6128 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 11, NOVEMBER 2014 Suppressing EMI in Power Converters via Chaotic SPWM Control Based on Spectrum Analysis Approach Hong Li, Member, IEEE, Yongdi Liu, Jinhu Lü, Fellow, IEEE, Trillion Zheng, Senior Member, IEEE, and Xinghuo Yu, Fellow, IEEE Abstract—This paper aims at developing a spectrum analysis approach for suppressing the electromagnetic interference (EMI) in power converters via chaotic sinusoidal pulse width modulation (CSPWM) control signals based on double Fourier series. In de- tail, we prove that the total harmonics of power converters under CSPWM control are the same with those of power converters under traditional SPWM control. Then, we introduce a novel spectrum analysis approach based on sawtooth carrier and double Fourier series. Moreover, a photovoltaic (PV) inverter is used to validate the proposed spectrum analysis approach based on the calculation of the output voltage spectrum for CSPWM control signals. In particular, this proposed method can also be used for the spectrum analysis of multiperiodic signals. Indeed, this devel- oped spectrum analysis approach provides a rigorous theoretical foundation for the CSPWM control in EMI suppression. Index Terms—Double Fourier series, electromagnetic interfer- ence (EMI), sinusoidal pulsewidth modulation (SPWM), spectrum calculation. I. I NTRODUCTION W ITH THE wide applications of power converters and the emergence of high-frequency full-controlled switching devices, sinusoidal pulse width modulation (SPWM) has be- come the main switching control method for inverters [1]–[7]. Compared with the phase-shifting technology, SPWM has some specific advantages, including the realization of frequency modulation and voltage regulation at the same time, rapid dynamic response, reducing or eliminating the harmonics in low-frequency band, and so on [8]. However, the harmonics in high-frequency band have received an increasing attention. Manuscript received October 29, 2013; revised December 28, 2013; accepted January 10, 2014. Date of publication February 26, 2014; date of current version June 6, 2014. This work was supported by the National Science and Technology Major Project of China under Grant 2014ZX10004-001-014; by the 973 Project under Grant 2014CB845302; by the National Natural Science Foundation of China under Grant 51007004, Grant 61025017, Grant 50937001, and Grant 11072254; by the Fundamental Research Funds for the Central Uni- versities under Grant 2012JBM096; by the Beijing Natural Science Foundation under Grant 3142015; by the Beijing Higher Education Young Elite Teacher Project under Grant YETP0569; and by the Specialized Research Foundation of Doctoral Subjects of Education Ministry under Grant 20114420110003. H. Li, Y. Liu, and T. Zheng are with the School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China (e-mail: hli@bjtu.edu.cn). J. Lü is with LSC, ISS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (e-mail: jhlu@iss.ac.cn). X. Yu is with the School of Electrical and Computer Engineering, Royal Melbourne Institute of Technology University, Melbourne, VIC 3001, Australia (e-mail: x.yu@rmit.edu.au). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2014.2308131 They are caused by the rapid turn-on and turn-off of switching devices under SPWM control. Moreover, the harmonics could result in the electromagnetic compatibility (EMC) of the con- verters out of limits as well as serious electromagnetic pollution [9]–[12]. To suppress the electromagnetic interference (EMI) and improve the EMC of power converters, the random PWM technique was proposed [13]–[15]. According to the imple- mentation method, the random PWM can be divided into three kinds: random switching frequency, random pulse position, and random switching [16], where each kind of random PWM is based on the generation of random signals. Since it is very dif- ficult to obtain the true random signals in practice, the pseudo- random signals are usually used to replace the aforementioned random PWMs [17], [18]. As we know now, chaotic signals are one kind of typical pseudorandom signals, which are easily obtained by the chaotic maps. Therefore, the chaotic PWM and chaotic SPWM (CSPWM) have attracted an increasing attention over the last decade [19]–[21]. Most of the aforementioned CSPWM approaches only focus on the operating principle analysis or the EMI suppression effectiveness test of power converters by using numerical simu- lations and experimental observations [22]–[24]. However, the spectrum quantitative analysis of CSPWM on EMI suppression is woefully inadequate, since the traditional spectrum calcu- lation methods are not able to deal with the chaotic signals effectively. Recently, many researchers have already realized the fundamental importance of theoretical analysis and begin to track these works [25]–[27]. For instance, a qualitative spectral analysis method was introduced to analyze the random frequency modulation and chaotic frequency modulation in [25], which can be used to predict the spectra peaks under different modulation indexes. In [26], Yang et al. analyzed the chaotic spectrum characteristics of time-frequency energy distribution based on wavelet transform and also explained the inherent mechanism of EMI suppression from the point of en- ergy spectrum. Moreover, Yang et al. applied statistical theory to further investigate the spectrum of chaotic PWM signals in [27]. However, the aforementioned approaches lack a rigorous theoretical analysis, where only the qualitative analysis results can be obtained. Based on the double Fourier transform of CSPWM control signals, this paper aims to introduce a new spectrum calculation method with rigorous theoretical analysis. It establishes a strict theoretical basis for the CSPWM control in EMI suppression and practical applications [28]–[34]. 0278-0046 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.