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三电平逆变器相较于传统的两电平逆变器具有输出电压谐波畸变率小、开关管电压应力小等优点，因而在大功率场合受到了越来越多的关注. 本文针对一种复合式单相三电平逆变器，对其中的分岔和混沌现象进行了深入的研究，建立了电流闭环比例控制下的一阶离散模型，得到了不同时间段内的频闪映射模型. 以比例系数k，负载电阻R，负载电感L及输入电压E为变化参数，研究了三电平逆变器的分岔现象：通过分岔图和李雅普诺夫指数谱分析了慢变尺度下比例系数、负载电感、负载电阻和输入电压对系统动态性能的影响；通过折叠图直观地观测到了快变尺度下不同比例系数、负载电感所导致的分岔过程. 最后搭建了Matlab/Simulink仿真模型，得到了电流闭环比例控制时电流i的时域波形，仿真结果与理论分析相一致. 研究表明，正确选择单相三电平逆变器的电路参数对于其稳定运行具有重要意义.Compared with traditional two-level inverter, three-level inverter has the advantages of low output voltage harmonic distortion, and small switch voltage stress, so it attracts more and more attention in high power applications. In this paper, the bifurcation and chaos in a single-phase three-level inverter are studied. The one-dimensional discrete iterated mapping model under proportional control is established, and the stroboscopic maps in different periods of time are obtained. The bifurcation phenomena in the single-phase three-level inverter are studied when the proportional coefficient k, load resistance R, load inductance L and input voltage E are used as changing parameters. Effects of all these parameters on the system dynamical performances are analyzed on a slow scale using the bifurcation diagram and Lyapunov index spectrum. The bifurcation processes on a fast scale caused by changing values of proportional coefficient and load resistance are visually observed using folded diagram. Finally, the time-domain waveforms with different proportional coefficients are obtained by Matlab/Simulink, which corresponds with the theoretical analysis. The results show that the correct circuit parameters of single-phase three-level inverter are very important for its stable operation.
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Keywords:
- three-level inverter /
- stroboscopic mapping /
- bifurcation /
- chaos
[1] David C H, David J J 1988 IEEE Trans. Circ. Syst. 35 1059
[2] Deane J H B 1992 IEEE Trans. Circ. Syst. I 39 680
[3] Tse C K, Chan W C Y 1995 26th Annual IEEE Power Electronics Specialists Conference Atlanta, GA, USA, June18–22, 1995 p608
[4] Zhou Y F, Qiu S S, Chen J N 2004 Proceedings of the CSEE 24 96 (in Chinese) [周宇飞, 丘水生, 陈军宁 2004 中国电机工程学报 24 96]
[5] Zhang B 2005 Transactions of China Electrotechnical Society 20 1 (in Chinese) [张波 2005 电工技术学报 20 1]
[6] Zhao Y B, Luo X S, Fang J Q, Wang B H 2005 Acta Phys. Sin. 54 5022 (in Chinese) [赵益波, 罗晓曙, 方锦清, 汪秉宏 2005 54 5022]
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[8] Bao B C, Xu J P, Liu Z 2008 J. Univ. Electron. Sci. Technol. China 37 397 (in Chinese) [包伯成, 许建平, 刘中 2008 电子科技大学学报 37 397]
[9] Li G L, Li C Y, Chen X Y, Mou X M 2012 Acta Phys. Sin. 61 170506 (in Chinese) [李冠林, 李春阳, 陈希有, 牟宪民 2012 61 170506]
[10] Robert B, Robert C 2002 Int. J. Contr. 75 1356
[11] Iu H H C, Robert B 2003 IEEE Trans. Circ. Syst. I 50 1125
[12] Robert B, Feki M, Iu H H C 2006 Int. J. Bifurc. Chaos 16 113
[13] Li M, Dai D, Ma X K 2008 Circ. Syst. Signal Process. 27 811
[14] Wang X M, Zhang B 2009 Trans. China Electrotech. Soc. 24 101 (in Chinese) [王学梅, 张波 2009 电工技术学报 4 101]
[15] Lei B, Xiao G C, Wu X L, Qi Y R 2011 Acta Phys. Sin. 60 090501 (in Chinese) [雷博, 肖国春, 吴旋律, 齐元瑞 2011 60 090501]
[16] Sun Y, Li M Y 2011 J. Xi’an Univ. Technol. 27 92 (in Chinese) [孙媛, 李敏远 2011 西安理工大学学报 27 92]
[17] Hu N H, Zhou Y F, Chen J N 2012 Acta Phys. Sin. 61 130504 (in Chinese) [胡乃红, 周宇飞, 陈军宁2012 61 130504]
[18] Wu J K, Zhou L W, Lu W G 2012 Acta Phys. Sin. 61 210202 (in Chinese) [吴军科, 周雒维, 卢伟国 2012 61 210202]
[19] Liu H C, Li F, Yang S 2013 Acta Phys. Sin. 62 110504 (in Chinese) [刘洪臣, 李飞, 杨爽 2013 62 110504]
[20] Wang X H, Ruan X B 2005 Proceedings of the CSEE 25 73 (in Chinese) [王学华, 阮新波 2005 中国电机工程学报 25 73]
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[1] David C H, David J J 1988 IEEE Trans. Circ. Syst. 35 1059
[2] Deane J H B 1992 IEEE Trans. Circ. Syst. I 39 680
[3] Tse C K, Chan W C Y 1995 26th Annual IEEE Power Electronics Specialists Conference Atlanta, GA, USA, June18–22, 1995 p608
[4] Zhou Y F, Qiu S S, Chen J N 2004 Proceedings of the CSEE 24 96 (in Chinese) [周宇飞, 丘水生, 陈军宁 2004 中国电机工程学报 24 96]
[5] Zhang B 2005 Transactions of China Electrotechnical Society 20 1 (in Chinese) [张波 2005 电工技术学报 20 1]
[6] Zhao Y B, Luo X S, Fang J Q, Wang B H 2005 Acta Phys. Sin. 54 5022 (in Chinese) [赵益波, 罗晓曙, 方锦清, 汪秉宏 2005 54 5022]
[7] Li S N, Zhang H, Ma X K, Li M 2006 J. Xi’an Jiaotong Univ. 40 454 (in Chinese) [李胜男, 张浩, 马西奎, 李明 2006 西安交通大学学报 40 454]
[8] Bao B C, Xu J P, Liu Z 2008 J. Univ. Electron. Sci. Technol. China 37 397 (in Chinese) [包伯成, 许建平, 刘中 2008 电子科技大学学报 37 397]
[9] Li G L, Li C Y, Chen X Y, Mou X M 2012 Acta Phys. Sin. 61 170506 (in Chinese) [李冠林, 李春阳, 陈希有, 牟宪民 2012 61 170506]
[10] Robert B, Robert C 2002 Int. J. Contr. 75 1356
[11] Iu H H C, Robert B 2003 IEEE Trans. Circ. Syst. I 50 1125
[12] Robert B, Feki M, Iu H H C 2006 Int. J. Bifurc. Chaos 16 113
[13] Li M, Dai D, Ma X K 2008 Circ. Syst. Signal Process. 27 811
[14] Wang X M, Zhang B 2009 Trans. China Electrotech. Soc. 24 101 (in Chinese) [王学梅, 张波 2009 电工技术学报 4 101]
[15] Lei B, Xiao G C, Wu X L, Qi Y R 2011 Acta Phys. Sin. 60 090501 (in Chinese) [雷博, 肖国春, 吴旋律, 齐元瑞 2011 60 090501]
[16] Sun Y, Li M Y 2011 J. Xi’an Univ. Technol. 27 92 (in Chinese) [孙媛, 李敏远 2011 西安理工大学学报 27 92]
[17] Hu N H, Zhou Y F, Chen J N 2012 Acta Phys. Sin. 61 130504 (in Chinese) [胡乃红, 周宇飞, 陈军宁2012 61 130504]
[18] Wu J K, Zhou L W, Lu W G 2012 Acta Phys. Sin. 61 210202 (in Chinese) [吴军科, 周雒维, 卢伟国 2012 61 210202]
[19] Liu H C, Li F, Yang S 2013 Acta Phys. Sin. 62 110504 (in Chinese) [刘洪臣, 李飞, 杨爽 2013 62 110504]
[20] Wang X H, Ruan X B 2005 Proceedings of the CSEE 25 73 (in Chinese) [王学华, 阮新波 2005 中国电机工程学报 25 73]
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