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

MRAS Observer for Sensorless Control of StandaloneDoubly 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 referenceadaptive system (MRAS) observer for the sensorless control of astandalone doubly fed induction generator (DFIG). The analysisallows the formal design of the MRAS observer of given dynamicsand further allows the prediction of rotor position estimation er-rors under parameter mismatch. The MRAS observer analysis isexperimentally implemented for the vector control of a standaloneDFIG feeding a load at constant voltage and frequency. Experi-mental results, including speed catching of an already spinningmachine, are presented and extensively discussed. Although themethod is validated for a standalone generator, the proposedMRAS observer can be extended to other applications of thedoubly fed induction machine.

Index Terms—Induction generator, induction motor drives,wind energy.

NOMENCLATURE

GeneralStator 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.

SuperscriptsEstimated value.Demanded value.

Manuscript received February 2, 2004; revised June 1, 2004. This work wassupported in part by Fondecyt under Grant 1010942, in part by The BritishCouncil, and in part by The University of Magallanes. Paper no. TEC-00019-2004.

R. Cárdenas, R. Peña, and J. Proboste are with the Electrical Engi-neering Department, University of Magallanes, Punta Arenas, Chile (e-mail:[email protected]).

G. Asher and J. Clare are with the School of Electrical and ElectronicEngineering, University of Nottingham, Nottingham NG7 2RD, U.K. (e-mail:[email protected]).

Digital Object Identifier 10.1109/TEC.2005.847965

SubscriptsStator fixed coordinates.Synchronous rotating coordinates.

, Rotor or stator quantities.0 Quiescent point.

I. INTRODUCTION

THE doubly fed induction generator (DFIG) has becomeone of the main generators for high-power variable speed

wind energy conversion systems (WECS). It has many advan-tages 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 frac-tion of the machine nominal power [1]. For the DFIG, sensor-less operation is desirable because the use of a position encoderhas several drawbacks in term of robustness, cost, cabling, andmaintenance.

Sensorless control of the variable speed doubly fed inductionmachine (DFIM) has been addressed by several researchers[3]–[10]. The earliest [3] proposes a rotor flux-based estimatorinvolving the integration of the rotor back-electromotive force(emf). This suffers from integration problems at low andzero rotor frequency and gives poor performance for operationaround synchronous speed. The sensorless control methods pre-sented in [4]–[8] are based on rotor current estimators in whichthe estimated current is compared to the measured current andthe rotor position is derived using an open-loop mathematicalidentity. The rotor speed is obtained via differentiation. In [4],for example, the rotor current is estimated in the stator frameusing stator variables, while in [6], the commercial productROTODRIVE is presented in which an alternative rotor currentestimator is proposed using load active and reactive power. In[7], a simpler implementation is proposed at the cost of reduceddynamics. It is noted that in all of these publications, the rotorposition accuracy and effect of parameter errors have not beenaddressed. The system dynamics and the formal estimatordesign procedures were also not considered.

This paper considers a stator-flux-based model referenceadaptive system (MRAS) structure for observing the rotorposition and speed of a DFIM. The similar rotor-flux basedMRAS applied to the squirrel-cage induction machine is wellknown [11]. The method has the advantages of simplicity andis amenable to analysis [12]. However, when applied to a cagemachine, it suffers from integrator drift effects at low excitationfrequency and its performance is dependent on resistanceparameters. As will be shown in this paper, neither of these

0885-8969/$20.00 © 2005 IEEE

CÁRDENAS et al.: MRAS OBSERVER FOR SENSORLESS CONTROL OF STAND-ALONE DFIGs 711

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

effects occur when applied to a DFIM. The MRAS method hasbeen reported in [9] and [10] in which simulations only werepresented for a DFIM operating at very low speed. As withother research into sensorless methods, the observer dynamics,the control design procedure, the sensorless accuracy, and theeffect of parameter variations are not considered in [9] and [10].These issues will be addressed in the present paper. Experi-mental validation over the speed ranges commonly associatedwith DFIGs will also be presented. The stator flux-based MRASobserver will be presented in its application to a vector-con-trolled standalone DFIG. However, it is understood that theprinciple of the MRAS structure is extendable to other DFIMdrive applications. Finally, the paper will also cover the startingregime in which the sensorless algorithm catches the speed ofthe pre-revolving shaft.

II. VECTOR CONTROL OF INDUCTION GENERATORS

FOR STANDALONE OPERATION

The proposed control system is shown in Fig. 1. As isappropriate for a standalone application, the vector controlscheme is indirect [13] and contains demands for frequencyand magnetizing current to set the constant stator frequency andvoltage (stator resistance compensation is omitted for simplicity)in the absence of a grid connection and irrespective of shaftspeed. The scheme is suitable for a variable speed diesel orwind drive. The MRAS observer is represented by the blockdiagrams inside the dotted box. Its output is the rotor angleused to modulate/demodulate the rotor currents and reference

voltages. The machine equations written in a synchronouslyrotating reference frame are [1], [2], and [13]

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

where the equivalent stator magnetizing current is suppliedentirely from the rotor. Aligning the axis of the referenceframe on the stator flux vector gives

(10)

Eliminating using the definition for given in (1) andeliminating using (10) yields, with

(11)

(12)


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

(13)

which forces the orientation of the reference frame along thestator flux vector position. The demodulation of the rotor de-mand 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 thestator frequency demand (50 Hz). This has the advantage thatthe orientation is shielded from measurement noise and statorvoltage harmonics, which may be a problem in a standaloneapplication [13].

Since the proposed sensorless control system is not affectedby the operation of the PWM front-end converter, the controlof this converter is considered outside the scope of this paper.A discussion about the control of the PWM front-end convertercan be found in [1] and [13].

III. MRAS OBSERVER FOR DFIM

A MRAS speed observer is used to estimate the rotationalspeed and rotor position of the DFIM. This observer is based ontwo models [11], [12]: the voltage model and the current model.In a stationary frame, the voltage model is used to obtain thestator flux as

(15)

The stator voltage drop will be small under rated op-eration so that the flux estimate of (15) is relatively insensitiveto . Using a stationary frame, the stator flux is obtained fromthe current model as

(16)

where is an estimation of the rotational speed. The currentis referred to the rotor frame. In the MRAS observer, the flux

obtained from (15) is used as the reference flux. By adjustingthe estimated rotational speed, the error between the referenceflux 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 speedobserver. The error calculated using (17) is driven to zero by aproportional-integral (PI) controller. The output of this PI con-troller is the estimated rotational speed used in (16). The imple-mentation of the MRAS observer is shown in Fig. 2. The voltagemodel is used to obtain the stator flux using a bandpass filteras a modified integrator to block the dc components of the mea-sured voltages and currents. Since and are at a frequencywell above the filter cut-off frequency, there is no deteriorationin integral action.

A. Small-Signal Model

The small-signal model for the MRAS observer is derivedusing a synchronous rotating frame. The error in coordi-nates is

(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 erroris

(20)

Referring (16) to a synchronously rotating frame yields

(21)

that is, the flux derived from the current model is not adc signal unless the estimated speed is equal to the real speed.Replacing in (21) yields

(22)

From (22), a variation is obtained as

(23)

using (23) and assuming , (i.e., in the quiescent point), is obtained as

(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 shownin 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 quiescentvalue of is used which implies that reactive power is sup-plied from the rotor-side converter, which must be the case forstandalone applications. In many grid-connected applications,especially in wind generation, reactive power generation viawill be preferred since the rotor-stator turns ratio is significantlygreater than unity. If this is not the case, and , then alter-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 proposedMRAS 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 tocatch the rotational speed of an already spinning machine [6].


Fig. 2. MRAS observer for the DFIM.

Fig. 3. Small-signal model of the proposed observer.

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

For the proposed sensorless systems, the speed catching pro-cedure considers the DFIG operating with scalar control of therotor current magnitude and the stator load disconnected. Thevoltage supplied to the machine rotor is demodulated using theestimated slip frequency which is calculated from (Fig. 1)and the speed estimated from the MRAS observer.

During the speed catching procedure, the stator frequency isnot equal to since the estimated speed differs from the realspeed. Therefore, the absolute error of the stator frequency, withrespect to the reference, can be used as an indicating parameterfor the MRAS convergence. Using coordinates for thestator voltage and flux, the electrical frequency can be estimatedas [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-fre-quency noise in . Once the MRAS observer has esti-mated the rotational speed correctly, the vector control of the

rotor currents and the control of the magnetizing currentare enabled. In this work, the vector-control system is enabledwhen the filtered values of Hz.

The principle of speed catching described above can be ex-tended to grid-connected systems. In this case, the generatedstator voltage vector under standalone control is adjusted untilit is synchronized with the supply voltage vector. When syn-

chronism is achieved, grid connection is enabled and the modeof vector control is changed to direct stator flux orientation [16].

C. Machine Parameter Sensitivity

For the MRAS observer proposed in this paper, incorrect es-timation of the machine inductances produces an incorrect esti-mation of the rotor angle. This angle is used to demodulate therotor currents and the demanded rotor voltages. The rotor angleestimation error can be obtained using a small-signal model. Thecurrent model of (16) can be rewritten as

(28)

where in (28) is referred to the stationary frame. The error inthe estimation of the rotor angle can be obtained using amodel of (28)

(29)

where . A variation causes a flux variation

(30)

The phase variation for can be calculated as

(31)

that is, if the machine is operating at steady-state and a variationis introduced in the MRAS observer parameters, then the

phase of the estimated flux will change according to (31). Thisphase error is corrected by the PI controller of the MRASobserver which drives the phase error between and tozero. However, this introduces an offset in the estimation ofthe rotor angle. Therefore, an incorrect estimation of the term

is equivalent to using a position encoder with an offsetin the measured rotor position.

For a vector-controlled standalone DFIG, the error in the es-timation of the rotor angle produces an incorrect demodulationof the rotor voltages, incorrect calculations of , , , and

, incorrect estimation of the machine torque, and couplingbetween the current control loops.

Small deviations in the estimation of do not affectthe accuracy of the steady-state speed obtained from the MRASobserver. This is because the error of (17) is driven to a zerosteady-state value only when both the estimated and referenceflux have the same phase and frequency. From (15) and (16), itis easily seen that the two estimates of stator flux have the samefrequency and phase only when .

The proposed MRAS observer is mainly affected by the in-correct estimation of . The reference flux obtained from(15) is robust against variations in the stator resistance and theMRAS observer is not affected by rotor resistance variations be-cause the rotor current is a measured quantity.

IV. EXPERIMENTAL RESULTS

The control system of Fig. 1 has been implemented using a2.5-kW DFIM driven by a dc machine. The experimental rig isshown in Fig. 5.


Fig. 5. Experimental rig.

Two PWM back-to-back inverters are connected to the rotorof the machine. The rotor-side PWM inverter is controlled usinga frequency of 1 kHz. Current transducers are used to measurethe rotor and stator currents. Two voltage transducers are usedto measure the stator voltage. A speed encoder of 10 000 pulsesper revolution is used to measure the rotational speed and rotorangle. The speed encoder is used only for comparison purposesand to control the dc drive machine. A microprocessor board isused to implement the MRAS observer and the whole sensorlessvector-control system.

The dc machine can be used to emulate a wind turbine or an-other prime mover according to the emulation technique pre-sented in [14]. For simplicity, the paper emulates the primemover using a second-order lowpass filter to filter the speed stepcommand from the host PC (Fig. 5). The output of the filter isthe reference sent to the dc machine speed control loop whichhas a natural frequency of 2 Hz; this is sufficient to performthe emulation considering the frequency content of most windprofiles.

Fig. 6 shows the speed catching performance of the MRASobserver with r/min. The top graphic shows the esti-mated speed and the bottom shows the rotor position error. TheMRAS speed observer converges after 18 s.

Fig. 7 shows the stator frequency and magnetizing currentduring speed catching. The frequency is in the top graphic andthe magnetizing current is in the bottom graphic. The MRASspeed observer has converged in 18 s and the stator electricalfrequency is 50 Hz for . However, because in thisapplication, a relatively narrow lowpass filter is used, the algo-rithm 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 enablingthe closed-loop control. The magnetizing current control loophas 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 rotorconverter within its rated current level.

Fig. 8 shows the axis rotor currents for the conditionsof Fig. 7. When the closed-loop control is enabled, the q-axisrotor current is controlled to zero, according to (13), to ensurethe orientation along the stator flux under no-load condition.The axis rotor current follows the output of the magnetizingcurrent controller. The current control loops have a natural

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 timeof 10–15 ms. This is sufficient for the present research sincehigher natural frequencies result in noisier waveforms withoutobservable improvement in the performance of the system.


Fig. 8. The d�q axis rotor currents.

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

Fig. 9 shows the performance of the MRAS observer trackingthe rotational speed. For this test, speed changes from 600 to1350 r/min (top graphic) and from 1350 to 600 r/min (bottomgraphic) in approximately 4 s. The acceleration is about 190r/min/s. Due to the large inertia of variable speed wind turbines[14], especially in high-power applications, this acceleration ismore than that expected for a DFIG in a WECS. For these ex-perimental results, a fixed load of approximately 1.2 kW (about50% of nominal load) is connected to the stator. A good trackingof the rotational speed, with an error of less than 5 r/min, hasbeen achieved with an MRAS observer having a closed-loopnatural frequency of 10 Hz which is about five times fasterthan the 2-Hz prime mover natural frequency.

Fig. 10 shows the estimated rotor angle and the rotor-angle es-timation error for steady-state operation with a rotational speedof about 600 r/min, and 1-kW load applied to the stator. Again,

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

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

the tracking performance is excellent. According to the exper-imental results, the estimated rotor angle has a negligible errorin steady-state when the machine inductances , are cor-rectly estimated.

Fig. 11 shows the performance of the MRAS observer whenthe DFIM is rotating at 700 r/min and a load impact of 1.4 kW(about 60% of nominal load) is connected and disconnectedfrom the stator. Load connection is shown in the bottom graphicand load disconnection is shown in the top graphic. The loadimpact produces a dip and an overshoot of about 100 r/min.The tracking of the speed by the MRAS observer is very goodin both cases. Fig. 12 shows the stator voltage correspondingto the load impacts of Fig. 11 with the vector-control systemusing the estimated rotor angle obtained from the MRAS ob-server (Figs. 1 and 2). The stator voltage is well regulated witha small dip and overshoot produced by the load impacts. Fig. 13shows the magnetizing and -axis currents corresponding to theconnection and disconnection of the 1.4-kW resistive load. Themagnetizing current is derived from the estimated axisflux as depicted in Fig. 1.

The regulation of the magnetizing and -axis currentsachieved with the proposed sensorless system is good even forthis relatively large load step.


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

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

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

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

Fig. 15. Rotor current and rotational speeds for dynamic operation throughsynchronous speed.

TABLE IEFFECTS OF MACHINE PARAMETERS VARIATION

or current is performed. Fig. 15 shows the performance ofthe sensorless control system for dynamic operation throughsynchronous speed. The current control loop operates witha good dynamic response and the sensorless control systemis tracking, with a small error, the speed obtained from theposition encoder.

The effects of incorrect estimation of the machine parametersare shown in Table I. This table shows the error in the rotorposition angles, the rotor currents, and the estimated rotationalspeeds obtained experimentally when is variedbetween 7% to 13%. The speed demand is 1000 r/min and thespeed estimate has zero error in steady-state. In Table I,is the rotor position error obtained experimentally and isthe rotor position error obtained using (31). According to theresults shown in Table I, the experimental results are in broadagreement with the rotor position error analysis of Section III-C.

Table I also shows the rotor currents and . For a givenload and magnetizing current, when the rotor position angle isincorrectly identified, the quadrature and direct currents changealthough the total rotor current magnitude remains constant.Incorrect estimation of the quadrature current produces anincorrect value of electrical torque when calculated accordingto (12). This may produce a low energy capture when controlof the DFIG electrical torque is used to drive a variable speedWECS 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 exper-

imentally tested for incorrect estimation of the stator resistanceof 100% of the real value. There was no noticeable effect inperformance.

V. CONCLUSION

This paper has presented an analysis and discussion ofsensorless control of DFIM using MRAS observers. Small-signal models have been derived for the analysis and the


design of the MRAS observer as well as for understanding theeffects of incorrect parameter estimation in the accuracy of theproposed MRAS observer. The proposed sensorless scheme hasbeen experimentally validated both in transient and steady-stateconditions. Several tests including load impacts, transient speedtracking performance, and speed catching on the fly have beenpresented showing the excellent performance of the proposedspeed-tracking scheme. Moreover, the experimental results arein broad agreement with the small-signal models proposed inthis paper.

Although this paper has discussed the application of anMRAS observer for a DFIG in standalone operation, thesmall-signal models and the effects of parameter sensitivity canbe extended to other applications of the DFIM, such as doublyfed induction motor drives.

APPENDIX

Parameters of the DFIM

Induction machine: stator 220 V delta, rotor 250 V star,2.5 kW, six poles, 960 r/min, , ,

, , . Externalinductances 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 gener-ator using back to back PWM converters supplying an isolated load froma variable speed wind turbine,” Proc. Inst. Elect. Eng., Electr. PowerAppl., pp. 380–387, Sep. 1996.

[2] B. Rabelo and W. Hofman, “Control of an optimized power flow inwind 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-fedinduction 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-orientedcontrol of a slipring induction generator for a 2.5 MW wind power plantfrom Nordex Energy GMBH,” in Proc. Eur. Power Electron. Conf., Graz,Austria, 2001.

[5] R. Datta and V. T. Ranganathan, “A simple position sensorless algorithmfor 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-fedinduction machine: converter optimization and field oriented controlwithout 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-fedmachine 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 orientedcontrol 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 MRAS-Luenberger 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 ma-chine,” in Proc. Int. Conf. Electrical Machines, Bruges, Belgium, Aug.26–28, 2002.

[11] C. Schauder, “Adaptive speed identification for vector control of induc-tion 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 perfor-mance 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 induc-tion machine for stand-alone wind energy applications,” in Proc. IEEEIndustry Application Annu. Meeting, Rome, Italy, Oct. 2000.

[14] R. Cárdenas, R. Peña, G. Asher, and J. Clare, “Emulation of wind tur-bines and flywheels for experimental purposes,” in Proc. Eur. PowerElectron. Conf., Graz, Austria, Aug. 2001.

[15] X. Xu and D. Novotony, “Implementation of direct stator flux orientationcontrol 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 usingback-to-back PWM converters and its applications to variable-speedwind-energy generation,” Proc. Inst. Elect. Eng., B, vol. 153, no. 3, pp.231–241, May 1996.

Roberto Cárdenas (S’95–M’97) was born inPunta Arenas, Chile. He received the ElectricalEngineering Degree from the University of Mag-allanes, Punta Arenas, in 1988 and the M.Sc. andPh.D. degrees from the University of Nottingham,Nottingham, U.K., in 1992 and 1996, respectively.

From 1989 to 1991, he was a Lecturer in theUniversity of Magallanes. He is currently with theElectrical Engineering Department, University ofMagallanes. His main interests are in control ofelectrical machines and variable-speed drives and

renewable energy systems.Dr. Cardenas is a member of the Institute of Electrical and Electronic Engi-

neers.

Rubén Peña (S’95–M’97) was born in Coronel,Chile. He received the electrical engineering degreefrom the University of Concepcion, Concepcion,Chile, in 1984 and the M.Sc. and Ph.D. degrees fromthe University of Nottingham, Nottingham, U.K., in1992 and 1996, respectively.

Currently, he is with the Electrical EngineeringDepartment, University of Magallanes, PuntaArenas, Chile. From 1985 to 1991, he was a Lecturerin the University of Magallanes. His main interestsare 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 En-gineering degree from the University of Magallanes,Punta Arenas, Chile, in 2004.

Currently, he is a Research Assistant in theElectrical Engineering Department, University ofMagallanes. His main interests are the control ofpower-electronics converters and ac drives.


Greg Asher (M’98) received the Electrical and Elec-tronic Engineering degree and the Ph.D. degree inBond Graph structures and General Dynamic Sys-tems from Bath University, Bath, U.K., in 1976 and1979, respectively.

He was appointed Lecturer in control with theSchool of Electrical and Electronic Engineering,University of Nottingham, Nottingham, U.K., in1984, where he developed an interest in motor drivesystems, particularly the control of ac machines. Hewas appointed Professor of electrical drives in 2000

and is currently Head of the School of Electrical and Electronic Engineering atthe University of Nottingham. He has published many research papers, receivedmore than $5M in research contracts, and has supervised 29 Ph.D. students.

Currently, he is Chair of the Power Electronics Technical Committee for theIndustrial Electronics Society. He was a member of the Executive Committeeof European Power Electronics (EPE) Association until 2003. He is a memberof the Institution of Electrical Engineers and is an Associate Editor of the IEEEIndustrial Electronics Society.

Jon Clare (M’90–SM’04) was born in Bristol, U.K.He received the B.Sc. and Ph.D. degrees in electricalengineering from The University of Bristol.

From 1984 to 1990, he was a Research Assistantand Lecturer at The University of Bristol, involvedin teaching and research in power-electronic sys-tems. Currently, he is with the Power Electronics,Machines and Control Group at the University ofNottingham, Nottingham, U.K., where he has beensince 1990. He is a Professor in power electronicsand Head of the Research Group. His research inter-

ests are power-electronic converters and modulation strategies, variable-speeddrive systems, and electromagnetic compatibility.

Prof. Clare is a member of the Institution of Electrical Engineers and is anAssociate Editor for IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS.

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