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基于单周期控制的自治性,建立了描述单周期控制Cuk功率因数校正(PFC)变换器动力学行为的非线性状态平均模型.在此基础上,采用谐波平衡法得出了该系统周期平衡态的近似解析表达式,继而通过判定Floquet乘子的变化趋势,准确地预测了该变换器首次失稳时分岔点的位置和类型,揭示了系统出现中尺度不稳定现象的物理机理.研究结果表明,该变换器周期闭轨稳定性的丧失,即Neimark-Sacker分岔的发生是最终导致中尺度振荡现象产生的根本原因.最后,电路实验验证了理论分析的正确性.这些研究结果不仅揭示了单周期控制Cuk PFC变换器中的中尺度分岔行为的本质,而且为系统电路参数的设计提供了理论依据.
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关键词:
- Cuk功率因数校正变换器 /
- 中尺度不稳定 /
- 谐波平衡法 /
- Floquet理论
Based on the autonomous character of one-cycle control, the average model of one-cycle controlled Cuk power factor correction converter can be derived. Subsequently, the approximate analytical expressions of periodic solutions are obtained by using the harmonic balance method. Furthermore, through analyzing the changing trend of Floquet multipliers, the location and the type of the first bifurcation point are predicted. Thus, the intrinsic mechanism of such an instability can also be explained. The results show that the intermediate-scale instability is due to the loss of stability of periodic solutions, which is named the Neimark-Sacker bifurcation in the circuit system. Finally, experimental results are presented for verification purpose. Our work has revealed the salient feature of the intermediate-scale instability, and provided a theoretical basis for facilitating design of the converter.-
Keywords:
- Cuk power factor correction converter /
- intermediate-scale instability /
- harmonic balance method /
- Floquet theory
[1] Aroudi A E, Orabi M, Salamero M L 2008 Int. J. Bifur. Chaos 18 3073
[2] Iu H H C, Zhou Y F, Tse C K 2003 Int. J. Circ. Theor. Appl. 31 611
[3] Wong S, Tse C K, Orabi M, Ninomiya T 2006 IEEE Trans. Circ. Syst. Ⅰ 53 454
[4] Wang F Q, Zhang H, Ma X K, Li X M 2009 Acta Phys. Sin. 58 6838 (in Chinese) [王发强、 张 浩、马西奎、李秀明 2009 物理学报 58 6838]
[5] Orabi M, Ninomiya T 2003 IEEE Trans. Ind. Electron. 50 1116
[6] Wang X M, Zhang B, Qiu D Y 2009 Acta Phys. Sin. 58 2248 (in Chinese) [王学梅、 张 波、丘东元 2009 物理学报 58 2248]
[7] Liu F 2008 Chin. Phys. B 17 2394
[8] Zou J L, Ma X K 2008 Acta Phys. Sin. 57 720 (in Chinese) [邹建龙、马西奎 2008 物理学报 57 720]
[9] Dai D, Tse C K, Zhang B, Ma X K 2008 Int. J. Circ. Theor. Appl. 18 2095
[10] Wang F Q, Zhang H, Ma X K 2010 IEEE Trans. Circuits Syst. Ⅰ 57 405
[11] Bento M A, Roberto E 2009 IEEE Trans. Ind. Appl. 45 268
[12] Hu Z B, Zhang B, Hu S F, Deng W H 2005 Proc. Chin. Soc. Electr. Eng. 25 19 (in Chinese) [胡宗波、张 波、胡少甫、邓卫华 2005 中国电机工程学报 25 19 ]
[13] Yang C, Smedly K M 2004 IEEE Trans. Power Electron. 19 1289
[14] Du X, Zhou L W, Luo Q M, Fu Z H 2006 Proc. Chin. Soc. Electr. Eng. 26 120 (in Chinese) [杜 雄、周雒维、罗全明、付志宏 2006 中国电机工程学报 26 120 ]
[15] Smedly K M, Cuk S 1995 IEEE Trans. Power Electron. 10 625
[16] Maksimovic D, Cuk S 1991 IEEE Trans. Power Electron. 6 476
[17] Erickson R W, Maksimovic D 2004 Fundermentals of Power Electronics (New York: Kluwer Academic Publishers) p27
[18] Iu H H C, Tse C K 2003 IEEE Trans. Circuits Syst. Ⅰ 50 679
[19] Nayfeh A H, Mook D T 1979 Nonlinear Oscillations (New York: John Wiley & Sons) p59
[20] Nayfeh A H, Balachandran B 1995 Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods ( New York : Wiley-VCH) p158
[21] Friedmann P, Hammond C E 1977 Int. J. Numer. Methods Eng. 11 1117
[22] Shen J H, Lin K C, Chen S H, Sze K Y 2008 Nonlin. Dyn. 52 403
[23] Seydel R 1999 Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos (New York: Springer-Verlag) p261
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[1] Aroudi A E, Orabi M, Salamero M L 2008 Int. J. Bifur. Chaos 18 3073
[2] Iu H H C, Zhou Y F, Tse C K 2003 Int. J. Circ. Theor. Appl. 31 611
[3] Wong S, Tse C K, Orabi M, Ninomiya T 2006 IEEE Trans. Circ. Syst. Ⅰ 53 454
[4] Wang F Q, Zhang H, Ma X K, Li X M 2009 Acta Phys. Sin. 58 6838 (in Chinese) [王发强、 张 浩、马西奎、李秀明 2009 物理学报 58 6838]
[5] Orabi M, Ninomiya T 2003 IEEE Trans. Ind. Electron. 50 1116
[6] Wang X M, Zhang B, Qiu D Y 2009 Acta Phys. Sin. 58 2248 (in Chinese) [王学梅、 张 波、丘东元 2009 物理学报 58 2248]
[7] Liu F 2008 Chin. Phys. B 17 2394
[8] Zou J L, Ma X K 2008 Acta Phys. Sin. 57 720 (in Chinese) [邹建龙、马西奎 2008 物理学报 57 720]
[9] Dai D, Tse C K, Zhang B, Ma X K 2008 Int. J. Circ. Theor. Appl. 18 2095
[10] Wang F Q, Zhang H, Ma X K 2010 IEEE Trans. Circuits Syst. Ⅰ 57 405
[11] Bento M A, Roberto E 2009 IEEE Trans. Ind. Appl. 45 268
[12] Hu Z B, Zhang B, Hu S F, Deng W H 2005 Proc. Chin. Soc. Electr. Eng. 25 19 (in Chinese) [胡宗波、张 波、胡少甫、邓卫华 2005 中国电机工程学报 25 19 ]
[13] Yang C, Smedly K M 2004 IEEE Trans. Power Electron. 19 1289
[14] Du X, Zhou L W, Luo Q M, Fu Z H 2006 Proc. Chin. Soc. Electr. Eng. 26 120 (in Chinese) [杜 雄、周雒维、罗全明、付志宏 2006 中国电机工程学报 26 120 ]
[15] Smedly K M, Cuk S 1995 IEEE Trans. Power Electron. 10 625
[16] Maksimovic D, Cuk S 1991 IEEE Trans. Power Electron. 6 476
[17] Erickson R W, Maksimovic D 2004 Fundermentals of Power Electronics (New York: Kluwer Academic Publishers) p27
[18] Iu H H C, Tse C K 2003 IEEE Trans. Circuits Syst. Ⅰ 50 679
[19] Nayfeh A H, Mook D T 1979 Nonlinear Oscillations (New York: John Wiley & Sons) p59
[20] Nayfeh A H, Balachandran B 1995 Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods ( New York : Wiley-VCH) p158
[21] Friedmann P, Hammond C E 1977 Int. J. Numer. Methods Eng. 11 1117
[22] Shen J H, Lin K C, Chen S H, Sze K Y 2008 Nonlin. Dyn. 52 403
[23] Seydel R 1999 Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos (New York: Springer-Verlag) p261
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