Dimensionless Approach to Multi-Parametric Stability Analysis of Nonlinear Time-Periodic Systems: Theory and Its Applications to Switching Converters
Dimensionless Approach to Multi-Parametric Stability Analysis of Nonlinear Time-Periodic Systems: Theory and Its Applications to Switching Converters
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DOI：
10.1109/tcsi.2012.2215798
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发表时间：
2013-02
期刊：
影响因子：
--
通讯作者：
Hao Zhang;Yuan Zhang-;Xikui Ma
中科院分区：
文献类型：
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作者：
Hao Zhang;Yuan Zhang-;Xikui Ma
本文提出了一种无量纲的方法来分析开关变换器的多参数稳定性行为，它可以用一个非线性时间周期（NTP）系统来表征。主要目的是分析多个电路参数如何影响导出的NTP系统的稳定模式，并简化这种NTP系统的参数复杂性。与以往的工作相比，该方法侧重于拓扑等价意义下的NTP系统的参数结式关系，并研究其在同胚NTP系统方面的稳定性。首先，提出了NTP系统的等效稳定性理论。然后，基于等效理论，引入规范化映射并推导出各种有趣的性质，从而制定无量纲方法。利用Galerkin方法求出了NTP系统在无量纲参数空间中的近似解，并利用特征值分析方法确定了其稳定性模式。最后，以单周控制Zeta功率因数校正变换器为例，详细讨论了该方法的应用。这些分析结果与实验测量结果吻合得很好。
This paper proposes a dimensionless approach to analyze the multi-parametric stability behavior of switching converters, which can be characterized by a nonlinear time-periodic (NTP) system. The main objective is to analyze how multiple circuit parameters affect the stability patterns of the derived NTP system and to simplify the parametric complexity of such NTP system. In contrast to previous work, the proposed method focuses on the parametric resultant relationships of the NTP system in the sense of topological equivalence, and investigates its stability in terms of the homeomorphic NTP system. Firstly, an equivalent stability theory of NTP systems is proposed. Then, based on the equivalent theory, a normalized map is introduced and various interesting properties are derived so as to formulate the dimensionless approach. Moreover, the approximate solution of the NTP system in dimensionless parameter space is calculated by using the Galerkin method, and its stability pattern is identified with the help of eigenvalue analysis approach. Finally, a case study of one-cycle controlled Zeta PFC converter is discussed in detail to exemplify the application of the proposed method. These analytical results agree well with those ones obtained from experimental measurements.