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Wavelet PWM Technique for Single-Phase Three-Level Inverters
Wavelet PWM Technique for Single-Phase Three-Level Inverters
Journal of Power Electronics. 2015. Nov, 15(6): 1517-1523
Copyright © 2015, The Korean Institute Of Power Electronics
  • Received : February 02, 2015
  • Accepted : June 12, 2015
  • Published : November 20, 2015
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About the Authors
Chun-Fang Zheng
Department of Shipbuilding Engineering, Guangzhou Maritime Institute, Guangzhou, China
zcf219@163.com
Bo Zhang
Department of Electric Power, South China University of Technology, Guangzhou, China
Dong-Yuan Qiu
Department of Electric Power, South China University of Technology, Guangzhou, China
Xiao-Hui Zhang
Department of Electric Power, South China University of Technology, Guangzhou, China
Le-Ming Xiao
Department of Shipbuilding Engineering, Guangzhou Maritime Institute, Guangzhou, China

Abstract
The wavelet PWM (WPWM) technique has been applied in two-level inverters successfully, but directly applying the WPWM technique to three-level inverters is impossible. This paper proposes a WPWM technique suitable for a single-phase three-level inverter. The work analyzes the control strategy with the WPWM and obtains the design of its parameters. Compared with the SPWM technique for a single-phase three-level inverter under the same conditions, the WPWM can obtain high magnitudes of the output fundamental frequency component, low total harmonic distortion, and simpler digital implementation. The feasibility experiment is given to verify of the proposed WPWM technique.
Keywords
I. INTRODUCTION
In recent years, Saleh has proposed and developed the wavelet modulation techniques on different two-level converters [1] - [5] . The wavelet modulation technique is based on establishing a non-dyadic type multi resolution analysis (MRA), which is required to support a non-uniform recurrent sampling–reconstruction process. The merits of this approach includes simpler realization by digital algorithm, higher magnitudes of the fundamental output voltage, and lower harmonic contents better than other types of modulation techniques. In [1] and [2] , the manner of implementation of a wavelet modulation technique for single-phase voltage source inverters was proposed. The manner of implementation of a wavelet modulation technique for three-phase voltage-source six-pulse inverters was proposed in [3] and [4] . In [5] , the manner of implementation of a wavelet modulation technique for AC–DC converters was proposed. Hence, the present research on the WPWM technique focuses on the two-level inverter.
Compared with the two-level inverter, the three-level inverter is a new type of high-voltage large capacity power converter with advantages of having improved voltage waveform on the AC side, smaller filter size, lower electromagnetic interference, and lower acoustic noise [6] . Therefore, three-level inverter options are attracting greater attention in the fields of the grid interconnection, new energy, fuel electromagnetic [7] , [8] . Because of the wide application of three-level inverters, the study of its control strategy has been increasingly highlighted [9] - [15] . One of commonly used control strategies is sinusoidal pulse width modulation (SPWM). The SPWM technique for two-level inverters only needs a modulating signal and a carrier signal, but the conventional SPWM technique for three-level inverters needs a modulating signal, two carrier signals, and a square signal. Thus, directly applying the WPWM technique to three-level inverters is impossible because the WPWM technique to two-level inverters can only generate two unipolar-controlled signals or two bipolar-controlled signals.
Thus, this paper presents the development and performance testing of the WPWM technique for single-phase three-level inverters. The single-phase three-level inverter with SPWM technique is reviewed in Section II. The single-phase three-level inverter with WPWM technique is proposed in Section III. The analysis of the WPWM technique for the single-phase three-level inverter is provided in Section IV. The experimental results are obtained in Section V. Conclusions are given in Section VI.
II. SINGLE-PHASE THREE-LEVEL INVERTER WITH SPWM TECHNIQUE
Fig. 1 shows the circuit schematic of an asymmetric single-phase three-level inverter [17] , [18] . The circuit is composed of a two-level bridge and a three-level bridge. C 1 and C 2 are the DC side filter capacitor. U d is the DC voltage source. When U d =E, Uao has three levels, i.e., +E/2, 0, and –E/2, and U bo has two levels: +E/2, and –E/2, which, in total, gives output voltage U ab five levels. The operation states of single-phase three-level inverter are listed in TABLE I .
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Scheme of the single-phase three-level inverter.
OPERATION STATES OF THE SINGLE-PHASE THREE-LEVEL INVERTER
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OPERATION STATES OF THE SINGLE-PHASE THREE-LEVEL INVERTER
A conventional SPWM scheme is shown in Fig. 2 [18] , which has a reference rectified sine wave ( V ref ) and two carrier signals ( v tri1 and v tri2 ). The comparison result of V ref and v tri1 is the control signal of A 1 ; the comparison result of V ref and v tri2 is the control signal of B 1 ; the comparison result of V ref and zero is the control signal of C 1 . Then, the control signals for switches S 1 S 6 can be derived by A 1 , B 1 , and C 1 , as shown in Fig. 3 , where S 1 = A 1 and
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;
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SPWM operation principle of the three-level inverter.
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Logic control scheme for switches S1–S6.
III. WPWM TECHNIQUE FOR SINGLE-PHASE THREE-LEVEL INVERTER
- A. Principle of the WPWM Technique
The WPWM technique is based on sampling–reconstructing a reference-modulating signal in a non-uniform recurrent manner using sets sampling and synthesis basis functions [1 , 2] . These sampling basis functions are generated as dilated and translated versions of the scale-based linearly-combined scaling function φ (j,k) ( t ) . Furthermore, synthesis basis functions are generated as dilated and translated versions of the scale-based linearly combined synthesis scaling function
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The scale-based linearly-combined scaling function is defined at scale j as
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and φ (j,k) ( t )= φ (2 j t - k ), where j =0, 1, 2, 3, … and ϕH ( t ) is the Harr scaling function that is given by
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Moreover, synthesis scaling function
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associated with φ ( t ) can be defined as
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Using these two dual scaling functions, a continuous-time signal xc ( t ) can be expanded as
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where j , k ∈ Z, where Z is the set of integer numbers. Such form of signal processing suggests that a continuous-time signal < xc ( t ), φ (2 j t - k )> can be recovered from its samples using sets of synthesis functions
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The work on [10] proved that the switching pulses for the inverter can be generated by using dilated and shifted versions of synthesis scaling function
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When each cycle of xc ( t ) is divided by a finite number of sample groups D , the length of the time interval of the sample group [ t d1 , t d2 ] changes as scale j changes, where
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In addition, based on the the procedure on how to implement the WPWM technique given in [1] , the flowchart for WPWM can be shown as Fig. 4 [16] , where Tm is the period of the reference sine wave.
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Flowchart of the WPWM technique implementation.
- B. WPWM Strategy for the Single-Phase Three-Level Inverter
According to the above flowchart of WPWM, once T m , j 0 and D are given, the time points ( t d1 and t d2 ) of each sample group can be calculated, and the driving pulses can be generated by the time points in each sample group, which can be integrated into two unipolar-controlled signals ( W 1 and W 2 ). However, the signals ( W 1 and W 2 ) cannot be used to control the switches of single-phase three-level inverter directly. Thus, based on Figs. 2 and 3 , the WPWM operation principle for the three-level inverter can be shown as Fig. 5 . W 1 and W 2 are generated according to the flowchart of the WPWM technique shown in Fig. 4 . Pulse P 1 has a half-cycle symmetry property, its frequency is the double of reference sine wave, and its pulse width can be varied to adjust the distribution of the output voltage levels, which will be discussed in detail in the following. Pulse C 1 is a square signal, and its frequency is the same as the reference sine wave. Then, the control signals for switches S 1 S 6 can be derived by the specific logic relationship among W 1 , W 2 , P 1 , and C 1 , as shown in Fig. 6 , where
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and
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WPWM operation principle of three-level inverter.
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Logic control scheme for the switches S1~S6 with WPWM technique.
Moreover, Fig. 6 shows that the WPWM control strategy for the single-phase three-level inverter can be implemented simply by a digital algorithm.
IV. ANALYSIS OF THE WPWM TECHNIQUE FOR THE SINGLE-PHASE THREE-LEVEL INVERTER
To verify the control strategy of the WPWM technique for the single-phase three-level inverter, a MATLAB/SIMULINK model is built and simulation is made by selecting D =30, f m =50 Hz ( f m is the frequency of the reference sine wave), j 0=0, the pulse width of P 1 is 50%, the simulation results of signals W 1 , W 2 , W 3 , P 1 , C 1 , and S 1 S 6 can be obtained, as shown in Fig. 7 . When input voltage U d =50 V, output voltage U ab is shown in Fig. 8 .
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Signals of W1, W2, W3, P1, C1, and S1S6 at D=30, fm=50 Hz, j0=0.
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Output voltage Uab.
According to the control strategy of the WPWM technique for the single-phase three-level inverter, the width and position of the pulses ( W 1 and W 2 ) generated by the WPWM technique are determined when D and j 0 are given, and C 1 is a determined square wave when the frequency of the reference sine wave is given. Therefore, the only way of changing the control signals for switches S 1 S 6 is by adjusting the pulse width of P 1 , the distribution of the output voltage levels is affected.
To analyze the effects of pulse P 1 on the distribution of the output voltage levels, this study selects D =30, f m =50 Hz, j 0=0, and input voltage U d =50 V as a sample object to be simulated based on the MATLAB/SIMULINK model of a single-phase three-level inverter, as shown in Fig. 2 . The pulse width of P 1 is chosen in the range of 10%–90%. The simulation results of the total harmonic distortion (THD) and the amplitude of fundamental voltage V 1 for output voltage U ab are shown in Figs. 9 and 10 , respectively. Fig. 9 shows that the THD is smallest when the pulse width of P 1 is about 62%. Fig. 10 shows that V 1 increases as the pulse width of P 1 increases, and V 1 can be larger than the input voltage when the pulse width is larger than 50%.
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THD of Uab vs. the pulse width of P1.
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V1of Uab vs. the pulse width of P1.
V. EXPERIMENTAL RESULTS
To verify the analysis of the WPWM technique for the single-phase three-level inverter, the algorithm of the WPWM technique is implemented by using DSP (TMS320LF2812), and the input voltage of the single-phase three-level inverter is 0V Vdc =50V , MOSFET IRFPE40 is selected as switch, TLP250 is used as driver, and pure resistance R = 50 Ω is used as the load. A photograph of the experimental setup is shown in Fig. 11 . Note that the value of the THD is tested by Fluke Norma 5000 Power Analyzer.
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Photograph of the experimental setup.
First, the experiments have been performed by choosing f m =50 Hz, j 0=0, D =30, and the pulse width of P 1 =40%, 50%, 60%, 62%, 63%, 70%, 80%, and 90%. The experimental results are shown in Fig. 12 . Fig. 12 (a) shows that the THD is smallest when the pulse width of P 1 is about 62%, and Fig. 12 (b) shows that V 1 increases as the pulse width of P 1 increases, which are consistent with the simulation results shown in Figs. 9 and 10 .
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Experimental results of the THD and V1vs. the pulse width of P1 at j0=0, fm=50 Hz, D=30.
Second, the experiments have been performed by choosing f m =50 Hz, j 0=0, the pulse width of P 1 =62%, and D =20, 30, 40. The experimental results are shown in Figs. 13 (a)-13(c). Fig. 13 shows that using the WPWM technique to control the single-phase three-level inverter is effective.
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Output voltage Uab and its spectrum of the single-phase three-level inverter by WPWM.
Finally, to validate the performance of the single-phase three-level inverter with the WPWM technique, this paper compares the WPWM with conventional SPWM, as shown in Fig. 2 . The algorithm of the conventional SPWM is implemented by using DSP (TMS320LF2812), and the experiments have been performed by choosing f m =50 Hz, m =1.0 ( m denotes the modulation index), the switching frequency f s =1 kHz ( D =20), f s =1.5 kHz ( D =30), and f s =2 kHz ( D =40). The experimental results are shown in Fig. 14 (a), (b), (c) respectively.
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Output voltage Uab and its spectrum of the single-phase three-level inverter by the SPWM.
The compared results between WPWM and SPWM from Figs. 13 and 14 are listed in TABLE II . From TABLE II , it can be concluded that (1) WPWM can get higher magnitudes of the fundamental component than SPWM; (2) WPWM technique can get smaller THD and more disperser spectrum than SPWM.
COMPARISON OF RESULTS BETWEEN WPWM AND SPWM FROMFIGS. 13AND14
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COMPARISON OF RESULTS BETWEEN WPWM AND SPWM FROM FIGS. 13 AND 14
VI. CONCLUSION
This study has developed the WPWM technique for single-phase three-level inverters. The design of the parameter for the WPWM is obtained by analyzing the magnitudes of the fundamental frequency component and harmonic distortion of its output voltage. The simulation and experimental results have shown that the proposed WPWM for the three-level inverter can obtain higher magnitudes of the output fundamental frequency component, lower THD, and simpler digital implementation than the SPWM, which will promote the application of WPWM technique in power electronics converters.
Acknowledgements
This research was supported in part by the Key Program of the National Natural Science Foundation of China under Grant 51437005, the National Natural Science Foundation of China under Grant 51277079, and the Guangzhou Science and Technology Project under Grant 201510010238.
BIO
Chun-Fang Zheng was born in China in 1978. She received her B.S. degree in Electrical Engineering from Nanchang University, Jiangxi, China, in 2000, the M.S. and Ph.D. degree in the Power Electronics and Power Drives from South China University of Technology, Guangzhou, China, in 2003,and 2006, respectively. From 2006 to 2010, she was an Engineer Supervisor in Emerson Network Power ASTEC Power Supply (Shenzhen) Co., Ltd., China, where she worked on the development of telecom power supply. Since 2013, she has been a Teacher in the School of Shipbuilding Engineering, Guangzhou Maritime Institute, Guangzhou, China. Her main research interests include design and control of power converters and inverters.
Bo Zhang was born in Shanghai, China, in 1962. He received his B.S. degree in Electrical Engineering from Zhejiang University, Hangzhou, China, in 1982, his M.S. degree in Power Electronics from Southwest Jiaotong University, Chengdu, China, in 1988, and his Ph.D. degree in Power Electronics from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1994. He is currently a Professor and the Vice Dean of the School of Electric Power, South China University of Technology, Guangzhou, China. He is the author or coauthor of more than 400 papers and the owner of 24 patents. His current research interests include nonlinear analysis and control of power electronics and AC drives.
Dong-Yuan Qiu was born in China in 1972. She received her B.S. and M.S. degrees from South China University of Technology, Guangzhou, China, in 1994 and 1997, respectively, and her Ph.D. degree from City University of Hong Kong, Kowloon, Hong Kong, in 2002. Since 2010, she has been a Professor in the School of Electric Power, South China University of Technology. Her main research interests include design and control of power converters, fault diagnosis, and sneak circuit analysis of power electronic systems.
Xiao-Hui Zhang was born in Fujian, China. She received her B.S. degrees in Electrical Engineering and Automation from Xiamen University, Xiamen, China, in 2014. She is currently working toward her M.S. degree in Power Electronics and Power Drives at South China University of Technology, Guangzhou, China. Her research interests include wavelet modulation.
Le-Ming Xiao was born in China in 1962. He received his B.S. degree in Shipbuilding Electronics from DaLian Maritime University, Liaoning, China, in 1983. He is currently a Professor and the Vice Dean of the Department of Shipbuilding Engineering, Guangzhou Maritime Institute, Guangzhou, China. His main research interests include marine electric energy conservation and its intelligent control.
References
Saleh S. A. , Moloney C. R. , Rahma M. A. “Developing a nondyadic MRAS for switching DC–AC inverters,” in Proc. IEEE 12th DSP Conf, Jackson Lake Lodge WY Sep. 2006 544 - 549
Saleh S. A. , Moloney C. R. , Rahman M. A. 2009 “Development and testing of wavelet modulation for single-phase inverters,” IEEE Trans. Ind. Electron. 56 (7) 2588 - 2599    DOI : 10.1109/TIE.2009.2019776
Saleh S. A. , Rahman M. A. 2010 “Development and testing of a new controlled wavelet modulated inverter for IPM motor drives,” IEEE Trans. Ind. Appl. 46 (4) 1630 - 1643    DOI : 10.1109/TIA.2010.2049814
Saleh S.A. , Moloney C. R. , Rahman M. A. 2010 “Analysis and development of wavelet modulation for three phase voltage source inverters,” IEEE Trans. Ind. Electron. 58 (8) 3330 - 3348    DOI : 10.1109/TIE.2010.2081957
Saleh S. A. , Rahman M. A. 2011 “Development and experimental validation of resolution-level controlled wavelet modulated inverters for three phase induction motor drives,” IEEE Trans. Ind. Appl. 47 (4) 1958 - 1970    DOI : 10.1109/TIA.2011.2156375
Saleh S. A. 2013 “The implementation and performance evaluation of 3φVS wavelet modulated AC-DC converters,” IEEE Trans. Power Electron. 28 (3) 1096 - 1106    DOI : 10.1109/TPEL.2012.2205945
Lai J.-S. , Peng F. Z. 1996 “Multilevel converters - a new breed of power converters,” IEEE Trans. Ind. Appl. 32 (3) 509 - 517    DOI : 10.1109/28.502161
Chang G. W. , Lin H.-W. , Chen S.-K. 2004 “Modeling characteristics of harmonic currents generated by high-speed railway traction drive converters,” IEEE Trans. Power Deliv. 19 (2) 766 - 773    DOI : 10.1109/TPWRD.2003.822950
Chao K.-H. , Chen P.Y. , Cheng C.-H. “A three-level converter with output voltage control for high-speed railway tractions,” The 33rd Annual Conf. IEEE Ind. Electron. Society (IECON) Taipei, Taiwan Nov. 2007 1793 - 1798
Tallam R. M. , Naik R. , Nondahl T. A 2005 “A carrier-based PWM scheme for neutral-point voltage balancing in three-level inverters,” IEEE Trans. Ind. Appl. 41 (6) 1734 - 1743    DOI : 10.1109/TIA.2005.858283
Song W. , Feng X. , Xiong C. “A neutral point voltage regulation method with SVPWM control for single-phase three-level NPC converters,” in Proc. IEEE VPPC Conference Sep. 2008 1 - 4
Salehi R. , Farokhnia N. , Abedi M. , Fathi S. H. 2011 “Elimination of low order harmonics in multilevel inverter using genetic algorithm,” Journal of Power Electronics 11 (2) 132 - 139    DOI : 10.6113/JPE.2011.11.2.132
Li Z. , Wang P. , Zhu H. , Chu Z. , Li Y. 2012 “An improved pulse width modulation method for chopper-cell-based multilevel inverters,” IEEE Trans. Power Electron. 27 (8) 3472 - 3481    DOI : 10.1109/TPEL.2012.2187800
Marzoughi A. , Imaneini H. , Moeini A. 2013 “An optimal selective harmonic mitigation technique for high power converters,” International Journal of Electrical Power and Energy Systems 49 34 - 39    DOI : 10.1016/j.ijepes.2012.12.007
Zhang M. , Huang L. , Yao W. , Lu Z. 2014 “Circulating harmonic current elimination of a CPS-PWM-based modualr mulitlevel converter with a plug-in repetitivecontroller,” IEEE Trans. Power Electron. 29 (4) 2083 - 2097    DOI : 10.1109/TPEL.2013.2269140
Zheng C. F. , Xu X. M. , Zhang B. , Qiu D. Y. “Inverter’s characteristic analysis under different parameters of Wavelet PWM Technique,” EPE’14 ECCE Europe Aug. 2014 1 - 7
Wang X.-H. , Ruan X. B. 2005 “SPWM control single-phase three-level inverter,” inProc. of the CSEE 25 (1) 73 - 76
Wu F. J. , Sun B. , Peng H. R. 2011 “Single-phase three-level SPWM scheme suitable for implementation with DSP,” Electronics Letters 47 (17) 994 - 996    DOI : 10.1049/el.2011.1969