modeling and analysis of static and dynamic...

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 2, MARCH 1998 323

Modeling and Analysis of Static and DynamicCharacteristics for Buck-Type Three-Phase PWM

Rectifier by Circuit DQ TransformationSoo-Bin Han,Member, IEEE,Nam-Sup Choi, Chun-Taik Rim, and Gyu-Hyeong Cho

Abstract—The static and dynamic characteristics of buck-typethree-phase pulse-width-modulation (PWM) rectifier are fullyanalyzed based on the dc and ac circuit models developed bythe circuit DQ transformation. Various static converter charac-teristics such as gain, real and reactive power, power factor, andunity power factor conditions are completely analyzed. Transitioncharacteristics are also analyzed by both exact small-signal modelwith full set of equations and simplified output model in explicitform. The usefulness of the models is verified through computersimulations and experiments with good agreements.

Index Terms—Circuit DQ transformation, current-source rec-tifier, PWM rectifier.

I. INTRODUCTION

PULSE-WIDTH-modulation (PWM) rectifiers have beenwidely used in recent years because of the increased

demand of high power factor and low harmonics in utilities.Buck type has unique advantages compared to the boost onein high-power applications due to its low-voltage stress andwide output voltage dynamic range [1]. A clear understandingof the characteristics of the practical buck-type rectifier whereinput LC filters are contained is, however, not easy due to theincreased dimension of system equation. The filter is used tosuppress the switching harmonics, but it causes the unwantedphase shift and degrades the power factor. It is found thatthe phase shift depends highly on the modulation index andthe phase angle of PWM switching pattern. This is why thecontrol of the converter is being so complicated for wide rangeoperation.

There have been proposed a few control methods of thebuck PWM rectifier, however most of them are based onsimple models only considering the steady-state properties[2], ignoring input filter characteristics [3] or using per-phasecircuit model [4]. It is quite evident that the applications ofsuch simple models can guarantee neither high performancenor good stability because the dynamics of real converter

Manuscript received February 26, 1996; revised June 3, 1997. Recom-mended by Associate Editor, P. N. Enjeti.

S.-B. Han is with the Electric Energy Division, Korea Institute of EnergyResearch, 71-2 Jang-Dong, Yusong-Gu, Taejon 305-343, Korea (e-mail:[email protected]).

N.-S. Choi is with the Department of Electrical Engineering, NationalFisheries University, 195 Kuk-Dong, Yosu, Chonam 550-749, Korea.

C.-T. Rim and G.-H. Cho are with the Department of Electrical Engineer-ing, Korea Advanced Institute of Science and Technology (KAIST), 373-1Kusong-Dong, Yusong-Gu, Taejon 305-701, Korea.

Publisher Item Identifier S 0885-8993(98)01945-0.

varies widely with the operating point. A model with a fullset of differential equations [5] describes the system precisely,but the dimensions of equations are of eighth order. Such anequational model requires the cumbersome and tedious matrixmanipulation which results in very complex functions givinglittle physical intuition about the rectifier operation.

In this paper, the complete models of the buck-type PWMrectifier are presented using the circuit DQ transform methodthat is very effective in analyzing the multiphase ac cir-cuits [6]–[8]. Equivalent dc and ac circuits which are linearand exact are obtained for the static and dynamic analyses,respectively. Various steady-state characteristics such as dctransfer function, real power, reactive power and power factoras functions of modulation index, phase angle, and loadvariations are investigated based on the dc circuits. Transitioncharacteristics with respect to control inputs and disturbancesare also analyzed based on the ac circuit of both state-spaceform and the transfer function form. Especially a simplifiedoutput model is supposed for practical control. Finally, variousexperimental results are included to verify the usefulness ofthe proposed models.

II. CIRCUIT DQ TRANSFORMATION OF THERECTIFIER

A. Process of Circuit DQ Transformation

The buck-type rectifier shown in Fig. 1 is basically a time-varying system due to the switch set although the othercircuit elements are linear time invariant (LTI). This impedesthe application of any well-established LTI circuit analysistechniques, but the circuit DQ transformation method enablesus to develop the complete circuit models by the followingthree steps [6], [7].

1) Partition the circuit into basic subcircuits.2) Transform each subcircuits into DQ equivalent circuits

based on the DQ transformation equations to eliminatethe time-varying nature of the switching system. Thethree-phase-balanced voltage sources, switching func-tions, power invariant DQ transformation matrix, anda related equation are given as follows:

(1)

0885–8993/98$10.00 1998 IEEE

324 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 2, MARCH 1998

Fig. 1. Partitioned circuit of the buck-type PWM rectifier.

Fig. 2. DQ transformed equivalent circuit of the rectifier.

(2)

and (3), shown at the bottom of page, and

(4)

where the fundamental components of switching func-

tions are only considered by ignoring harmonics, andrepresents the modulation index of PWM switching

function. These relations are applied to each subcircuitsto produce time invariant circuits.

3) Reconstruct the transformed subcircuits by connectingthe nodes of adjacent subcircuits.

According to the above rule, the rectifier whose circuitelements and switches are assumed to be ideal is divided bysix basic subcircuits as shown in Fig. 1. The equivalent LTIcircuit model of the rectifier is obtained as shown in Fig. 2 byrejoining transformed subcircuits.

(3)

HAN et al.: MODELING AND ANALYSIS OF STATIC AND DYNAMIC CHARACTERISTICS 325

Fig. 3. Simplified circuit of Fig. 2, where� = �2.

B. Simplification of Equivalent Circuit

The equivalent circuit can be simplified further withoutsacrificing generality by selecting with as shown inFig. 3. This is justified that the of the DQ transformationmatrix in (3) can be chosen arbitrarily independent of thesystem operation. Another way of simplification iscase, however, this is not so much helpful for easy analysisof the rectifier.

The circuit shown in Fig. 3 represents the whole dynamiccharacteristics of the rectifier, hence, this can be used fordynamic performance simulations where the nonlinear controlvariables, and , are not fixed to some constant values. It isfound from Fig. 3 that the system order is reduced to six andthe system stability is changed only by the modulation index

so far as all passive circuits elements are kept constant. Notethat the power angle does not change the systempoles, but changes the zeros. These characteristics could alsobe understood through complicated equational analysis orexperience, but none of the previous works shows so unifiedand simple physical views as this does. Now this circuit ofFig. 3 needs to be simplified further for the specific analysespurposes such as following dc and ac analyses.

III. STEADY-STATE ANALYSIS

A dc equivalent circuit representing the steady-state charac-teristics of the converter is obtained from Fig. 3 by shorteningall the inductors and opening all the capacitors as shownin Fig. 4. In the dc circuit, instantaneous circuit variablesand varying parameters have stationary values

. We represent the electrical dc variables ascapital letter and denote the steady-state parameters by addingsubscript “ ,” and the expression of various circuit variables isfollowed by the representation of Fig. 1. The ac-side inductorresistance is ignored in the dc analysis since it is normally verysmall, and this simplifies the analysis for the main features ofthe system greatly. Now the analysis is straightforward.

Since the input currents of two gyrators are identical asshown in Fig. 4

(5)

or

(6)

so

(7)

The other dc variables are as follows:

(8)

(9)

(10)

A. DC Output Characteristic

It is noted from (7) that the rectified output voltage isindependent of load resistance . This indicates the outputvoltage of the converter can be regarded as an ideal voltagesource controlled by phase differenceand modulation index

, which is just a dual characteristic of the boost-typeconverter where the rectified output current is equivalent toa controlled ideal current source [7].

It is also noted that the dc gain ranges from zero to somemaximum. It can be much higher than unity if the resonancefrequency of the ac-side LC filter is set to be nearthe line frequency . But it is limited to a certain value inthe real system, where the resonant frequency of the filter isdesigned much higher than the line frequency, which resultsin a little increase in the dc gain. Fig. 5 shows that the voltagegain can be controlled by switching function parameters suchas phase angle and modulation index . The circuitparameters used in the analysis are given in Appendix A.


Fig. 4. DC circuit of the rectifier.

Fig. 5. DC voltage gain.

B. Real and Reactive Powers

The real power generated from ac source is obtained as

(11)

where

(12)

Reactive power is obtained by

(13)

The first term of (13) represents the variable reactive powerterm generated from the converter, which is controlled byfor a specific . This indicates that reactive power can becontrolled lagging or leading only by the phase difference,where is predetermined to produce a certain output power.The second term means the constant leading VAR generatedby the input LC filter. Hence, the converter must generate thesame amount of lagging reactive power as this second term

to obtain unity power factor at the source side. The reactiveand real powers normalized by are shown in Fig. 6as functions of phase and modulation index of the switchingfunction.

C. Power Factor and Unity PF Operation

Power factor is given by

PF

(14)

The power factor can be unity when the reactive poweriscontrolled to be zero. From (13), the unity PF condition isgiven as

or

for(15)

If the parameter of (12) is less than , the powerfactor cannot be unity. This condition can occur when theload resistance is large, which is also a dual property ofthe boost-type converter when the load resistance is small[7]. Fig. 7(a) shows that power factor can be controlledas functions of control parameters, and , but thereare restricted ranges where power factor cannot be unity.Although there are two points for the power factor to beunity, only one of them, placed between 0and 45 , can beused in practice since usable output voltage is obtained. Inthis region, the rectifier can supply the maximum power withhigh power factor, but in the region of between 45and 90 ,power utilization is not efficient and the power factor greatlychanges with the phase difference. Fig. 7(b) shows the unityPF condition varies with load, and the range is narrower forlighter load.

Under the unity power factor condition of (15), the rectifierhas some interesting characteristics. For example, the output


(a) (b)

Fig. 6. Power characteristics. (a) Real power. (b) Reactive power.

(a) (b)

Fig. 7. Power factor characteristics. (a) Power factor. (b) Unity power factor condition.

inductor current becomes

(16)

It is noted that the dc-side voltage and the real power as wellas the current can be controlled only by the modulation indexnearly independent of phase difference under the unity PFcondition.

D. Operation Characteristics over All Range

The knowledge of operation over whole range is useful forthe design and control of the rectifier. Fig. 8 shows how thegain, real power, reactive power, and power factor operatewith the various operating points. The gain and the real powerare higher as the phase difference goes to zero and modulationindex is higher, but the reactive power has maximum leadingpower at 45 and maximum lagging power at 45. Theinternal resistance, of course, changes the magnitude of theelectrical quantities, but the general tendency is not affectedgreatly. For an analysis including the internal resistance, therelations of steady state in Appendix B must be used.

IV. DYNAMIC CHARACTERISTICS ANALYSIS

A. Small-Signal Perturbation Analysis

In this section, the dynamic characteristics of the PWMrectifier, i.e., the small-signal perturbation responses withrespect to the control parameters such as phase differenceand modulation index , are analyzed. The circuit of Fig. 3is perturbed since the system is nonlinear with respect tothe control variables [6]. A small-signal perturbed circuitis shown in Fig. 9 by excluding the dc term and higherorder perturbation terms. A complete state-space equation isobtained from this small-signal model as follows:

(17)


Fig. 8. Operation characteristics as functions of phase difference and modulation index.

Fig. 9. Perturbed ac circuit for small-signal analysis [v1 =3

2(v̂s sin �o + �̂Vs cos �o) andv2 =

3

2(v̂s cos �o � �̂Vs sin �o)].

However, it is hardly possible to analyze manually eitherthe circuit of Fig. 9 or the equation of (17), hence, the signalflow graph is used as shown in Fig. 10. The analysis results aresummarized in Appendix B, where various transfer functionswith respect to the inputs of the control variables and thesource disturbance are derived, respectively. Still it is not easyto analyze the signal flow graph of Fig. 10, however, this is themost feasible way of analyzing such a sixth-order convertersystem among the analysis techniques ever found. This analyt-ical result can be used for the controller design, which guar-antees stable and fast responses for wide operating range. It isfound from (17) or Appendix B that the dynamic characteris-tics of the buck-type PWM rectifier are summarized as follows.

1) System poles are dependent only on the modulationindex when the circuit parameters are fixed. In the real

system, however, the load varies and the rectifierpoles approach to the origin as the load resistanceincreases.

2) Output transfer functions with respect to the modulationindex are independent of the phase difference, but varyby the modulation index, output voltage, and outputcurrent.

3) Zeros of the output transfer functions with respect to thephase difference or source disturbance are independentof the modulation index while dc gains are dependent.

4) Fig. 11 shows the dynamics change greatly with theoperating point. The system property is changed fromthe minimum phase system at to nonminimumphase system with positive zero in the right-half planeat .


Fig. 10. Perturbed signal flow graph with respect to variations of control parameters� and m.

Fig. 11. Bode diagram of transfer function̂vco=m̂.

B. Simplified Dynamic Characteristic

Analytically, the previous exact ac models are quite prefer-able, however, in the engineering sense they are still toocomplicated to apply in practice. Hence, it is necessary to de-velop more simplified model for practical application purpose.Fortunately, the converter has two distinct characteristics. Oneis the fast response dominated by the ac-side LC filters, andanother is the slow response dominated by the dc-side LCfilter. They are coupled with each other through the rectifierswitch set, equivalently a transformer.

If the control objectives are power factor correction andstable and fast output voltage/current regulations, a slow

Fig. 12. Simplified output model.

(a)

(b)

Fig. 13. Real PWM switching function. (a) PWM strategy(m = As=Ac).(b) Resulting switching function.

response circuit is more dominant over a fast response one.In this case, the ac-side circuits are regarded as ideal voltagesources at a specific operating point, and the fast responsecharacteristic is ignored. Thus, a simplified output model isobtained as shown in Fig. 12, where the ac-side filters areassumed to be in the steady state while the dc-side filter isassumed to be in the transient state. There are three perturbedvoltage sources as

(18)


(a)

(b)

Fig. 14. Verification of small-signal model in comparison with numerical calculation of full-order differential equations. (a) Phase currentias. (b)Output current io.

(19)

(20)

The simplified model of Fig. 12 is quite different from thesimple output model ignoring ac input characteristics becausethis model has full information about input ac filters andcurrent operating point. The accuracy of this simplified modelis determined by the degree of separation between the polesof ac filters and those of dc filters. This simplified ac circuitmodel is quite useful for a fast and simple controller designwith plenty of physical insights.

V. VERIFICATION OF MODELS BY SIMULATION

Since the purpose of this paper is to provide exact and easyunderstandable models, the verifications are done first by thecomputer simulations to avoid erroneous disturbances imposedby many practical situations in the experiment. The computersimulations enable us to simulate various considerations withgreat ease, very low cost, and little time consumption.

The simulations are done by the numerical calculation of theeighth-order time-varying differential equations of (21), givenat the bottom of the next page, for the original rectifier ofFig. 1, and a fourth/fifth-order Runge–Kunta method is usedas a numerical algorithm. In these equations, source voltages

and of (1) are used with andand can be any switching functions from various PWM


(c)

Fig. 14. (Continued.) Verification of small-signal model in comparison with numerical calculation of full-order differential equations. (c) Output voltagevo.

Fig. 15. Verification of simplified model for output current in comparison with the numerical calculation.

methods. For general performance comparison, we use bothreal switching functions of the modified PWM [9] as shownin Fig. 13 and ideal switching functions defined in (2) withthe switching pattern harmonics excluded.

There are three time steps in simulation. The first is forsource voltage perturbation, and the second and third are formodulation index and phase difference perturbations as shownin Fig. 14. The system is started at with and

(21)


Fig. 16. Comparison of three models for an extreme case.

Fig. 17. Experimental and simulated waveforms by dc model in steady state atmo = 0:9 and �o = 5� (2 ms/div).

, all initial conditions are zeros. When the systemreaches to a steady-state condition, the modulation index isabruptly increased by 10% at ms. After reachinganother steady-state condition, the phase difference is nowincreased by 5 at ms.

It is noted that when source voltages are applied abruptly atthe start, high inrush current flows due to the resonance withthe ac-side LC filter and this also drive the dc-side currentand voltage to have high peak values. So careful processis needed at the starting point. In the real PWM case, it isobserved that much ripples in output currentexist by the

harmonics of switching function, but the average trajectoryof the ripple is almost identical with the ideal switchingfunction case. This shows that the circuit DQ transformedmodel describes averaging behavior of the rectifier and itis identical to the ideal switching function model. Althoughthe switching harmonics are reflected in the output current,the line-side current and output dc voltage havelittle harmonics due to the filtering effect of ac- and dc-side LC filters, respectively. The small-signal responses ofFig. 14 verify that the numerical calculation method and thesmall-signal model show almost the same transient response


(a) (b)

(c)

Fig. 18. Experiments of steady-state characteristics. (a) Output capacitor voltage. (b) Real power. (c) Reactive power.

(a) (b)

Fig. 19. Demonstration of variation of unity power factor condition according to load variation atmo = 0:8. (a) In the case ofRo = 10 and�o = 5�. (b) In the case ofRo = 20 and �o = 25�.

characteristics. Especially the response of the system withideal switching function is almost identical to the small-signalresponse. Only a negligible error occurs in the case of thephase perturbation due to the exclusion of the higher orderterms during the small-signal model.

The simplified output model of Fig. 12 is also verifiedthrough the simulations as shown in Fig. 15. It is identifiedfrom Fig. 15 that there are same mismatches in the response,

however, the simplified output model could be useful forpractical situations. This model does not guarantee wideapplication areas which include some extreme cases. The roleof it could be understood that gives physical insight andusefulness for rough design.

An example for an extreme case where the input ac filtershave lower poles than the output dc filters is shown in Fig. 16with the case of the small-signal model for comparison. Here,


the outputs and are changed to 2 mH, 50F, and15 , respectively. Note that the small-signal model is stillvalid for this extreme case while the simplified model is not.

There is some uncertainty in the parameter of the converter.The values of input-side inductors are not easily determinedsince they include the line and source inductors that may varywith the structure changes in power lines or power facilities.Considering this uncertainty the exactness of the model isrelatively not so much important than the simplified one in thereal situation. This is another reason why the simplified outputmodel is useful even though it has some amount of error.

VI. EXPERIMENT

By comparison of the solution of numerical full-orderdifferential equation, it has been shown that the model basedon the circuit DQ transformation is sufficiently accurate andmore effective to estimate the behavior of the converter. Now,to confirm the effectiveness of the model in real system,various experiments of a scaled-down 1-kVA converter ofFig. 1 are performed by using IGBT as main switch. Converteris designed as the values of Appendix A and .Converter waveforms and various electrical quantities aremeasured by Lecroy’s DSO scope 9354M and Voltech’s poweranalyzer PM3000A, respectively.

A. Experiment Results of Steady-State Characteristics

Fig. 17 shows the whole steady-state waveforms of the buckPWM rectifier at the operation condition of and

. Detected signal of source voltage of phase andgate signal of switch , converter unfiltered output voltage

, converter input current , converter output current ,converter filtered output voltage , phase current of phase

and ac-side capacitor voltage between phaseand phase,, are shown sequentially at identical trigger position.

Detected signal of source voltage , which operates as areference signal of the system, is synthesized from the sensingsignal of line to line voltages by the relation

. Fig. 17 also includes simulated waveforms of ,, and by inverse transformation from the values

of dc model, and this shows all fundamental componentswaveforms both the ac and dc side can be exactly calculated.From these, the waveform of unfiltered output voltagecanbe easily calculated by using instantaneous switching function[9].

Various steady-state characteristics of Figs. 5 and 6 in thereal system are verified as shown in Fig. 18. The valuescalculated from the steady-state relations in Appendix Bincluding the internal resistance are nearly identical to themeasured values. Around the phases of 90and 90 , somemismatch is occurred due to the effect of used snubbers, butit is negligible in the main operation of rectifier.

Fig. 19 demonstrates the analysis of Fig. 7(b) which showsthat unity power factor condition changes by the load variation.When the load varies from to , unitypower factor condition moves from toat .

Fig. 20. Transient state response of step change (10 ms/div).

Fig. 21. Demonstration of the rectifier dynamics operated as nonminimumphase system (5 ms/div).

B. Experiment Results of Transient Characteristics

Fig. 20 shows the dynamic characteristics of the case wherethe operating point at , changes to thepoint of , and after 30 ms, the operating pointchanges again to the point of whose operation wasestimated by Fig. 14(b). From Fig. 20, It is known that thedynamics between the rising step response and the falling stepresponse is different, the falling step response has some longerdelay before the falling process.

It is expected that the dynamics of the converter can beoperated as nonminimum phase system in Fig. 11. To showthis clearly, a step response experiment from to

is performed in stiff condition of load and. Fig. 21 shows the result that at the instance of step

change, negative direction of change is happened before thevoltage drop, which shows the phenomena of the nonminimumphase system where some zeros are in the right-half plane. Inhigh-order system such as this rectifier, the effect of positivezero is occurred as a simple delay in dynamic response or the


(B-1)

(B-2)

negative initial slope of the response for a command. Anyway,such a delay in start of the response may impede the successfuldesign of the high performance controller, so careful analysisshould be performed for the fast and wide range operatedcontrol.

VII. CONCLUSION

The buck-type PWM rectifier is completely analyzed usingcircuit DQ transformation. Exact LTI dc and ac equivalentcircuits in a unified form are induced and full set of equationsare derived in explicit form. From the dc circuit, variouscharacteristics such as gain, powers, power factor, unity powerfactor condition, and the practical behavior including com-ponent and load variations are analyzed clearly. From theac perturbation circuits, the system dynamic characteristicequations of small-signal dynamic model and simplified outputmodel are fully derived. The circuit models are verifiedthrough computer simulations and experiments with goodagreement, so it is very useful to estimate all the electricalvalues of the designed converter and to design the controller.

APPENDIX APWM RECTIFIER PARAMETERS

The parameters used for the buck-type PWM rectifier areas follows unless otherwise stated:

mH, F, , , mH,F, , rad/s.

APPENDIX BTABLE OF TRANSFER FUNCTIONS

A. Characteristic Equations

B. Control Variable to Output Transfer Functions

[see (B-1) at the top of the page] and

C. Source Perturbation to Output Transfer Functions

See (B-2) at the top of the page and


D. Steady-State Relations

where

REFERENCES

[1] N. R. Zargari, G. Joos, and P. D. Ziogas, “A performance comparisonof PWM rectifiers and synchronous link converters,”IEEE Trans. Ind.Electron., vol. 41, pp. 560–562, 1994.

[2] N. R. Zargari and G. Joos, “A three phase current source type PWMrectifier with feed-forward compensation of input displacement factor,”in IEEE PESC Conf. Rec., 1994, pp. 363–368.

[3] S. Hiti, V. Vlatkovic, D. Borojevic, and F. C. Lee, “A new controlalgorithm for three phase PWM buck rectifier with input displacementfactor compensation,”IEEE Trans. Power Electron., vol. 9, pp. 173–179,1994.

[4] X. Wang and B. T. Ooi, “Real-time multi-DSP control of three phasecurrent source unity power factor PWM rectifier,” inIEEE IAS Conf.Rec., 1992, pp. 1376–1383.

[5] O. Ojo and I. Bhat, “Analysis of three phase PWM buck rectifier undermodulation magnitude and angle control,” inIEEE IAS Conf. Rec., 1993,pp. 917–925.

[6] C. T. Rim, D. Y. Hu, and G. H. Cho, “Transformers as equivalent circuitsfor switches: General proofs andD-Q transformation-based analyzes,”IEEE Trans. Ind. Applicat., vol. 26, pp. 777–785, 1990.

[7] C. T. Rim, N. S. Choi, G. C. Cho, and G. H. Cho, “A complete dcand ac analysis of three phase controlled-current PWM rectifier usingcircuit D-Q transformation,”IEEE Trans. Power Electron., vol. 9, pp.390–396, 1994.

[8] W. H. Kwon and G. H. Cho, “Analysis of static and dynamic charac-teristics of practical step-up nine-switch matrix converter,”Proc. Inst.Elect. Eng. B, vol. 140, pp. 139–146, 1993.

[9] P. D. Ziogas, Y. G. Kang, and V. R. Stefanovic, “PWM controltechniques for rectifier filter minimization,”IEEE Trans. Ind. Applicat.,vol. IA-21, pp. 1206–1213, 1985.

Soo-Bin Han (M’95) was born in Korea on June 9,1958. He received the B.S. degree in electronic engi-neering from Hanyang University, Seoul, Korea, in1981, and the M.S. and Ph.D. degrees in electricalengineering from the Korea Advanced Institute ofScience and Technology (KAIST), Taejon, Korea,in 1986 and 1997, respectively.

He has been a Senior Researcher at Korea In-stitute of Energy Research since 1986, engaged inthe various projects concerning electric energy sav-ing/storage technologies, fuel cell power generation,

and resonant inverter. His research interests include modeling and control ofpower converter systems, control of fuel cell power plant, and DSP-basedcontrol systems.

Nam-Sup Choi was born in Korea on March 5,1963. He received the B.S. degree in electricalengineering from Korea University, Seoul, Korea, in1987, and the M.S. and Ph.D. degrees in electricalengineering from the Korea Advanced Institute ofScience and Technology (KAIST), Taejon, Korea,in 1989 and 1994, respectively.

He was a Researcher at the Information andElectronics Institute in KAIST 1994. He has beenAssistant Professor in the Department of ElectricalEngineering, Yosu National Fisheries University,

Chonnam, Korea, since 1995. His research interests include modeling andsimulation of switching power converters and high-power inverters, includingmultilevel PWM inverters.

Chun-Taik Rim , photograph and biography not available at the time ofpublication.

Gyu-Hyeong Cho received the Ph.D. degree inelectrical engineering from the Korea Advanced In-stitute of Science and Technology (KAIST), Korea,in 1981.

He was with the Westinghouse R&D Center until1983. Since 1984, he has been with KAIST, wherehe was appointed Professor in 1991. During 1989,he was a Visiting Professor at the University ofWisconsin, Madison. He is interested in power elec-tronics, but since 1993 he has also been interestedin the area of CMOS/BiCMOS analog-integrated

circuits including A/D converters, smart power IC’s, RF IC’s for wirelesscommunications, flat panel displays, etc.

Dr. Cho is a Member of the Institute of Electrical/Electronics Engineersof Korea.

modeling and analysis of static and dynamic...

Documents