In this paper, a new chaotic pulse width modulation (PWM) scheme is proposed and implemented to reduce the conducted electro-magnetic interference (EMI) in motor drives. The key is the use of logistic mapping to chaoize a frequency-modulated signal which then modulates the carrier frequency. Compared with the sinusoidal PWM and random PWM, the proposed scheme not only suppresses the peaky EMI, but also avoids the occurrence of low-order noises and mechanical resonance. Both simulation and experimental results are given to support the validity. © 2007 IEEE.published_or_final_versio

Chau, KT

Liu, C

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Wang, Z

IEEE Transactions on Magnetics

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Title Improvement of electromagnetic compatibility of motor drivesusing chaotic PWMAuthor(s) Wang, Z; Chau, KT; Liu, CCitationThe 10th Joint Magnetism and Magnetic Materials – InternationalMagnetics Conference (MMM–INTERMAG), Baltimore, MD., 7-11January 2007. In IEEE Transactions on Magnetics, , 2007, v. 43 n.6, p. 2612-2614Issued Date 2007URL http://hdl.handle.net/10722/57469Rights©2007 IEEE. Personal use of this material is permitted. However,permission to reprint/republish this material for advertising orpromotional purposes or for creating new collective works forresale or redistribution to servers or lists, or to reuse anycopyrighted component of this work in other works must beobtained from the IEEE.2612 IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 6, JUNE 2007Improvement of Electromagnetic Compatibility of Motor DrivesUsing Chaotic PWMZheng Wang, K. T. Chau, and Chunhua LiuDepartment of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, ChinaIn this paper, a new chaotic pulse width modulation (PWM) scheme is proposed and implemented to reduce the conducted electro-magnetic interference (EMI) in motor drives. The key is the use of logistic mapping to chaoize a frequency-modulated signal which thenmodulates the carrier frequency. Compared with the sinusoidal PWM and random PWM, the proposed scheme not only suppresses thepeaky EMI, but also avoids the occurrence of low-order noises and mechanical resonance. Both simulation and experimental results aregiven to support the validity.Index Terms—Chaos, EMC, EMI, motor drives, PWM.I. INTRODUCTIONI N the field of variable-speed motor drives, there is a trend forpushing up switching frequencies of pulse width modulation(PWM) inverters to reduce both volume and weight. This trendinevitably contributes to an increasing level of electromagneticinterference (EMI). It leads to degrade the electromagnetic com-patibility (EMC) for electronic devices [1]. Consequently, EMClegislation is increasingly stringent in many countries.In recent years, random PWM (RPWM) schemes, includingboth nonoptimized and optimized ones, have been developedto improve the EMC of motor drives [2]. The RPWM can ef-fectively spread the discrete spectral power over a continuousspectrum by varying the widths of individual switching inter-vals randomly. The optimized version can further even out thespectral power distribution. However, these schemes have ig-nored the consideration of low-order harmonic frequencies andthe system natural frequency. So, they inevitably introduce low-order noises, and increase the possibility to create mechanicalresonance [3].Because of the deterministic but random-like behavior, chaosis becoming attractive for application to motor drives [4]. Re-cently, it has been identified that the use of chaotic PWM toreplace sinusoidal PWM (SPWM) can reduce EMI in motordrives [5]. This chaotic PWM scheme employs the Bernoullishift map to chaoize an amplitude-modulated signal which thenmodulates the carrier frequency, so-called the chaotically ampli-tude-modulated PWM (CAMPWM). Although the CAMPWMtakes the advantage of easier implementation than the RPWMwhich needs a truly random source, their performance compar-ison is absent. Also, the CAMPWM is inflexible to tune thespectral power distribution, and is limited to those chaotic mapssatisfying some specific characteristics, namely the mixing rateand probability density function.In this paper, a chaotically frequency-modulated PWM(CFMPWM) scheme is proposed and implemented, which notonly suppresses the peaky EMI, but also avoids the occurrenceof low-order noises and mechanical resonance. Both simulationand experimental results will be given to compare the powerspectra resulting from SPWM, CFMPWM, and RPWM. More-Digital Object Identifier 10.1109/TMAG.2007.893712Fig. 1. Conducted EMI in motor drives.over, a comparison between CFMPWM and CAMPWM willbe given and discussed.II. PROPOSED CFMPWMIn general, the total conducted EMI is caused by two mecha-nisms: the common-mode (CM) noise which is related tocapacitive coupling of switching voltage into the line impedancestabilizing network (LISN), and the differential-mode (DM)noise which is related to switching current. Fig. 1 showstypical current flows of the conducted EMI in motor drives.The key of the CFMPWM is to modulate the switching fre-quency by chaotic sequences. The corresponding carrier signalis given by(1)(2)where is the nominal switching frequency, is the devia-tion frequency, is the modulation frequency, andis the chaotic sequences generated by the logistic mapwith . Hence, the spectrum of canbe expressed as(3)where is the frequency modulation index, isthe harmonic order, is the Fourier order, is the im-0018-9464/$25.00 © 2007 IEEEAuthorized licensed use limited to: The University of Hong Kong. Downloaded on October 8, 2008 at 04:16 from IEEE Xplore.  Restrictions apply.WANG et al.: IMPROVEMENT OF ELECTROMAGNETIC COMPATIBILITY OF MOTOR DRIVES USING CHAOTIC PWM 2613Fig. 2. Logistic map: (a) Bifurcation diagram; (b) Lyapunov exponent.pulse function, and is the magnitude coefficient. Ac-cording to the Carson’s rule, if , 98% of the power aroundis distributed to the discrete terms atwithin a limited frequency range .Fig. 2(a) shows the bifurcation diagram of against . It illus-trates that can be used to tune the spectral power distributionamong no frequency modulation (FM), periodic FM, multi-pe-riodic FM and chaotic FM. When , chaos occursand the corresponding Lyapunov exponent is positive as shownin Fig. 2(b).Based on a practical 3-phase 400-W 220-V 4-pole inductionmotor drive, the mechanical resonant frequency of the rotor canbe estimated by using the Holzer method. Given Hzand kHz, it deduces kHz andHz so as to avoid overlapping with the mechanical resonant fre-quency of 10.2 kHz. Hence, three indicators are defined to as-sess the EMC of this motor drive. Since the conducted EMIwith a frequency exceeding 9 kHz is stringently limited by theVDE standards, the maximum power spectral density (PSD) ofand within 9–150 kHz is used as the first indicator.In order to evaluate the content of low-order noises while thepower spectrum is mainly from to , thepower of and within 4.99–5.01 kHz is used as thesecond indicator. In order to evaluate the possibility of mechan-ical resonance at 10.2 kHz, the power of and within10.19–10.21 kHz is used as the third indicator. Therefore, theCFMPWM is created by tuning equal to 3.9 so that the firstindicator is minimum while the others are low.III. SIMULATION RESULTSComputer simulation of the whole system is carried out byusing the Matlab Simulink. The corresponding power spectraare plotted by a Matlab function, namely the periodogrammethod. The power spectra of and using SPWM,CFMPWM, and RPWM are computed from zero to 150 kHzunder the same and . Figs. 3–5 show the correspondingpower spectra within 0–22.5 kHz so as to depict their spectralpower distributions.First, by comparing the maximum PSD of theirspectra within 9–150 kHz, namely 21.3 dBm/Hz for SPWM,10.8 dBm/Hz for CFMPWM and 7.3 dBm/Hz for RPWM,it shows that the CFMPWM and RPWM have remarkableimprovements over the SPWM. Similarly, by comparing thosespectra, namely 31.4 dBm/Hz for SPWM, 10.2 dBm/Hzfor CFMPWM, and 6.2 dBm/Hz for RPWM, it further showsthat the CFMPWM and RPWM have remarkable improvementsover the SPWM. Thus, it indicates that both the CFMPWMFig. 3. Simulated power spectra of SPWM: (a) V ; (b) V .Fig. 4. Simulated power spectra of CFMPWM: (a) V ; (b) V .Fig. 5. Simulated power spectra of RPWM: (a) V ; (b) V .and RPWM have much better performance than the SPWM insuppressing the peaky EMI.Second, by comparing the power of their spectra within4.99–5.01 kHz, namely dBm for SPWM, dBmfor CFMPWM, and 2.5 dBm for RPWM, it shows that theCFMPWM has a significant improvement over the RPWM.Similarly, by comparing those spectra, namelydBm for SPWM, dBm for CFMPWM and dBm forRPWM, it further shows that the CFMPWM has a significantimprovement over the RPWM. Thus, this comparison indicatesthat the CFMPWM has much better performance than RPWMin avoiding low-order noises.Third, by comparing the power of their spectra within10.19–10.21 kHz, namely dBm for SPWM, dBmfor CFMPWM, and dBm for RPWM, it illustrates thatthe CFMPWM provides a much greater attenuation than theRPWM. Similarly, by comparing those spectra, namelydBm for SPWM, dBm for CFMPWM, anddBm for RPWM, it further illustrates that the CFMPWM pro-vides a much greater attenuation than the RPWM. Thus, it in-dicates that the CFMPWM has much better performance thanRPWM in avoiding mechanical resonance.It should be noted that even though the SPWM of-fers the lowest spectral power within 4.99–5.01 kHz and10.19–10.21 kHz, its severely peaky EMI will create annoyingAuthorized licensed use limited to: The University of Hong Kong. Downloaded on October 8, 2008 at 04:16 from IEEE Xplore.  Restrictions apply.2614 IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 6, JUNE 2007Fig. 6. Measured power spectra of SPWM: (a) V ; (b) V .Fig. 7. Measured power spectra of CFMPWM: (a) V ; (b) V .Fig. 8. Measured power spectra of RPWM: (a) V ; (b) V .acoustic noise in motor drives. This problem precludes theSPWM competing with CFMPWM and RPWM.IV. EXPERIMENTAL RESULTSFor experimental verification, an IGBT-based voltage sourceinverter is constructed to supply the aforementioned inductionmotor. The CFMPWM scheme is implemented by a single-chipTMS320F240 microcontroller. All power spectra are directlymeasured by using the LeCroy WR6050 power spectrum an-alyzer. Figs. 6, 7, and 8 show the measured power spectra ofSPWM, CFMPWM, and RPWM, respectively. The resolutionbandwidth is set to be 15 Hz. It can be seen that the measuredspectra well agree with the simulated counterparts as shownin Figs. 3, 4, and 5. Hence, it experimentally verifies that theproposed CFMPWM not only effectively suppresses the peakyEMI, but also exhibits high immunity to low-order noises andmechanical resonance.Fig. 9. Simulated power spectra of CAMPWM: (a) V ; (b) V .V. FURTHER COMPARISONIn order to compare the CFMPWM with the CAMPWM,the power spectra of and using CAMPWM arecomputed under the same logistic map, and . Fig. 9shows their distributions within 0–22.5 kHz. The maximumPSD within 9–150 kHz, the power within 4.99–5.01 kHz, andthe power within 10.19–10.21 kHz of using CAMPWMare 14.4 dBm/Hz, dBm, and dBm, respectively,whereas those using CFMPWM are only 10.8 dBm/Hz,dBm, and dBm, respectively. Relative data of aresimilar. Hence, it confirms that the proposed CFMPWM canoffer better spectral performances than the CAMPWM.VI. CONCLUSIONBy using the logistic map to chaoize the frequency-modu-lated signal for the carrier frequency, a new CFMPWM has beenproposed and implemented to improve EMC of motor drives.Both simulation and experimental results have confirmed thatthe proposed CFMPWM can effectively suppress the peaky EMIwhich usually occurs in SPWM, and can avoid the possibilityof low-order noises and mechanical resonance which gener-ally occur in RPWM. Moreover, the CFMPWM can offer betterspectral performances than the CAMPWM.ACKNOWLEDGMENTThis work was supported and funded by a Grant (HKU7154/04E) from the Research Grants Council, Hong Kong SpecialAdministrative Region, China.REFERENCES[1] A. M. Sitzia, A. E. Baker, T. W. Preston, A. Puzo, and A. Pons, “Finiteelement analysis for power electronics EMC applications,” IEEE Trans.Magn., vol. 32, no. 3, pp. 1517–1520, May 1996.[2] F. Blaabjerg, J. K. Pedersen, L. Oestergaard, R. L. Kirlin, A. M. Trzy-nadlowski, and S. Legowski, “Optimized and non-optimized randommodulation techniques for VSI drives,” EPE J., vol. 6, pp. 46–53, Sep.1996.[3] W. C. Lo, C. C. Chan, Z. Q. Zhu, L. Xu, D. Howe, and K. T. Chau,“Acoustic noise radiated by PWM-controlled induction machinedrives,” IEEE Trans. Ind. Electron., vol. 47, pp. 880–889, Aug. 2000.[4] K. T. Chau and Z. Wang, “Design of permanent magnets to chaoizedoubly salient permanent magnet motors for electric compaction,” J.Appl. Phys., vol. 99, pp. 08R306:1–08R306:3, Apr. 2006.[5] A. Bellini, G. Franceschini, R. Rovatti, G. Setti, and C. Tassoni, “Gen-eration of low-EMI PWM patterns for induction drives with chaoticmaps,” IEEE IECON, pp. 1527–1532, 2001.Manuscript received October 31, 2006 (e-mail: zwang@eee.hku.hk).Authorized licensed use limited to: The University of Hong Kong. Downloaded on October 8, 2008 at 04:16 from IEEE Xplore.  Restrictions apply.

Improvement of electromagnetic compatibility of motor drives using chaotic PWM

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Improvement of electromagnetic compatibility of motor drives using chaotic PWM

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