A New Stator Resistance Tuning Method for Stator-Flux-Oriented Vector-Controlled Induction Motor Drive
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1 1148 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 6, DECEMBER 2001 A New Stator Resistance Tuning Method for Stator-Flux-Oriented Vector-Controlled Induction Motor Drive Epaminondas D. Mitronikas, Athanasios N. Safacas, Member, IEEE, and Emmanuel C. Tatakis Abstract Field-oriented-controlled induction motor drives have been widely used over the last several years. Conventional direct stator-flux-oriented control schemes have the disadvantage of poor performance in the low-speed operating area when the stator flux is calculated using the voltage model, due to the stator resistance uncertainties and variations. In this paper, a new closed-loop stator-flux estimation method for a stator-flux-oriented vector-controlled induction motor drive is presented in which the stator resistance value is updated during operation. This method is based on a simple algorithm capable of running in a low-cost microcontroller, which is derived from the dynamic model of the induction machine. The effects of stator resistance detuning, especially in the low-speed operating region, are investigated and simulation results are shown. The motor drive system as well as the control logic and the resistance estimator are simulated and characteristic simulation results are derived. In addition, the proposed control scheme is experimentally implemented and some characteristic experimental results are shown. The simulation as well as the experimental results reveal that the proposed method is able to obtain precise flux and torque control, even for very low operating frequencies. Index Terms Field-oriented control, induction machine, statorflux orientation, stator resistance identification. I. INTRODUCTION THE concept of vector control for induction motors has become very popular during the last years as the ability of accurate motor torque control allows the construction of high-performance motor drive systems. Combined with the low cost and the structure robustness of the induction machine, this has led to replacement of the direct current machines by induction motors in many applications the last few years [1] [3]. Several vector control techniques have been proposed, which can be separated into two categories, according to the method used for the flux vector orientation: direct and indirect control schemes. In direct control schemes, the flux vector is calculated using the stator terminal quantities, while indirect methods use the machine slip frequency value to achieve field orientation. However, both methods require the knowledge of machine parameters, which are not precisely known in general. Indirect control schemes require knowledge of the machine inductances as well as the rotor time constant, while in direct schemes only Manuscript received September 6, 2000; revised June 1, Abstract published on the Internet October 24, The authors are with the Laboratory of Electromechanical Energy Conversion, Department of Electrical and Computer Engineering, University of Patras, Rio-Patras, Greece ( e.mitronikas@ee.upatras.gr; a.n.safacas@ee. upatras.gr; e.c.tatakis@ee.upatras.gr). Publisher Item Identifier S (01)10287-X. the stator resistance value has to be known for flux estimation. Depending on the specific method, these parameters highly affect the flux vector calculation precision. In past work [4] it has been shown that these parameters not only cannot be precisely known, but also vary during operation. Variations can exceed 50% of the startup value. In particular, for the stator-flux-oriented direct control method which will be used in the present work, the stator resistance value is not dominant in the highspeed range, so a possible estimation error will not affect the stator flux calculations. In low-speed operation, the stator resistance value becomes critical for the calculations and a stator resistance variation in the traditional open-loop stator flux observer will produce a significant estimation error. In addition, open-loop observers are characterized from steady-state errors and poor performance under noisy environments. To overcome this problem, several closed-loop stator flux estimators have been proposed in the last years [5] [9]. Closedloop schemes have the capability to provide more accurate flux estimation and have less sensitivity to parameter variations. Some proposed solutions involve the use of artificial neural networks (ANNs) [5] or neuro-fuzzy contollers [6] to directly obtain the flux value. A slightly different way is to use an ANN [7] or an observer for tuning the stator resistance while the stator flux is calculated using the well-known voltage model of the machine. Furthermore, signal injection techniques have been used to obtain flux estimation with minimum errors [8]. As these sophisticated methods require hardware with high computing capabilities, some more simplified heuristic approaches have been proposed such as in [9], which utilizes a speed sensor and the induction machine equations to update the stator resistance in the low-speed operating range. Several of the simplified approaches lead to more inexpensive hardware, without significant performance degradation. In this paper, a new closed-loop stator flux estimator for a stator-flux-oriented vector-controlled induction motor drive is presented. Assuming that flux calculation errors are due to stator resistance variations, the estimation algorithm corrects the stator resistance value in order to eliminate the error. The overall control algorithm, including the flux estimator, should fit the following requirements: 1) decoupled stator flux and electromagnetic torque control; 2) stator current limiting under all operating conditions; 3) stator resistance updating and correct flux estimation based only on stator voltage and current measured values; 4) Simplification of the required algorithms, so that the necessary computing power can be the minimum possible /01$ IEEE
2 MITRONIKAS et al.: NEW STATOR RESISTANCE TUNING METHOD 1149 The control system has been designed and the overall system has been simulated using the MATLAB/SIMULINK software. Furthermore, the machine and control equations are derived, effects of the stator resistance variations in the conventional controllers are presented, the proposed stator resistance identification algorithm is discussed and simulation results are shown. II. DYNAMIC MODEL OF THE INDUCTION MACHINE The model of the squirrel-cage induction machine can be expressed in terms of - and -axes quantities resulting in the following equations: (1) where definitions are given in (2) (7) at the bottom of the page. The meaning of the symbols in (2) (7) are as follows: stator and rotor resistances; stator and rotor leakage inductances; mutual inductance; and -axes stator flux components; and -axes stator current components; and -axes stator voltage components; angular rotor speed; angular speed of the reference frame. As it can be seen in (2) (7), the machine model is not restricted in the stator reference frame, but is expressed in an arbitrary frame, defined by the value of. Thus, it is possible to express (1) in a way which describes the electrical dynamics of the machine in the stator, rotor, or flux orientation. The torque and the mechanical equation can be written as follows: where is the moment of inertia, is the number of pole pairs, is the electromagnetic torque, and is the load torque. A simulation model of the induction machine has been built using the above equations, expressed in a stationary reference frame ( ). III. EFFECT OF STATOR RESISTANCE VARIATIONS IN STATOR-FLUX-ORIENTED VECTOR-CONTROLLED DRIVES In classical stator-flux-oriented direct vector control methods, the stator flux vector is estimated as the integral of the voltage drop in the stator resistance subtracted from the stator voltage vector, as described by (9) In conventional controllers, a constant value of stator resistance is considered. However, in practice, the stator resistance of an induction motor changes during operation due to variation of the stator windings temperature. This fact introduces errors in the flux calculation. The same kind of errors could be caused (8) (9) (2) (3) (4) (5) (6) (7)
3 1150 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 6, DECEMBER 2001 Fig. 1. Variation of stator resistance during simulation. Fig. 3. Simulation results of motor operation at 7.5 Hz without stator resistance updating. (a) Stator flux magnitude. (b) Stator flux position error. Fig. 2. Simulation results of motor operation at 2.5 Hz without stator resistance updating. (a) Stator flux magnitude. (b) Stator flux position error. by stator resistance estimation errors. Despite this, flux calculations are proven to be accurate in the high-speed operating range, as the voltage drop in the stator resistance is negligible. However, at low speeds, this drop becomes significant compared with the stator voltage. Stator flux is a vector quantity, so there will be a magnitude and position error in the stator flux estimation. The magnitude error is often smaller and affects less the control efficiency, leading to bad torque regulation and, therefore, deterioration of the system dynamic response. The position error is a more serious problem, as in very low speeds it can lead to controller failure. To investigate the vector controller behavior under stator resistance changes, a simulation model of the conventional stator-flux-oriented controller has been made using MATLAB software. During the simulation progress, the stator resistance of the induction machine is subject to variations, as shown in Fig. 1. Although the resistance variations in the real machine are usually slower, this does not affect the quality of the results. Given a constant reference flux of 1 Wb, the estimation error for the stator flux is investigated. As the flux is a vector quantity, the error in magnitude and position estimation is shown for different operating frequencies, as demonstrated in Figs From the figures, it is clear that both the magnitude and position estimation errors are decreasing as the operating frequency Fig. 4. Simulation results of motor operation at 12.5 Hz without stator resistance updating. (a) Stator flux magnitude. (b) Stator flux position error. Fig. 5. Simulation results of motor operation at 45 Hz without stator resistance updating. (a) Stator flux magnitude. (b) Stator flux position error. increases. For the high-frequency operating range these errors become negligible, while they become significant in the very low operating frequencies.
4 MITRONIKAS et al.: NEW STATOR RESISTANCE TUNING METHOD 1151 IV. ESTIMATION OF THE STATOR RESISTANCE VARIATIONS To overcome the problem of stator resistance variations in the stator-flux-oriented vector control technique, a closed-loop estimation scheme should be preferred instead. The basic concept of the proposed closed-loop estimator is analyzed in detail. In a conventional digital stator flux estimator with sampling period, the following equations are derived from (9) for the - and -axes components of stator flux expressed in a stationary reference frame: (10) (11) where. Considering that is the actual and is the estimated resistance value, then the estimation error for the stator resistance is given by Combining (10) (12) the following equations stand: (12) (13) (14) According to (13) and (14) and assuming that a flux estimation is introduced on step ( ) due to a resistance change, the following equations are obtained: (15) (16) Having this flux error, we can use (17) and (18) of the rotor in order to derive appropriate mathematical expressions which should be used to eliminate the flux estimation error (17) (18) By multiplying both equations in (17) and (18) with the values and, respectively, (19) is derived (19) current vector is perpendicular to the rotor flux vector, so we can write (22) The constancy of in a controlled drive system is ensured in the steady-state operation. It can be easily understood that it is advisable to express (22) using the stator and flux current components. Therefore, equations written in matrix form in (1) are solved in order to express the rotor current and flux and components with respect to the stator quantities, as follows: (23) (24) Substituting rotor values in (22) from (23) and (24), we can obtain (25) If, the estimated value of the stator resistance is identical to the actual value. In the opposite case where, the estimated values and are not the same as the actual ones. Considering that this difference is due to the stator resistance estimation error, we have to change the value of so that the value becomes zero. This can be done inside the calculation procedure of the stator flux estimator [Fig. 6(a)]. For the digital estimation scheme, the following equation yields for the actual flux components: If the flux value is not correctly estimated, we can write (26) (27) Subtracting the above equations, the following equation is obtained: As the derivative of is given by (20), (21) can be obtained (20) (21) (28) It is well known that the stator resistance changes are very slow compared with the sampling period. As a small resistance estimation error will produce a small flux error, we can say that the actual and the estimated flux are almost equal. Considering this, the following approximations are valid: Note that, in (21), the quantity is the inner product of the rotor current and rotor flux vectors. If the rotor flux is kept constant, this inner product equals zero, because the derivative becomes zero. It means that the rotor (29)
5 1152 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 6, DECEMBER 2001 (a) (b) Fig. 6. Block diagram of (a) the whole proposed system and (b) the flux and torque control unit. From (15), (16), and (28) (30), we obtain (30) TABLE I OUTPUT VOLTAGE OF THE INVERTER WITH RESPECT TO THE SWITCHING STATE (31) We can ascertain that the mathematical expression is always positive. This is due to the fact that the second summand of the expression is always positive, while the first one is the inner product of the vectors and which is also nonnegative. It is, therefore, clear that error is proportional to the stator resistance estimation error. Based on this, one can note the following: if the quantity is positive, then is positive. In this case, the estimated value is smaller than the real one and, therefore, should be increased. In the opposite case ( ), the estimated value of should be reduced. This process is repeated until a zero value of is reached. The final value of which is estimated this way is considered to be the actual stator resistance value and is used in the vector control unit [Fig. 6(a)]. It can be noticed that the proposed stator resistance error estimation technique is basically derived from (22). This equation obviously shows an inner product between rotor flux and current vector. A nonzero value occurs when there is an error in stator flux estimation, which, as shown by (23) and (24), af-
6 MITRONIKAS et al.: NEW STATOR RESISTANCE TUNING METHOD 1153 Fig. 7. Simulation results for motor operating at 2.5 Hz. (a) Actual stator resistance. (b) Estimated stator resistance. (c) Stator flux magnitude. (d) Stator flux position error. Fig. 8. Simulation results of step changes in reference torque during machine startup. (a) Motor torque. (b) Stator current. (c) Motor speed. fects also the rotor flux and current vector estimation. It is well known that the stator flux estimation error decreases as the frequency increases. Therefore, the proposed method is especially designed for the low-speed operating range and can be capable of obtaining good results, even at very low speeds of operation. V. SIMULATION SCHEME OF THE PROPOSED SYSTEM The block diagram of the overall control system is shown in Fig. 6(a). The blocks enclosed within the dashed lines represent the control, flux estimation, and stator resistance estimation logic and are implemented in the real system using a microprocessor unit, by the use of software routines. As in the real system, the control technique is implemented using a digital processor, it is essential that the simulation model is designed to approach as close to reality as possible. In a real control system, the sampling frequency is restricted due to hardware limitations (processor frequency) combined with the code complexity. As all the recently developed microprocessors have multitasking capabilities, an attempt to divide the control system into separate groups could lead to better utilization of the CPU capabilities. In this way, each group refers to a process with its own time constant. The switching technique, the stator flux vector estimation, and the vectors rotation have to do with the machine electrical values, which have extremely low time constants. For this reason, they are grouped into a highest speed, highest priority routine, executing at the switching frequency (period ). The flux-torque controller calculates the appropriate currents in and axes to obtain the required flux and torque value. Its algorithm is executed in lower frequency (period ) and the stator resistance estimation routine is executed with the same frequency. The speed control loop has the lowest priority. For the simulation of the whole drive system according to Fig. 6, a mathematical model has been developed based on the induction motor equations and the equations for estimating the stator resistance which have been derived in Section III. In addition, a mathematical model for all the remaining drive system units was necessary to complete the simulation model. These relations are described in the following paragraphs. A. Voltage-Source Inverter A conventional three-phase voltage-source inverter has been used. For the inverter simulation, the output voltage is determined from the switching signal, where, according to the following equation: (32) When, the upper switching element of the inverter leg is conducting. When it is zero, then the lower switching element of the corresponding inverter leg is conducting. B. Induction Motor Model The induction motor model described by (1) (8), expressed in the stationary reference frame, has been developed in the MATLAB/SIMULINK environment. The model is modified so that the stator resistance is an input signal to it. In this way, it is possible to simulate any changes in the stator resistance value. C. Pulsewidth-Modulation (PWM) Technique A modified three-phase ramp-comparison current controller [8] has been used to implement the PWM. The ramp-comparison controller has been preferred instead of the conventional current hysteresis controller or a sinusoidal PWM technique, as
7 1154 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 6, DECEMBER 2001 Fig. 9. Basic structure of the experimental system. it combines advantages of both of them: it offers almost instant current control with constant switching frequency and good harmonic content. A carrier frequency of 10 khz has been chosen. D. Current and Voltage Measurements The microcontroller is able to measure the stator currents via an A/D conversion unit. The measurement delay and quantization error introduced by a typical 10-bit A/D conversion unit is included in the simulation model of the measurement devices. As the three-phase windings of the induction motor are star connected with unconnected neutral, only two of the three phase currents are measured from which the third is calculated. For the measurement of stator voltages, the dc-link voltage is measured. Considering the structure of the conventional threephase voltage-source inverter, the three phase voltages can be calculated according to the switching state of the inverter, using Table I. E. Stator-Flux Estimation Two of the stator phase currents and the dc-bus voltage are fed to the input of the stator-flux estimation block. From these values, the and components of the stator currents and voltages are calculated in the stationary reference frame. In order to obtain precise results, an average value for the stator voltage is calculated for each switching period. For the estimation of and components of the stator flux, (10) and (11) are used, respectively. The sampling frequency is the same as the PWM frequency. In order to take into account the corrections that the stator resistance estimator inserts, the resistance value is given by the following equation: (33) is the correction value produced by the output of the stator resistance estimator. Fig. 10. Actual and estimated stator resistance value (experimental results). F. Stator-Resistance Tuning Equation (31) shows a monotonic relation between the stator resistance estimation error, and the value, calculated from (27). Although it is possible to calculate and update the stator resistance value from the former, this would lead to increased requirements in computational power. Therefore, as discussed in Section IV, it is preferred that the correct resistance value is tracked utilizing the sign of the error. In the stator resistance estimation unit, the error value is calculated according to (27). According to the sign of, the estimated stator resistance value is decreasing or increasing until the correct resistance value is reached. Each estimator loop gives a small, constant resistance correction value, which has the sign of the value. The stator resistance tracking which is implemented in this way converges when the estimated value of the stator resistance equals the ac-
8 MITRONIKAS et al.: NEW STATOR RESISTANCE TUNING METHOD 1155 Fig. 11. Stator currents during torque transients (experimental results, I : 7.5 A/div; t: 100 ms/div). (a) Step change from 20 to 10 N1m. (b) Step change from 10 to 20 N1m. tual value. During operation, this will be done very quickly, as the stator resistance of the motor actually changes very slowly compared to the loop execution time. As expected, the stator resistance estimator is sensitive to large transients of the stator flux magnitude, although, even in this case, it quickly converges to the actual value after transient. However, this is not actually a problem, as in stator-flux-oriented schemes the stator flux is kept constant at the normal operation region. To help convergence, the estimator is turned off for a short period of time during machine startup. G. Vector Control Unit Once stator-flux orientation is achieved, the machine torque equation described by (8) reduces to (34) Vector control is achieved by selecting the proper current vector in order to obtain constant flux magnitude and to regulate torque as requested by the user. Stator flux is controlled by the -axis component of the current, while torque is controlled selecting the proper value of the current -axis component, as defined by (34). In Fig. 6(b), the block diagram of the vector control unit is shown. VI. SIMULATION RESULTS The above-presented system has been simulated using MATLAB software. An induction machine with a rated power of 2.2 kw has been used. The machine parameters are described in the Appendix. Hereafter, we present some simulation results during operation of the system. A constant reference flux of 1Wb is assumed and the stator resistance value changes during operation. The actual and estimated resistance value are shown in Fig. 7(a) and (b). In Fig. 7(c) and (d), the stator flux magnitude and the stator flux position error are illustrated. Compared with Fig. 2, where no stator resistance updating is applied, it is clear that the proposed scheme achieves good performance as it achieves compensation of the stator resistance changes. In Fig. 8, the current transients during step changes in the torque reference as well as the motor shaft speed are shown. VII. EXPERIMENTAL RESULTS An experimental 16-bit microprocessor-based controller has been used to experimentally verify proper operation of the proposed technique. The structure of the experimental system is shown in Fig. 9. The Siemens SAB164CI microcontroller operating at 20 MHz has been chosen. The unit has a fixed-point ALU, so all the machine parameters and equations are transformed in a normalized per-unit system. The chip is equipped with a fast A/D conversion unit, which is used for the current and voltage measurements. The main advantage of the SAB164CI is the peripheral event controller, a powerful peripheral, which gives the processor the ability to complete tasks related to peripheral units with the minimum possible CPU intervention. In this way, the computing power of the CPU is not wasted. The control program consists of two combined tasks, which are running in parallel, as shown in Fig. 9. The first task which consists of the PWM and flux calculations is executed with highest speed and priority and the second one which consists of the vector control calculations and resistance estimation routines is running with lower speed. For evaluation purposes, data are collected using an additional routine, and transferred to the host computer through the programming environment upon user request. Therefore, in Fig. 10, the stator resistance estimator output during machine startup is demonstrated. In this figure, it can be noticed that the calculation method takes account of the
9 1156 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO. 6, DECEMBER 2001 proposed method requires no mechanical sensors and can be implemented in a low-cost microprocessor. It has been proven that, with the proposed method, an accurate estimation of the stator flux is achieved. As a result of this, torque control can be precise, even in the low-speed range, offering good dynamic performance of the asynchronous machine. APPENDIX PARAMETERS OF INDUCTION MOTOR A. Parameters Used for Simulation of the Induction Motor Rated power, 2.2 kw; rated voltage, 380 V; four poles; inertia, W s ; stator resistance ( ), ; rotor resistance ( ), ; stator leakage inductance, H; rotor leakage inductance, H; magnetizing inductance, H. (a) B. Parameters of the Induction Machine Used in the Experimental Setup Rated power, 5.5 kw; rated voltage, 380 V; four poles; stator resistance ( ), 0.72 ; stator leakage inductance, H; rotor leakage inductance, H; magnetizing inductance, H. REFERENCES (b) Fig. 12. Experimental results. (a) Stator flux in the stationary reference frame. (b) Torque meter output during constant torque operation. Reference torque is 20 N1m. cable resistance between the inverter and the machine as well as the stator resistance. The actual machine resistance is shown with the dotted line, the solid line shows the estimator output, and the dashed-dotted line shows the resistance of the cable. It is clear that the estimator quickly converges to the actual resistance value. In Fig. 11, the stator phase current of the machine is shown during step changes in the machine torque reference which is changed from 10 to 20 N m and vice versa. Fig. 12(a) demonstrates the and components of the stator flux expressed in a stationary reference frame. Finally, Fig. 12(b) shows the machine torque output, measured in the rotor shaft using a strain-gauge-based torque meter. VIII. CONCLUSION In this paper, a new closed-loop stator-flux estimator taking account of the stator resistance changes has been presented. The [1] G. O. Garcia, R. M. Stephan, and E. H. Watanabe, Comparing the indirect field-oriented control with a scalar method, IEEE Trans. Ind. Electron., vol. 41, pp , Apr [2] M. P. Kazmierkowski and A. B. Kasprowicz, Improved direct torque and flux vector control of PWM inverter-fed induction motor drives, IEEE Trans. Ind. Electron., vol. 42, pp , Aug [3] Y. T. Kao and C. H. Liu, Analysis and design of microprocessor-based vector-controlled induction motor drives, IEEE Trans. Ind. Electron., vol. 39, pp , Feb [4] R. Marino, S. Peresada, and P. Tomei, On-line stator and rotor resistance estimation for induction motors, IEEE Trans. Contr. Syst. Technol., vol. 8, pp , May [5] A. Ba-Razzouk, A. Cheriti, G. Olivier, and P. Sicard, Field-oriented control of induction motors using neural-network decouplers, IEEE Trans. Power Electron., vol. 12, pp , July [6] V. Lovati, M. Marchesoni, M. Oberti, and P. Segarich, A microcontroller-based sensorless stator flux-oriented asynchronous motor drive for traction applications, IEEE Trans. Power Electron., vol. 13, pp , July [7] L. A. Cabrera, M. E. Elbuluk, and I. Husain, Tunning the stator resistance of induction motors using artificial neural network, IEEE Trans. Power Electron., vol. 12, pp , Sept [8] J. I. Ha and S. K. Sul, Sensorless field-orientation control of an induction machine by high-frequency signal injection, IEEE Trans. Ind. Applicat., vol. 35, pp , Jan./Feb [9] T. G. Habetler, F. Profumo, G. Griva, M. Pastorelli, and A. Bettini, Stator resistance tuning in a stator-flux field-oriented drive using an instantaneous hybrid flux estimator, IEEE Trans. Power Electron., vol. 13, pp , Jan [10] E. D. Mitronikas, E. C. Tatakis, and A. N. Safacas, A simplified stator resistance estimator for a speed sensorless stator flux field oriented controller, in Proc. Int. Conf. Electrical Machines, Espoo, Finland, Aug , 2000, pp [11] I. Boldea and S. A. Nasar, Vector Control of AC Drives. Boca Raton, FL: CRC Press, [12] J. Faiz and M. B. B. Sharifian, Different techniques for real time estimation of an induction motor rotor resistance in sensorless direct torque control for electric vehicle, IEEE Trans. Energy Conversion, vol. 16, pp , Mar
10 MITRONIKAS et al.: NEW STATOR RESISTANCE TUNING METHOD 1157 Chamber of Greece. Epaminondas D. Mitronikas was born in Agrinio, Greece, in He received the Dipl.-Eng. degree in electrical and computer engineering in 1995 from the Department of Electrical and Computer Engineering, University of Patras, Rio-Patras, Greece, where he is currently working toward the Ph.D. degree in electrical engineering. His research interests include power electronics, electrical machines, and simulation and control of electric motor drive systems. Mr. Mitronikas is member of the Technical Athanasios N. Safacas (M 76) was born in Amphilohia, Greece, in He received the Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering from Karlsruhe University, Karlsruhe, Germany, in 1967 and 1970, respectively. During 1971, he was with Siemens, Karlsruhe, Germany. Since 1975, he has been a Professor with the Department of Electrical and Computer Engineering, University of Patras, Rio-Patras, Greece, where he is also the Director of the Electromechanical Energy Conversion Laboratory. His teaching and research activities are in the areas of electrical machines, power electronics, and electric motor drive systems. Prof. Safacas is Member of the VDE, CIGRE, EPE Association, AVERE, IASTED, and the Technical Chamber of Greece. Emmanuel C. Tatakis was born in Alexandria, Egypt, in He received the Electrical Engineering Dipl. degree from the University of Patras, Rio-Patras, Greece, and the Ph.D. degree in applied sciences from the University of Brussels, Brussels, Belgium, in 1981 and 1989, respectively. He is currently an Assistant Professor in the Department of Electrical and Computer Engineering, University of Patras. His teaching activities include power electronics and electrical machines. His research interests include switch-mode power supplies, resonant converters, power-factor correction, electric drive systems, photovoltaic systems, educational methods on electrical machines, and power electronics. Dr. Tatakis is member of the European Power Electronics Association, Société Royale Belge des Electriciens, and Technical Chamber of Greece.
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