Study on Bifurcation and Chaos in Boost Converter Based on Energy Balance Model

Quanmin NIU, Zhizhong JU

.

DOI: 10.4236/epe.2009.11006                

Abstract

Based on boost converter operating in discontinuous mode, this paper proposes an energy balance model (EBM) for analyzing bifurcation and chaos phenomena of capacitor energy and output voltage when the converter parameter is varying. It is found that the capacitor energy and output voltage dynamic behaviors exhibit the typical period-doubling route to chaos by increasing the feedback gain constant K of proportional controller. The accurate position of the first bifurcation point and the iterative diagram of the capacitor energy with every K can be derived from EBM. Finally, the underlying causes for bifurcations and chaos of a general class of nonlinear systems such as power converters are analyzed from the energy balance viewpoint. Com-paring with the discrete iterative model, EBM is simple and high accuracy. This model can be easily devel-oped on the nonlinear study of the other converters.

Keywords

power converter, nonlinear, bifurcation, chaos, energy balance model

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Middlebrook R D and Cuk S, "A general unified approach to modeling switching-converter power stage," IEEE Power Electron. Spec. Conf. Rec., pp. 18-34, 1976.
[2]	Mario di Bernardo and Francesco Vasca, "Discrete-time for the analysis of bifurcations and chaos in DC/DC converters," IEEE Transactions on Circuit System Ⅰ, Vol. 47, No. 2, pp. 130-143, 2000.
[3]	Ma Xikui, Li Ming, Dai Dong, ZhaoHao, et al., "Reviews of res- earch on complex behavior of power electronic circuits and systems," Transactions of China Electrotechnical Society, Vol. 21, No. 12, pp. 1-11, 2006.
[4]	C. K. Tse, "Flip bifurcation and chaos in the three-state boost switching regulators," IEEE Transactions on Circuit System Ⅰ, Vol. No. 1, pp. 16-23, 1994.
[5]	C. K. Tse, Y. M. Lai, and H. H. C. Iu, "Hopf bifurcation and chaos in a free-running current-controlled Cuk switching regulator," IEEE Transactions on Circuit SystemⅠ, Vol. 47, No. 4, pp. 448-457, 2000.
[6]	Guohui Yuan, Soumitro Banerjee, Edward Ott, et al., "Border- collision bifurcations in the buck converter," IEEE Transactions on Circuit SystemⅠ, Vol. 45, No. 7, pp. 707-716, 1998.
[7]	H. H. C. Iu and C. K. Tse, "Bifurcation behavior in parallel- connected buck converters," IEEE Transactions on Circuit System Ⅰ, Vol. 48, No. 2, pp. 233-240, 2001.
[8]	Zhang Bo, Li Ping, and Qi Qun, "Method for analyzing and modeling bifurcation and chaos in DC/DC converters," Peoceedings of CSEE, Vol. 22, No. 11, pp. 81-86, 2002.
[9]	Liu Weizeng, Zhang Hao, and Ma Xikui, "Analysis of intermittent bifurcations and chaos phenomena in boost PFC converters bystroboscopic map," Proceedings of CSEE, Vol. 25, No. 1, pp. 43-48, 2005.
[10]	Qu Ying and Zhang Bo, "The precise mathematical discrete model of buck converter in DCM and its analysis for bifurcation stability," Acta Electronica Sinica, Vol. 30, No. 8, pp. 1253-1256, 2002.
[11]	Ma Xikui, Liu Weizeng, and Zhang Hao, "Analysis of fast-scale bifurcations and chaos phenomena in boost PFC converter," Proceedings of CSEE, Vol. 25, No. 5, pp. 61-67, 2005.