simulation Paper 7

IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 3, AUGUST 2002 253

Teaching Nonlinear Modeling, Simulation, andControl of Electronic Power Converters Using

MATLAB/SIMULINKVitor Fernão Pires, Member, IEEE,and José Fernando A. Silva, Senior Member, IEEE

Abstract—This paper describes an efficient method to teachanalysis and simulation of power electronic converters to un-dergraduate students, using system level nonlinear state-spacemodels. System-level modeling of power electronic converters re-produces only the ideal switching behavior of the semiconductorsand is a useful concept for the numerical simulation of power con-verters, since simulations present no convergence problems andrequire little computational time. Switched state-space models,programmed in the MATLAB/SIMULINK software package,can be advantageously used to simulate power converters atthe system level and also to design and study their controllers.Switched state-space nonlinear models should be obtained usinga theoretical framework suitable for the enhanced control ofvariable structure power systems. Since the method is inherentlynonlinear, no approximated linear models are needed; and sincestate-space models are used, modern control techniques (slidingmode, neural networks, fuzzy logic) for power converters caneasily be used. This paper summarizes the proposed methodologyand gives some examples.

Index Terms—Electronic power converters, power convertercontrol, power converter modeling, power converter simulation.

I. INTRODUCTION

COMPUTER simulation plays an important role in the de-sign, analysis, and evaluation of power electronic con-

verters and their controllers. Designing and developing powerelectronic circuits without suitable computer simulation is ex-tremely laborious, error-prone, time-consuming, and expensive.Therefore, it is essential to teach, at the undergraduate level,power converter modeling and simulation, together with the dy-namic behavior of the converter, using a theoretical frameworksuited for controller design and development.

Nowadays, a variety of software tools, such as SPICE [1]–[3],EMTP [4], SABER [5], CASPOC [6], SIMPLORER [7], [8],SPECTRE [9], etc., is available to simulate electrical and elec-tronic circuits. The most used simulators are SPICE or PSPICE[10], [11], user-friendly programs designed to perform analysisof low power analog electronic circuits.

Several power electronics professors [12]–[14] have usedSPICE to simulate the behavior of power electronics converters.

Manuscript received July 23, 2001; revised February 11, 2002.V. F. Pires is with Centro de Automática Universidade Técnica de Lisboa,

Escola Superior Tecnologia Setúbal, Inst. Politécnico de Setúbal, Setúbal2914-508, Portugal (e-mail: [email protected]).

J. F. A. Silva is with Centro de Automática Universidade Técnica de Lisboa,Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa Codex1096, Portugal.

Publisher Item Identifier S 0018-9359(02)05061-6.

SPICE simulation has, therefore, become a part of severalpower electronics courses. SPICE is fitted with physical modelsof semiconductors and switching devices. Physical modelingproduces well-detailed results, but leads to high calculation ef-fort and often introduces convergence problems during transientsimulation (SPICE has 86% success rate [15]). To overcomethese convergence problems, the power semiconductors areusually fitted with suitably designed snubbers. Students andteachers [13], [14], [16] are, therefore, committed to solvingthe convergence problems and to reducing the computing timeand memory needed, both time consuming tasks.

With suitable snubber circuits and device values, SPICEis able to perform the time-domain, steady-state behaviorand transient analysis needed to study most power electroniccircuits. However, some built-in capabilities of SPICE, suchas dc operating point and small signal ac frequency analysis,are not usable for power converters. SPICE ac frequencyanalysis does not provide the dynamic transfer functions ofpower converters, because of the switching operation of thepower semiconductors. Therefore, two simulation packages areoften needed [17]. Furthermore, because of the huge amountof memory and CPU time required to converge problems,SPICE cannot easily handle the usually long, transient analysisbehavior of complex switching converter topologies [17], [18].Since most physical details are not needed in the study of powerelectronics, some well-known authors [18] have used macromodels of the semiconductor switching devices to improveconvergence and increase simulation speed.

The authors have been using SPICE as an instructional toolto teach power converters at an introductory level. The successrate in examinations shows that student ability to understand thebehavior of several power electronics converters have been in-creased. Despite this success, the continual use of SPICE simu-lations leads to a loss of student commitment and ability to dothe mathematical modeling needed for more advanced courses,such as control of power converters. Students concentrate onthe skills needed to obtain convergence of the solutions withclosed-loop control and tend to use only well established con-verter controllers. They often use trial and error methods to de-sign high-performance controllers for power converters. There-fore, undergraduate students should also learn some nonlinearmathematical modeling and converter control. Additionally, stu-dents should take advantage of the mathematical models theyhave derived to perform the simulation of the power electronicconverters with closed-loop control.

0018-9359/02$17.00 © 2002 IEEE

254 IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 3, AUGUST 2002

To reach this goal, students should be able to analyze powersemiconductor circuits using classic network theory withoutgoing through complicated mathematics. The derived modelsshould be suitable for implementing a computer simulation ofthe power converter. This accomplishment can be a powerfulmotivation for the somewhat tedious mathematical modelingwork, because students tend to prefer the automatic use ofthe computer, encouraged by its well-known relevance as apowerful tool for research and development.

“MATLAB/SIMULINK” software [19] is widely used for thesimulation of almost all types of dynamic systems. This soft-ware package is also valuable for teaching and learning since itprovides a series of standard routines and software toolboxes,such as a control toolbox, system identification blocks, non-linear control design block set, and neural networks block set,which enable students to perform system simulation, identifica-tion, and control.

The latest versions of MATLAB/SIMULINK include a“Power System Blockset” [20]. This toolbox features electricalmodels of power semiconductors and the most commonly usedpower devices (machines, transformers, power lines, voltagesources), and allows simulation of power systems and powerelectronics. This package is valuable for simulating well-knowntopologies several of which are included as demonstrations,but it tends to generate too many algebraic loops on morecomplex or novel power topologies. These algebraic loops aredifficult to handle (because they are inherent to the modelingmethod) and are time consuming, often preventing simulationconvergence. Furthermore, this toolbox does not easily allowopen-loop or closed-loop simulation of series associations ofpower rectifiers, nor does it study the steady and the tran-sient-states in cases of unbalanced or distorted and/or pollutedpower supply. Considering the approach of [18] with PSPICEand SIMPLORER, the authors think that a system-level sim-ulation, considering only the ideal switching and functionalbehavior of power semiconductors, would be desirable forMATLAB/SIMULINK. The system-level simulation is fastenough and free of algebraic loops and convergence problems(SIMULINK has built-in integration methods suited to dealwith stiff systems). Therefore, it could avoid the problems ofthe “Power System Blockset” mentioned above. Additionally,the system-level derived models to implement in SIMULINKcan be used for closed-loop controller design, since they areswitched state-space models. This advantage is lost when usingthe “Power System Blockset” or “SIMPLORER.”

Considering the increasing capabilities of“MATLAB/SIMULINK” for the simulation of dynamicsystems [21], it is advantageous to adapt the ideal models ofsemiconductors and simulation methods presented here forthis software since only one software package is needed. Thesimulation time is short (a few seconds); an excellent graphicalinterface is available with parametric identification of thesystem and the ability to choose the numerical integrationmethod and toolboxes for closed-loop control. In addition,the SIMULINK package offers the benefits of a hierarchicalstructure and uses “MATLAB” as its mathematical engine.If required, the modeling method here proposed could beadapted to other programs. Since the goal is to teach nonlinear

mathematical modeling and control and the simulation ofpower converters, this paper shows, in Section II, how towrite system-level models of power electronics circuits. InSection III, examples of pulse width modulation (PWM) ac/dcand dc/ac power electronic converters are given.

The simulation models described are quite suitable to studypower electronics converters in drives or other applicationswhose simulation times are not too long, since only the idealbehavior of the power switches is considered.

This work was initially developed for research in the area ofnew topologies for power electronics. However, further develop-ments allowed its use as a valuable teaching aid. Therefore, thiswork presents a new way to teach undergraduate students thedynamic behavior of power electronics circuits without cuttingdown the analytic skills needed to learn and synthesize powerconverter controllers. The new method can also be used as veri-fication of analytical methods, allowing students to check theirmathematical work quickly and use it for power converter be-havior and controller development.

II. M ODELING PROCEDURE

To obtain a nonlinear model easily for power electroniccircuits, students need only to apply Kirchhoff’s circuit laws.To avoid the use of complex mathematics, the electrical andsemiconductor devices must be represented as ideal compo-nents (zero ON voltages, zero OFF currents, zero switchingtimes). Therefore, auxiliary binary variables can be usedto determine the state of the switches. Then, students mustensure that the equations obtained by the use of Kirchhoff’slaws should include all the permissible states due to powersemiconductor devices being ON or OFF.

The steps to obtain a system-level modeling and simulation ofpower electronic converters are listed below. The two last stepsobtain the controller(s) and perform closed-loop simulations.

1) Determine the state variables of the power circuit in orderto write its switched state-space model [22].

2) Assign integer variables to the power semiconductor (orto each switching cell) ON and OFF states (generally, ifthe circuit includes power switches, it needs 2topolo-gies minus those forbidden by topological restrictions).

3) Determine the conditions governing the states of thepower semiconductors or the switching cell.

4) Assume the main operating modes of the converter(continuous or discontinuous conduction or both) or themodes needed to describe all the possible circuit opera-tional modes. Then, apply Kirchhoff’s laws and combineall the required stages into a switched state-space model,which is the desired system-level model.

5) Write this model in the integral form, or transform the dif-ferential form to include the semiconductors logical vari-ables in the control vector: the converter will be repre-sented by a set of nonlinear differential equations.

6) Implement the derived equations with “SIMULINK”blocks (open-loop system simulation is then possible tocheck the obtained model).

7) Use the obtained switched space-state model to designlinear or nonlinear controllers for the power converter.

PIRES AND SILVA: TEACHING NONLINEAR MODELING, SIMULATION, AND CONTROL OF ELECTRONIC POWER CONVERTERS 255

Fig. 1. Buck dc/dc regulator (first quadrant chopper).

8) Perform closed-loop simulations and evaluate converterperformance.

III. EXAMPLES

A. Buck DC/DC Regulator

Consider the buck regulator of Fig. 1. Students should be ableto preview the continuous and discontinuous conduction modesof operation. Using the procedure outlined in Section II, themodeling steps are the following.

Step1) The state variables of the Fig. 1 chopper areand.

Step2) The states of the power switch can be representedby a switching variable defined as

if is driven ON ANDif is OFF.

(1)

Step3) To model operation in the continuous and discontin-uous conduction modes, the states of the power diode

can be described by the binary variable

if ANDif AND . (2)

Therefore, the voltage (Fig. 1) is

(3)

Step4) Applying Kirchhoff’s laws to Fig. 1, students canwrite

(4)

and

(5)

Step5) For a resistor load , the inductor current andoutput voltage can be obtained by integrating (4) and(5) over time

(6)

and

(7)

Step6) Using “MATLAB/SIMULINK,” the subsystem de-scribing the behavior of the current (6) and voltage

(a)

(b)

Fig. 2. (a) Block diagram to model thei current,v andv voltagesof the circuit of Fig. 1; (b) Block diagram showing the control method, theconverter load and output devices.

(7) is shown in Fig. 5(a). The voltage and areobtained using respectively (3) and (1).

Step7) A simple control method [Fig. 2(b)] is used to set theinput current. The power switch is driven on by theclock signal (clocked turn-on) and driven off when the

current exceeds a defined value (peak-currentturn-off). This defined value is a step from 3 A to9 A at 0.4 ms.

Step8) The algorithm for solving the differential equationsand the step size should be chosen before runningany simulation. This example considers a 10-kHzswitching frequency and 100 time steps per period.The Runge–Kutta 4–5 algorithm, with a step size of10 s, has been selected. Simulations of the dc/dc Buckconverter were made using 5 , 0, 2 mH,

0, 5 mF, 50 V, 15 V, 0A.

Students can easily change the component values and verifywhat happens to the voltages and currents. Fig. 3(a) shows the

current, which has a step from 3 A to 9 A at 0.4 ms, thecurrent and the Clk clock pulses. Fig. 3(b) shows the

and voltages. From 0 to 0.4 ms operation is in thediscontinuous conduction mode, and equals when the

current is zero. From 0.4 ms to 1 ms operationis in the continuous conduction mode, and is zero whenswitch Q1 is off. The converter simulations and graphics displaytook only 10 s on a 166-MHz Pentium.

B. AC/DC Single Phase Converter

Single-phase pulse-width modulated (PWM) voltage-sourced, switch-mode rectifiers (Fig. 4) are used in industrialapplications, such as uninterruptible power supply (UPS)systems and ac/dc power supplies for telecommunicationsequipment. They are capable of bidirectional power flow,operation with near unity power factor, and input current with


(a)

(b)

Fig. 3. Main waveforms of the buck converter; (a)i andi currents andthe Clk clock pulses; (b) thev andv voltages.

Fig. 4. Single-phase voltage source switch-mode rectifier.

low harmonic content, and they can behave as power factorpreregulators. Therefore, it is important for most students ofelectrical engineering to study the behavior of these powerconverters alone or with their controllers.

Using the procedure outlined in Section II, the modeling stepsare:

Step1) The state variables of the rectifier of Fig. 4 are chosento be and .

Step2) To avoid shorting the output capacitor (and de-stroying the power semiconductors), the two switchesof each bridge leg must be in complementary states(topological restriction). Therefore, the semiconductorsare grouped into two switching cells, whose states

can be represented by the switching variables,( ) defined as

if OR is ON ANDAND are OFF

AND are OFF ANDOR is ON.

(8)

Step3) Students should note that the diodes impose 0.Therefore, the conditions governing the states of thepower semiconductors considered in (8), are related toswitch drive signals and to diode bias voltages and cur-rents. Therefore, according to (8)

if is driven ON AND is driven OFF

OR if OR then

and

if is driven OFF AND is driven ON

OR if then (9)

Step4) Applying Kirchhoff’s laws to Fig. 4, students caneasily write

(10)

and

(11)

and

(12)

where the switching function is given by (13). Thisdefinition assumes continuous conduction mode in theboost mode, and two-level operation, typical of voltagesource PWM reversible rectifiers

if ANDif AND .

(13)

Considering the voltage (11) and current (12),again applying Kirchhoff’s laws, students can easily ob-tain the switched, state-space equations of the PWM rec-tifier

(14)

and

(15)

Step5) For a resistor load , the converter input currentand output voltage can be obtained by integrating(14) and (15)

(16)

and

(17)

Step6) Using “MATLAB/SIMULINK,” the subsystem de-scribing the behavior of the boost inductor current (16) isshown in detail in Fig. 5. This subsystem “Single-Phase


Fig. 5. Block diagram describing the behavior of the input current of the singlephase ac/dc converter.

Fig. 6. Block diagram for the model of the circuit of Fig. 4.

ac/dc Converter, with the inductor (, ) in the sourceline” is then included in the implementation of equation(17) as shown in Fig. 6. The bounded integrator ensures apositive . The figure also presents a closed-loop con-troller for the input current ( ) (“current controller”),which is explained in the next step.

Step7) Sliding mode [23], [24] is used to control the inputcurrent . Equation (14), written in the controllabilitycanonical form, shows the first order dependence ofon the switching function . Therefore, a sliding surface

, able to enforce the control goal andalso provide robustness and system-order reduction, is

(18)

Using sliding mode stability ( ) and alsoconsidering (18) (14), the control law (19) is derived. It definesthe switching function to obtain , which isa sinusoidal wave in phase with the input voltage. This actionachieves a near unity power factor. As power switches (e.g.,MOS power transistors, or insulated gate bipolar transistors)present upper bounds for their switching frequency, a positiveconstant and the current ripple 2 are designed to achieveswitching frequencies suitable for the power semiconductorsused

S1 S4 are driven ON

and S2 S3 are driven OFFand

S2 S3 are driven ON

and S1S4 are driven OFF (19)

The approach considered here is similar to current mode con-trol, but a PWM modulator is not needed. The semiconductorsare driven ON or OFF just when needed at variable switchingfrequency.

Fig. 7. Block diagram of the input current controller.

(a)

(b)

Fig. 8. (a): Reference for the input current (i ). (b) Input current (i ) andscaled input voltage (V =15).

The “current controller” subsystem (Fig. 7) outputs theswitching function . The block “product” generates thesinusoidal reference . A step is used to change the phaseof this reference [Fig. 8(a)], enabling power factors close to 1before the step and close to1 (for inverter operation) after thestep. Block “sum_3” implements (18), and block “” togetherwith “Relay3” (with hysteresis width 2 ) implement (19).

The derived input current controller is encased in the rec-tifier model (Fig. 6). The use of subsystems is encouraged, en-abling alternative controller testing by simple replacement of theexisting controller with a new block, whose output must be theswitching variable . The study of the rectifier with three-leveloperation is possible just by allowing 1 0 1 .

Step8) Simulations will allow students to verify that this con-troller draws input current with sinusoidal shape, alsopresenting near unity power factor. Operation in the in-verter mode is also studied. Prior to running the simula-


tions, the algorithm for solving the differential equationsand the step size must be chosen. For this example, con-sidering switching frequencies around 5 kHz and about20 time steps per period, the Dormand–Prince (ode5) al-gorithm, with a step size of 10 s, has been selected.Simulations of the single-phase ac/dc converter weremade using 100 , 10 000 F, 10mH, 0.01 , 220 V, 0 220 Vand 0 0 A.

Students can easily change the component values and verifywhat happens to the voltages and currents. Fig. 8(a) shows the

, which is designed to be in phase with the input voltage(50-Hz sinusoid) during the first 30 ms, but to be in oppositephase during the next 30 ms. This situation allows testing thecurrent controller, as the rectifier operates in the rectifier regionand then in the inverter region, if the current controller is fastenough. Fig. 8(b) confirms that the controller performs with therequired speed as the input current follows the reference, exceptfor the unavoidable ripple. The rectifier input current is almostsinusoidal in shape and is in phase, or is 180out of phase,with the voltage source, providing power factors close to 1 or

1, respectively [Fig. 8(b)]. Students can note the rectifier orinverter operation at unity power factor and can easily confirmthese results in laboratory classes. The converter simulationsand graphics display took 12 s on a 166-MHz Pentium, whichis fast enough to be used in teaching classes. Recent computers,running at 1 GHz or more, can cut down this time by at least afactor of 5.

Proposed Exercises:

I) Use a sinusoidal PWM modulator with a triangular car-rier to perform open-loop simulations. Design an av-erage current mode controller and compare the perfor-mance obtained with that presented in Fig. 8(b).

II) Derive a three-level control by rewriting equation(13). Use two “relay” blocks (Fig. 7) to implementthe new equation. Repeat simulations and compareperformance.

C. AC/DC Three-Phase Converter

Three-phase PWM voltage-source converters (Fig. 9) aresuited to high power industrial applications and capable ofbidirectional power flow, near unity power factor operation.They can behave as power factor compensators, and the ACcurrents can be almost sinusoidal waveforms with low har-monic content. The converter model can be obtained using theconcepts already presented in the previous example.

Step 1) Consider the AC currents and DC voltage(Fig. 9) as the state variables.

Step 2), 3) The switching function, which representsthe states of the switches, can be defined according to (20).This definition prevents internal shorts in the voltage sourceswitch-mode converter, ensuring that the two switches of eachbridge leg are always in complementary states (topologicalrestriction)

if is ON or is ONif is ON or

is ON(20)

Fig. 9. Three-phase voltage source switch-mode converter.

Step 4) Students can verify that, from Kirchhoff’s laws, thispower converter can be described by the following state-spaceequations ( 1 2 3):

(21a)

(21b)

with

(22)

where the voltages are functions of the output voltage (),and the state of the switches (variable), according to (23)

(23)

Now applying steps 5) through 6), the SIMULINK block di-agram is obtained (Fig. 10). The block diagram includes theAC current controller and two input voltages (only two of thethree-phase variables are independent in this three-wire con-verter).

Step 7) To obtain sinusoidal ac currents, a sliding modecontroller can be used. For simplicity, one switching function

for each converter leg should be defined according to (24),as in (19)

ifif

(24)Simulations were made using 100 , 10 000

F, 10 mH, 0.01 , and 220 V, withintegration settings and initial conditions similar to those of theprevious example. Again, the ac current reference [Fig. 11(a)]is designed to show rectifier and inverter operation (converterreversibility). Students can verify that ac currents track the ref-erence [Fig. 11(b)], and are in phase, or 180out of phase, rela-tive to the corresponding input voltage [Fig. 11(b)]. Power fac-tors close to 1 or 1 are achieved. It is also verified that thepower flows [Fig. 11(c) and (d)] to the ac source voltages, when


Fig. 10. Block diagram for the model of the three-phase ac/dc converter.

Fig. 11. (a) Reference waveform for the ac currenti . For t � 0.05 s the converter will operate in the inverter mode. (b) Currenti and voltage sourceV =15. (c) Three-phase ac currents showing the transition from rectifier to inverter att = 0.05 s. (d) Output voltageV , showing that, in the inverter mode(t � 0.05 s), the capacitor is delivering energy to the three-phase ac system. (e) Converter leg voltageu . (f) Line-to-line output voltageV .

the current reference is reversed, since the capacitor voltage de-creases. The simulation time was about 35 s using a 166-MHzPentium, which is fast enough for the classroom.

These examples highlight a simple method to integrate theteaching of power converter modeling, simulation, and control.More exercises can be proposed to derive other controllers.Changing the controller is straightforward: replace the con-troller block with the new design, provided that it outputs 1 or 0to drive the switches “ON” or “OFF.” For instance, a sinusoidalPWM modulator can be used to control the output voltage, andthe capacitor value can be increased to store enough energyto allow almost constant dc voltage supply in the invertermode. Then, for a dc voltage of 400 V the converter leg

voltage is plotted in Fig. 11(e) and the line-to-line voltage, is shown in Fig. 11(f). The presence of two

and three voltage levels in these voltages is clearly illustrated.Validation of the simulations in the laboratory is a very im-

portant step since it enables students to gain or enhance insightin the simulation method and, above all, it increases experiencein handling the problems of real power converters.

Proposed Exercises:

III) Repeat exercise I) of the previous example for thisconverter. Compare the result with that presented inFigs. 11(e) and 8(f).

IV) Evaluate the ac current ripple and compare it with thedesign value. Explain the differences.


Fig. 12. Association of two three-phase converters connected back to back.

Fig. 13. SIMULINK block diagram for the association of two three-phase converters connected back to back.

V) Design a space vector current controller, applying theConcordia transformation to the ac currents and plot-ting the converter leg voltages in the plane. Eval-uate and compare the obtained current ripple.

D. Extension to Associations of Electronic Power Converters

One of the main areas of power electronics is the study of con-verters to supply ac machines from the mains. Two three-phaseconverters connected back-to-back (Fig. 12) enable operationat variable torque and/or speed and unity power factor. This as-sociation is advantageous since, removing the high frequencyac current harmonics, the mains seems to supply a pure resistor.This scheme can be also used in UPS. For these applications, theline-side converter operates in rectifier mode (ac/dc converter),while the load-side converter operates in inverter mode (dc/acconverter), supplied by the dc link capacitor voltage.

Fig. 13 shows the block diagram used in the“MATLAB/SIMULINK” program to simulate the circuitpresented in Fig. 12. In this example both converters featurecurrent controllers. Fig. 14 shows the output currents of thedc/ac converter. Students can then be encouraged to designthe dc voltage controller and ac output voltages, as well astorque and speed controllers.

Fig. 14. Three-phase output currents of the dc/ac converter.

IV. CONCLUSION

This paper has outlined and illustrated a method to obtainnonlinear, switched, state-space models of power converters,suited for simulation and control design. As the methodologyuses state-space models, electronic power converters, asso-ciations of power converters, and electromechanical devicesor drives, with elaborate control systems, can be effectivelysimulated. Associations of electromechanical systems and/orelectronic power converters, which are often complex anddifficult to analyze and to converge, due to stiffness, canalso be studied. Simulation times are a few tens of seconds,


and no convergence problems were found. The somewhattedious work needed to obtain the switched, state-space modelof the converter, which is a theoretical frame necessary forcontroller design, can be advantageously used to performthe simulation. Therefore, this methodology is an effectivetool to teach undergraduate students to simulate electronicpower converters dynamics and their control design. Usingthe “MATLAB/SIMULINK” software package, students orpower converter control engineers are provided with a powerfulsimulation and control tool for power converters. Several ac/dcand dc/ac converters have been successfully simulated. Theexamples given illustrate the considerable potential of thepresented techniques as teaching aids.

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Vitor Fernão Pires (M’96) received the B.S. degreein electrical engineering from Institute Superiorof Engineering, Lisbon, Portugal, and the M.S.and Ph.D. degrees in electrical and computer engi-neering from Technical University of Lisbon (UTL),Portugal, in 1988, 1995, and 2000, respectively.

Since 1991, he has been a member of the teachingstaff at Electrical Engineering Department, SuperiorTechnical School of Setúbal—Polytechnic Instituteof Setúbal, Setúbal, Portugal. Currently, he is aProfessor, teaching power electronics and control

of power converters. He is also a Researcher at Centro de Automática, UTL.His present research interests include the areas of low-distortion rectifiertopologies, converter control, modeling, and simulation.

José Fernando A. Silva (M’91–SM’00) born inMonção Portugal in 1956, received the Dipl.Ing. inelectrical engineering and the Ph.D. degree in elec-trical and computer engineering (power electronicsand control), from Institute Superior of Engineering(IST), Technical University of Lisbon (UTL),Lisbon, Portugal, in 1980 and 1990, respectively.

He is currently an Associate Professor of PowerElectronics at IST, teaching power electronics andcontrol of power converters and a Researcher atCentro de Automática, UTL. His main research

interests include power semiconductor devices, modeling and simulation, newconverter topologies, and sliding mode control of power converters. He hasauthored or coauthored one book, one book chapter, and over one hundredpapers.

Documents

simulation Paper 7