电压型双频率控制开关变换器的动力学建模与多周期行为分析

吴松荣; 何圣仲; 许建平; 周国华; 王金平

doi:10.7498/aps.62.218403

摘要

在断续导电模式下, 建立了电压型双频率控制开关变换器的动力学模型, 并推导了相应的特征值方程. 根据动力学模型, 采用分岔图研究了电路参数变化时变换器存在的边界碰撞分岔行为和周期2, 周期3,周期4等多周期行为, 结果表明: 变换器经历了周期1态、多周期态、周期1态的分岔路由; 周期态的转变均是由边界碰撞分岔引起的. 根据特征值方程, 采用Lyapunov指数研究了变换器的稳定性, 结果表明: 随着电路参数的变化, Lyapunov指数始终小于零, 变换器一直工作于稳定的周期态, 验证了电压型双频率控制开关变换器的周期3行为并不意味着变换器会必然发生混沌. 通过电路仿真, 分析了负载变化时变换器的时域波形、相轨图和频谱图, 验证了动力学模型的可行性和理论分析的正确性. 实验结果验证了文中的仿真结果.

关键词:

Abstract

A dynamical model is proposed and the corresponding characteristic aligns are derived for voltage-mode bi-frequency controlled switching converter operating in discontinuous conduction mode. According to the dynamical model, the border-collision bifurcation and multi-period behaviors, such as period-2, period-3, period-4, and so on, are studied using bifurcation diagrams as the circuit parameters are varied. It is found that the converter behaves along the bifurcation route of period-1, multi-period, and period-1, and the change of period state is induced by border-collision bifurcation. Based on the characteristic equation, the converter stability is investigated by the Lyapunov exponent. It is shown that Lyapunov exponent is always smaller than zero with the variation of circuit parameters and the converter operates in stable period state all the time. Also, it is validated that period-3 behavior of voltage-mode bi-frequency controlled switching converter does not predicate its inevitable chaos. Time-domain waveforms, phase portraits, and frequency spectra of voltage-mode bi-frequency controlled switching converter are analyzed by circuit simulation, which validates the feasibility of dynamical model and the correctness of theoretical analysis. Simulation results are verified by experiments in this paper.

Keywords:

作者及机构信息

1.
磁浮技术与磁浮列车教育部重点实验室, 西南交通大学电气工程学院, 成都 610031;

2.
合肥工业大学电气与自动化工程学院, 合肥 230009

基金项目: 国家自然科学基金(批准号: 51177140)、四川省青年科技基金(批准号: 2013JQ0033) 和中央高校基本科研业务费专项资金 (批准号: 2682013ZT20, SWJTU11CX032) 资助的课题.

Authors and contacts

1.
Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China;

2.
School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51177140), the Sichuan Provincial Youth Science and Technology Fund (Grant No. 2013JQ0033), and the Fundamental Research Funds for the Central Universities of China (Grant Nos. 2682013ZT20, SWJTU11CX032).

参考文献

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[2]	Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[3]	Banerjee S, Parui S, Gupta A 2004 IEEE Trans. Circuits Syst. II 51 649
[4]	Sha J, Bao B C, Xu J P, Gao Y 2012 Acta Phys. Sin. 61 120501 (in Chinese) [沙金, 包伯成, 许建平, 高玉 2012 61 120501]
[5]	Aroudi A El, Bernadero L, Toribio E, Olivar G 1999 IEEE Trans. Circuits Syst. I 46 1374
[6]	Wang F Q, Ma X K, Yan Y 2011 Acta Phys. Sin. 60 060510 (in Chinese) [王发强, 马西奎, 闫晔 2011 60 060510]
[7]	Iu H H C, Tse C K, Pjevalica V, Lai Y M 2001 Int. J. Circ. Theor. Appl. 29 281
[8]	Zhou G H, Bao B C, Xu J P 2013 Int J Bifurcation and Chaos 23 1350062
[9]	Zhou Y F, Chen J N, IU H H C, Tse C K 2008 Int J Bifurcation and Chaos 18 121
[10]	Maity S, Tripathy D, Bhattacharya T K, Banerjee S 2007 IEEE Trans. on Circuits and Systems I 54 1120
[11]	Zhou G H, Xu J P, Bao B C 2010 Acta Phys. Sin. 59 2272 (in Chinese) [周国华, 许建平, 包伯成 2010 59 2272]
[12]	Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[13]	Zhou G H, Xu J P, Bao B C 2012 Int J Bifurcation and Chaos 22 1250008
[14]	Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[15]	Yang P, Bao B C, Sha J, Xu J P 2013 Acta Phys. Sin. 62 010504 (in Chinese) [杨平, 包伯成, 沙金, 许建平 2013 62 010504]
[16]	Yang N N, Liu C X, Wu C J 2012 Chin. Phys. B 21 080503
[17]	He S Z, Zhou G H, Xu J P, Bao B C, Yang P 2013 Acta Phys. Sin. 62 110503 (in Chinese) [何圣仲, 周国华, 许建平, 包伯成, 杨平 2013 62 110503]
[18]	Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese) [王发强, 张浩, 马西奎 2008 57 2842]
[19]	Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 1522 (in Chinese) [王发强, 张浩, 马西奎 2008 57 1522]
[20]	Wang J P, Xu J P, Zhou G H, Mi C B, Qin M 2011 Acta Phys. Sin. 60 048402 (in Chinese) [王金平, 许建平, 周国华, 米长宝, 秦明 2011 60 048402]
[21]	Wang J P, Xu J P, Xu Y J 2011 Acta Phys. Sin. 60 058401 (in Chinese) [王金平, 许建平, 徐扬军 2011 60 058401]
[22]	Zhang X, Bao B C, Wang J P, Ma Z H, Xu J P 2012 Acta Phys. Sin. 61 160503 (in Chinese) [张希, 包伯成, 王金平, 马正华, 许建平 2012 61 160503]
[23]	Wang J P, Xu J P, Qin M, Mu Q B 2003 Proceeding of the CSEE 30 1 (in Chinese) [王金平, 许建平, 秦明, 牟清波 2010 中国电机工程学报 30 1]
[24]	Xu J P, Wang J P 2011 IEEE Trans Industrial Electronics 58 3658

施引文献

[1]	Chan W C Y, Tse C K 1997 IEEE Trans. Circuits Syst. I 44 1129
[2]	Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[3]	Banerjee S, Parui S, Gupta A 2004 IEEE Trans. Circuits Syst. II 51 649
[4]	Sha J, Bao B C, Xu J P, Gao Y 2012 Acta Phys. Sin. 61 120501 (in Chinese) [沙金, 包伯成, 许建平, 高玉 2012 61 120501]
[5]	Aroudi A El, Bernadero L, Toribio E, Olivar G 1999 IEEE Trans. Circuits Syst. I 46 1374
[6]	Wang F Q, Ma X K, Yan Y 2011 Acta Phys. Sin. 60 060510 (in Chinese) [王发强, 马西奎, 闫晔 2011 60 060510]
[7]	Iu H H C, Tse C K, Pjevalica V, Lai Y M 2001 Int. J. Circ. Theor. Appl. 29 281
[8]	Zhou G H, Bao B C, Xu J P 2013 Int J Bifurcation and Chaos 23 1350062
[9]	Zhou Y F, Chen J N, IU H H C, Tse C K 2008 Int J Bifurcation and Chaos 18 121
[10]	Maity S, Tripathy D, Bhattacharya T K, Banerjee S 2007 IEEE Trans. on Circuits and Systems I 54 1120
[11]	Zhou G H, Xu J P, Bao B C 2010 Acta Phys. Sin. 59 2272 (in Chinese) [周国华, 许建平, 包伯成 2010 59 2272]
[12]	Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[13]	Zhou G H, Xu J P, Bao B C 2012 Int J Bifurcation and Chaos 22 1250008
[14]	Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[15]	Yang P, Bao B C, Sha J, Xu J P 2013 Acta Phys. Sin. 62 010504 (in Chinese) [杨平, 包伯成, 沙金, 许建平 2013 62 010504]
[16]	Yang N N, Liu C X, Wu C J 2012 Chin. Phys. B 21 080503
[17]	He S Z, Zhou G H, Xu J P, Bao B C, Yang P 2013 Acta Phys. Sin. 62 110503 (in Chinese) [何圣仲, 周国华, 许建平, 包伯成, 杨平 2013 62 110503]
[18]	Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese) [王发强, 张浩, 马西奎 2008 57 2842]
[19]	Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 1522 (in Chinese) [王发强, 张浩, 马西奎 2008 57 1522]
[20]	Wang J P, Xu J P, Zhou G H, Mi C B, Qin M 2011 Acta Phys. Sin. 60 048402 (in Chinese) [王金平, 许建平, 周国华, 米长宝, 秦明 2011 60 048402]
[21]	Wang J P, Xu J P, Xu Y J 2011 Acta Phys. Sin. 60 058401 (in Chinese) [王金平, 许建平, 徐扬军 2011 60 058401]
[22]	Zhang X, Bao B C, Wang J P, Ma Z H, Xu J P 2012 Acta Phys. Sin. 61 160503 (in Chinese) [张希, 包伯成, 王金平, 马正华, 许建平 2012 61 160503]
[23]	Wang J P, Xu J P, Qin M, Mu Q B 2003 Proceeding of the CSEE 30 1 (in Chinese) [王金平, 许建平, 秦明, 牟清波 2010 中国电机工程学报 30 1]
[24]	Xu J P, Wang J P 2011 IEEE Trans Industrial Electronics 58 3658

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