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14 2 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL 24 . NO I . J A N U A R Y I F E B R U A R Y I O X X

Analysis and Realization of a PulsewidthM odulator Based on V oltageSpace VectorsAbstract-The metho d of using a space vector concep t for deriving theswitching instants for pulsewidth-modulated voltage source inverters is

compared with the commonly used established sinusoidal concept. Afterdeducing the switching times from assumptions for minimum currentdistortion, the resulting mean voltage values are shown and the differ-ences between these and the established sinusoidal PW M are elaborated.Based on an analytical calculation, the current distortions and torqueripples are evaluated and compared with those of established sinusoidalpulsewidth modulation. The realization of a pulsewidth modulator isdescribed in the range of syn chronous sinusoidal pulsewidth modulation,which generates-by software-symmetrical synch ronou s pulse patterns.The performance has been proved by laboratory tests.

INTRODUCTIONARIABLE-FREQUENCY ac drives are increasinglyV sed for various applications in industry and traction.

Due to the improvement of fast-switching semiconductorpower devices, voltage source inverters with pulsewidth-modulated (PWM) control, as shown in Fig. 1, find particu-larly growing interest.

Control methods that generate the necessary PWM patternshave been discussed extensively in the literature. Two basicconcepts may be distinguished: for small and medium-sizedrives, the current-controlled PWM has proved to b e advanta-geous. For big drives employing inverters with low switchingfrequency, PWM voltage control is more advantageous.How ever, this method is also an option for small and medium-size drives. A detailed description of the basic methods may befound in [I] and [2]. This paper deals with PWM voltagecontrol methods.

PWM VOLTAGE ONTROL ETHODSIf the switching frequency fJ is high compared to the

fundamental output frequency fi f the inverter (frequencyratio zT 2 9, 0 . * 15), sampling methods with sinusoidalreference s igna ls , e .g . , n a u a l sampl ing [3] or regularsampling [4], may be used. These methods aim at generatingan inverter output voltage with sinusoidally modulated pulse-

Paper IPCSD 87-19, approved by the Industrial Drives Committee of theIEEE Industry Applications Society for presentation at the 1986 IndustryApplications Society Annual Meeting, Denver, C O, Septem ber 28-October 3 .Manuscript released for publication April 14, 1987.H. W . van der Broeck is with Philips Forschu ngslaboratoriu m Aache n,Weisshausstrasse, 5100 Aachen, West Germany.

H . C. Skudelny and G . V. Stanke ar e with the Institut fur Stromrichtertech-nik und Electrische Antribe, Jagerstrasse 17/19, 5100 Aachen, WestGermany.lEEE Log Number 8716204.

---- ~Fig 1. Induction motor drlve with pulsewidth-modulated vvltdge w u r c einverterwidths. They will be referred to as established sinusoidalmodulation in this paper. If the switching frequency is aninteger multiple of the fund amental output frequency, this willbe called synchronized sinusoidal modulation, in contrast tofree-running sinusoidal modulation, where the switchingfrequency and the fundamental output frequency are indepen-dent of each other.

Sinusoidal modulation maintains good performance of thedrive in the entire range of operation between zero and 100-percent modulation index m. f the modulation index exceedsunity, sinusoidal modulation is no longer possible. In thisrange of operation it is useful to apply optimized PWM withprecalculated switching points, which are stored in a look-uptable. Optimized PWM is also recommended for low-fre-quency ratios. It is practical to calculate the notches off-line i nsuch a way that current ripple or losses or torque pulsations areminimized.

SINUSOIDALODULATI ONIn the following the sinusoidal modulation will be discussed

in more detail. For this purpose an inverter leg, as shown i nFig. 2(a), is represented by an equivalent circuit. shown inFig. 2(b).

If the changeover switch is operated according to sinusoidalmodulation, the line-to-center voltage U , follows a shape asshown for instance in Fig. 3 in per-unit notation. The meanvalue of the voltage u averaged over each cycle of theswitching frequency follows a staircase shape, which will bereplaced with a smoothed curve u ( t ) for sufficiently highfrequency ratios zr. This curve will be called mean valueherein. In a symmetrical three-phase inverter the mean line-to-center voltages are

0093-9994/88/0100-0142$01OO O 1988 IEEE

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V A N DE R BROECK er ul.: PULSEWIDTH MODULATOR BASED ON VOLTAGE SPACE VECTORS 143

(a ) (b)F I ~ .. (a ) Inverter leg. (b) Inverter leg equivalent circuit.

-it-llf,- ,

Fig. 3 . Single-phase inverter output voltage by established sinusoidalmodulat ion.

However, the instantaneous values of the voltages depend onthe method of pulsing. It has been shown that a symmetry ofthe pulses within one switching period, as shown in Fig. 7, isparticularly advantageous [11, [ I I]. F or fixed-frequency ratiosthat are multiples of three. this concept results in equal shapesof the three phase-to-center voltages:

(3)f ,flz r = - = 3 n ( n = 1 , 2 , 3 , - . e ) .The upper limit of the phase-to-center voltage for sinusoidal

modulation is theoretically m = 1 with zl = 1. This is only 78percent of the value that would be reached by square-waveoperation.

SPACE-VECTORODULATIONA different approach to PWM modulation is based on thespace vector representation of the voltages in the CY,3 plane.

The CY ,3 components are found by Park transform, where thetotal power, as well as the impedances, remains unchanged(see also (23) ). This concept was discussed in publicationssuch as [4]-[6]. For our purpose the basic ideas are summa-rized.

The three machine voltages are represented by a voltagespace vector 0.here are eight states available for this vectoraccording to eight switching positions of the inverter, whichare depicted in Fig. 4.

W e define a mean space vector U , which is almost constantduring a switching period. This vector generates the funda-mental behavior of the machine, e.g. , currents and torque.The difference space vector U - u causes the current harmon-ics. Fo r discussing the current harmonics, a simplifiedequivalent circuit of the induction machine according to Fig.5(c ) can be used.

For the quality of PWM control, the deviation of themachine currents from the fundamental currents is highlyimportant. For the ideal case of sufficiently high frequencyratios, cycles of switching states can be found wherein the

2

-. ->

(b )vectors .Fig. 4. (a) Inverter switching states. (b) Inverter output voltage space

(a ) (b )+

-e

u-u(C)Equivalent circuit of induction machine. (a) Single-phase representa-tion. (b) Simplification for harmonic current calculation. (c) S implificationfo r space vector calculation.

Fig. 5 .

mean voltage vector is equalized to the fundamental voltagevector and the average deviation curren t vector becomes zero .

Within one switching state the deviation current vectorchanges by the amount

1 t 2 - !L , I 1A?_ =- { (I??-U ) dt = m i n (4)

wheret , beginning of switching state.t2 end of switching state.

An optimum PWM modulation is expected ifthe maximum deviation of the current vector for severalthe cycle time is as short as possible.switching states becomes as small as possible, and

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1 4 4 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO I , J A N U A R Y I FE B R U A R Y 1988These conditions are met in general if

only the three switching states adjacent to the referencevector are used, andthe cycle wherein the average voltage vector becomesequal to the reference vector consists of three successiveswitching states only.

To obtain minim um switching frequen cy of each inverter leg itis necessary to arrange the switching sequence in such a waythat the transition from one state to the next is performed byswitching only one inverter leg.

It can be seen in the switching diagram of Fig. 4 that theseconditions are met if starting from one zero state the inverterlegs are switched in the relevant sequence ending at the otherzero state. If, for instance, the reference v ector sits in sector I,the switching sequence has to be *812721812721*.Hence it follows for a switching cycle in sector I:

ira dt+ I oa dt. ( 5 )+ s::+" TI fT 2For sufficiently high switching frequency the reference spacevector Gref s assumed constant d u r i y one switching cycle.

Taking into accou nt that the states Ug an d bo are constantan d oa = 0, one finds (see Fig. 6 )

( 6 )If the space vectors in this equation are described in

-00 TI+Oa * T2=Uref Tz.rectangular coordinates, it follows that

Hencesi n (60" -7)

sin 60"T l = T z . a -sin yT z = T z .a . sin 60"

(9)

T7=TX= To= Tz - T2- T I . (1 1)For the sectors 11-VI the same rules apply. This results in a

definite switching order according to Fig. 7, which showsexactly the same symmetry as derived for established sinusoi-dal modulation [ 11.

Fig. 6 . Determination of switching times.

+TZ 4Fig. 7. Optimum pulse pattern of space vector PW M

PWM concepts, the mean values of the phase-to-centervoltages averaged over on e switching cycle are evaluated. Forsector I one finds

2= - . a U, sin (7+60" )6

=2a + U , . sin (7-30") (13)

Taking into account the necessary changes in the other sectors,one finds for the fundamental periodU , ( t ) = a . U ,

( 2 sin w1 fo r 0 5 w , t 30"

U, ( )= - U, (- )= - U ,( - T / 2 ) (16)To compare the results of the space-vector PWM with other U l ( t ) =U2 ( t - T/3)=U3(t+ T / 3 ) . (17)

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V A N DER BROECK el at.: PULSEWIDTH MODULATOR BASED ON VOLTAGE SPACE VECTORS 1 4 5

30" 90"

Fig. 8. Mean inverter output voltages by space vector P W M .Hence the phase-to-phase voltages are

4u 1 2 ( f ) = ~ l ( f ) - ~ 2 ( f ) = - auq sin ( ~ , f + 3 0 ~ )18 )4Both the phase-to-center voltage ul and the phase-to-phasevoltage U , , are shown in Fig. 8 in per-unit notation. It turnsout that with space-vector PWM, the phase-to-phase voltagewhich is seen by the machine is sinusoidal. as expected.However, the phase-to-center voltage is not sinusoidal. Tounderstand this result we have to recall that the Parktransformation, which defines the compon ents of the spacevectors, is not definitely reversible. Harmonics of triplenorders may be added to the phase voltages without affectingthe Park components and the value of the phase-to-phasevoltages. Once this curve is known it could be substituted forthe sinusoidal reference signal in a normal three-phasemodulator. In fact an infinite number of curves could besynthesized as reference curves for P WM modulators. Somehave been mentioned in the literature, e.g. [SI, [9].

Comparing the phase-to-phase voltages according to theestablished PWM and the space-vector PWM, one finds

4m = - . .3Looking at Fig. 4 one finds that the maximum value for asinusoidal PWM is a = 4 1 2 .

This leads to the maximum modulation index in the case ofspace vector PWM:

rn,,,, = 2 / & . ( 2 1 )This is approximately 15 percent more than with establishedPWM [SI, [9]. The amplitude of the maximum voltagefundamental reaches about 90 percent of the respective square-wave fundamental.

COMPARISONF SINUSOIDALW M A N D SPACE V E C T O R PW MIt has been found in the previous section that with space-vector modulation a modulation index of rn = 1.15 can be

reached without any constraint, whereas with sinusoidalmodulation, notches are suppressed and low-order harmonicsoccur in the range of overmodulation rn > 1. In addition, theharmonic content of the inverter output voltages and currents

is less for the space-vector method than for its counterpart.This is demonstrated in Fig. 9, which shows the results ofsimulation runs with exact modeling of the modulationprocedures. In either case the same frequency ratio zr = 21and the same modulation index rn = 0.9 have been used.Because the phase-to-phase voltage, which has the shape ofup, is more favorable for the space-vector P W M, the harmoniccontent of the current and the torque pulsations are signifi-cantly reduce d. T o demonstrate the differences between thetwo modulation concepts, an analytical solution is used alsofor the sinusoidal PWM [ IO] , [ l l ] .

Under the same assumptions as those described for thespace-vector PWM, a single-phase approach is used as a firststep. On the basis of an equivalent circuit for the inductionmachine , as show n in Fig. 5 (b), the phase-to-center voltage,the mean phase-to-center voltage, and the harmon ic content ofthe current are shown in Fig. 10.

In analytical form the harmonic content of the current is

p=I, 2, 3 .For the symmetrical three-phase machine with open neutralthe harmonic content of the phase currents can be derived fromthe line-to-line voltages. Under the symmetry conditions thatwe have supposed both for established sinusoidal modulationand space vector modulation (refer to Fig. 7), the Parkcomp onents of the harmonic content of the stator currents canbe derived by superim posing the single-phase values (22) [101,[ l l ] :

The harmonic content of the stator currents can be calculatedin a similar way:[ = [ 1 / 2 - 1 / 2 - 1 / 21 - 2 1 . [ . (24)

1-C - 1 / 2 - 1 / 2 1To compare the copper losses, the rms value of the

harmonic machine current is to be evaluated. Since theharmonic content is orthogonal to the fundamental cu rrent, theadditional copper losses due to current harmonics can becalculated independently. By integration of (23) and (24) onefinds for sinusoidal PWM

3 4 . h 9- m 2 - - . m3+- m Ji T 8

3 . 48(25)

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146 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS. VOL 24 . NO I . JANUARY 'FEBRUARY I W X

(b)Simulation of PWM inverter-fed induction machine. (a) Establishedsinusoidal PW M ( f , / f i = 21; rn = 0.9). (b) Space-vector PWM ( f , / f i =21 ; rn = 0.9).

Fig. 9.

--1 + '

Fig. 10. Voltage pulse and resulting harmonic current within one pulseperiod for single-phase system .

A similar calculation for the space-vector concept yields3 4J3 9 3 9&- m2- -m3+- m4

7r 8 2 sa3 . 48

(26)Fig. 11 shows the evaluation of these equations in per-unitnotation with Tc = I : , (&L, /UJ2.

- 2

VECTOR-PWM

-- -0 00 02 OL 0 6 0 8 1 0 11 5rn --Fig 11 Square of rms harmonic current

f ,":PI SIN-PWM

0 ' ~ r n0 2 n(a )

SPACE -VE C TOR - PWM

1 , , . , ,' 6 1 rn' 3 '0 Z n

(b )Fi g 12 (a) Envelope curve fo r establlshed sinurotdal PWM ( T r , =TH_fs.L,*/(Uq$)) (b) Space vector PWM

Ip=Z?Tf, t-For cross-reference to the fundamental quantities the idealno-load machine current may be used:

Next the torque pulsations are compared for the two PWMmodes. If one assu mes that the airgap flux is purely sinu soidal,the torque pulsations are described by the following:

where the angle cp describes the position within the fundnmen-tal period with respect to the zero crossing of U , . Thisequation is to be evaluated for both PWM modes. As therelation between cp and t depends on the point of operationand cannot be represented in simple analytical form, a nenvelope curve will be derived:

The torque pulsations do not exceed the following limits:

For both PW M methods the envelope curves are plotted i nFig. 12 . As expected, a strong dependence on the modulationindex m appears. Then the maxima of these curves ar eevaluated as a function of the modulation index. These valuesare given in analytical form for sinusoidal PWM and for

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V A N DER BROECK ci u l. PULSEWIDTH MODULATOR BASED ON VOLTAGE SPACE VECTORS 147space-vector PWM in ( 3 1) and (32), respectively:

In (32) a slight inaccuracy in the range rn > 1 was acceptedlor the sake of a simple rsul t .

The evaluation of (31) and (32) is depicted in Fig. 13. It isapparent that the space-vector PWM concept results incoiisiderably less torque pulsations than the sinusoidal PWM.Again in Fig. 13 the torque pulsations are plotted in per-unitnotation. For comparison with the fundamental quantities thepull-out torque may be used. This is under ideal assumptions:

(33)PW M MODULATOR

A modulator for practical use in high-power thyristorinverters or GT O inverters should be capable of the followingmodes of operation: free-running sinusoidal mo dulation,synchronous sinusoidal modulation, and optimized PWMincluding overmodulation and square-wave operation. Asmooth transition between these modes is highly desirable. Aversatile modulator with a general strategy and a high degreeof tlexibility can be realized by means of a microprocessor.The real-time form ing of the inverter gate pulses, ho wever, istime critical. For this reason this is usually the task of separatecounters. which are controlled by the microprocessor.

One problem of this solution is the synchronization of thepulse frequency with the fundamental working frequency,which is necessary for small frequency ratios (about z7 30).

For synchronized pulsing the clock frequency of thecounters isf C L K = 2 n; . 27 . i (34)

where n, is the resolution of the entire pulse cycle. For anadequate resolution of the pulse angle the counter frequencymay reach the megahertz range.

I f this frequency is derived from a higher referencefrequency by dividing, only a limited number of frequencyratios is possible due to the technological upper limit of thereference freq uency. If the counter frequency is generated byphase-locked-loop (PLL) circuits, some other problems arisedu e to PLL transients if the frequency ratio is changed, or dueto the symmetry requirements of the pulse angles. Theseproblems may be overcome by very complex PLL arrange-ments using several PLL loops. It seems to be more practicalto adjust the switching frequency by means of software. In thiscase the counters are clocked with fixed stabilized frequency ,and the time positions of the notch angles are loaded into thecounters by the microprocessor. Therefore the microprocessorhas to calculate the count value fo r the cycle time T, from thedigital value of the reference fundamental frequency and the

0 0.2 0 . i 0.6 0,8 1,O 1,15m -Fig. 13 .

suitable frequency ratio:Peak values of torque harmonics with FL = i . fsL,*/(Uq.$)orestablished sinusoidal and space-vector PWM.

(35)

The cycle time then has to be multiplied with the pulsewidthratio derived from the reference curve for the PWM (see (9)an d (IO)).

DESIGN F A PWM-CONTROLLEROn the basis of the space vector concept a PWM controller

was developed. It covers all modes of operation that werementioned in the previous section. The referen ce values of thefundamental output voltage, which for synchronous modula-tion have to be the amplitude and the frequency, are given inpurely digital form. This enables the modulator to beinterfaced directly with a superimposed digital drive controlsystem.As an example the synchronous sinusoidal modulation isdepicted in Fig. 14. As described previously the referencecurve and the cycle time ar e calculated by software in a space-vector reference frame . The hardware c ounters for the regularsampling procedure could be organized either in the space-vector system or in the three-phase system. The authorspreferred the three-phase arrangement as depicted in Fig. 14 .The sampling instants are fixed for strongly symmetricalpulsing, and a software counter, which is loaded with thenumber of cycles per sector, selects for every frequencyratio the suitable sam pling values in the reference cu rves. T hereference cu rves, as seen in Fig. 8 , are calculated piecewise intwo channels an d multiplied with the m odulation index and thecycle time. Th e sector distributor selects the respective valuesfor the three phases. As the regular sampling m ethod is used.only one reference value is needed for each switching cycle. Anew value of the frequency ratio can be started only at thebeginning of a 60" sector. T hus fully symmetric pulse patternsare generated. Since with space-vector PWM the currentdistortion in the sym metry ax is of the pulses is zero (see Fig.lo), this ensures pulse ratio transitions without current andtorque transients.As an example of the performance of this modulation, Fig. 15 shows the oscillogram of voltage and current as measuredat a laboratory test bed with no load and a fundamentalfrequency of about 23 Hz . O ne sees that the frequency ratio ischanged without any current transient.Operation in another mode is possible by just calling theappropriate subroutine. The fundamental frequency and the

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148

rWLd3-4-.I-OI/)

IIL .

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VO L 24, NO I , JANUARYiFEBRUARY 1188

_ _a2cc-

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VAN DER BROECK ei al. : PULSEWIDTH MODULATOR BASED ON VOLTAGE SPACE VECTORS 149

10

I !214 I

III1111111111111II I 1 1 lUUUUUUI lornI p=21-1-p=15 c_I

Fig. 15. Measured shape of motor curr ent and line-to-line voltage with pulseratio changing.

modulation index can be changed independently. The transi-tion from one mode to another is without current transients.The described modulator was realized by means of an 8086microprocessor. Although rather complex programs areneeded, the modulator is capable of switching frequencies upto 2 kHz.

CONCLUSIONIt was shown that sinusoidal modulation generated in aspace vector representation has the advantages of lowercurrent harmonics and a possible higher modulation indexcomp ared with the three-phase sinusoidal modulation meth od.

A modulator on the basis of an 8086 microprocessorsuitable of operating in the free-running mode, in thesinusoidal modulation mode, and in the fixed-pattern modewas developed. As an example the operation of this modu latorwas shown in the sinusoidal modulation mode.

NOMENCLATURE

tdT-TH - c p)

DC source voltage.Phase-to-center voltage.Per-unit value of U,(t).Fundamental amplitude ofMean value of U ( t ) fo rswitching period T = l/f,.Park components of voltage.Phase-to-phase voltage.Voltage space vector.Machine currents (star con-nection).Park components of I A , I B ,IC .Harmonic content of currentfor single-phase calculation.RMS value of harmonic con-tent of current.RMS value of fundamentalmachine current at no-load.Flux, crest value.Torque pulsation.Envelo pe curve of torque pul-sations.

u,w.

= 27rfit = U l t

Peak value of torque pulsa-tions.Fundamental pull-out torque.Fundamental frequency.Switching frequency.Frequency ratio.Modulat ion index.Leakage factor .Leakage inductance.Leakage inductance for cal-culation of torque pulsations.Phase angle 0 5 y 5 6 0 .Phase angle 0 5 cp 5 360.

REFERENCESA. Schonung and H. Stemm ler, Static frequency changer s withsubharm onic control in conjunction with reversible variable-speed a x .drives, Brown-Boveri Rev., vol. 51, pp. 555-577, 1964.A. B. Plunkett , A current-control led PWM transistor inverter drive,in Conf. Record of 1979 IEEE-IAS Ann . Meeting, pp. 785-792.J . Zubek, A. Abbondanti , and C. Nordby, Pulsewidth modulatedinverter motor drive with improved modulation, IEEE Trans. Ind.Appl . , vol. IA-11, no . 6, pp. 695-703, Nov./Dec. 1975.G. Pfaff, A. Weschta, and A. Wick, Design and experimental resultsof a brushless ac servo-drive, in Conf. Rec. 1982 IEEE-IAS Ann .Meeting, pp. 692-697.J . Eibel and R. Jotten, Control of a 3-level switching inverter, feedinga 3-phase a.c. machine, by a microprocessor, ETG-Fachberichte,A. Bellini, G . Figalli, and G. Ulivi, A three-phase modulationtechnique suitable to supply induction motors, in Conf. Record ofIPEC 1983, Tokyo, pp. 396-406.K. Kovacs and I. Racz, Transiente Vorgange in Wech selstromm a-schinen, Bd . I and 11.Budapest: Verlag der Ungarischen Akademie derWissenschaften, 1959.J . Schorner, Bezugsspannung zur Umrichtersteuerung, ETZ-B, vol.27 , no. 7, pp. 151-152, 1975.D. Grant , J . Houldsworth, and K . Lower, The effect of word lengthon the harmonic content of microprocessor-based PW M waveformgenerators , in Conf. Rec. 1983 IEEE-IAS Annual Meeting, pp .H. van der Broeck and H. C . Skudeln y, Analytical analysis of theharmonic effects of a PWM ac d r ive , IEEE Trans. Power Electron.,vol . 3, no. 4, Apr. 1988.H. van der Broeck, Vergleich von spannungseinpragenden Wech-selrichtern mit zwei und drei Zweigpaaren zur Speisung einer Drehstro-masynchronmaschine unter Verwendung der Pulsweitenmodulationhoher Taktzahl, Dissertation , Rheinisch-Westfalische TechnischeHochschule, Aachen, 1985.S. Bowes and M. Mount, Microprocessor control of PWM invert-ers , in IEE Proc., vol. 128, Pt. B, no. 6, Nov. 1981, pp. 293-305.B. Bose and H. Sutherland, A high-performance pulse-width modula-

vel. 11, pp. 217-222, 1982.

643-650.

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150 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL 24 NO I , JANUARYIFEBKUARY I OR Xtor tor an inverter-fed drive system using a microcomputer, in Conf.Rec. 1982 Ann, Meeting IEEE-IAS, p p . 847-853

[I41 K Manch and M Ito, A mult imicroprocessor ac drive control ler, inCon!. Rec. 1980 IEEE-IAS Annual Meeting, pp 634-640[15] B Cook, A. Cantoni, and R Evans, A microprocessor based, 3-phase pulse width modulator, in Conf. Rec. 1982 Znt. Semiconduc-tor Power Converter Conf. of IEEE-IAS, pp 375-384A. Pollmann, A digital pulsewidth inodulator employing advancedmodulation techniques, IEEE Trans. Ind. Appl., vol IA-19, no 3 ,pp 409-414, M ayiJune 1983

Hans-Christoph Skudelny ( M 7 9 ) W ~ S orn 1111932 He received the Dip1 In g degree in 1957 mt lthe Dr Ing degree in 1960. both froni AdihenUniversit) of TechnologyFro m 1961 to 1973 he wds with Brow n-Bover i &Cie AG, Mannheim, Germany. where he workedin the fields of power electronics an d trdctio? Hebecame a Professor of power elei t ronics m d electrica l drives at Aachen University ot rechnology in1973 Hi s main re\edrch interebts ar e Lonvertercircuits, industrial and trdction drives. an d bd tery

[161

electric vehiclesHeinz W. va n der Broeck was born in Fussenich,Germany, on Novem ber 25, 1952 He received theIng Grad degree in electr~cal ngineering from theFachhochschule, Koln, Germany, in 1975, and theDip1 Ing. degree in electrical engineering from theAachen Universlty of Technology, Germany, in1980 University ot Technology, Gerrndny in I9X

From 1980 to 1987 he was on the scientific staffof the Institute of Power Electronic? and ElectricalDrives at the Aachen University of Technology In1985 he received the Dr Ing degree from the sameUniversity Since 1987 he ha s been with the Philips Research Laboratory.Aachen, Germ any

Georg V . Stanke was born in Baden Bden . G crmany, on July 25, 1956 He received the Dip1 Ingdegree in electrical engineering from the Aichen

In 1983 he joined the InTtitute ot Power Electrimics an d Electricdl Drives of the baiw bniver\ity upply