IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 2, FEBRUARY 2014 687

Improved Active Power Filter Performancefor Renewable Power Generation Systems

Pablo Acuna, Member, IEEE, Luis Moran, Fellow, IEEE, Marco Rivera, Member, IEEE,Juan Dixon, Senior Member, IEEE, and Jose Rodriguez, Fellow, IEEE

Abstract—An active power filter implemented with a four-legvoltage-source inverter using a predictive control scheme is pre-sented. The use of a four-leg voltage-source inverter allows the com-pensation of current harmonic components, as well as unbalancedcurrent generated by single-phase nonlinear loads. A detailed yetsimple mathematical model of the active power filter, including theeffect of the equivalent power system impedance, is derived andused to design the predictive control algorithm. The compensationperformance of the proposed active power filter and the associ-ated control scheme under steady state and transient operatingconditions is demonstrated through simulations and experimentalresults.

Index Terms—Active power filter, current control, four-leg con-verters, predictive control.

NOMENCLATURE

AC Alternating current.dc Direct current.PWM Pulse width modulation.PC Predictive controller.PLL Phase-locked-loop.vdc dc-voltage.vs System voltage vector [vsu vsv vsw ]T .is System current vector [isu isv isw ]T .iL Load current vector [iLu iLv iLw ]T .vo VSI output voltage vector [vou vov vow ]T .io VSI output current vector [iou iov iow ]T .i∗o Reference current vector [i∗ou i∗ov i∗ow ]T .in Neutral current.Lf Filter inductance.Rf Filter resistance.

Manuscript received July 4, 2012; revised October 13, 2012 and December27, 2012; accepted March 21, 2013. Date of current version August 20, 2013.This work was supported in part by the Chilean Fund for Scientific and Tech-nological Development (FONDECYT) through project 1110592, in part by theBasal Project FB 0821, and in part by the CONICYT Initiation into Research2012 11121492 Project. Recommended for publication by Associate EditorM. Malinowski.

P. Acuna and L. Moran are with the Department of Electrical Engineering,Universidad de Concepcion, Concepcion 4030000, Chile (e-mail: pabloacuna@udec.cl; lmoran@udec.cl).

M. Rivera is with the Department of Industrial Technologies, Universidad deTalca, Curico 685, Chile (e-mail: marcoriv@utalca.cl).

J. Dixon is with the Department of Electrical Engineering, Pontificia Univer-sidad Catolica de Chile, Santiago 340, Chile (e-mail: jdixon@ing.puc.cl).

J. Rodriguez is with the Department of Electronics Engineering, UniversidadTecnica Federico Santa Marıa, Valparaıso 1680, Chile (e-mail: jrp@usm.cl).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2257854

I. INTRODUCTION

R ENEWABLE generation affects power quality due to itsnonlinearity, since solar generation plants and wind power

generators must be connected to the grid through high-powerstatic PWM converters [1]. The nonuniform nature of powergeneration directly affects voltage regulation and creates volt-age distortion in power systems. This new scenario in powerdistribution systems will require more sophisticated compensa-tion techniques.

Although active power filters implemented with three-phasefour-leg voltage-source inverters (4L-VSI) have already beenpresented in the technical literature [2]–[6], the primary contri-bution of this paper is a predictive control algorithm designedand implemented specifically for this application. Traditionally,active power filters have been controlled using pretuned con-trollers, such as PI-type or adaptive, for the current as well asfor the dc-voltage loops [7], [8]. PI controllers must be de-signed based on the equivalent linear model, while predictivecontrollers use the nonlinear model, which is closer to real op-erating conditions. An accurate model obtained using predictivecontrollers improves the performance of the active power filter,especially during transient operating conditions, because it canquickly follow the current-reference signal while maintaining aconstant dc-voltage.

So far, implementations of predictive control in power con-verters have been used mainly in induction motor drives[9]–[16]. In the case of motor drive applications, predictivecontrol represents a very intuitive control scheme that han-dles multivariable characteristics, simplifies the treatment ofdead-time compensations, and permits pulse-width modulatorreplacement. However, these kinds of applications present dis-advantages related to oscillations and instability created fromunknown load parameters [15]. One advantage of the proposedalgorithm is that it fits well in active power filter applica-tions, since the power converter output parameters are wellknown [17]. These output parameters are obtained from theconverter output ripple filter and the power system equivalentimpedance. The converter output ripple filter is part of the activepower filter design and the power system impedance is obtainedfrom well-known standard procedures [18], [19]. In the case ofunknown system impedance parameters, an estimation methodcan be used to derive an accurate R–L equivalent impedancemodel of the system [20].

This paper presents the mathematical model of the 4L-VSIand the principles of operation of the proposed predictive controlscheme, including the design procedure. The complete descrip-tion of the selected current reference generator implementedin the active power filter is also presented. Finally, the pro-posed active power filter and the effectiveness of the associated

0885-8993 © 2013 IEEE

688 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 2, FEBRUARY 2014

Fig. 1. Stand-alone hybrid power generation system with a shunt active power filter.

Fig. 2. Three-phase equivalent circuit of the proposed shunt active powerfilter.

control scheme compensation are demonstrated through simula-tion and validated with experimental results obtained in a 2 kVAlaboratory prototype.

II. FOUR-LEG CONVERTER MODEL

Fig. 1 shows the configuration of a typical power distributionsystem with renewable power generation. It consists of varioustypes of power generation units and different types of loads.Renewable sources, such as wind and sunlight, are typically usedto generate electricity for residential users and small industries.Both types of power generation use ac/ac and dc/ac static PWMconverters for voltage conversion and battery banks for long-term energy storage. These converters perform maximum powerpoint tracking to extract the maximum energy possible fromwind and sun. The electrical energy consumption behavior israndom and unpredictable, and therefore, it may be single- orthree-phase, balanced or unbalanced, and linear or nonlinear.An active power filter is connected in parallel at the point ofcommon coupling to compensate current harmonics, currentunbalance, and reactive power. It is composed by an electrolyticcapacitor, a four-leg PWM converter, and a first-order outputripple filter, as shown in Fig. 2. This circuit considers the powersystem equivalent impedance Zs , the converter output ripplefilter impedance Zf , and the load impedance ZL .

The four-leg PWM converter topology is shown in Fig. 3. Thisconverter topology is similar to the conventional three-phaseconverter with the fourth leg connected to the neutral bus of thesystem. The fourth leg increases switching states from 8 (23) to16 (24), improving control flexibility and output voltage quality[21], and is suitable for current unbalanced compensation.

Fig. 3. Two-level four-leg PWM-VSI topology.

The voltage in any leg x of the converter, measured from theneutral point (n), can be expressed in terms of switching states,as follows:

vxn = Sx − Sn vdc , x = u, v, w, n. (1)

The mathematical model of the filter derived from the equiv-alent circuit shown in Fig. 2 is

vo = vxn − Req io − Leqd iodt

(2)

where Req and Leq are the 4L-VSI output parameters expressedas Thevenin impedances at the converter output terminals Zeq .Therefore, the Thevenin equivalent impedance is determinedby a series connection of the ripple filter impedance Zf and aparallel arrangement between the system equivalent impedanceZs and the load impedance ZL

Zeq =ZsZL

Zs + ZL+ Zf ≈ Zs + Zf . (3)

For this model, it is assumed that ZL � Zs , that the resistivepart of the system’s equivalent impedance is neglected, andthat the series reactance is in the range of 3–7% p.u., which isan acceptable approximation of the real system. Finally, in (2)Req = Rf and Leq = Ls + Lf .

III. DIGITAL PREDICTIVE CURRENT CONTROL

The block diagram of the proposed digital predictive currentcontrol scheme is shown in Fig. 4. This control scheme is basi-cally an optimization algorithm and, therefore, it has to be im-plemented in a microprocessor. Consequently, the analysis hasto be developed using discrete mathematics in order to consideradditional restrictions such as time delays and approximations

ACUNA et al.: IMPROVED ACTIVE POWER FILTER PERFORMANCE FOR RENEWABLE POWER GENERATION SYSTEMS 689

Fig. 4. Proposed predictive digital current control block diagram.

[10], [22]–[27]. The main characteristic of predictive control isthe use of the system model to predict the future behavior of thevariables to be controlled. The controller uses this informationto select the optimum switching state that will be applied to thepower converter, according to predefined optimization criteria.The predictive control algorithm is easy to implement and tounderstand, and it can be implemented with three main blocks,as shown in Fig. 4.

1) Current Reference Generator: This unit is designed to gen-erate the required current reference that is used to compensatethe undesirable load current components. In this case, the sys-tem voltages, the load currents, and the dc-voltage converterare measured, while the neutral output current and neutral loadcurrent are generated directly from these signals (IV).

2) Prediction Model: The converter model is used to predictthe output converter current. Since the controller operates indiscrete time, both the controller and the system model must berepresented in a discrete time domain [22]. The discrete timemodel consists of a recursive matrix equation that represents thisprediction system. This means that for a given sampling time Ts ,knowing the converter switching states and control variables atinstant kTs , it is possible to predict the next states at any instant[k + 1]Ts . Due to the first-order nature of the state equations thatdescribe the model in (1)–(2), a sufficiently accurate first-orderapproximation of the derivative is considered in this paper

dx

dt≈ x[k + 1] − x[k]

Ts. (4)

The 16 possible output current predicted values can be ob-tained from (2) and (4) as

io [k + 1] =Ts

Leq(vxn [k] − vo [k]) +

(1 − Req Ts

Leq

)io [k].

(5)As shown in (5), in order to predict the output current io at

the instant (k + 1), the input voltage value vo and the converteroutput voltage vxN , are required. The algorithm calculates all16 values associated with the possible combinations that thestate variables can achieve.

3) Cost Function Optimization: In order to select the optimalswitching state that must be applied to the power converter, the16 predicted values obtained for io [k + 1] are compared withthe reference using a cost function g, as follows:

g[k + 1] = (i∗ou [k + 1] − iou [k + 1])2

+ (i∗ov [k + 1] − iov [k + 1])2

+ (i∗ow [k + 1] − iow [k + 1])2

+ (i∗on [k + 1] − ion [k + 1])2 . (6)

The output current (io) is equal to the reference (i∗o ) wheng = 0. Therefore, the optimization goal of the cost function isto achieve a g value close to zero. The voltage vector vxN thatminimizes the cost function is chosen and then applied at thenext sampling state. During each sampling state, the switchingstate that generates the minimum value of g is selected from the16 possible function values. The algorithm selects the switchingstate that produces this minimal value and applies it to theconverter during the k + 1 state.

IV. CURRENT REFERENCE GENERATION

A dq-based current reference generator scheme is used to ob-tain the active power filter current reference signals. This schemepresents a fast and accurate signal tracking capability. This char-acteristic avoids voltage fluctuations that deteriorate the currentreference signal affecting compensation performance [28]. Thecurrent reference signals are obtained from the correspondingload currents as shown in Fig. 5. This module calculates the ref-erence signal currents required by the converter to compensatereactive power, current harmonic, and current imbalance. Thedisplacement power factor (sin φ(L)) and the maximum totalharmonic distortion of the load (THD(L)) defines the relation-ships between the apparent power required by the active powerfilter, with respect to the load, as shown

SAPF

SL=

√sin φ(L) + THD(L)

2

√1 + THD(L)

2(7)

where the value of THD(L) includes the maximum compensableharmonic current, defined as double the sampling frequency fs .The frequency of the maximum current harmonic componentthat can be compensated is equal to one half of the converterswitching frequency.

The dq-based scheme operates in a rotating reference frame;therefore, the measured currents must be multiplied by thesin(wt) and cos(wt) signals. By using dq-transformation, thed current component is synchronized with the correspondingphase-to-neutral system voltage, and the q current componentis phase-shifted by 90◦. The sin(wt) and cos(wt) synchronizedreference signals are obtained from a synchronous referenceframe (SRF) PLL [29]. The SRF-PLL generates a pure si-nusoidal waveform even when the system voltage is severely

690 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 2, FEBRUARY 2014

Fig. 5. dq-based current reference generator block diagram.

distorted. Tracking errors are eliminated, since SRF-PLLs aredesigned to avoid phase voltage unbalancing, harmonics (i.e.,less than 5% and 3% in fifth and seventh, respectively), and off-set caused by the nonlinear load conditions and measurementerrors [30]. Equation (8) shows the relationship between the realcurrents iLx(t) (x = u, v, w) and the associated dq components(id and iq )

[idiq

]=

√23

[sin ωt cos ωt

− cos ωt sin ωt

]⎡⎢⎢⎣

1 −12

−12

0√

32

−√

32

⎤⎥⎥⎦⎡⎣ iLu

iLv

iLw

⎤⎦.

(8)A low-pass filter (LFP) extracts the dc component of the phase

currents id to generate the harmonic reference components −id .The reactive reference components of the phase-currents areobtained by phase-shifting the corresponding ac and dc compo-nents of iq by 180◦. In order to keep the dc-voltage constant,the amplitude of the converter reference current must be mod-ified by adding an active power reference signal ie with thed-component, as will be explained in Section IV-A. The re-sulting signals i∗d and i∗q are transformed back to a three-phasesystem by applying the inverse Park and Clark transformation,as shown in (9). The cutoff frequency of the LPF used in thispaper is 20 Hz

⎡⎢⎣

i∗ou

i∗ov

i∗ow

⎤⎥⎦ =

√23

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

1√2

1 0

1√2

−12

√3

2

1√2

−12

−√

32

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦

×

⎡⎢⎣

1

0

0

0

sinωt

cos ωt

0

− cos ωt

sin ωt

⎤⎥⎦

⎡⎢⎣

i0

i∗di∗q

⎤⎥⎦ . (9)

The current that flows through the neutral of the load is com-pensated by injecting the same instantaneous value obtained

Fig. 6. Relationship between permissible unbalance load currents, the cor-responding third-order harmonic content, and system current imbalance (withrespect to positive sequence of the system current, is ,1 ).

from the phase-currents, phase-shifted by 180◦, as shown next

i∗on = − (iLu + iLv + iLw ) . (10)

One of the major advantages of the dq-based current refer-ence generator scheme is that it allows the implementation ofa linear controller in the dc-voltage control loop. However, oneimportant disadvantage of the dq-based current reference framealgorithm used to generate the current reference is that a second-order harmonic component is generated in id and iq under un-balanced operating conditions. The amplitude of this harmonicdepends on the percent of unbalanced load current (expressed asthe relationship between the negative sequence current iL,2 andthe positive sequence current iL,1). The second-order harmoniccannot be removed from id and iq , and therefore generates athird harmonic in the reference current when it is convertedback to abc frame [31]. Fig. 6 shows the percent of system cur-rent imbalance and the percent of third harmonic system current,in function of the percent of load current imbalance. Since theload current does not have a third harmonic, the one generatedby the active power filter flows to the power system.

ACUNA et al.: IMPROVED ACTIVE POWER FILTER PERFORMANCE FOR RENEWABLE POWER GENERATION SYSTEMS 691

Fig. 7. DC-voltage control block diagram.

A. DC-Voltage Control

The dc-voltage converter is controlled with a traditional PIcontroller. This is an important issue in the evaluation, sincethe cost function (6) is designed using only current references,in order to avoid the use of weighting factors. Generally, theseweighting factors are obtained experimentally, and they are notwell defined when different operating conditions are required.Additionally, the slow dynamic response of the voltage acrossthe electrolytic capacitor does not affect the current transientresponse. For this reason, the PI controller represents a simpleand effective alternative for the dc-voltage control.

The dc-voltage remains constant (with a minimum value of√6 vs(rms)) until the active power absorbed by the converter

decreases to a level where it is unable to compensate for itslosses. The active power absorbed by the converter is controlledby adjusting the amplitude of the active power reference signalie , which is in phase with each phase voltage. In the blockdiagram shown in Fig. 5, the dc-voltage vdc is measured andthen compared with a constant reference value v∗

dc . The error(e) is processed by a PI controller, with two gains, Kp and Ti .Both gains are calculated according to the dynamic responserequirement. Fig. 7 shows that the output of the PI controller isfed to the dc-voltage transfer function Gs , which is representedby a first-order system (11)

G (s) =vdc

ie=

32

Kpvs

√2

Cdcv∗dc

. (11)

The equivalent closed-loop transfer function of the given sys-tem with a PI controller (12) is shown in (13)

C(s) = Kp

(1 +

1Ti · s

)(12)

vdc

ie=

ω 2n

a · (s + a)s2 + 2ζωn · s + ω2

n

. (13)

Since the time response of the dc-voltage control loop doesnot need to be fast, a damping factor ζ = 1 and a natural angularspeed ωn = 2π · 100 rad/s are used to obtain a critically dampedresponse with minimal voltage oscillation. The correspondingintegral time Ti = 1/a (13) and proportional gain Kp can becalculated as

ζ =

√38

Kpvs

√2Ti

Cdcv∗dc

(14)

ωn =

√32

Kpvs

√2

Cdcv∗dcTi

. (15)

TABLE ISPECIFICATION PARAMETERS

aNote: Vbase = 55 V and Sbase = 1 kVA.

V. SIMULATED RESULTS

A simulation model for the three-phase four-leg PWM con-verter with the parameters shown in Table I has been developedusing MATLAB-Simulink. The objective is to verify the currentharmonic compensation effectiveness of the proposed controlscheme under different operating conditions. A six-pulse rec-tifier was used as a nonlinear load. The proposed predictivecontrol algorithm was programmed using an S-function blockthat allows simulation of a discrete model that can be easily im-plemented in a real-time interface (RTI) on the dSPACE DS1103R&D control board. Simulations were performed considering a20 [μs] of sample time.

In the simulated results shown in Fig. 8, the active filter startsto compensate at t = t1 . At this time, the active power filter in-jects an output current iou to compensate current harmonic com-ponents, current unbalanced, and neutral current simultaneously.During compensation, the system currents is show sinusoidalwaveform, with low total harmonic distortion (THD = 3.93%).At t = t2 , a three-phase balanced load step change is generatedfrom 0.6 to 1.0 p.u. The compensated system currents remainsinusoidal despite the change in the load current magnitude. Fi-nally, at t = t3 , a single-phase load step change is introduced inphase u from 1.0 to 1.3 p.u., which is equivalent to an 11% cur-rent imbalance. As expected on the load side, a neutral currentflows through the neutral conductor (iLn ), but on the source side,no neutral current is observed (isn ). Simulated results show thatthe proposed control scheme effectively eliminates unbalancedcurrents. Additionally, Fig. 8 shows that the dc-voltage remainsstable throughout the whole active power filter operation.

VI. EXPERIMENTAL RESULTS

The compensation effectiveness of the active power filter iscorroborated in a 2 kVA experimental setup. A six-pulse rec-tifier was selected as a nonlinear load in order to verify the ef-fectiveness of the current harmonic compensation. A step loadchange was applied to evaluate the transient response of the dc-voltage loop. Finally, an unbalanced load was used to validatethe performance of the neutral current compensation. Becausethe experimental implementation was performed on a dSPACEI/O board, all I/O Simulink blocks used in the simulations are100% compatible with the dSPACE system capabilities. Thecomplete control loop is executed by the controller every 20 μs,while the selected switching state is available at 16 μs. An aver-age switching frequency of 4.64 kHz is obtained. Fig. 9 shows

692 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 2, FEBRUARY 2014

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Fig. 8. Simulated waveforms of the proposed control scheme. (a) Phase toneutral source voltage. (b) Load Current. (c) Active power filter output current.(d) Load neutral current. (e) System neutral current. (f) System currents. (g) DCvoltage converter.

the transient response of the compensation scheme. Fig. 9(a)shows that the line current becomes sinusoidal when the activepower filter starts compensation, and the dc-voltage behavesas expected. Experimental results shown in Fig. 9(b) indicatethat the total harmonic distortion of the line current (THDi) isreduced from 27.09% to 4.54%. This is a consequence of thegood tracking characteristic of the current references, as shownin Fig. 9(d). In Fig. 10, the transient response of the active powerfilter under a step load change is shown. The line currents remainsinusoidal and the dc-voltage returns to its reference with a typ-ical transient response of an underdamped second-order system(maximum overshoot of 5% and two cycles of settling time).In this case, a step load change is applied from 0.6 to 1.0 p.u.Finally, the load connected to phase u was increased from 1.0to 1.3 p.u. The corresponding waveforms are shown in Fig. 11.Fig. 11(a) shows that the active filter is able to compensate thecurrent in the neutral conductor with fast transient response.

Fig. 9. Experimental transient response after APF connection. (a) Load Cur-rent iLu , active power filter current iou , dc-voltage converter vdc , and systemcurrent isu . Associated frequency spectrum. (c) Voltage and system waveforms,vsu and isu , isv , isw . (d) Current reference signals i∗ou , and active power filtercurrent iou (tracking characteristic).

Moreover, Fig. 11(b) shows that the system neutral current ionis effectively compensated and eliminated, and system currentsremain balanced even if an 11% current imbalance is applied.

ACUNA et al.: IMPROVED ACTIVE POWER FILTER PERFORMANCE FOR RENEWABLE POWER GENERATION SYSTEMS 693

Fig. 10. Experimental results for step load change (0.6 to 1.0 p.u.). LoadCurrent iLu , active power filter current iou , system current isu , and dc-voltageconverter vdc .

Fig. 11. Experimental results for step unbalanced phase u load change (1.0to 1.3 p.u.). (a) Load Current iLu , load neutral current iLn , active powerfilter neutral current ion , and system neutral current isn . (b) System currentsisu , isv , isw , and isn .

VII. CONCLUSION

Improved dynamic current harmonics and a reactive powercompensation scheme for power distribution systems with gen-eration from renewable sources has been proposed to improvethe current quality of the distribution system. Advantages ofthe proposed scheme are related to its simplicity, modeling, andimplementation. The use of a predictive control algorithm forthe converter current loop proved to be an effective solutionfor active power filter applications, improving current tracking

capability, and transient response. Simulated and experimentalresults have proved that the proposed predictive control algo-rithm is a good alternative to classical linear control methods.The predictive current control algorithm is a stable and robustsolution. Simulated and experimental results have shown thecompensation effectiveness of the proposed active power filter.

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Pablo Acuna (M’12) received the B.S. degree and theGraduate degree in electronics engineering in 2004and 2007, respectively, from the University of Con-cepcion, Concepcion, Chile, where he is currentlyworking toward the Ph.D. degree.

His current research interests include the areas ofthree-phase ac/dc static-power converters, and activepower filters applications using field programmablegate arrays and microcontroller systems-on-a-chip.

Luis Moran (F’05) received the Ph.D. degree fromConcordia University, Montreal, QC, Canada, in1990.

Since 1990, he has been with the Departmentof Electrical Engineering University of Concepcion,Concepcion, where he is a Professor. He has writ-ten and published more than 30 papers in activepower filters and static Var compensators in IEEETransactions. His main areas of interests are in acdrives, power quality, active power filters, FACTS,and power protection systems.

Dr. Moran is the principal author of the paper that got the IEEE OutstandingPaper Award from the Industrial Electronics Society for the best paper pub-lished in the IEEE TRANSACTION ON INDUSTRIAL ELECTRONICS during 1995,and the coauthor of the paper that was awarded in 2002 by the IAS Static PowerConverter Committee.

Marco Rivera (S’09–M’11) received the B.Sc. de-gree in electronics engineering and M.Sc. degree inelectrical engineering from the Universidad de Con-cepcion, Chile, in 2007 and 2008, respectively andthe Ph.D. degree from the Department of Electron-ics Engineering, Universidad Tecnica Federico SantaMarıa, Valparaıso, Chile, in 2011, with a scholarshipfrom the Chilean Research Fund CONICYT.

During 2011 and 2012, he was at a Post Doctoralposition and as a part-time Professor of Digital SignalProcessors and Industrial Electronics at Universidad

Tecnica Federico Santa Marıa, and currently he is a Professor in Universidadde Talca, Chile. His research interests include matrix converters, predictiveand digital controls for high-power drives, four-leg converters, renewable en-ergies, and development of high performance control platforms based on field-programmable gate arrays.

Juan Dixon (M’90–SM’95) received the B.S. de-gree in electrical engineering from the Universidadde Chile, Santiago, Chile, in 1977, and the M.S.Eng.and Ph.D. degrees from McGill University, Montreal,QC, Canada, in 1986 and 1988, respectively.

In 1976, he was with the State TransportationCompany in charge of trolleybuses operation. In1977 and 1978, he was with the Chilean RailwaysCompany. Since 1979, he has been with the Depart-ment of Electrical Engineering, Pontificia Universi-dad Catolica de Chile, Santiago, where he is currently

a Professor. He has presented more than 70 works in international conferencesand has published more than 30 papers related with power electronics in IEEETransactions and IEE proceedings. His research interests include electric trac-tion, power converters, PWM rectifiers, active power filters, power-factor com-pensators, multilevel, and multistage converters. He has consulting work relatedwith trolleybuses, traction substations, machine drives, hybrid electric vehicles,and electric railways. He has created an electric vehicle laboratory where he hasbuilt state-of-the-art vehicles using brushless dc machines with ultracapacitorsand high specific-energy batteries.

Jose Rodriguez (M’81–SM’94–F’10) received theEngineering degree in electrical engineering fromthe Universidad Tecnica Federico Santa Marıa, inValparaıso, Chile, in 1977, and the Dr.-Ing. de-gree in electrical engineering from the University ofErlangen, Erlangen, Germany, in 1985.

He has been with the Department of Electron-ics Engineering, Universidad Tecnica Federico SantaMarıa, since 1977, where he is currently a Full Pro-fessor and Rector. He has coauthored more than 350journal and conference papers. His main research in-

terests include multilevel inverters, new converter topologies, control of powerconverters, and adjustable-speed drives.

Dr. Rodriguez is member of the Chilean Academy of Engineering.