tables II and III produces the same effect. The same algorithm can be used to generate the PWM based on Table II or Table III. C. Scalar Modulation The same technique employed with the previous configuration to define a scalar modulation to control the FSI can be and during which used in this case. The pulsewidths and must be kept conducting in order to the switches obtain at the output of the FSI the desired reference voltage, are determined by

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Fig. 4. Block diagram of the digital current controller.

The discrete-time current–voltage representation given by (45)–(48) can be obtained by using the forward shift operator. This simplified representation allows us to derive decoupled control laws that have the same complexity of proportional integral (PI) controllers. For this simplified model, the current controller written in vector notation is (49)

(43) (44) Note that (30) and (31) are also valid as a general relationship between the vector and scalar PWM for the two-phase machine. D. Steady-State Analysis The steady-state voltages and currents of a two-phase machine are given by (12) and (13). The amplitudes of the times greater than those fundamental phase currents are determined for the first configuration [Fig. 1(a) plus Fig. 1(b)]. Also, it can be shown that the ac current in the capacitors is of the phase current. in the In this case, to obtain the same maximum voltage, plane, the dc-bus voltage must be times that of the dc times lower than that required when using bus for the SSI, the three-phase machine with FSI [Fig. 1(a) plus Fig. 1(b)]. V. CURRENT CONTROLLER The most inner loop is the current control loop, normally required when the machine is controlled by using fieldorientation principles. This section focuses on the design of the digital current control loop for the proposed configurations. The model used to design the current controller is obtained coordinates [9] and is from the machine model written in given by (45) (46) Terms

and

are counter emf’s given by (47) (48)

where and and are the gains of the controller. This paper did not consider the compensation of terms due and The gains of the controller are determined to according to the optimum damping criteria [10]. The gains proportional, and integral, of the equivalent continuoustime controller are computed and, from those, the discrete-time and are obtained by the Tustim approximation. gains Fig. 4 presents a generic block diagram of the current control strategy to be employed with the proposed configurations for the synchronous reference frame. In the figure, represents the coordinate transform block to the and converts the quantities from the synchronous Block PWM FSI IM represents stator reference frame the PWM voltage-source inverter plus the induction machine. corresponds to the current controller. Block Block implements the matrix transformation given by (1). Note included in this block provides a general that the term representation for the three configurations, as explained below. In the case of the first configuration [Fig. 1(a) plus Fig. 1(b)], will give the same result of (8) the output of the Block Similarly, in the and (9) when case of the second configuration [Fig. 1(a) plus Fig. 1(c)], the output will give the result of (26) and (27) if where Of course, can only be achieved if and the compensation of are known. Finally, in the case of the two-phase machine, and are equivalent to and respectively. Another alternative to implement the current control loop is to use an analog solution based on the hysteresis approach that is required in [11]. In this case, the compensation of the second configuration is achieved by the controller itself, and it is not necessary to know the machine parameters. VI. SIMULATION RESULTS Next, simulation results obtained for the configurations being investigated are presented for the sake of comparison. For this purpose, the induction machines were considered to

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Fig. 5. Stator currents and ripple currents for all configurations. (a) Three-phase machine. (b) Two-windings machine. (c) Two-phase machine.

have the same parameters, and the dc-bus voltage was selected so that the maximum voltage was obtained for all and configurations. In this way, the amplitudes of vectors in Fig. 2(a), for the three-phase machine, become equal to and respectively, in Fig. 2(b), the amplitudes of vectors . For results for the two-windings machine, in which in Figs. 5, 7, and 8, the scalar modulation that always use two vectors of small amplitudes is employed, i.e., Table III is applied to the three-phase machine and Table II is applied to the two-windings machine. currents obtained for the machines Fig. 5 presents the current for the machine in in Fig. 1(b) and (d) and the the Fig. 1(c). In all cases, the modulation index is switching frequency is 2.0 kHz, and the stator frequency is 50 Hz. The machine with two windings has been considered so that The current ideal, i.e., are compared to ideal waveforms presented in these figures, obtained with the assumption that the current waveforms machine is supplied with an ideal sinusoidal voltage source. Such comparison is made via the current ripple which is also represented in the figures. The currents for the cases of Fig. 1(b) and (d) and currents for the case of Fig. 1(c) are similar. A comparison of the currents shows that the ripple is slightly higher for the two-phase machine. The ripple for the two-windings machine is equivalent to that of the three-phase machine, but, in this case, Fig. 6 shows the phase current (actual and reference suin the plan perimposed) and space-vector locus of when the inverter supplies an induction machine with two windings. These results, obtained when a hysteresis current control loop is employed, show that the induction machine due to operates correctly. The deformation of vector is always present in the process, independently of the type of current control strategy being employed. Fig. 7 presents the THD of the voltage supplied to the machine for all configurations and with a standard three-phase machine supplied by an SSI, as a function of the modulation index. The two-windings machine has been considered as so that The THD presented ideal, i.e.,

Fig. 6. Stator current and space-vector locus of v i obtained for the case of the two-windings machine.

Fig. 7. THD of the output voltage.

in Fig. 7 has been computed by (50) is the total root mean square value and is where the root mean square value of the fundamental component. The THD’s are almost the same for the four cases when the However, the THD for modulation index is close to the two-phase machine is the highest one for a low modulation index. The THD constitutes a good criteria for evaluating the heating and losses of the machine in each one of the configurations. , in each The electromagnetic torque of the machine, one of the configurations in Fig. 1, with a modulation index of 0.8, is presented in Fig. 8. Note that the ripple of the


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Fig. 10. Stator current for the configuration composed of Fig. 1(a) plus Fig. 1(c). Fig. 8. Electromagnetic torque waveforms for all configurations. (a) Three-phase machine. (b) Two-windings machine. (c) Two-phase machine. COMPARISON

TABLE IV THREE CONFIGURATIONS

OF THE

good in all cases. However, it can be noted that there exists a small error between the reference and measured currents in the second configuration. This indicates that the compensation can be improved. of Fig. 9. Stator current for the configuration composed of Fig. 1(a) plus Fig. 1(b).

electromagnetic torque is slightly higher for the two-phase machine. VII. EXPERIMENTAL RESULTS The drive system is composed of the static power converter, an induction machine, and a microcomputer (PC-Pentium133 MHz). The generation of the command signals for the converters, the data acquisition, and the control law are implemented in a microcomputer-based platform that is equipped with appropriate plug-in boards and sensors. The plug-in board has five analog–digital converters (AD573), each one having its own antialiasing filter and sample–hold (AD582), and programmable timer circuits to control the power converter. Figs. 9 and 10 show the experimental test results obtained for configurations of Fig. 1(a) plus Fig. 1(b) and Fig. 1(a) plus Fig. 1(c) at 50 Hz. In these figures, the reference and the actual stator current of axis and axis are plotted. The reference with an abrupt change current waveform was The transient change reduces the in its amplitude at amplitude of the reference from 0.8 to 0.4 A and always occurs The closed-loop performance is quite at the instant

VIII. COMPARISON

OF THE

CONFIGURATIONS

Table IV presents the comparison chart between the configurations in Fig. 1, operating at the same power. In this table, the amplitude of the fundamental the dc-bus voltage and phase current component of phase voltage and the amplitude of the ac capacitors current are given. and are normalized relatively to the values of a three-phase machine supplied with an SSI, whereas is normalized relatively to the phase current amplitude of the three-phase machine. In the case of the configuration of is considered. Except Fig. 1(c), the ideal case where for the dc-bus voltage, the machine of Fig. 1(b) presents the best performance. The harmonic distortion for both the three-phase and the two-windings machine is similar, but only if the homopolar impedance is null. Instead, the two-phase machine presents a higher harmonic distortion for low values of the modulation index. Both the converter cost and the processing hardware of the three configurations are identical for all configurations. A single six-pack insulated gate bipolar transistor converter can be employed, in which one of the legs is used as the rectifier and the other two as the inverter. The equivalent

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configuration with a standard three-phase machine (SSI plus a single-phase rectifier) needs one additional leg, which is indicative of the cost increase. The processing power required to implement the proposed systems depends on what parts of the control strategy are implemented in software. If the overall drive strategy must be implemented via software, then a digital signal processor is indicated. However, if, for instance, the current controller is implemented with analog circuitry, then the remaining control function fits quite well for a microcontroller. The machine prices are almost similar. However, in several countries, the lack of demand causes low industrial production of the two-phase machine, increasing its price. This makes the configuration with the machine in Fig. 1(d) more expensive than the others. IX. CONCLUSION This paper has investigated the utilization of three configurations of induction motor drives to implement low-cost systems for low-power applications. These configurations use the same power converter and three different induction machine arrangements: three-phase machine, two-windings machine, and two-phase machine. Comparing all the configurations, operating at same power, the following can be observed: 1) the second configuration [Fig. 1(a) plus Fig. 1(c)] demands the lowest dc-bus voltage; 2) the first configuration [Fig. 1(a) plus Fig. 1(b)] demands the smallest phase current; and 3) the first configuration [Fig. 1(a) plus Fig. 1(b)] presents the lowest harmonic distortion. The voltage rating of the two-windings machine mentioned above corresponds to the ideal case, in which However, in practical case, so that the voltage applied by the FSI presents an internal voltage drop which depends on the current. This makes the implementation of the digital current controller more complex. The configuration with a three-phase machine presents the best performance for the features analyzed, except for the dcbus voltage. Therefore, this configuration is the most suitable for low-power applications. The studies for the three-phase machine and the twowindings machine can be considered for the case of failure in a three-phase machine with SSI. In this case, there will be an increase of the robustness of the three-phase drive. REFERENCES [1] H. W. van der Broeck and J. D. van Wyk, “A comparative investigation of three-phase induction machine drive with a component minimized voltage-fed inverter under different control options,” IEEE Trans. Ind. Applicat., vol. 20, pp. 309–320, Mar./Apr. 1984. [2] P. Enjeti and A. Rahman, “A new single phase to three phase converter with active input current shaping for low cost ac motor drives,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1990, pp. 935–942. [3] G. Kim and T. A. Lipo, “Vsi-pwm rectifier/inverter system with a reduced switch count,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1995, pp. 2327–2332. [4] F. Blaabjerg, S. Freysson, H. H. Hansen, and S. Hansen, “Comparison of a space-vector modulation strategy for a three phase standard and a component minimized voltage source inverter,” in Proc. EPE Conf., 1995, pp. 1.806–1.813. [5] C. B. Jacobina, E. R. C. da Silva, A. M. N. Lima, and R. L. A. Ribeiro, “Vector and scalar control of a four switch three phase inverter,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1995, pp. 2422–2429.

[6] M. F. Rahman and L. Zhong, “A current-forced reversible rectifier fed single-phase variable speed induction motor drive,” in Conf. Rec. PESC’96, 1996, pp. 114–119. [7] T.-H. Liu, J.-R. Fu, and T. A. Lipo, “A strategy for improving reliability of field-oriented controlled induction motor drives,” IEEE Trans. Ind. Applicat., vol. 29, pp. 910–918, Sept./Oct. 1993. [8] R. L. A. Ribeiro, C. B. Jacobina, E.R. C. da Silva, and A. M. N. Lima, “Ac/ac converter with four switch three phase structures,” in Conf. Rec. PESC’96, 1996, pp. 134–139. [9] L. A. de S. Ribeiro, C. B. Jacobina, and A. M. N. Lima, “Real-time estimation of the electrical parameters of an induction machine using sinusoidal pwm voltage waveforms,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1997, pp. 746–752. [10] H. Buhler, Reglages Echantillonnes, vol. 1. Lausanne, Switzerland: Presses Polytechnique Romandes–Dunod, 1983. [11] D. M. Brod and D. W. Novotny, “Current control of vsi-pwm inverters,” IEEE Trans. Ind. Applicat., vol. 21, pp. 526–570, May/June 1985.

Cursino Brandão Jacobina (S’78–M’78) was born in Correntes, Pernambuco, Brazil, in 1955. He received the Bachelor’s degree in electrical engineering from the Federal University of Para´ıba, Campina Grande, Para´ıba, Brazil, in 1978 and the Diplôme d’Etudes Approfondies (DEA) and the doctoral degrees from the Institut National Polytechnique de Toulouse, Toulouse, France, in 1980 and 1983, respectively. Since 1978, he has been with the Electrical Engineering Department, Federal University of Para´ıba, where he is currently a Professor of Electrical Engineering. His research interests include electrical drives, power electronics, control systems, and system identification.

Maur´ıcio Beltrão de Rossiter Corrêa was born in Maceió, Alagoas, Brazil, in 1973. He received the Bachelor’s and Master’s degrees in electrical engineering in 1996 and 1997, respectively, from the Federal University of Para´ıba, Campina Grande, Para´ıba, Brazil, where he is currently working towards the Doctoral degree. Since 1997, he has been a faculty member of the Escola Técnica Federal de Alagoas, Palmeira dos Indios, Alagoas, Brazil. His research interests include power electronics and electrical drives.

Edison Roberto Cabral da Silva (M’92–SM’95) was born in Pelotas, Brazil, in 1942. He received the B.C.E.E. degree from the Polytechnic School of Pernambuco, Recife, Pernambuco, Brazil, the M.S.E.E. degree from the University of Rio de Janeiro, Rio de Janeiro, Brazil, and the D.Eng. degree from the University Paul Sabatier, Toulouse, France, in 1965, 1968, and 1972, respectively. In 1967, he joined the Electrical Engineering Department, Federal University of Para´ıba, Campina Grande, Para´ıba, Brazil, where he is currently a Professor of Electrical Enginering and Director of the Research Laboratory on Industrial Electronics and Machine Drives. In 1990, he was with COPPE, Federal University of Rio de Janeiro, and, from 1990 to 1991, he was with WEMPEC, University of Wisconsin, Madison, as a Visiting Professor. His current research work is in the area of power electronics and motor drives. He was the General Chairman of the 1984 Joint Brazilian and Latin-American Conference on Automatic Control sponsored by the Brazilian Automatic Control Society. Dr. Da Silva is a member of the IEEE Industry Applications, IEEE Industrial Electronics, and IEEE Power Electronics Societies. He is currently a Memberat-Large of the Executive Board of the IEEE Industriy Applications Society.


Antonio Marcus Nogueira Lima (S’77–M’89) was born in Recife, Pernambuco, Brazil, in 1958. He received the Bachelor’s and Master’s degrees in electrical engineering from the Federal University of Para´ıba, Campina Grande, Para´ıba, Brazil, in 1982 and 1985, respectively, and the Doctoral degree in 1989 from the Institut National Polytechnique de Toulouse, Toulouse, France. He was with the Escola Técnica Redentorista, Campina Grande, Para´ıba, Brazil, from 1977 to 1982 and was a Project Engineer with Sul-América Philips, Recife, Pernambuco, Brazil, from 1982 to 1983. Since September 1983, he has been with the Electrical Engineering Department, Federal University of Para´ıba, where he is currently a Professor of Electrical Engineering. His research interests are in the fields of electrical machines and drives, electronic instrumentation, control systems, and system identification.

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