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This paper deals with the issue of modeling method by perturbation solution to the single-phase AC-DC converter. A continuous circuit that includes a single-phase AC-DC converter is inducted first. And then a differential equation is presented with two parameters, which are controlling parameter and small perturbation parameter. A strict proof indicates that this equation can be solved by the regular perturbation. The compareison between the result and the simulation figures of PSCAD/EMTDC, shows that the result is correct and simple, thus avoiding the requirements for large computation capacity. Finally, the physical significance of the two parameters is analyzed, showing that they may incur the period-doubling chaos. This method not only fits the single-phase AC-DC converter circuit, but also meets the need of two-phase or N-phase circuits.
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Keywords:
- nonlinear oscillation /
- chaotic analysis /
- regular perturbation /
- single-phase AC-DC converter
[1] Yu Y X, Luan W P 2011 J. Tianjin Univ. 44 377 (in Chinese) [余贻鑫, 栾文鹏 2011 天津大学学报 44 377]
[2] Hao L L, Xue Y S, Dong Z Y, Wu Q H, Xu T S 2010 Automation of Electric Power Systems 34 11 (in Chinese) [郝丽丽, 薛禹胜, Dong Z Y, Wu Q H, 徐泰山 2010 电力系统自动化 34 11]
[3] van der Pol B 1920 Radio Rev. 1 701
[4] Zhou H Q, Ju P, Song Z P, Jin Y Q, Sun G Q 2011 Proceeding of The CSEE 31 19 (in Chinese) [周海强, 鞠平, 宋忠鹏, 金宇清, 孙国强 2011 中国电机工程学报 31 19]
[5] Liu H T, Gong L N 2010 Power System Protection and Control 38 1 (in Chinese) [刘海涛, 龚乐年 2010 电力系统保护与控制 38 1]
[6] Cha X M, Zhang Y, Cheng Y, Fan Y P 2012 Trans. China Electrotech. Soc. 27 24 (in Chinese) [查晓明, 张扬, 成燕, 樊友平 2012 电工技术学报 27 24]
[7] Zha X M, Zhang Y, Sun J J, Fan Y P 2012 Acta Phys. Sin. 61 020505 (in Chinese) [查晓明, 张扬, 孙建军, 樊友平 2012 61 020505]
[8] Wu Y F, Zhang S P, Sun J W 2011 Acta Phys. Sin. 60 020511 (in Chinese) [吴勇峰, 张世平, 孙金玮 2011 60 020511]
[9] Hefner A R, Diebolt D M 1994 IEEE Trans. Power Elec. 9 233
[10] Mo J Q, Lin Y H, Lin W T 2005 Acta Phys. Sin. 54 3974 (in Chinese) [莫嘉琪, 林一骅, 林万涛 2005 54 3974]
[11] Feigenbaum M J, Jensen M H, Itamar P 1986 Phys. Rev. Lett. 57 1503
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[1] Yu Y X, Luan W P 2011 J. Tianjin Univ. 44 377 (in Chinese) [余贻鑫, 栾文鹏 2011 天津大学学报 44 377]
[2] Hao L L, Xue Y S, Dong Z Y, Wu Q H, Xu T S 2010 Automation of Electric Power Systems 34 11 (in Chinese) [郝丽丽, 薛禹胜, Dong Z Y, Wu Q H, 徐泰山 2010 电力系统自动化 34 11]
[3] van der Pol B 1920 Radio Rev. 1 701
[4] Zhou H Q, Ju P, Song Z P, Jin Y Q, Sun G Q 2011 Proceeding of The CSEE 31 19 (in Chinese) [周海强, 鞠平, 宋忠鹏, 金宇清, 孙国强 2011 中国电机工程学报 31 19]
[5] Liu H T, Gong L N 2010 Power System Protection and Control 38 1 (in Chinese) [刘海涛, 龚乐年 2010 电力系统保护与控制 38 1]
[6] Cha X M, Zhang Y, Cheng Y, Fan Y P 2012 Trans. China Electrotech. Soc. 27 24 (in Chinese) [查晓明, 张扬, 成燕, 樊友平 2012 电工技术学报 27 24]
[7] Zha X M, Zhang Y, Sun J J, Fan Y P 2012 Acta Phys. Sin. 61 020505 (in Chinese) [查晓明, 张扬, 孙建军, 樊友平 2012 61 020505]
[8] Wu Y F, Zhang S P, Sun J W 2011 Acta Phys. Sin. 60 020511 (in Chinese) [吴勇峰, 张世平, 孙金玮 2011 60 020511]
[9] Hefner A R, Diebolt D M 1994 IEEE Trans. Power Elec. 9 233
[10] Mo J Q, Lin Y H, Lin W T 2005 Acta Phys. Sin. 54 3974 (in Chinese) [莫嘉琪, 林一骅, 林万涛 2005 54 3974]
[11] Feigenbaum M J, Jensen M H, Itamar P 1986 Phys. Rev. Lett. 57 1503
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