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-leg voltage-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 unbalanced current generated by single-phase nonlinear loads. A detailed yet simple mathematical model of the active power filter, including the effect of the equivalent power system impedance, is derived and used to design the predictive control algorithm. The compensation performance of the proposed active power filter and the associ-ated control scheme under steady state and transient operating conditions is demonstrated through simulations and experimental results.

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.v

d c dc-voltage.v

s System voltage vector [vs u vs v vs w ]T .

is System current vector [is u is v is w ]T .iL Load current vector [iL u iL v iL w ]T .

vo VSI output voltage vector [vo u vo v vo w ]T .io VSI output current vector [io u io v io w ]T .

io∗ Reference current vector [io∗ u io∗ v io∗ w ]T .in Neutral current.Lf Filter inductance.R

f Filter resistance.

Manuscript received July 4, 2012; revised October 13, 2012 and December 27, 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 the Basal Project FB 0821, and in part by the CONICYT Initiation into Research 2012 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 de Talca, 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, Universidad Tecnica´ Federico Santa Mar´ıa, Valpara´ıso 1680, Chile (e-mail: jrp@usm.cl).

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

Digital Object Identifier 10.1109/TPEL.2013.2257854

I. INTRODUCTION

ENEWABLE generation affects power quality due to its

Rnonlinearity, since solar generation plants and wind power generators must be connected to the grid through high-power static PWM converters [1]. The nonuniform nature of power generation directly affects voltage regulation and creates volt-age distortion in power systems. This new scenario in power distribution systems will require more sophisticated compensa-tion techniques.

Although active power filters implemented with three-phase four-leg voltage-source inverters (4L-VSI) have already been presented in the technical literature [2]–[6], the primary contri-bution of this paper is a predictive control algorithm designed and 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 as for the dc-voltage loops [7], [8]. PI controllers must be de-signed based on the equivalent linear model, while predictive controllers use the nonlinear model, which is closer to real op-erating conditions. An accurate model obtained using predictive controllers improves the performance of the active power filter, especially during transient operating conditions, because it can quickly follow the current-reference signal while maintaining a constant 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, predictive control represents a very intuitive control scheme that han-dles multivariable characteristics, simplifies the treatment of dead-time compensations, and permits pulse-width modulator replacement. However, these kinds of applications present dis-advantages related to oscillations and instability created from unknown load parameters [15]. One advantage of the proposed algorithm is that it fits well in active power filter applica-tions, since the power converter output parameters are well known [17]. These output parameters are obtained from the converter output ripple filter and the power system equivalent impedance. The converter output ripple filter is part of the active power filter design and the power system impedance is obtained from well-known standard procedures [18], [19]. In the case of unknown system impedance parameters, an estimation method can be used to derive an accurate R–L equivalent impedance model of the system [20].

This paper presents the mathematical model of the 4L-VSI and the principles of operation of the proposed predictive control scheme, including the design procedure. The complete descrip-tion of the selected current reference generator implemented in 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. 3. Two-level four-leg PWM-VSI topology.Fig. 2. Three-phase equivalent circuit of the proposed shunt active power filter.

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

II. FOUR-LEG CONVERTER MODEL

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

The four-leg PWM converter topology is shown in Fig. 3. This converter topology is similar to the conventional three-phase converter with the fourth leg connected to the neutral bus of the system. The fourth leg increases switching states from 8 (23 ) to 16 (24 ), improving control flexibility and output voltage quality [21], and is suitable for current unbalanced compensation.

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

vx n = Sx − Sn vd c , x = u, v, w, n. (1)The mathematical model of the filter derived from the equiv-alent

circuit shown in Fig. 2 is

vo = vx n − Re q io − Le q

d io(2)dt

where Re q and Le q are the 4L-VSI output parameters expressed as Thevenin impedances at the converter output terminals Ze q . Therefore, the Thevenin equivalent impedance is determined by a series connection of the ripple filter impedance Zf and a parallel arrangement between the system equivalent impedance Zs and the load impedance ZL

Ze q =Zs ZL

+ Zf ≈ Zs + Zf . (3)Zs + ZLFor this model, it is assumed that ZL Zs , that the resistive part of the

system’s equivalent impedance is neglected, and that the series reactance is in the range of 3–7% p.u., which is an acceptable approximation of the real system. Finally, in (2)Re q = Rf and Le q = Ls + Lf .

III. DIGITAL PREDICTIVE CURRENT CONTROL

The block diagram of the proposed digital predictive current control 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 has to be developed using discrete mathematics in order to consider additional restrictions such as time delays and approximations

689

[k + 1] −

io w [k + 1])2

+ (i∗ [k + 1] i [k + 1])2 . (6)o n −

o n

The output current (io ) is equal to the reference (i∗o ) when g = 0. Therefore, the optimization goal of the cost function is to achieve a g value close to zero. The voltage vector vx N that minimizes the cost function is chosen and then applied at the next sampling state. During each sampling state, the switching state that generates the minimum value of g is selected from the 16 possible function values. The algorithm selects the switching state that produces this minimal value and applies it to the converter during the k + 1 state.

dx

≈

x[k + 1] − x

dt Ts

IV. CURRENT REFERENCE GENERATION

A dq-based current reference generator scheme is used to ob-tain the active power filter current reference signals. This scheme presents a fast and accurate signal tracking capability. This char-acteristic avoids voltage fluctuations that deteriorate the current reference signal affecting compensation performance [28]. The current reference signals are obtained from the corresponding load currents as shown in Fig. 5. This module calculates the ref-erence signal currents required by the converter to compensate reactive power, current harmonic, and current imbalance. The displacement power factor (sin φ(L

) ) and the maximum total harmonic distortion of the load (THD(L ) ) defines the relation-

(4) ships between the apparent power required by the active power filter, with respect to the load, as shown

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

io [k + 1] = Leq (vx n [k] − vo [k]) +T

s

(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

converter output voltage vx N , are required. The algorithm

calculates all 16 values

associated with the possible combinations that the

state variables can achieve.3) Cost Function Optimization:

In order to select the optimal switching state that must be applied to the power converter, the 16 predicted values obtained for io [k + 1] are compared with the reference using a cost function g, as follows:

g[k + 1] = (i∗o u [k

+ 1] −

[10], [22]–[27]. The main characteristic of predictive control is the use of the system model to predict the future behavior of the variables to be controlled. The controller uses this information to select the optimum switching state that will be applied to the power converter, according to predefined optimization criteria. The predictive control algorithm is easy to implement and to understand, 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 compensate the undesirable load current components. In this case, the sys-tem voltages, the load currents, and the dc-voltage converter are measured, while the neutral output current and neutral load current are generated directly from these signals (IV).

2) Prediction Model: The converter model is used to predict the output converter current. Since the controller operates in discrete time, both the controller and the system model must be represented in a discrete time domain [22]. The discrete time model consists of a recursive matrix equation that represents this prediction system. This means that for a given sampling time s , knowing the converter switching states and control variables at instant 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 that describe the model in (1)–(2), a sufficiently accurate first-order approximation of the derivative is considered in this paper

+ (i∗o

w

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

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

io u [k

+ 1])2

+ (i∗o v

[k + 1]

− io v

[k +

1])2

SA P F

=

sin φ(L ) + THD

SL 1 + THD(where the value of THD(L ) includes the maximum compensable harmonic current, defined as double the sampling frequency fs . The frequency of the maximum current harmonic component that can be compensated is equal to one half of the converter switching frequency.

The dq-based scheme operates in a rotating reference frame; therefore, the measured currents must be multiplied by the sin(wt) and cos(wt) signals. By using dq-transformation, the d current component is synchronized with the corresponding phase-to-neutral system voltage, and the q current component is phase-shifted by 90◦. The sin(wt) and cos(wt) synchronized reference signals are obtained from a synchronous reference frame (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 are designed 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 measurement errors [30]. Equation (8) shows the relationship between the real currents iL x (t) (x = u, v, w) and the associated dq components (id and iq )

11 1

− −iL ui

d 2 sin ωt cos ωt 2 2= iL v .

i q − cos ωt sin ωt √3 √33

−2 2 (8)Fig. 6. Relationship between permissible unbalance load currents, the cor-

A low-pass filter (LFP) extracts the dc component of the phase responding third-order harmonic content, and system current imbalance (with

currents id to generate the harmonic reference components −id . respect to positive sequence of the system current, is , 1 ).

The reactive reference components of the phase-currentsare

obtained by phase-shifting the corresponding ac and dc compo-nents of iq by 180◦. In order to keep the dc-voltage constant,

from the phase-currents, phase-shifted by 180◦, as shown nextthe amplitude of the converter reference current must be mod-ified by adding an active power reference signal ie with the

d-component, as will be explained in Section IV-A. The re- i∗ =−

(i + i + i ) . (10)sulting signals id∗ and iq∗ are transformed back to a three-phase o n L u L v L w

system by applying the inverse Park and Clark transformation,as shown in (9). The cutoff frequency of the LPF used in this

One of the major advantages of the dq-based current refer-paper is 20 Hzence generator scheme is that it allows the implementation of

11 0

a linear controller in the dc-voltage control loop. However, one

√ important disadvantage of the dq-based current reference frame2

io∗ u = 1 1 √algorithm used to generate the current reference is that a second-

2 3 order harmonic component is generated in id and iq under un-i∗

o v balanced operating conditions. The amplitude of this harmonic√ − 2 23io∗w

2de pends on the percent of unbal anced load current (expressed as

√1 1 the relationship between the negative sequence current iL ,2 and3

√ − −2 2 the positive sequence current iL ,1 ). The second-order harmonic2

1 0 0 i0cannot be removed from id and iq , and therefore generates athird harmonic in the reference current when it is converted

×0 sin ωt cos ωt i∗ . (9) back to abc frame [31]. Fig. 6 shows the percent of system cur-−

sin ωtd

0 cos ωt i rent imbalance and the percent of third harmonic system current,q∗ in function of the percent of load current imbalance. Since the

The current that flows through the neutral of the load is com- load current does not have a third harmonic, the one generatedpensated by injecting the same instantaneous value obtained by the active power filter flows to the power system.

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

TABLE ISPECIFICATION PARAMETERS

Fig. 7. DC-voltage control block diagram.

A. DC-Voltage ControlThe dc-voltage converter is controlled with a traditional PI

controller. This is an important issue in the evaluation, since

the cost function (6) is designed using only current references, aNote: Vbase = 55 V and Sbase = 1 kVA.

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. V. SIMULATED RESULTSAdditionally, the slow dynamic response of the voltage across

A simulation model for the three-phase four-leg PWM con-the electrolytic capacitor does not affect the current transientverter with the parameters shown in Table I has been developedresponse. For this reason, the PI controller represents a simpleusing MATLAB-Simulink. The objective is to verify the currentand effective alternative for the dc-voltage control.

harmonic compensation effectiveness of the proposed control√

The dc-voltage remains constant (with a minimum value ofscheme under different operating conditions. A six-pulse rec-6 vs(rm s) ) until the active power absorbed by the converter

decreases to a level where it is unable to compensate for its tifier was used as a nonlinear load. The proposed predictive

control algorithm was programmed using an S-function blocklosses. The active power absorbed by the converter is controlledthat allows simulation of a discrete model that can be easily im-by adjusting the amplitude of the active power reference signal

plemented in a real-time interface (RTI) on the dSPACE DS1103ie , which is in phase with each phase voltage. In the blockR&D control board. Simulations were performed considering adiagram shown in Fig. 5, the dc-voltage vd c is measured and

20 [μs] of sample time.then compared with a constant reference value vd∗ c . The error

(e) is processed by a PI controller, with two gains, Kp and Ti . In the simulated results shown in Fig. 8, the active filter starts

to compensate at t = t1 . At this time, the active power filter in-Both gains are calculated according to the dynamic responserequirement. Fig. 7 shows that the output of the PI controller is jects an output current io u to compensate current harmonic com-

fed to the dc-voltage transfer function Gs , which is represented ponents, current unbalanced, and neutral current simultaneously.

During compensation, the system currents is show sinusoidalby a first-order system (11)waveform, with low total harmonic distortion (THD = 3.93%).

√ At t = t2 , a three-phase balanced load step change is generated

G (s) =

vd c

=3 Kp vs 2

. (11)from 0.6 to 1.0 p.u. The compensated system currents remain

ie 2 Cd c v∗ sinusoidal despite the change in the load current magnitude. Fi-d c nally, at t = t3 , a single-phase load step change is introduced in

The equivalent closed-loop transfer function of the given sys- phase u from 1.0 to 1.3 p.u., which is equivalent to an 11% cur-tem with a PI controller (12) is shown in (13) rent imbalance. As expected on the load side, a neutral current

flows through the neutral conductor (iL n ), but on the source side,

C(s) = Kp 1 + 1no neutral current is observed (is n ). Simulated results show that

(12) the proposed control scheme effectively eliminates unbalancedT s

i · currents. Additionally, Fig. 8 shows that the dc-voltage remains

2 stable throughout the whole active power filter operation.vd c =

ω n · (s + a)a . (13)

ie s2 + 2ζ ωn · s + ωn2 VI. EXPERIMENTAL RESULTS

Since the time response of the dc-voltage control loop does The compensation effectiveness of the active power filter isnot need to be fast, a damping factor ζ = 1 and a natural angular corroborated in a 2 kVA experimental setup. A six-pulse rec-speed ωn = 2π · 100 rad/s are used to obtain a critically damped tifier was selected as a nonlinear load in order to verify the ef-response with minimal voltage oscillation. The corresponding fectiveness of the current harmonic compensation. A step loadintegral time Ti = 1/a (13) and proportional gain Kp can be change was applied to evaluate the transient response of the dc-calculated as voltage loop. Finally, an unbalanced load was used to validate

the performance of the neutral current compensation. Becausethe experimental implementation was performed on a dSPACE

3 Kp vs √2Tiζ = (14) I/O board, all I/O Simulink blocks used in the simulations are

8 Cd c v∗ 100% compatible with the dSPACE system capabilities. Thed c

complete control loop is executed by the controller every 20 μs,

3 Kp vs √

.ωn = 2 (15) while the selected switching state is available at 16 μs. An aver-

2 Cd c vd∗ c Ti age switching frequency of 4.64 kHz is obtained. Fig. 9 shows

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

Fig. 8. Simulation results: (a) Grid voltages, (b) Grid Currents (c) Unbalanced load currents, (d) Inverter Currents.

the transient response of the compensation scheme. Fig. 9(a) shows that the line current becomes sinusoidal when the active power filter starts compensation, and the dc-voltage behaves as expected. Experimental results shown in Fig. 9(b) indicate that the total harmonic distortion of the line current (THDi ) is reduced from 27.09% to 4.54%. This is a consequence of the good tracking characteristic of the current references, as shown in Fig. 9(d). In Fig. 10, the transient response of the active power filter under a step load change is shown. The line currents remain sinusoidal 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 1.0 to 1.3 p.u. The corresponding waveforms are shown in Fig. 11. Fig. 11(a) shows that the active filter is able to compensate the current in the neutral conductor with fast transient response.

Fig. 9. Experimental transient response after APF connection. (a) Load Cur-rent iL u , active

power filter current io u , dc-voltage converter vd c , and system current is u . Associated

frequency spectrum. (c) Voltage and system waveforms, vs u and i s u , is v , is w . (d) Current

reference signals i∗o u , and active power filter current io u (tracking characteristic).

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

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

Fig. 10. Experimental results for step load change (0.6 to 1.0 p.u.). Load Current iL u , active power filter current io u , system current is u , and dc-voltage converter vd c .

Fig. 11. Experimental results for step unbalanced phase u load change (1.0 to 1.3 p.u.). (a) Load Current iL u , load neutral current iL n , active power filter neutral current io n , and system neutral current is n . (b) System currents is u , is v , is w , and is n .

VII. CONCLUSION

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

capability, and transient response. Simulated and experimental results 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 robust solution. Simulated and experimental results have shown the compensation effectiveness of the proposed active power filter.

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

His current research interests include the areas of three-phase ac/dc static-power converters, and active power filters applications using field programmable gate arrays and microcontroller systems-on-a-chip.

Luis Moran´ (F’05) received the Ph.D. degree from Concordia University, Montreal, QC, Canada, in 1990.

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

Dr. Moran´ is the principal author of the paper that got the IEEE Outstanding Paper 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 Power Converter Committee.

Marco Rivera (S’09–M’11) received the B.Sc. de-gree in electronics engineering and M.Sc. degree in electrical engineering from the Universidad de Con-cepcion,´ Chile, in 2007 and 2008, respectively and the Ph.D. degree from the Department of Electron-ics Engineering, Universidad Tecnica´ Federico Santa Mar´ıa, Valpara´ıso, Chile, in 2011, with a scholarship from the Chilean Research Fund CONICYT.

During 2011 and 2012, he was at a Post Doctoral position and as a part-time Professor of Digital Signal Processors and Industrial Electronics at Universidad

Tecnica´ Federico Santa Mar´ıa, and currently he is a Professor in Universidad de Talca, Chile. His research interests include matrix converters, predictive and 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 Universidad de 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 Transportation Company in charge of trolleybuses operation. In 1977 and 1978, he was with the Chilean Railways Company. 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 conferences and has published more than 30 papers related with power electronics in IEEE Transactions 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 related with trolleybuses, traction substations, machine drives, hybrid electric vehicles, and electric railways. He has created an electric vehicle laboratory where he has built state-of-the-art vehicles using brushless dc machines with ultracapacitors and high specific-energy batteries.

Jose´ Rodriguez (M’81–SM’94–F’10) received the Engineering degree in electrical engineering from the Universidad Tecnica´ Federico Santa Mar´ıa, in Valpara´ıso, Chile, in 1977, and the Dr.-Ing. de-gree in electrical engineering from the University of Erlangen, Erlangen, Germany, in 1985.

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

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

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