Waveform Distortion Caused by High Power Adjustable Speed Drives, Part 2 Probabilistic Analysis

7/28/2019 Waveform Distortion Caused by High Power Adjustable Speed Drives, Part 2 Probabilistic Analysis

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Waveform Distortion Caused by High PowerAdjustable Speed DrivesPart 11: Probabilistic AnalysisD. Castaldo, F. De Rosa, R. Langella, A. Sollazzo, A. TestaAbstractWaveformdistortion caused by high po we r adjustable speed d rives is considered in a probabi listic scenario . In acompanion pape r, two high computational eflci enc y drive models, one using the Line Com mutated Inverter andthe other the Pulse Width Modu lated Inverter, have been prop osed . These models are used inside a simu lationprocedure fo r the probabi listic ana lysis ofwaveform distortion on both the supply and motor sides of the two kindsof drives considered. The results obtained considering both mechanical and supply voltage variability are pre-sented and comm ented.

1 IntroductionHigh power adjustable speed drives (ASDs) arewell known to be generators of harmonic and interhar-monic distortion of curren ts and voltages in both sup-ply system and supplied motors. Th is happens for boththe most popular solutions using the L ine Comm utatedInverter (LCI) and the Pulse Width Modulated (PWM)Inverter. On th e supply side, the problem is the reduc-tion of quality of electrical energy due to individualharmonic components, total harmonic distortion andwaveform peak variation caused in voltages, for all theother loads supplied. On the motor side, the main prob-lems are the increased mechanical, thermal, vibrationand electrical stresses, caused on the motor by the volt-age distortion; especially in the case of ASDs withP W M nverters, the peak voltage increments can bevery remarkable and, consequently, the insulation ishighly stressed. When the consequences of d istortioncannot be accepted, filters have to be installed on the

supply or the supplied side, or on both. Moreover,sometimes i t is necessary to derate the main compon-ents (f.i. supply transformer and/or m otors) [1-51.The limits on the voltage and current disto rtion inthe Standards are defined on the basis of probab ilisticapproaches [6], [7]. In fact, current distortion dependson a large number of quantities such as those related tomechanical load, supplying system conditions and theother load behaviours. As these quan tities vary in time,the current component frequencies, amplitudes andphase angles, and then the peak value vary. Conse-quently the distorted voltages vary in time, so it be-comes useful to represent all the involved quantities interms of random variables.Provisional analyses to fo recast the Standard limitcompliance must be based on probabilistic models andit is necessary to use simulation tools. Among these, thewell known Monte Carlo Method [8], whose mainadvantage lies in the possibility of simulating a wide

variety of random supply and load characteristics, isone of the m ost attractive solutions. The m ain problemis the computational burden due to the high num ber ofsolutions required to ensure the simulation accuracy. Inpart I of this paper, two high efficiency models ofASDs have been proposed to cope with this problem.In this part of the paper, a simu lation procedu re isproposed to perform probabilistic analyses of thewaveform distortion caused by ASD s, also taking intoaccount the characteristics of the industrial plant inwhich they operate.

2 Simulation procedure2.1 Description

The strong correlation existing among all quant-ities affecting the waveform distortion, in particularthose related to time , makes the probabilistic modellingvery difficult to handle. A possible simulation pro-cedure, able to take into accou nt these correlations in acomprehensive way, is the Monte C arlo simulation.The simulation procedure can be implemented ac-cording to the flux diagram of Fig. 1.The random generation of the inpu t quantity valuesof both the supplying and motor sides, has to be doneaccording to proper probability density functions (pdf)which, in general, are multivariate pdf with a largenumber of variates.The pdf of the supply ing side quan tities, in partic-ular the fundamental and the o ther voltage frequencycomponents (amplitudes and arguments) for each sys-tem phase, can be derived from measurements or hy-pothesized according to proper scenarios. The pdf ofthe load demand can be obtained starting from the fore-casted working conditions of the specific mechanicalload considered. Experience on similar studies is alsouseful in certain cases.

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- * -

+Input data7 1 andom generationI

.cI AS D,Modelling!

Control system

Distortion evaluation4

Output statistics

&Fig. 1. Flux diagram of the simulation procedure ETEP

Deterministic models of the ASD can be used toobtain the waveforms of the electrical quantities of in-terest. For the high power ASDs using LCI or PWM in-verters, proper models of the control system and of theconversion system have been proposed in Part I. Thecontrol models permit to represent the operating condi-tions setting-stage and are able to take into accoun t thevariations of supplying system parameters, in partic-ular fundamental supplying voltage. The proposedmodels are characterized by high computational effi-ciency, but, in principle, any kind of different modelscan be included in the simulation procedure.Concerning distortion evaluation, it results useful(and necessary for the subsequent statistical treatmen t)to sacrifice the frequency resolution during D l Tanalysis and details about the single componentspresent in the result storage stage. Both goals are ob-tained f. i. following the IEC standard [9], which fixesthe frequency resolution to 5 Hz and groups all inter-harmonic components between two adjacent har-monics in a single index that is the r.m.s. value of all thecomponents included.It is worthwhile noting that also the storage and thestatistic treatment of output quantities is a serious prob-lem due to the need of using jpdf. In fact, in general, forthe purpose of harmonic penetration studies and for ap -plication in evaluations related to waveform peak val-ues, it is necessary to preserve all the inform ation aboutphase angles and correlations among different quant-ities. For some applications, the interest of the analysisis restricted to single output variation causes and/orsimplifications are possible for output data. This is thecase of some compatibility previsions, in which it ispossible to take advantage of the use of marginal pdfsfor both input and output data. In these cases, the sim-ulation procedure may result simplified or degeneratein a deterministic procedure applied to a certainnumber of case s, with the use of proper weighting fac-tors to properly combine the deterministic results in astatistic.

2.2 Tw o remarkable applicationsTw o applications of the simulation procedure pro-posed are here considered.The former deals with the impact of ASD s on theindustrial plants in which they operate in terms of injec-tion of harmonic and interharmonic currents into the

supplying system. The IEC and IEEE standards [6], [7]define compatibility levels generally based on statisticfigures such as 95 % or 99.9 % percentiles of the am-plitude variations of disturbances registered over de-fined periods of observation.The latter is related to ASDs' voltage distortion im-pact on the asynchronous motors they feed, causing areduction of their useful life due to increased insula-tion, mechan ical, thermal and vibration stresses. A cor-rect design of the moto rs is based on the evaluation oftheir expected useful life. Concerning the stress com-ponents which determine the useful life, the effects oflow frequency individual components (interharmonics)or distortion cumulated effects on peak value seem par-ticularly im portant [ 5 ] , [lo].For both applications, a comprehensive probabi-listic modelling is necessary because the know ledge ofthe probability density function, and not of singlefigures alone, is needed to asses distortion levels.The statistical figures needed for compatibilitytests are very easy to evaluate starting from pdf. A moredifficult and complex problem is the useful life evalu-ation because it must be solved, in gene ral, using com-plex electro-therm al models. A simplified model is re-ported in the Appendix.

3 Numerical experimentsThe simulation procedure has been carried out ap-plied to two d ifferent types of ASDs, depicted in Fig. 2and fully re ferred in 1131, [141.The generation of the input parameter values, bothfor the motor and supply side, presents some criticalaspects related to the conversion system behaviour.Referring to the supplying side parameters, themain problem is constituted by the amplitude variation

of voltages at the fundam ental frequency whose effectsare very relevant.Referring to the motor side quantities, speed in par-ticular, creates very c ritical problems in terms of signal

AC Loado-+-m++--

Rectifier DC Link Inverter TC Power supply

Fig. 2. a) Scheme of LCI asynchronous motor drive;b) Scheme of PWM asynchronous motor drive

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Output driv e frequency,f, + ETEPFig. 3. Pdf of output drive frequenc ies

periodicity assessmen t.The signals fundamental perioddepends on the motor speed and results as the inverseof the Fourier fundamental frequency, that is to say themaximum common devisor among all the frequenciescontained in the signal [15], [16]. In principle, verysmall Fourier frequency could occur; this means thatthe signals of interest should be calculated and ana-lyzed for a very long period. From an engineeringpoint of view, it is not necessary to take into accounttoo small working condition variations. Hence, the au-thors experience suggests that output frequ encies canbe approximated by partitioning the range of interestwith a frequency resolution of 0.5 Hz. This resolutiondoes not turn out to be too critical for the analysis of theconversion system and, at the same time, is accurateenough to take into account the working condition vari-ability.The output frequency,f,, has been considered asbeing variable from 17.5 to 50 Hz. The output powerand voltage have been considered to be proportional tothe output frequency. Fig. 3 show s the pdf of the outputfrequency, referring to realistic conditions in whichsome main speeds are more frequent [171.Furthermore, the fundamental supplying voltage,U,,, s modeled in a Gaussian scenario. In particular,the majority of dete rminations(99.75 %) falls in the in-terval (Uacn +5 %), assuming, for the sake of simpli-city, phase symmetry and the same mean value, Uac,(nominal rms value), for all the working conditions.The pdf of the supply voltage is partitioned by intro-ducing a proper num ber of classes, as shown in Fig. 4,and, to each of these classes, the supplying voltagevalue and probability are associated.

r.rn.s. voltage fo r LCI case study+5700 5900 6000 6100 V 6300

2315 2450 2500 2550 V 2625r.m.s.voltage for PW M case study4

Fig. 4. Partitioning of the Gaussian pdf of the supplyingvoltages

The ab sence of a statistical correlation between U,,andf, is assumed for the sake of simplicity even if otherstudies of the authors [181 have demonstrated how cor-relations can be important in the most general case.Once assumed this hypothesis, for each of the outputfrequencies, the supplying voltage randomness can betaken into accoun t by running, in a Monte Car10 pro-cedure, the simplified models for a very large numberof voltage determinations.In the following, two cases are considered. Theformer refers to a scenario in which only output drivefrequency variations are considered. The latter consid-ers also the supp lying voltage amplitude variations andgives an idea of their consequences. The results ob-tained for each of the applications discussed in section2.2 are reported.3.1 Input current distortion

For the sake of brevity, only som e IEC groups [9]have been selected. The choice of the main harmonicgroup C5 (5* harmonic) and its nearest interharm onicsgroups C4, (between 4thand 5th harmonics) and C5,5(between 5 and 6thharmonics).3.1.1 Variable frequen cy, constant supply voltage

Fig. 5 shows the relative and cumulative frequencyhistograms obtained for the PWM (a, b, c) and the LCI(d, e, f) drives. In particular, it can be ob served that:- in all the figures, the histograms present a great dis-persion of values;- the 95 % percentile is close to the maximum valuefor all the histograms except the case of Fig. 5fwhere it assumes a low value;the harmonic maximum values are greater for thePWM than for the LCI drive, while the contraryhappens for interharmonics, and these considera-tions apply also for the other group s not represent-ed in Fig. 5;- Fig. 5c and Fig. 5f show how the 95 % percentile isgreater for the PWM than for the LCI drive in spiteof the previous considerations about the maximumvalues;Fig. 5b and Fig. 5c evidence a bimodal behaviour,while Fig. 5e and Fig. 5f show a mono-modal be-haviour;in Fig. 5c and Fig. 5e the highest probability valuesare associated to the worst case.Fig. 6 shows the histograms of the Total Interhar-monic Distortion factor, TID [171, obtained for the PWMand LCI d rives. Comparing the results, it is evident howthe 95 % percentile in F ig. 6a is sensibly lower than the95 %percentile in Fig. 6b. This confirms in quantitativeterms the well-known fact that the P W M rive interhar-monk distortion is lower than that of the LCI drive.

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3.1.2 Variable frequen cy, variable supply voltageThe histogram s for gro ups C4,5, C5, C5,5 are shownin Fig. 7. Comparing the results of Fig. 7a, Fig. 7b,Fig. 7c with those in Fig. 5a, Fig. 5b, Fig. 5c, it can beobserved that:

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Fig. 5. Relative and cumulative frequency histograms for variable mechanical co nditions and constant supplying voltage.a) C4,5, b) C5, c) C5,5 or the PWM drive;d) C4,5,e) C5, f ) C5,5 for the LCI drive

Fig. 6. TID relative and cumulative frequency histograms.a) PWM drive, b) LCI drive

- the histogram shape is quite similar;- slight variations affect the maximum values;- the probability of the worst case in Fig. 7a andFig. 7c is lower than the probability in Fig. 5a andFig. 5c ; the same happens for the 95 % percentilevalues.

Comparing the results of Fig. 7d, Fig. 7e, Fig. 7fwith those in Fig. 5d, Fig. 5e, Fig. 5f, it can be observedthat:- al the h istogram shapes present appreciable changes;- in particular, Fig. 7e shows an evident bimodalbehaviour (differently from Fig. 5e);

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Fig. 7. Relative and cumulative frequency histograms for variable mechanical conditions and variable supplying voltage.a) C4 5 , b)C5, c) C5,5or the PWM drive;d) C& , e) C5, f) C5,5or the LC I drive- the probabilities of the worst cases in Fig. 7d,Fig. 7e, Fig. 7f are low er than those in Fig. 5d,Fig. 5e, Fig. 5f;the 95% percentiles in Fig. 7d, Fig. 7e, Fig. 7f

present different (greater or lower) values both forharmonic and interharmonic groups.The aforementioned considerations demonstrate

that supplying voltage variations bring about relevantvariations in estimating probabilistic parameters.Finally, Fig. 8 shows the histograms of the TID.Comparing the results in Fig. 8a with those in Fig. 6adoes not ev idence noticeable variations. Different con-siderations can be deve loped comparing the results inFig. 8b with those in Fig. 6b: a more pron ounced modal

-

Fig. 8. TID relative and cumulative frequency histograms. a) PWM drive; b) LCI drive

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Fig. 9. PWM drive: a) variable frequency-constant supply voltage; b) variable frequency-variable supply voltagevalue and a 10% decrease on the 95 % percentile areappreciated in the LCI drive case. and, then, to express kp as:U3.2 Outputvoltage distortion kp =Pi =("U ~ M A X100]L,f (2 )For both the cases of variable frequency-constantsupply voltage and variable frequency-variable supplyvoltage, statistics of harm onic and interharmonic volt-ages were obtained, including the statistic of the peakvalue.Fig. 9 shows, for the PWh4 drive, the relative andcumulative frequency histograms of the peak value ofthe distorted voltages as a percentage of 2449 V, whichturned out to be the maximum observed peak value. Bycomparing Fig. 9a and Fig. 9b, the effects of the v oltagevariability on the histogram shapes are evident, withgreat effects on the standard deviations and lower ef-fects on the mean values. Voltage variability reflects it-self on the variance of the PWM output peak voltage.Different possibilities are ava ilable to use the re-sults of Fig. 9 for insulation sizing or testing. H ere, ref-erence is made to the insulation voltage, Ui, epresent-ing the nom inal peak voltage considered for sizing andbeing different from the Uplnof eq. (A2) where Ui re-fers to the more general case in w hich the amount of thedistortion is of the same order of quantity of U as itis typical for the motors driven by modem A S d G h e r eit is not possible to refer to the fundamental voltagepeak value Upln.Considenng that Ui could not be, for economic rea-sons, the maximum possible value of Up, iYp ~AX,t i suseful to consider a size factor,Sf,epresentmg the per-centage of the m aximum peak voltage to be consideredfor sizing:

where the quantity in brackets is the random variable inFig. 9. For each Sf hoice, the relative frequencies ofthe corresponding kp values can be obtained by divid-ing the x axis values of Fig. 9 by a factor equal to SpThe results obtained for different choices of Sf rereported in Tab. 1. The corresponding Ui and E[$] arealso reported. E[L] /L , are estimated with reference toFig. 9a and Fig. 9b by using both the eq. (A3) and itssimplified expression of eq. (A4).The following considerations can be made:- a choice of Sf n the interval between 93 % and

94 %would give nominal values for the expectedlife;- the increased value of the standard deviation ofFig. 9b produces little reduction of the expectedlife (about 1 %);the sim plification introduced by eq. (A 4) has neg-ligible effects on the results in each case (about1%) as expected due to the low value of the stand-ard deviation.Fig. 10 shows the LCI drive relative and cumu-lative frequency histograms of the peak value of thedistorted voltages as a percentage of 6978 V, whichwas the maximum observed peak value. By comparingFig. 10a and Fig. lob, the effects of the voltage varia-bility on the histogram shapes are perceptible but, inthis case, with smaller consequences on both the stand-ard deviations and the mean values.Tab. 2 is the equivalent of Tab . 1 for the LCI drive.The following considerations can be made:a choice of Sf n the interval between 84 % and85 % would give nominal values for the expectedlife;

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"*I E[L] /L ,Fig. 9a E [ L ] /L ,Fig. 9bFig. 9a Fig. 9b By eq. (A31 By eq. (A4) By eq. (A3) By eq. (A4)Sf % I u, [VI

92 2253 1.014 1.014 0.881 0.882 0.872 0.88293 2278 1.003 1.003 0.97 0.972 0.962 0.97294 2302 0.992 0.992 1.070 1.07 1.059 1.071

Tab. 1. PWM drive: motor life variation for different Sf alues360 ETEPVol. 13, No. 6, NovemberDecember2003


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Fig. 10. LCI drive: a) variable frequency-constant supply voltage; b) variable frequency-variable supply voltage

EFpI E [ L ] / L ,Fig. 10a E[L] /L ,Fig. 10bFig. 10a Fig. 10b By eq. (A3) By eq. (A4) By eq . (A3) By eq. (A4)Sf % I ui [Vl83 5792 0.924 0.924 0.888 2.033 0.887 2.026

84 5862 0.9 13 0.9 13 0.989 2.264 0.988 2.25785 5932 0.902 0.902 1.100 2.5 18 1.099 2.5 10

Tab. 2. LCI drive: motor life variation for different Sf alues

- the eq. (A4) is applied outside its validity condi-tions; so, the simplification introduced has verynegative effects on results in each case (mo re than100%) as expected due to the high value of thestandard deviation.It is interesting to note the different results in termsof Sf alues which give nominal useful lives, obtainedfor the PWM (93-94 %) and LCI (84-85 %) drives.This is the consequence of th e different shapes of thepdfs, which are more ev ident in the sm all black histo-grams in the sam e scale reported in the top left side ofFig. 9 and Fig. 10.Furthermore, if Ui values are assumed equal toU ],.,MAX, Sf ould be equal to 61 % for the PWM and9 % for the LCI drive. So, the useful life of the PWMdriven motor would be reduced to ridiculous values andthe useful life of the LCI increased to anti-econom icalnon-useful great values.It is important to underline that the effected motorlife estimations have not included the effects of thevoltage spikes produced by commutation.

4 ConclusionWaveform distortion caused by high power Ad just-able Speed Drives has been considered in a probabilis-tic scenario. Reference is made to two high computa-

tional efficiency models of ASDs, proposed in a com-panion paper, one using the Pulse Width ModulatedInverter and the other the Line Commutated Inverter.They have been used inside a simulation procedure forth e probabilistic analysis of waveform distortion onboth the supply and motor sides of the two types ofASDs considered. The results obtained by considering

both mechanical and supply voltage variability condi-tions have been presented and commented.The paper dem onstrates the usefu lness of the prob-abilistic modelling based on simulation and on the useof high computational efficiency ASD models. It ispossible to obtain com plete statistics of the main quant-ities of interest:- absorbed harmon ic and interharmonic currents forthe application of com patibility tests as requestedby standards;output voltages for motor side component sizingpurposes.-

5 AppendixA simplified expression of the electro-the rmal lifemodel of M V L V com ponents insulation, referring tothe life in nominal operating temperature and neglect-ing further warming up due to harm onics, is [ 5 ] :

L ( k p ) =L ( k p ,O n ) ==[Lo xp(-Bcgn)] kpnp =Lnk p n p , ( Al l

where L is the insulation life, Lo its value at nominal si-nusoidal voltage and reference temperature,$ he peakfactor defined in the following, np and B model para-meters, ce = ( l /Oo - l/On) the conventional thermalstress, On the nominal absolute temperature, and Oo thereference temperature.The peak factor is defined as:

I.

(A2)

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where U is the peak value of the disto rted voltage, andUpln s ti e nominal peak value of the fundamental volt-age.The useful life can be estimated starting from themonitoring of the voltage over a certain period, Tp,and,then, assuming that the pattern of the voltage is almostthe same during the future life of the components. Theexpected relative value of the component useful life is[ I l l :

In [12], assuming that the standard deviation, akp,is sufficiently small (f.i.


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ETEP[171 Carbone, R.; Lungella, R.; Testa, A.: Simplified Prob-abilistic modelling of AC/DC /AC Power Conv erter In-terharmonic D istortion. 6h Int. C onf. on ProbabilisticMethods Applied to Power Systems (PMAPS ), Madei-ra/Portugal, 20 00[181 Castaldo, D .; Lungella, R.; Testa, A. : ProbabilisticAspects of Harmonic Impedances. Int. Conf. IEEEWinter Power Meeting, New Y or W S A , 2002

Manuscript received on March 5, 2003

The authorsDaniele Castaldo (1972) was born inCercolaDtaly. He received the de greein Computer Science Engineeringfrom the University of Naples, in1998. He is w orking towards the Ph.D.degree in Electrical Energy Conversi-on at the Secon d University of Naples,Aversdtaly. He is a student memberof IEEE Power Engineering Society.(Dipartimento di Ingegneria dellin-formazione, S econda Universith degliStudi di Napoli, Via Rom a, 29 - 81031 - Aversa (CE)/Italy,Phone: +3908 15010239, Fax: ++3908 15037042, E -Mail:[email protected])Francesco De Rosa (19 74) was born inCapuaDtaly. He received the degree inElectronic Engineering from the Se-cond University of Naples, in 2000.He is working towards the Ph.D. inElectrical Energy Conversion at theSecond University of Naples, AversdItaly. He is a student mem ber of IEE EPower Engineering Society. (Diparti-mento di Ingegneria dellinformazio-ne, Seconda Universith degli Studi diNapoli, Via Roma, 29 - 81031 - Aversa (CE)/Italy, Phone:+3908 15010239, Fax: ++3908 15037042, E-M ail: [email protected])

Roberto Langella (1972) was born inNapleshtaly. He received the degreein Electrical Engineering from theUniversity of Naples, in 1996, and thePh.D. degree in Electrical EnergyConversion from the Second Univer-sity of Naples, in 2000. He is curren tlyassistant professor in Electrical PowerSystems at S econd University of Nap-les, Aversdtaly. He is a member ofIEEE P ower E ngineering Society. (Di-partimento di Ingegneria dellinforrnazione, Seconda Uni-versith degli Studi di Napoli, Via R oma, 29 - 1031 - Aversa(CE)/Italy, Phone: +390815010239, Fax: ++390815037042,E-Mail: [email protected])Adolfo Sollazzo (1975) was born inCapuaD taly. He received the degree inElectronic Engineering from the Se-cond University of Naples, in 2001.He is working towards the Ph.D. de-gree in Electrical Energy Conversionat the Second University of Naples,Aversdtaly. (Dipartimento di Inge-gneria dellinformazione, SecondaUniversith degli Studi di Napoli, ViaRoma, 29 - 81031 - Aversa (CE)/Italy, Phone: +390815010239, Fax: ++390815037042,E-Mail: [email protected])Alfred0 Testa (1950 ) was born in Nap-les/Italy. He received the degree inElectrical Engineering from the Uni-versity of Naples, in 1975. He is a Pro-fessor in Electrical Power Systems atthe Second University of Naples,Aversdtaly. He is engaged in resear-ches on electrical power systems reli-ability and harmonic analysis. He is amember of IEEE Power EngineeringSociety and of AEI (the Italian Insti-tute of Electrical Engineers). (Dipartimento di Ingegneriadellinforrnazione, Seconda Universith degli Studi di Napoli,Via Roma, 29 - 81031 - Aversa (CE)/Italy, Phone:+3908150 10239, Fax: ++3908 15037042, E-Mail: alfredo .testa@ ieee.org)

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Waveform Distortion Caused by High Power Adjustable Speed Drives, Part 2 Probabilistic Analysis