Application of chaotic modulation to ac motors forharmonic suppression

Wei Cui *, K. T Chau #, Zheng Wang #, J.Z Jiang *

* Shanghai Key Laboratory ofPower Station Automation Technology, School ofMechatronics andAutomation,Shanghai University, Shanghai, China

# Department ofElectrical and Electronic Engineering, The University ofHong Kong, Hong Kong, Chinacwmail@,staff shu. edu. cn, ktchau@,eee. hku. hk, jzhjiang@,mail. shu. edu. cn

Abstract- Instead of avoiding the occurrence of chaos in motor The key of the proposed low EMI modulation strategy is todrives, chaos is positively utilized in this paper. A new chaotic adopt the chaotic sequence to generate PWM patterns so thatpulse width modulation (PWM) scheme is proposed and the periodicity of the power spectrum of the motor current canimplemented for ac motors, which functions to significantly be disrupted and a more evenly distributed current spectrumsuppress the harmonic peaks and hence the acoustic noise. The with lower harmonic peaks can be obtained. In this paper, ankey is to employ the Chua's circuit for generation of the desired analogue chua's circuit shown in Fig. 1 has been implementedchaotic sequence. By using a practical induction motor, both to obtain the necessary chaotic sequence. The chua's circuitcomputer simulation and experimental results verify that thecchaotic PWM takes definite advantages over the conventionalPWM and random PWM, namely the harmonic peak suppression diL Iand simple hardware implementation.. - - Vc2

dit LKeywords-Chaotic modulation; Chua's circuit; Harmonic dVC2 I C (G)suppression cdt C2 C2

1. INTRODUCTION dt Cl (VcI)± (VC2-Vci)

The steep variation of the voltage in the PWM-VSI where f(Vcl) describes the characteristic of negativeconverters working at high switching frequency will produce resistance and G = I/ R.high frequency components in the motor currents, which aremainly responsible for most of the electromagnetic emissions CbVc] ± (Gb - Ga)E Vt1 <Einterference (EMI) issues[1]-[3]. The fixed switching f(Vcl) GaVCI - E< Vcl < E (2)frequency technique usually used in most converters will result lin impulsive and periodic high-frequency current spectra while tGbVC] ± (GaGb)E > Ethe dominant frequencies are densely concentrated at amultiple of the switching frequency. Depending on the R Rdeployed power, such current peaks are usually high enough to __cause EMI problems. Therefore, it is desirable to spread out thefrequency spectrum of the harmonic current so as to eliminatethe presence of the large-amplitude harmonic currentsconcentrated around the specific frequency [4]-[20].

The purpose of this paper is to propose a low EMI non- +tperiodic modulation strategy based on chaotic sequence (_obtained on the chua's circuit. With the adoption of the chaos- LC2 2based PWM technique, the resulting power spectrum of the 2 _ _Vmotor current can be compelled to be continuous, while theharmonic peak can be reduced by 15dB. Both computersimulation and experimental results will be given to verify theproposed modulation strategy. L

II. IMPLEMENTATION OF CHAOTIC SEQUENCE

Figi.1 Chua's circuit.

1-4244-0726-5/06/$20.00 '2006 IEEE 2343

Due to the negative resistance, the chua's circuit can produce where 0(t) is the frequency modulated phase angle which cancontinuous chaotic output with the proper selection of circuit be further express as:parameters. A digital control system shown in Fig.2 has beendesigned to sample the analog output voltage of the chua's0()5 tA F (r) d (6)circuit and stores the sampled discrete sequence in a unitized J mform. According to the research [24], the obtained discrete °sequence is still chaotic by inheriting the stochastic nature ofthe original chaotic system. V

|Chua's ||circuit |g

Se uene Modulaor2 SamplFng and PM ator.

I I ~~~~~~~~BaseCarrierI

Control pulse | MC. ~~~~~~~~Fig.3. Accomplishment of Chaos-based PWM Generator.

Fig.2.Hardware setup used to sample the chaoticsequence.

As the frequency deviation laws are non-periodic which isbased on the chaotic sequence, thus the modulated signal

III. CHAOTIC MODULATION IMPLEMENTATION power densely concentrated around specific frequencies are

The frequeny m d fappreciably spread and the peak interference is effectivelyThefaperequecy:oduate funtio as(3)is itrouce in suppressed. Fig.3 and Fig.4 show the possible scheme of thethe paper: chaos-based PWM generator and the block diagram of the

N proposed chaotic modulation sine-triangle PWM controlFm(t)= irn ZXk(t-tk) (3) system respectively. The chaotic sequence generator is

N>oo k=1

The modulated signal can be obtained through its incessantiteration with: - _PMXk+] f(xk ), k=0,,2, (4)wheref is the mapping function, therefore a chaotic sequence PWM duty cycleslike {xk: k =0,1,2, } can be obtained. genationandfire

In this paper, the mapping is realized based on the sample circuitsequence obtained from the chua' s circuit. Because thesequence is established on the chua's circuit, it shows the idealnature of auto correlation and cross correlation. The discrete Referen f tchaotic sequence Fm (t) is used as the frequency deviation + Genetorsignal regulating the modulation, while the control F() |parameters f- and f determine the central frequency andmaximal deviation of the frequency modulator, respectively. Feqa ^Chati sThe output ofthe frequency modulator can be expressed as: |mdl inMr ||l

Fig.4. Chaos-based SPWM\ control system for induction motor.

2344

implemented using a lookup table contained in the ROM of dsp, N owhose contents have been generated in an offline manner. If Zthe quantity numbers are large enough, thus there will be no m -20effect on the resulting current spectrum. The chaotic -4 0

lsignal Fm(t) is then applied to frequency modulator. As can ,1be seen from the figure, the chaotic modulation is a very u 60simple addition to an existing sine-triangle modulator.

IV. SIMULATION AND EXPERIMENTAL RESULTS -80An off-the-shelf SPWM inverter has been modified to

include the chaos-based PWM scheme and the schematic of the . I Icontrol system is shown in Fig.4. Based on the scheme, an u -120experimental platform is also developed. Both computer asimulations and experiments have been conducted based on a - 14013-phase induction motor (see Table 1). In all the results given, X 0 2 4 6 8 10the output frequency fr is 50Hz, the carrier frequency fc is Frequency (KHz)IkHz, the peak frequency deviation fA is 100Hz and the (b)modulation index M is 1. The simulated currents and their Fig.5. Simulated current (a) and its harmonic spectrum (b) with the

conventional SPWM pattern.corresponding harmonic spectra are shown in Fig.5 and 6 withand without the chaos-based PWM scheme, respectively. It 5can be clearly seen that the energy spectrum of the motorcurrent is compelled to spread evenly with chaos-based 3modulation, leading to an effective suppression of harmoniccurrent peaks by lOdB at least, compared with the case of <conventional SPWM scheme. Based on the experimentalJplatform as shown in Fig.7, Fig.8 and 9 shows the measured acurrents and their corresponding harmonic spectra with and t -1without the chaos-based PWM scheme respectively. Harmonicspectra for larger frequency-range with and without the chaos- -3based PWM scheme are also shown in Fig.10. Due to thelimited sampling capability of the oscillograph, the harmonicanalysis of measured current can only be done below 50kHz. 25However, it still matches well with the simulation results, 10 20 30 40hence verifying the good harmonic suppression capability of Time (ms)the proposed modulation scheme. (a)

5 NOD-20

3 ~~~~~~~-40-60

4-3-5~~~~~~~~~~~~~8

03 10 21040Feunc0K zTime(ins) (b)~~~~IA

ATIL~ ~~~(a

Fi ....Experimental.......platform.......

............................................................(b............(a)... Fig...Me sure.curent(a).nd.is.h rmonc.sp ctru.(b.of.he.c aos-ase

............~~~SWI4patrn (l /iv lm /dv 2 dBdv,lk zdi)

...(b).(a)Fi.8... Mesue.cren.a)an.tshrmnc.petum().ih.hconenioalPW..pater.(A/i..lO s/i...O B/i. .....di

2346.

characteristics of a spread spectrum technique for conducted EMIsuppression," IEEE Trans. on Power Electronics, vol.15, no.2, 2000,pp.399-410

[6] M.Vilathgamuwa, J.Deng, and K.J.Tseng, "EMI suppression with..................................switching frequency.modulated.dc-dc.converte...... Industry

Applications, vol.5, no.6, 1999, pp.27-33[7] D.A.Steve, B.Chambers, D.Howe, "Easing EMC problem in switched

mode power converters by random modulation of the PWM carrierfrequency," IEEEAPEC'96 Record, 1996, pp.317-332

[8] A.Wang, and S.R.Sanders, "Random and programmed pulse-widthmodulation technique for voltage-controlled inverter drive systems," in

Proc, APEC'91, pp.100-106[9] A.M.Trzynadlowski, S.Ji, and S.Legowiski, "Random pulse width

modulation of delta inverter for automotive applications," in ConferenceRecord ofIEEE IASAnnual Meeting, 1991, pp.826-833

[10] G.Setti, R.Rovatti, S.Callegari, and A.Bellini, "Chaos-based generation oflow-EMI PWM control signals for induction motor drives," in ProInt,Symp. On Nonlinear Theory and Its Applications NOLTA'01, vol.2,Miyagi, Japan, Oct.2001, pp.629-632

[11] A.Bellini, G.Franceschini, R.Rovatti, G.Setti, "Generation of low-EMI(b) PWM Patterns for Induction Motor Drives with Chaotic Maps", the

Fig.10. Measured harmonic spectrums for larger frequency-range: the Conference Record of The 27th Annual Conference of the IEEE Industryconventional SPWM pattern (a) and the chaos-based SPWM pattern (b) Electronics Society, 2001, pp. 1527-1532(20dB/div, 5kHz/div). [12] G.H. Thomas, M.D. Deepakraj, "Acoustic noise reduction in sinusoidal

PWM drives using a randomly modulated carrier," IEEE Trans. onPower Electronics, Vol. 6, No. 3, 1991, pp.356-3 63.

TABLE I. [13] A.M.Trzynadlowski, and S.Legowiski, "Random pulse width modulation

technique for voltage -controller power inverters," in Conference Record

Parameters Data ofIEEE IASAnnual Meeting 1987, pp.863-868Rated Voltage 220 V [14] J.T.Boys, and P.G.Handley, "Spread spectrum switching: low noise

Rated Current 2 AV modulation technique for PWM inverter drives," Proc of IEE, Part B,Rated Frequency 50Hz [1]vol.139, no.3, 1992, pp.252-260Rated Powerequey 750 [15] G.Setti, R.Rovatti, S.Callegarl, "Spectral properties of chaos-based FMRated power 750W signals: theory and simulation results," IEEE Trans. on Circuits andRated Speed 1500 rpm Systems, vol.50, no.1, 2003, pp.3-15No. of Phases 3 [16] J.H.B.Deane,D.C.Hamill, "Improvement of Power Supply EMC byNo. of Poles 4 Chaos," IEE Electronics Letter, vol.32, no.12, 1996,pp.1045

[17] G.Setti, R.Rovatti, S.Callegari, and M.Balestra, "Control of Chaosstatistics for the generation of timing signals with improved EMC," in

ACKNOWLEDGMENT Chaos and Bifurcation Control: Theory and Applications-Part I: ChaosControl. NewYork: Springer-Verlag, 2003, ch.20

This work was funded by Shanghai Leading Academic [18] H.Kragh, and F.Blaabjerg, "Reduction of the acoustic noise effects fromDiscipline Project (Project No. T0103) and Research Grants PWM-VSI inverter controlled AC drives by music and randomCouncil ofHong Kong, China (Project No. HIKU 7035/OlE). modulation," in Proc. PCC'93, pp.85-92

[19] F.Blaabjerg, J.K.Pedersen, "Digitally implemented random modulationREFERENCES strategies for ac and switched reluctance drives," in Proc. IECON'93,

pp.676-682[1] F. Lin, D.Y. Chen, "Reduction of power supply EMI emission by [20] T.Tanaka, H.Kameda, and T.Ninomiya, "Noise analysis of DC-to-DC

switching frequency modulation," IEEE Trans. on Power Electronics, converter with random switching control,' in Proc of INTELEC'91,Vol.9, No. 1, 1994, pp. 132-137. pp.283-290

[2] R.Redl, "Electromagnetic environmental impact of power electronics [21] L.O.Chua, " The genesis of Chua's circuit," Archiv fur Elektronik undequipment," Proceedings ofIEEE, vol.89, no.6, 1994, pp.926-938 Ubertragungstechnik, vol.46, no.4, 1992, pp.250-257

[3] Q.Zhaoming, W.Xin, L.Zhengyu,and M.H.Pong, "Status of [22] R.Madan, Ed., Chua's Circuit: A paradigm for chaos. NewYork: Worldelectromagnetic compatibility research in power electronics," IEEE Scientific, 1993PIEMC 2000 Record,2000, pp.46-56 [23] L.Q. Chua, M. Komuro, "The double scroll family, Part I and II [J],"

[4] R.A.Scholtz,"The origin of spread spectrum," IEEE Trans. on IEEE Trans. on Circuit and System, Vol.30, No.11, 1986, pp.1072-1118.Communications, vol.30, 1982, pp.822-854 [24] X.G. Cai, S.S. Qiu, "A chua's circuit-based chaotic spread spectrum

[5] K.K.Tse, H.S-H.Chung, S.Y.Hui, H.C.So, "Analysis and spectral sequence," Journal of South China University of Technology, Vol.28,No.1, 2000, pp. 5-9.