Lyapunov Exponent Calculation and Dynamics Properties of DC-DC Converter with Constant Power Load
Huang Liangyu1, 2, Lu Yimin1, 2
1. College of Electrical Engineering Guangxi University Nanning 530004 China; 2. Guangxi Key Laboratory of Power System Optimization and Energy Technology Nanning 530004 China
Abstract：The Lyapunov exponents of a DC-DC converter with constant power load cannot be calculated at the switching points because of the inexistence of Jacobi matrixes at these points. Aiming at this problem, this paper studies the Lyapunov exponent algorithm of such system using the local maps to construct the system compound Poincaré mapping. Thus, the piece-wise smooth nonlinear dynamic properties of the system can be analyzed according to the Lyapunov exponents. The calculating process is illustrated by the example of a Buck converter with constant power load. Both the local maps of non-switching and switching stage are deduced in detail. Then compound Poincaré mapping of system is constructed based on these two local maps. The theoretical results are verified by the numerical and circuit simulations. It is shown that the accuracy of Lyapunov exponents is improved by introducing the local mapping of load switching. The proposed method can also be extended to the other kind of switching power converters with nonlinear load or nonlinear source.
黄良玉, 陆益民. 带恒功率负载DC-DC变换器的Lyapunov指数计算和动力学特性分析[J]. 电工技术学报, 2017, 32(24): 97-106.
Huang Liangyu, Lu Yimin. Lyapunov Exponent Calculation and Dynamics Properties of DC-DC Converter with Constant Power Load. Transactions of China Electrotechnical Society, 2017, 32(24): 97-106.
[1] 李响, 郝瑞祥, 游小杰, 等. 一种级联电力电子变压器直流电压平衡控制策略[J]. 电工技术学报, 2017, 32(2): 238-245. Li Xiang, Hao Ruixiang, You Xiaojie, et al. A DC voltage balance control strategy for the cascaded power electronic transformer[J]. Transactions of China Electrotechnical Society, 2017, 32(2): 238- 245. [2] 包伯成, 冯霏, 潘赛虎. 脉冲跨周期调制连续导电模式Buck变换器低频波动现象及其抑制技术[J]. 电工技术学报, 2014, 29(4): 38-44. Bao Bocheng, Feng Fei, Pan Saihu. Low-frequency oscillation phenomenon and its suppression technique in pulse skipping modulation CCM Buck converter[J]. Transactions of China Electrotechnical Society, 2014, 29(4): 38-44. [3] 李学生, 张新闻, 常玉峰, 等. 基于半导体功率损耗的小型风电变换器可靠性研究[J]. 电力系统保护与控制, 2015, 43(19): 16-21. Li Xuesheng, Zhang Xinwen, Chang Yufeng, et al. Small wind power converter reliability research based on semiconductor power loss[J]. Power System Protection and Control, 2015, 43(19): 16-21. [4] 刘月贤, 王天钰, 杨亚宇, 等. 电动汽车充放电系统建模与仿真[J]. 电力系统保护与控制, 2014, 42(13): 70-76. Liu Yuexian, Wang Tianyu, Yang Yayu, et al. Modeling and simulation of electric vehicles' charge and discharge system[J]. Power System Protection and Control, 2014, 42(13): 70-76. [5] 许正平, 李俊. 双向全桥DC-DC变换器高效能控制研究与实现[J]. 电力系统保护与控制, 2016, 44(2): 140-146. Xu Zhengping, Li Jun. Research and implementation of bidirectional full bridge DC-DC converter with high-efficiency control[J]. Power System Protection and Control, 2016, 44(2): 140-146. [6] 杨玉岗, 邹雨霏, 代少杰, 等. DCM模式下交错并联磁集成双向DC/DC变换器的稳态性能分析[J]. 电工技术学报, 2015, 30(11): 60-70. Yang Yugang, Zou Yufei, Dai Shaojie, et al. Steady state performance analysis of the interleaving and magnetically integrated bidirectional DC/DC conver- ter under DCM mode[J]. Transactions of China Electrotechnical Society, 2015, 30(11): 60-70. [7] 易桂平. 电网电压不平衡条件下微网恒功率控制策略研究[J]. 电工技术学报, 2015, 30(14): 377-387. Yi Guiping. Micro-grid constant power control strategy analysis under grid voltage imbalance[J]. Transactions of China Electrotechnical Society, 2015, 30(14): 377-387. [8] 韦李军, 黄萌, 孙建军, 等. 带恒功率负载的光伏-储能混合发电系统非线性行为分析[J]. 电工技术学报, 2017, 32(7): 128-137. Wei Lijun, Huang Meng, Sun Jianjun, et al. Nonlinear analysis of photovoltaic battery hybrid power system with constant power loads[J]. Transa- ctions of China Electrotechnical Society, 2017, 32(7): 128-137. [9] Barabanov N, Ortega R, Griñó R, et al. On existence and stability of equilibria of linear time-invariant systems with constant power loads[J]. IEEE Transa- ctions on Circuits and Systems I: Regular Papers, 2016, 63(1): 114-121. [10] Emadi A, Khaligh A, Rivetta C H, et al. Constant power loads and negative impedance instability in automotive systems: definition, modeling, stability, and control of power electronic converters and motor drives[J]. IEEE Transactions on Vehicular Tech- nology, 2006, 55(4): 1112-1125. [11] Singh S, Fulwani D, Kumar V. Robust sliding-mode control of DC/DC Boost converter feeding a constant power load[J]. IET Power Electronics, 2015, 8(7): 1230-1237. [12] Zhao Y, Qiao W, Ha D. A sliding-mode duty-ratio controller for DC/DC Buck converters with constant power loads[J]. IEEE Transactions on industry Appli- cations, 2014, 50(2): 1448-1458. [13] Sanchez S, Ortega R, Griñó R, et al. Conditions for existence of equilibrium points of systems with constant power loads[J]. IEEE Transactions Circuits and Systems-I, 2014, 61(7): 2204-2211. [14] Marco C, Lin Z, Antonello M. Why ideal constant power loads are not the worst case condition from a control standpoint[J]. IEEE Transactions on Smart Grid, 2015, 6(6): 2596-2606. [15] Liu X B, Ma S H, Li Z X, et al. Large signal stability analysis for constant power loads with RC parallel damping filters[C]//17th International Conference on Electrical Machines and Systems (ICEMS), Hangzhou, 2014: 2796-2801. [16] Lu X N, Sun K, Guerrero J M, et al. Stability enhancement based on virtual impedance for DC microgrids with constant power loads[J]. IEEE Transactions on Smart Grid, 2015, 6(6): 2770-2783. [17] Herrera L, Wang J. Stability analysis and controller design of DC microgrids with constant power loads[C]// Proceedings of IEEE Applied Power Electronics Conference and Exposition, Charlotte, NC, 2015: 691-696. [18] Xie F, Yang R, Zhang B. Bifurcation and border collision analysis of voltage-mode-controlled flyback converter based on total ampere-turns[J]. IEEE Transactions Circuits and System-I, 2011, 58(9): 2269-2280. [19] Zamani N, Ataei M, Niroomand M. Analysis and control of chaotic behavior in Boost converter by ramp compensation based on Lyapunov exponents assignment: theoretical and experimental investi- gation[J]. Chaos, Solitons and Fractals, 2015, 81: 20-29. [20] Wang L, Wei X. Computation of Lyapunov exponents for a current-programmed Buck Boost converter[C]// Autonomous Decentralized System on the 2nd Inter- national Workshop, Washington DC, 2002: 273- 276. [21] 李小峰, 马西奎, 李明. DC/DC变换器的最大Lyapunov指数计算及其非线性特性的实验研究[J]. 电工技术学报, 2005, 20(4): 21-27. Li Xiaofeng, Ma Xikui, Li Ming. Calculation of largest Lyapunov exponent and laboratorial verification of nonlinear behavior for DC/DC converters[J]. Transactions of China Electrotechnical Society, 2005, 20(4): 21-27. [22] Jin L, Lu Q S, Twizell E H. A method for calculating the spectrum of Lyapunov exponents by local maps in non-smooth impact-vibrating systems[J]. Journal of sound and Vibration, 2006, 298(4-5): 1019-1033. [23] 李清都, 郭建丽. 切换系统Lyapunov指数的算法及应用[J]. 物理学报, 2014, 63(10): 100501(9). Li Qingdu, Guo Jianli. Algorithm for calculating the Lyapunov exponents of switching system and its application[J]. Acta Physica Sinica, 2014, 63(10): 100501(9). [24] 徐德鸿, 马皓, 汪槱生. 电力电子技术[M]. 北京:科学出版社, 2006. [25] Wang J, Howe D. A power shaping stabilizing control strategy for DC power systems with constant power loads[J]. IEEE Transactions on Power Electronics, 2008, 23(6): 2982-2989. [26] 徐慧东. 非光滑动力系统周期解的分岔研究[D]. 成都: 西南交通大学, 2008. [27] 张思进. 机械碰撞运动中的非光滑动力学[M]. 长沙: 湖南大学出版社, 2008. [28] Maniktala S. 精通开关电源设计[M]. 王健强, 译. 2版. 北京: 人民邮电出版社, 2015.
2017, Vol. 32 
