MRAS Observer for Sensorless Control of Standalone ... - IEEE Xplore

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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 20, NO. 4, DECEMBER 2005

MRAS Observer for Sensorless Control of Standalone Doubly Fed Induction Generators Roberto Cárdenas, Member, IEEE, Rubén Peña, Member, IEEE, José Proboste, Greg Asher, Senior Member, IEEE, and Jon Clare, Senior Member, IEEE

Abstract—This paper presents an analysis of a model reference adaptive system (MRAS) observer for the sensorless control of a standalone doubly fed induction generator (DFIG). The analysis allows the formal design of the MRAS observer of given dynamics and further allows the prediction of rotor position estimation errors under parameter mismatch. The MRAS observer analysis is experimentally implemented for the vector control of a standalone DFIG feeding a load at constant voltage and frequency. Experimental results, including speed catching of an already spinning machine, are presented and extensively discussed. Although the method is validated for a standalone generator, the proposed MRAS observer can be extended to other applications of the doubly fed induction machine. Index Terms—Induction generator, induction motor drives, wind energy.

NOMENCLATURE

, ,

,

General Stator or rotor flux. Magnetizing, rotor, stator inductance. Rotor, stator resistance. Stator or rotor current. Stator or rotor voltage. Stator leakage coefficient. Total leakage coefficient. Electrical torque. Time constant. Number of poles. Induction machine rotational speed. Electrical frequency. Slip frequency. Rotor position angle. Slip angle. Electrical angle. Magnetizing current. Superscripts Estimated value. Demanded value.

Manuscript received February 2, 2004; revised June 1, 2004. This work was supported in part by Fondecyt under Grant 1010942, in part by The British Council, and in part by The University of Magallanes. Paper no. TEC-000192004. R. Cárdenas, R. Peña, and J. Proboste are with the Electrical Engineering Department, University of Magallanes, Punta Arenas, Chile (e-mail: [email protected]). G. Asher and J. Clare are with the School of Electrical and Electronic Engineering, University of Nottingham, Nottingham NG7 2RD, U.K. (e-mail: [email protected]). Digital Object Identifier 10.1109/TEC.2005.847965

, 0

Subscripts Stator fixed coordinates. Synchronous rotating coordinates. Rotor or stator quantities. Quiescent point. I. INTRODUCTION

T

HE doubly fed induction generator (DFIG) has become one of the main generators for high-power variable speed wind energy conversion systems (WECS). It has many advantages when compared with the squirrel-cage induction generator [1], [2] since the power converters are in the rotor circuit and, for restricted speed range applications, are rated at only a fraction of the machine nominal power [1]. For the DFIG, sensorless operation is desirable because the use of a position encoder has several drawbacks in term of robustness, cost, cabling, and maintenance. Sensorless control of the variable speed doubly fed induction machine (DFIM) has been addressed by several researchers [3]–[10]. The earliest [3] proposes a rotor flux-based estimator involving the integration of the rotor back-electromotive force (emf). This suffers from integration problems at low and zero rotor frequency and gives poor performance for operation around synchronous speed. The sensorless control methods presented in [4]–[8] are based on rotor current estimators in which the estimated current is compared to the measured current and the rotor position is derived using an open-loop mathematical identity. The rotor speed is obtained via differentiation. In [4], for example, the rotor current is estimated in the stator frame using stator variables, while in [6], the commercial product ROTODRIVE is presented in which an alternative rotor current estimator is proposed using load active and reactive power. In [7], a simpler implementation is proposed at the cost of reduced dynamics. It is noted that in all of these publications, the rotor position accuracy and effect of parameter errors have not been addressed. The system dynamics and the formal estimator design procedures were also not considered. This paper considers a stator-flux-based model reference adaptive system (MRAS) structure for observing the rotor position and speed of a DFIM. The similar rotor-flux based MRAS applied to the squirrel-cage induction machine is well known [11]. The method has the advantages of simplicity and is amenable to analysis [12]. However, when applied to a cage machine, it suffers from integrator drift effects at low excitation frequency and its performance is dependent on resistance parameters. As will be shown in this paper, neither of these

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CÁRDENAS et al.: MRAS OBSERVER FOR SENSORLESS CONTROL OF STAND-ALONE DFIGs

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Fig. 1. Sensorless vector-control scheme for a standalone DFIG.

effects occur when applied to a DFIM. The MRAS method has been reported in [9] and [10] in which simulations only were presented for a DFIM operating at very low speed. As with other research into sensorless methods, the observer dynamics, the control design procedure, the sensorless accuracy, and the effect of parameter variations are not considered in [9] and [10]. These issues will be addressed in the present paper. Experimental validation over the speed ranges commonly associated with DFIGs will also be presented. The stator flux-based MRAS observer will be presented in its application to a vector-controlled standalone DFIG. However, it is understood that the principle of the MRAS structure is extendable to other DFIM drive applications. Finally, the paper will also cover the starting regime in which the sensorless algorithm catches the speed of the pre-revolving shaft.

voltages. The machine equations written in a synchronously reference frame are [1], [2], and [13] rotating (1) (2) (3) (4) (5) (6) (7) (8) (9)

II. VECTOR CONTROL OF INDUCTION GENERATORS FOR STANDALONE OPERATION The proposed control system is shown in Fig. 1. As is appropriate for a standalone application, the vector control scheme is indirect [13] and contains demands for frequency and magnetizing current to set the constant stator frequency and voltage (stator resistance compensation is omitted for simplicity) in the absence of a grid connection and irrespective of shaft speed. The scheme is suitable for a variable speed diesel or wind drive. The MRAS observer is represented by the block diagrams inside the dotted box. Its output is the rotor angle used to modulate/demodulate the rotor currents and reference

is supplied where the equivalent stator magnetizing current axis of the reference entirely from the rotor. Aligning the frame on the stator flux vector gives (10) using the definition for Eliminating using (10) yields, with eliminating

given in (1) and

(11) (12)

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where . Since the last two terms in (5) are zero for is seen to be small, and from (11) constant flux operation, can be controlled using . The rotor it is thus seen that current can be controlled according to

A. Small-Signal Model The small-signal model for the MRAS observer is derived coordiusing a synchronous rotating frame. The error in nates is

(13) which forces the orientation of the reference frame along the stator flux vector position. The demodulation of the rotor demand voltages uses the slip angle derived from (14) where is estimated from the MRAS observer. In this work, the stator flux angle is derived from a free-running integral of the stator frequency demand (50 Hz). This has the advantage that the orientation is shielded from measurement noise and stator voltage harmonics, which may be a problem in a standalone application [13]. Since the proposed sensorless control system is not affected by the operation of the PWM front-end converter, the control of this converter is considered outside the scope of this paper. A discussion about the control of the PWM front-end converter can be found in [1] and [13].

(18) The small-signal model for the error is (19) For this small-signal system, it is assumed that . Also , because the system is oriented along the stator flux . Therefore, the small-signal model for the error is (20) Referring (16) to a synchronously rotating frame yields (21) that is, the flux derived from the current model is not a dc signal unless the estimated speed is equal to the real speed. in (21) yields Replacing (22)

III. MRAS OBSERVER FOR DFIM A MRAS speed observer is used to estimate the rotational speed and rotor position of the DFIM. This observer is based on two models [11], [12]: the voltage model and the current model. In a stationary frame, the voltage model is used to obtain the stator flux as

From (22), a variation

is obtained as (23)

using (23) and assuming ), is obtained as

, (i.e., in the quiescent point

(15) will be small under rated opThe stator voltage drop eration so that the flux estimate of (15) is relatively insensitive to . Using a stationary frame, the stator flux is obtained from the current model as (16) is an estimation of the rotational speed. The current where is referred to the rotor frame. In the MRAS observer, the flux obtained from (15) is used as the reference flux. By adjusting the estimated rotational speed, the error between the reference flux and the flux estimated from (16) is reduced. The error in coordinates is defined as (17) Equations (15)–(17) are used to implement the MRAS speed observer. The error calculated using (17) is driven to zero by a proportional-integral (PI) controller. The output of this PI controller is the estimated rotational speed used in (16). The implementation of the MRAS observer is shown in Fig. 2. The voltage model is used to obtain the stator flux using a bandpass filter as a modified integrator to block the dc components of the measured voltages and currents. Since and are at a frequency well above the filter cut-off frequency, there is no deterioration in integral action.

(24) is obtained as

(25) Using (20), (24), and (25), the small-signal model for the MRAS observer is obtained. The small-signal model is shown in Fig. 3. A sketch of the root locus, including the PI controller, is shown in Fig. 4. With reference to (24) and Fig. 3, it is seen that the quiescent is used which implies that reactive power is supvalue of plied from the rotor-side converter, which must be the case for standalone applications. In many grid-connected applications, especially in wind generation, reactive power generation via will be preferred since the rotor-stator turns ratio is significantly , then altergreater than unity. If this is not the case, and native measures of MRAS error (e.g., rotor flux) are necessary; such measures will be considered in a future paper. From the control loop of Fig. 3 and the root locus of Fig. 4, it is concluded that the bandwidth attainable with the proposed MRAS configuration is limited only by noise considerations. B. Speed Catching Operation of the MRAS Observer It is desirable for a sensorless standalone DFIG to be able to catch the rotational speed of an already spinning machine [6].


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chronism is achieved, grid connection is enabled and the mode of vector control is changed to direct stator flux orientation [16]. C. Machine Parameter Sensitivity For the MRAS observer proposed in this paper, incorrect estimation of the machine inductances produces an incorrect estimation of the rotor angle. This angle is used to demodulate the rotor currents and the demanded rotor voltages. The rotor angle estimation error can be obtained using a small-signal model. The current model of (16) can be rewritten as

Fig. 2. MRAS observer for the DFIM.

(28) where in (28) is referred to the stationary frame. The error in the estimation of the rotor angle can be obtained using a model of (28) Fig. 3.

Small-signal model of the proposed observer.

(29) where

. A variation

causes a flux variation (30)

The phase variation for

can be calculated as (31)

Fig. 4. Sketch of root locus for the control system of Fig. 3.

For the proposed sensorless systems, the speed catching procedure considers the DFIG operating with scalar control of the rotor current magnitude and the stator load disconnected. The voltage supplied to the machine rotor is demodulated using the (Fig. 1) estimated slip frequency which is calculated from and the speed estimated from the MRAS observer. During the speed catching procedure, the stator frequency is since the estimated speed differs from the real not equal to speed. Therefore, the absolute error of the stator frequency, with respect to the reference, can be used as an indicating parameter coordinates for the for the MRAS convergence. Using stator voltage and flux, the electrical frequency can be estimated as [15] (26) and the absolute value of the stator frequency error is given by (27) A first-order lowpass filter is used to eliminate the high-frequency noise in . Once the MRAS observer has estimated the rotational speed correctly, the vector control of the rotor currents and the control of the magnetizing current are enabled. In this work, the vector-control system is enabled Hz. when the filtered values of The principle of speed catching described above can be extended to grid-connected systems. In this case, the generated stator voltage vector under standalone control is adjusted until it is synchronized with the supply voltage vector. When syn-

that is, if the machine is operating at steady-state and a variation is introduced in the MRAS observer parameters, then the phase of the estimated flux will change according to (31). This is corrected by the PI controller of the MRAS phase error and to observer which drives the phase error between in the estimation of zero. However, this introduces an offset the rotor angle. Therefore, an incorrect estimation of the term is equivalent to using a position encoder with an offset in the measured rotor position. For a vector-controlled standalone DFIG, the error in the estimation of the rotor angle produces an incorrect demodulation , , , and of the rotor voltages, incorrect calculations of , incorrect estimation of the machine torque, and coupling current control loops. between the Small deviations in the estimation of do not affect the accuracy of the steady-state speed obtained from the MRAS observer. This is because the error of (17) is driven to a zero steady-state value only when both the estimated and reference flux have the same phase and frequency. From (15) and (16), it is easily seen that the two estimates of stator flux have the same . frequency and phase only when The proposed MRAS observer is mainly affected by the in. The reference flux obtained from correct estimation of (15) is robust against variations in the stator resistance and the MRAS observer is not affected by rotor resistance variations because the rotor current is a measured quantity. IV. EXPERIMENTAL RESULTS The control system of Fig. 1 has been implemented using a 2.5-kW DFIM driven by a dc machine. The experimental rig is shown in Fig. 5.

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Fig. 5. Experimental rig.

Two PWM back-to-back inverters are connected to the rotor of the machine. The rotor-side PWM inverter is controlled using a frequency of 1 kHz. Current transducers are used to measure the rotor and stator currents. Two voltage transducers are used to measure the stator voltage. A speed encoder of 10 000 pulses per revolution is used to measure the rotational speed and rotor angle. The speed encoder is used only for comparison purposes and to control the dc drive machine. A microprocessor board is used to implement the MRAS observer and the whole sensorless vector-control system. The dc machine can be used to emulate a wind turbine or another prime mover according to the emulation technique presented in [14]. For simplicity, the paper emulates the prime mover using a second-order lowpass filter to filter the speed step command from the host PC (Fig. 5). The output of the filter is the reference sent to the dc machine speed control loop which has a natural frequency of 2 Hz; this is sufficient to perform the emulation considering the frequency content of most wind profiles. Fig. 6 shows the speed catching performance of the MRAS r/min. The top graphic shows the estiobserver with mated speed and the bottom shows the rotor position error. The MRAS speed observer converges after 18 s. Fig. 7 shows the stator frequency and magnetizing current during speed catching. The frequency is in the top graphic and the magnetizing current is in the bottom graphic. The MRAS speed observer has converged in 18 s and the stator electrical . However, because in this frequency is 50 Hz for application, a relatively narrow lowpass filter is used, the algorithm automatically enables the vector-control system at about , when the filtered frequency error is within 0.5 Hz. This ensures that the speed estimation is stable before enabling the closed-loop control. The magnetizing current control loop has a demand value of 6.5 A and a natural frequency of 2 Hz; this is sufficient to control the flux level while operating the rotor converter within its rated current level. axis rotor currents for the conditions Fig. 8 shows the of Fig. 7. When the closed-loop control is enabled, the q-axis rotor current is controlled to zero, according to (13), to ensure the orientation along the stator flux under no-load condition. axis rotor current follows the output of the magnetizing The current control loops have a natural current controller. The

Fig. 6. Speed catching of the MRAS observer.

Fig. 7. Stator frequency and magnetizing current during speed catching.

frequency of about 60 Hz corresponding to a step settling time of 10–15 ms. This is sufficient for the present research since higher natural frequencies result in noisier waveforms without observable improvement in the performance of the system.


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Fig. 10. Estimated rotor angle and estimation error for 600 r/min. Top: estimated angle. Bottom: position error.

Fig. 8.

0

The d q axis rotor currents.

Fig. 11. Rotational speeds for load impacts of 1.4 kW. Top: Load disconnection. Bottom: Load connection.

Fig. 9. Speed tracking using the MRAS observer. Top: speed change from 600 to 1350 r/min. Bottom: speed change from 1350 to 600 r/min.

Fig. 9 shows the performance of the MRAS observer tracking the rotational speed. For this test, speed changes from 600 to 1350 r/min (top graphic) and from 1350 to 600 r/min (bottom graphic) in approximately 4 s. The acceleration is about 190 r/min/s. Due to the large inertia of variable speed wind turbines [14], especially in high-power applications, this acceleration is more than that expected for a DFIG in a WECS. For these experimental results, a fixed load of approximately 1.2 kW (about 50% of nominal load) is connected to the stator. A good tracking of the rotational speed, with an error of less than 5 r/min, has been achieved with an MRAS observer having a closed-loop natural frequency of 10 Hz which is about five times faster than the 2-Hz prime mover natural frequency. Fig. 10 shows the estimated rotor angle and the rotor-angle estimation error for steady-state operation with a rotational speed of about 600 r/min, and 1-kW load applied to the stator. Again,

the tracking performance is excellent. According to the experimental results, the estimated rotor angle has a negligible error , are corin steady-state when the machine inductances rectly estimated. Fig. 11 shows the performance of the MRAS observer when the DFIM is rotating at 700 r/min and a load impact of 1.4 kW (about 60% of nominal load) is connected and disconnected from the stator. Load connection is shown in the bottom graphic and load disconnection is shown in the top graphic. The load impact produces a dip and an overshoot of about 100 r/min. The tracking of the speed by the MRAS observer is very good in both cases. Fig. 12 shows the stator voltage corresponding to the load impacts of Fig. 11 with the vector-control system using the estimated rotor angle obtained from the MRAS observer (Figs. 1 and 2). The stator voltage is well regulated with a small dip and overshoot produced by the load impacts. Fig. 13 shows the magnetizing and -axis currents corresponding to the connection and disconnection of the 1.4-kW resistive load. The is derived from the estimated axis magnetizing current flux as depicted in Fig. 1. The regulation of the magnetizing and -axis currents achieved with the proposed sensorless system is good even for this relatively large load step.

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Fig. 15. Rotor current and rotational speeds for dynamic operation through synchronous speed. TABLE I EFFECTS OF MACHINE PARAMETERS VARIATION

Fig. 12. Stator quadrature voltage for load impacts of 1.4 kW. Top: Load disconnection. Bottom: Load connection.

Fig. 13. The i and i currents for load impacts of 1.4 kW. Top: Load disconnection. Bottom: Load connection.

Fig. 14. Rotor current and estimated speed for synchronous operation.

Fig. 14 shows the rotational speeds and the rotor current for steady-state operation at the synchronous velocity with 60% of the nominal load applied to the stator. The rotor current is a dc signal with some noise produced by the PWM switching. Unlike previous work [3], the estimation of the rotor speed is very good at synchronous operation because in the proposed sensorless control system, no integration of the rotor voltage

or current is performed. Fig. 15 shows the performance of the sensorless control system for dynamic operation through synchronous speed. The current control loop operates with a good dynamic response and the sensorless control system is tracking, with a small error, the speed obtained from the position encoder. The effects of incorrect estimation of the machine parameters are shown in Table I. This table shows the error in the rotor position angles, the rotor currents, and the estimated rotational is varied speeds obtained experimentally when between 7% to 13%. The speed demand is 1000 r/min and the speed estimate has zero error in steady-state. In Table I, is the rotor position error obtained experimentally and is the rotor position error obtained using (31). According to the results shown in Table I, the experimental results are in broad agreement with the rotor position error analysis of Section III-C. and . For a given Table I also shows the rotor currents load and magnetizing current, when the rotor position angle is incorrectly identified, the quadrature and direct currents change although the total rotor current magnitude remains constant. Incorrect estimation of the quadrature current produces an incorrect value of electrical torque when calculated according to (12). This may produce a low energy capture when control of the DFIG electrical torque is used to drive a variable speed WECS to the optimal tip-speed ratio of the wind turbine [1], [13], [14], [16]. In addition to studying the effects of incorrect estimation of , the performance of the MRAS observer has been experimentally tested for incorrect estimation of the stator resistance of 100% of the real value. There was no noticeable effect in performance. V. CONCLUSION This paper has presented an analysis and discussion of sensorless control of DFIM using MRAS observers. Smallsignal models have been derived for the analysis and the


design of the MRAS observer as well as for understanding the effects of incorrect parameter estimation in the accuracy of the proposed MRAS observer. The proposed sensorless scheme has been experimentally validated both in transient and steady-state conditions. Several tests including load impacts, transient speed tracking performance, and speed catching on the fly have been presented showing the excellent performance of the proposed speed-tracking scheme. Moreover, the experimental results are in broad agreement with the small-signal models proposed in this paper. Although this paper has discussed the application of an MRAS observer for a DFIG in standalone operation, the small-signal models and the effects of parameter sensitivity can be extended to other applications of the DFIM, such as doubly fed induction motor drives.

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[11] C. Schauder, “Adaptive speed identification for vector control of induction motors without rotational transducers,” IEEE Trans. Ind. Appl., vol. 28, no. 5, pp. 1054–1061, Oct. 1992. [12] R. Blasco-Gimenez, G. M. Asher, and M. Sumner, “Dynamic performance limitations for MRAS based sensorless induction motor drives, part 1: stability analysis for the closed loop drive,” Proc Inst. Elect. Eng. B, pp. 113–122, Mar. 1996. [13] R. Peña, R. Cárdenas, G. Asher, and J. Clare, “Vector controlled induction machine for stand-alone wind energy applications,” in Proc. IEEE Industry Application Annu. Meeting, Rome, Italy, Oct. 2000. [14] R. Cárdenas, R. Peña, G. Asher, and J. Clare, “Emulation of wind turbines and flywheels for experimental purposes,” in Proc. Eur. Power Electron. Conf., Graz, Austria, Aug. 2001. [15] X. Xu and D. Novotony, “Implementation of direct stator flux orientation control on a versatile DSP system,” Proc. IEEE Trans. Ind. Appl., vol. 27, no. 4, pp. 694–700, Jul./Aug. 1991. [16] R. Pena, J. Clare, and G. Asher, “Doubly-fed induction generators using back-to-back PWM converters and its applications to variable-speed wind-energy generation,” Proc. Inst. Elect. Eng., B, vol. 153, no. 3, pp. 231–241, May 1996.

APPENDIX Parameters of the DFIM Induction machine: stator 220 V delta, rotor 250 V star, , , 2.5 kW, six poles, 960 r/min, , , . External inductances of 30 mH have been added to the rotor.

REFERENCES [1] R. S. Peña, G. M. Asher, and J. C. Clare, “A doubly fed induction generator using back to back PWM converters supplying an isolated load from a variable speed wind turbine,” Proc. Inst. Elect. Eng., Electr. Power Appl., pp. 380–387, Sep. 1996. [2] B. Rabelo and W. Hofman, “Control of an optimized power flow in wind power plants with doubly-fed induction generators,” in Proc. Power Electronics Specialist Conf., Acapulco, México, Jun. 2003, pp. 1563–1568. [3] L. Xu and W. Cheng, “Torque and reactive power control of a doubly-fed induction machine by position sensorless scheme,” IEEE Trans. Ind. Appl., vol. 31, no. 3, pp. 636–641, May/Jun. 1995. [4] U. Rädel, D. Navarro, G. Berger, and S. Berg, “Sensorless field-oriented control of a slipring induction generator for a 2.5 MW wind power plant from Nordex Energy GMBH,” in Proc. Eur. Power Electron. Conf., Graz, Austria, 2001. [5] R. Datta and V. T. Ranganathan, “A simple position sensorless algorithm for rotor side field oriented control of wound rotor induction machine,” IEEE Trans. Ind. Electron., vol. 48, no. 4, pp. 786–793, Aug. 2001. [6] L. Morel, H. Godfroid, A. Mirzaian, and J. M. Kauffmann, “Double-fed induction machine: converter optimization and field oriented control without position sensor,” Proc. Inst. Elect. Eng., Electr. Power Appl., vol. 145, no. 4, pp. 360–368, Jul. 1998. [7] E. Bogalecka and Z. Krzeminski, “Sensorless control of a double-fed machine for wind power generators,” in Proc. Eur. Power Electron. Conf.-Power Electron., Machines Control, Dubrovnik and Cavtat, Slovenia, 2002. [8] B. Hopfensperger, D. J. Atkinson, and R. A. Lakin, “Stator-flux oriented control of a doubly-fed induction machine without position encoder,” Proc. Inst. Elect. Eng., Electr. Power Appl., vol. 147, no. 4, pp. 241–250, Jul. 2000. [9] R. Ghosn, C. Asmar, M. Pietrzak-David, and B. De Fornel, “A MRASLuenberger sensorless speed control of doubly fed induction machine,” in Proc. Eur. Power Electron. Conf., Toulose, France, 2003. [10] , “A MRAS-sensorless speed control of doubly fed induction machine,” in Proc. Int. Conf. Electrical Machines, Bruges, Belgium, Aug. 26–28, 2002.

Roberto Cárdenas (S’95–M’97) was born in Punta Arenas, Chile. He received the Electrical Engineering Degree from the University of Magallanes, Punta Arenas, in 1988 and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. From 1989 to 1991, he was a Lecturer in the University of Magallanes. He is currently with the Electrical Engineering Department, University of Magallanes. His main interests are in control of electrical machines and variable-speed drives and renewable energy systems. Dr. Cardenas is a member of the Institute of Electrical and Electronic Engineers.

Rubén Peña (S’95–M’97) was born in Coronel, Chile. He received the electrical engineering degree from the University of Concepcion, Concepcion, Chile, in 1984 and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively. Currently, he is with the Electrical Engineering Department, University of Magallanes, Punta Arenas, Chile. From 1985 to 1991, he was a Lecturer in the University of Magallanes. His main interests are in control of power electronics converters, ac drives, and renewable energy systems.

José Proboste was born in Puerto Natales, Chile, on March 21, 1976. He received the Electrical Engineering degree from the University of Magallanes, Punta Arenas, Chile, in 2004. Currently, he is a Research Assistant in the Electrical Engineering Department, University of Magallanes. His main interests are the control of power-electronics converters and ac drives.

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Greg Asher (M’98) received the Electrical and Electronic Engineering degree and the Ph.D. degree in Bond Graph structures and General Dynamic Systems from Bath University, Bath, U.K., in 1976 and 1979, respectively. He was appointed Lecturer in control with the School of Electrical and Electronic Engineering, University of Nottingham, Nottingham, U.K., in 1984, where he developed an interest in motor drive systems, particularly the control of ac machines. He was appointed Professor of electrical drives in 2000 and is currently Head of the School of Electrical and Electronic Engineering at the University of Nottingham. He has published many research papers, received more than $5M in research contracts, and has supervised 29 Ph.D. students. Currently, he is Chair of the Power Electronics Technical Committee for the Industrial Electronics Society. He was a member of the Executive Committee of European Power Electronics (EPE) Association until 2003. He is a member of the Institution of Electrical Engineers and is an Associate Editor of the IEEE Industrial Electronics Society.

Jon Clare (M’90–SM’04) was born in Bristol, U.K. He received the B.Sc. and Ph.D. degrees in electrical engineering from The University of Bristol. From 1984 to 1990, he was a Research Assistant and Lecturer at The University of Bristol, involved in teaching and research in power-electronic systems. Currently, he is with the Power Electronics, Machines and Control Group at the University of Nottingham, Nottingham, U.K., where he has been since 1990. He is a Professor in power electronics and Head of the Research Group. His research interests are power-electronic converters and modulation strategies, variable-speed drive systems, and electromagnetic compatibility. Prof. Clare is a member of the Institution of Electrical Engineers and is an Associate Editor for IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS.