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建立了谷值V2控制Boost变换器的离散迭代映射模型，在此基础上得到了输入电压、输出电容及其等效串联电阻（equivalent series resistance，ESR）变化时的分岔图，推导了不动点处的雅可比矩阵，利用特征值和最大Lyapunov指数对系统进行了稳定性分析，并验证了分岔图的正确性. 重点研究了输入电压和输出电容及其ESR对谷值V2控制Boost变换器的动力学特性的影响. 研究结果表明，输入电压增大时，变换器从周期1态经历1次倍周期分岔和边界碰撞分岔进入混沌状态；输出电容及其ESR具有相同的分岔路由，随着输出电容及其ESR的逐渐减小，变换器具有从周期1态经历周期2态、周期4态、周期8 态、逐渐演变到混沌态的动力学行为. 最后，用仿真和实验结果验证了本文理论分析的正确性.A discrete iterative map model of valley V2 controlled Boost converter is established, based on which the bifurcation diagrams are obtained with the variation of input voltage, output capacitance and its equivalent series resistance (ESR). Jacobi matrix at a fixed point is also derived, and according to it, the converter stability is analyzed using characteristic values and maximum Lyapunov exponent, thus the correctness of bifurcation analysis is validated. The effect of input voltage, output capacitance and its ESR on the dynamic characteristics of valley V2 controlled Boost converter is mainly investigated. It is found that as the input voltage increases continuously, the valley V2 controlled Boost converter changes from continuous conduction mode (CCM) period-1 to CCM period-2 due to period-doubling bifurcation, and comes into CCM chaos due to border collision bifurcation. The converter has the same bifurcation routes at output capacitance and its ESR: with gradual reduction of output capacitance or its ESR, the valley V2 controlled Boost converter behaves the evolutive dynamic behavior from CCM period-1 to CCM period-2, CCM period-4, CCM period-8, and CCM chaos. Finally, the simulation and experimental circuits are set up, and the correctness of theoretical analysis is verified by simulation and experimental results.
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Keywords:
- Boost converter /
- valley V2 control /
- Jacobi matrix /
- characteristic value
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[37] -
[1] Goder D, Pelletier W R 1996 Proceeding of HFPC'1996 p19
[2] [3] Li J, Lee F C 2009 IEEE Tran. Circuits and Systems, Part I, 57 2552
[4] [5] Wang F Y, Xu J P, Xu J F 2005 Proc. CSEE 25 67 (in Chinese)[王凤岩, 许建平, 许峻峰 2005 中国电机工程学报 25 67]
[6] [7] 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]
[8] [9] Zhou G H, Xu J P, Sha J, Jin Y Y 2011 IEEE ECCE Asia p2788
[10] [11] Zhou G H, Xu J P, Wang J P 2014 IEEE Transactions on Industrial Electronics 61 1280
[12] Wang F Y 2005 Ph.D. Dissertation (Southwest Jiaotong University) (in Chinese)[王凤岩2005 博士学位论文(西南交通大学)]
[13] [14] Zhou Y F, Chen J N, Tse C K, Ke D M, Shi L X, Sun W F 2004 Acta Phys. Sin. 53 3676 (in Chinese)[周宇飞, 陈军宁, 谢智刚, 柯导明, 时龙兴, 孙伟峰 2004 53 3676]
[15] [16] [17] Zhou G H, Xu J P, Bao B C, Zhang F, Liu X S 2010 Chin. Phys. Lett. 27 090504
[18] [19] 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]
[20] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[21] [22] [23] Lu W G, Zhou L W, Luo Q M, Du X 2007 Acta Phys. Sin. 56 6275 (in Chinese)[卢伟国, 周雒维, 罗全明, 杜雄 2007 56 6275]
[24] [25] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[26] [27] Bao B C 2013 An Introduction to Chaotic Circuits (Science Press) p164 (in Chinese)[包伯成 2013 混沌电路导论 (科学出版社)第164页]
[28] Dai D, Ma X K, Li X F 2003 Acta Phys. Sin. 52 2729 (in Chinese)[戴栋, 马西奎, 李小峰 2003 52 2729]
[29] [30] [31] 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]
[32] [33] Bao B C, Xu J P, Liu Z 2009 Acta Phys. Sin. 58 2949 (in Chinese)[包伯成, 许建平, 刘中 2009 58 2949]
[34] 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]
[35] [36] Zhang B, Li P, Qi Q 2002 Proc. CSEE 22 81 (in Chinese)[张波, 李萍, 齐群 2002 中国电机工程学报 22 81]
[37]
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