The Influence of the Harmonics in the Contactless Power Transfer Systems

Transcription

1 6H NERNAONA CONFERENCE ON MODERN OWER SYSEMS MS5, 8- MAY 5, CUJ-NAOCA, ROMANA he nfluence of the Harmonics in the Contactless ower ransfer Systems oana-gabriela Sîrbu an Dan-Gabriel Stănescu Department of Electrical, ower Systems an Aerospace Engineering University of Craiova Craiova, Romania Abstract New aspects concerning the behavior of the inuctively couple contactless power transfer systems are presente in this paper. he main analysis focuses on the interaction between the contactless power transfer circuit an the.c.-a.c. converter. he influence of the voltage harmonics introuce by this converter on the transfer performances is stuie. he analysis inclues not only etails on the power transferre to the resistive loa, but also aspects on the transfer efficiency. he influence of the semiconuctor elements switching frequency on the system performances is presente, too. Finally some conclusions are epicte as concerns the necessity of using filtering circuits between these two components of the system. Keywors contactless power transfer system; circuit analysis; harmonics; efficiency. NRODUCON he problems concerning the contactless power transfer represente an still represent interest subjects for the researchers community [], []. Even if the operating principle is well-nown, there are some aspects that are not fully explaine an there are some components of the system for which it is necessary to fin out improve solutions. he technical papers publishe in the last few years try to offer solutions an alternatives to each problem, motivating with arguments each choice. hus one coul observe that some structures have alreay been settle for the contactless power transfer system an that they epen on the application type. Even that it is use for the electric vehicle battery charging [], [3] [6], for small omestic evices or for accurate meical evices, the system general structure is almost the same. t inclues: the source, the conversion equipment (an inverter in case of a.c. source or an a.c.-.c.-a.c conversion group in case of an a.c. source), the magnetically couple circuits an the loa. For a.c. loa an aitional equipment is neee, i.e. an a.c. -.c. converter (rectifier) [3] []. n this wor we focus on the stuy of the inverter - inuctively couple circuit group. For this purpose a series connection of the elements was consiere in the two couple circuits. As inverter we opte for a mipoint inverter type because of its simplicity an as cheaper solution []. he analyses of the output voltage of the inverter an of its harmonic content were mae firstly. hen through a circuit analysis the harmonics of the primary circuit an of the seconary circuit currents were etermine. Using these harmonic currents the performances of the system were analyze for each harmonic an globally, by calculating the loa active power, the generate active power at the inverter output an the efficiency. he results were analyze comparatively as function of the harmonic orer an as function of the operating (funamental) frequency. Finally the contribution of the harmonics on the power transfer efficiency was emphasize an some conclusions coul be formulate.. HEORECA ASECS ON HE CONACESS OWER RANSFER SYSEM he iagram of the inverter - couple circuits group stuie here is presente in Fig.. he mipoint inverter has only two switching elements an two capacitors, being thus the cheapest type of monophase inverter. he elements of the two couple circuits can have the same values or, in the general case, can be ifferent. Depening on the position of the two coils, the coupling inuctances an can have ifferent or the same values. As loa we consiere a resistance R. f the supply voltage is U, each switching element is in conuction moe only a half of the perio. hus the voltage u at the inverter output is a perioic signal that is given by the relation: U / pentru t, / u ( t) U / pentru t /, his voltage was represente in Fig. uring one perio corresponing to the operating frequency f of 5 Hz ( / f ). Being a perioic function this voltage can be written using the trigonometric Fourier series []: A u ( t) A cost B sint his wor was supporte by the strategic grant OSDRU/59/.5/S/ 3355, roject D 3355 (4), co-finance by the European Social Fun within the Sectorial Operational rogram Human Resources Development

2 6H NERNAONA CONFERENCE ON MODERN OWER SYSEMS MS5, 8- MAY 5, CUJ-NAOCA, ROMANA U + C D u (t) i (t) R C C R * * i (t) R C inverter D inuctive contactless power transfer circuit Fig.. Contactless power transfer system iagram. U B B ( ) his result is obvious if we tae into account the fact that the function () is a crenel function [], i.e. an o function that fulfill also the relation u ( t) u ( t). Consequently the output voltage u can be written as a trigonometric Fourier series having the form: ( t) B sin u t Fig.. Supply voltage of the inuctive contactless power transfer circuit, u (t), uring one perio, for f = 5 Hz. where is the harmonic orer. By calculating the series coefficients [] of the output voltage u given by (), we obtaine: A u ( t)t A u ( t) cos( t)t U B u ( t) sin( t)t cos So the coefficients of the continuous component an of the cosine components are zero. As concerns the sine components the coefficients of even orer are zero, too. We can easily notice that the coefficients of the sine components can be calculate with the relations: Because we can etermine now each harmonic of the ( ) output voltage u o, we can use their phasor transform U to calculate the harmonics of the currents i ( t) an i ( t) of the primary an of the seconary circuits (Fig. ): U R R R j C j C Using the notations ( ) X C j j j. ( ) X j C A R R R X X, ( ) R R X B R X the rms values obtaine for the -th orer harmonic of the currents are: 34

3 6H NERNAONA CONFERENCE ON MODERN OWER SYSEMS MS5, 8- MAY 5, CUJ-NAOCA, ROMANA U A B R R X A B U Using these formulae we can etermine the active power consume by the loa an the active power offere by the inverter for each harmonic: R R g * g ReU U R R A A B X B an consequently the efficiency, calculate for each harmonic:, / R g f the total active power at the resistive loa or at the inverter output is wante, they can be calculate by summation: R t R g t g Because the harmonic components are nown the total harmonic istortion HD can be etermine for any electrical quantity Y (voltage or current) with [3] [5]: () (3) Y Y () () (3) Y Y Y HD Fig. 3. Harmonic specter of the supply voltage u (t), rezulting from analytical calculus, for f = 5 Hz. Some of the results obtaine for this system are presente further on. Fig, 3 shows the harmonic specter of the output voltage u. One can notice that the funamental harmonic has the highest value, but the o orer harmonics brings an important contribution, too. Fig. 4 an Fig. 5 present the harmonic specters of the primary an of the seconary currents, if the operating frequency is equal to the resonance frequency. We can observe that the preominant harmonic of the primary circuit current is of the thir orer, even if the funamental has a value close to it. n the same time in the seconary circuit the funamental current has the main weight. Because the resistive loa active power epens only on the seconary current an not on the primary one, the active power calculate for each harmonic showe a specter similar to the current i, where the main contribution is brought by the funamental an to a certain extent by the thir orer harmonic (Fig. 6). hese formulae can be introuce in a program (for example using the MAAB software [6]) an the results can be represente graphically in a suggestive manner for an easier interpretation.. HARMONC ANAYSS ON A CASE SUDY We preforme the harmonic analysis on a system with the following parameters: the.c. supply voltage U V, the circuits parameters R R., 37.5μH, R 5, C C 3 nf, 6.5μH (corresponing to a coupling coefficient c. 7 ). Because the elements of the two circuits have the same values one can say that the system is symmetrical. he resonance frequencies of the circuits are f f 5 Hz. Fig. 4. Harmonic specter of the primary circuit current i (t), for f = 5 Hz. 34

4 6H NERNAONA CONFERENCE ON MODERN OWER SYSEMS MS5, 8- MAY 5, CUJ-NAOCA, ROMANA Fig. 5. Harmonic specter of the secunary circuit current i (t), for f = 5 Hz. Fig. 6. Active power corresponing to the loa resistance R as function of the harmonic orer, for f = 5 Hz. Fig. 8. ower transfer efficiency as function of the harmonic orer, for f = 5 Hz. he active power generate by the inverter, for the same operating frequency, represente for each harmonic (Fig. 7) showe a big similarity with the Fig. 6. his fact is confirme by the graphical representation of the efficiency of the power transfer as function of harmonic orer (Fig. 8). We can remar that when the operation frequency is equal to the resonance frequency the efficiency is always higher than 94%, the biggest value (almost %) being for the funamental. We wante to analyze what happens if we change the operating frequency. We consiere a frequency lower than the resonance frequency, lower than half of f f 5 Hz, i.e. f 7 Hz. n this case we notice that the thir harmonic is preominant in the seconary current specter, but also in the active power consume by the resistive loa (Fig. 9). n fact in Fig. 9 one can see that the active power corresponing to the funamental is almost negligible. he thir harmonic is preominant also in the active power offere by the inverter. Consequently in the efficiency graphic as function of the harmonic orer the funamental has a efficiency of only 64 %, while the highest efficiency is obtaine for the thir harmonic (Fig. ). Fig. 7. Active power generate by the supply system as function of the harmonic orer, for f = 5 Hz. Fig. 9. Active power corresponing to the loa resistance R as function of the harmonic orer, for f = 7 Hz. 343

5 6H NERNAONA CONFERENCE ON MODERN OWER SYSEMS MS5, 8- MAY 5, CUJ-NAOCA, ROMANA Fig.. ower transfer efficiency as function of the harmonic orer, for f = 7 Hz. Fig.. Active power corresponing to the loa resistance R as function of the funamental frequency of the supply voltage u (t). By choosing a frequency higher than the resonance frequency f 5 Hz, for example f Hz, the funamental becomes preominant not only at the seconary current, but also at the primary circuit current (Fig. ). hus in this case the power transfer is ue mainly to the funamental, when the efficiency if over 94%. he analysis was repeate successively for ifferent values of the operating frequency f. he main results were centralize in able. With (6) the total harmonic istortion for the primary current (HD) an for the seconary current (HD) were calculate, as well as the total efficiency of the power transfer with a relation similar to (4). Fig.. Harmonic specter of the primary circuit current i (t), for f = Hz. his is ue to the fact that the thir harmonic correspons to a frequency in the vicinity of the resonance frequency. One can say that in this case the power transfer is mae especially through the harmonics. We observe that for frequencies much lower that the resonance frequency the harmonics (especially the thir orer ones) are ominant, taing over the function of power transfer. For frequencies in the vicinity of the resonance frequency f or higher than its value, the funamental is preominant an the efficiency reaches high values, of more than 95%. his fact explains why the total harmonic istortion calculate for the two currents is important for f f. ABE. COMARAVE RESUS OF SOME CASES AS CONCERNS HE EECRCA QUANES FOR HE DSORED REGME AND FOR HE FUNDAMENA Case f [Hz] HD [%] HD [%] [%] [W] [W] [%] f<<f f<f f<f, R max f=f f>f f=3 f f>>f () [A] () [A] () R () g () 344

6 6H NERNAONA CONFERENCE ON MODERN OWER SYSEMS MS5, 8- MAY 5, CUJ-NAOCA, ROMANA he ifferent behavior for various values of the frequencies can be explaine also if we represent the active power corresponing to the resistive loa as function of the operating frequency (Fig. ). hus we remare that the resonance frequency correspons to a minimum of the active power. wo peas of active power are obtaine for the frequencies 5.5 Hz an 75 Hz. his type of variation can be explaine by the frequency splitting phenomena that appear at the couple circuits in series configuration [7]. f we choose the frequency corresponing to the first maximum ( f 5.5 Hz ) we obtaine the maximum active power transferre to the loa that is ue mainly to the funamental (76.5 W for the frequency of 5.5 Hz, by comparing with 33 W obtaine for the resonance frequency). n the same time, because the funamental is ominant, the HD has a minimum in this case. he analysis shows that it is recommene that the operation frequency must be chosen equal or higher than the resonance frequency of the circuits. Also the frequencies when the highest values of active power are obtaine must be nown an even chosen as operating frequency if a maximum power transfer an a maximum efficiency have to be obtaine. n all cases because of the voltage harmonics introuce by the converter the currents in the two circuits - an implicitly the active powers - have harmonics; their weight epens on the operating frequency. Even if these harmonics create istortions to the electrical quantities they bring a positive contribution to the power transferre to the loa. By consiering a filter in this system (between the inverter an the couple circuits) we coul limit the harmonics an implicitly the total transferre power. f one chooses an operating frequency equal to a frequency that correspon to an active power pea, the funamental is preominant so that a filtering system is not necessary any more. V. CONCUSON he paper analyzes the inuctively couple circuits of a contactless power transfer system in correlation with the.c.- a.c. converter that supplies this system. hus the harmonics introuce by the converter are etermine an analyze an they are use afterwars in the stuy of the couple circuits. he harmonic content is etermine an explaine not only for voltages an currents, but also for the generate power an the loa active power as well as for the power transfer efficiency. We conclue that in certain cases the harmonics can bring an important contribution to the power transfer an in these cases a filter in this system coul affect in a negative manner the performances of the system. his stuy brings a contribution on the harmonic behavior of the contactless power transfer system, by taing into account the inverter operation. he conclusions epicte here can be useful in a thoroughgoing stuy on the contactless power transfer systems an in the esign of these systems. REFERENCES [] D. Niculae,. Dumitriu, M. orache, A. lie an. Manache, Magnetic resonant couplings use in wireless power transfer to charge the electric vehicle batteries, roceeings of the 4-th nternational Symposium on Electrical Engineering an Energy Converters, Suceava, September -3,, pp [] C. ăcurar, V. Ţopa, A. Răcăşan an C. Munteanu, nuctance computation an layout optimization for spiral inuctor, Buletinul AGR, no. 3, pp ,. [3] S. Choi, J. Huh, W.Y. ee an C.. Rim, Asymmetric coil sets for wireless stationary EV chargers with large lateral tolerance by ominant fiel analysis, EEE ransactions on ower Electronics, vol.9, no., pp , December 4. [4] S. i an C.C. Mi, Wireless power transfer for electric vehicle applications, EEE Journal of Emerging an Selecte opics in ower Electronics, p.-4. in press. [5] S. A. Sabi an N. M.. an, Wireless power transfer for electric vehicle, 4 EEE 8th nternational ower Engineering an Optimization Conference (EOCO4), 4-5 March 4, angawi, he Jewel of Keah, Malaysia, pp [6] C. Song, D. H. Jung, E. Song, Y. Cho, S. Kim, J. Kim an J. Kim, Electromagnetic interference reuction metho from hanhel resonant magnetic fiel charger (HH-RMFC) for electric vehicle, 4 EEE Wireless ower ransfer Conference (WC), Jeju, South Korea, 8-9 May 4, p.5-8, 4. [7] S. C. Moon, B. C. Kim, S. Y. Cho, C. H. Ahn an G. W. Moon, Analysis an esign of a wireless power transfer system with an intermeiate coil for high efficiency, EEE ransactions on nustrial Electronics, vol.6, no., pp , November 4. [8] R. revisan an A. Costanzo, A -W contactless energy transfer system base on a rotary transformer for sealing rollers, EEE ransactions on nustrial Electronics, vol.6, no., pp , November 4. [9] F. uri, R. Wiengarten, V. Reising, A. Kratser, mpact of the woring frequency on wireless power transfer systems, CM Europe 4, May 4, Nuremberg, Germany, pp [] W. Zhong an S. Y. R. Hui, Maximum energy efficiency tracing for wireless power transfer systems, EEE ransactions on ower Electronics, p.-, in press. [] A. Bitoleanu, S. vanov an M. opescu, Static Convertors (Convertoare statice), Craiova: nfome, 997. [] C.. Mocanu, Electric Circuit heory (eoria circuitelor electrice), Bucharest: Diactica si eagogica, 979. [3]. M. Nicolae, Electric Energy Quality in Electroenergetical Systems of imite ower (Calitatea energiei electrice in sisteme electroenergetice e putere limitată), Bucharest: ehnica, 998, pp.7-. [4].G. Sîrbu an. M. Nicolae, Analysis an simulation of an electric riving inverter use in electric urban traction, Annals of the University of Craiova, Electrical Engineering series, vol. 3, no. 3, pp.36-4, 6 [5]. G. Sîrbu, Software tools for electrical signals processing, Acta Electrotehnica, Special issue, vol. 5, no. 5, pp ,. [6] M. Ghinea an V. Fireţeanu, MAAB - Numerical Calculus. Graphics. Applications (MAAB - Calcul numeric. Grafică. Aplicaţii), Bucharest: eora, 3. [7] W. Q. Niu, J. X. Chu, W. Gu an A. D. Shen, Exact analysis of frequency splitting phenomena of contactless power transfer systems, EEE ransactions on Circuits an Systems -: Regular papers, vol. 6, no.6, pp , June