Abstract：Dynamic response and stability criterion and adaptability of state space averaging method for periodic piecewise linear system, which is linear time invariant system at each stage, is investigated by its detail model. It is proved that arbitrary state variable sequence with interval of switching period is linear time invariant discrete system and its analytical solution is obtained. Based on the solution, this paper presents state space exact averaging method and characteristic matrix method to estimate system stability, which shows that state space averaging method are the approximation of these methods. Analogy to concept of Lyapunov stability, concept and stability criterion of periodic stability of equilibrium curve is presented, which can lay strict foundation for dynamic response and stability analysis of switching converter. The algorithm is validated by simulation test.
王刚, 马伟明, 付立军, 康军, 马凡. 周期分段线性系统稳定性理论[J]. 电工技术学报, 2010, 25(12): 84-91.
Wang Gang, Ma Weiming, Fu Lijun, Kang Jun, Ma Fan. Stability Theory of Periodic Piecewise Linear System. Transactions of China Electrotechnical Society, 2010, 25(12): 84-91.
[1] 马伟明．交直流电力集成技术[J]．中国工程科学, 2002, 4(12)：53-59． Ma Weiming. AC-DC power integration techniques[J]. Engineering Science, 2002, 4(12): 53-59. [2] 陈坚．电力电子学—电力电子变换和控制技术[M].北京：高等教育出版社, 2002． [3] Shortt D J, Lee F C. Improved switching converter model using averaging and discrete techniques[J]. IEEE Transactions on Aerospace and Electronic Systems, 1983, AES-19(2): 190-202. [4] 蔡宣三, 龚绍文．高频功率电子学——直流-直流变换部分[M]．北京：科学出版社, 1993． [5] Middlebrook R D, Cuk S. A general unified approach to modeling switching-converter power stages[C]. IEEE PESC, 1976: 23-25. [6] Brand L, Bass R M. Extension of averaging theory for power electronics systems[J]. IEEE Transactions on Power Electronics, 1996, 11(4): 542-553. [7] 卢强, 王仲鸿, 韩英铎．输电系统最优控制[M]．北京：科学出版社, 1982． [8] 郑大钟．线性系统理论[M]．北京：清华大学出版社, 2002． [9] Emadi Ali, Khaligh Alireza, Rivetta Claudio 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 Technology, 2006, 55(4): 1112-1125. [10] Ferraro L. D, Capponi F. G. Stability conditions for multi-converter power systems[C]. IEEE Conference on Vehicle Power and Propulsion, 2005: 137-142. [11] 徐德鸿．电力电子系统建模及控制[M]．北京：机械工业出版社, 2006．
2010, Vol. 25 
