Abstract This paper is concerned with the nonlinear dynamics of Cascaded H-Bridge Converter under PR (Proportional Resonant) control. First, a stroboscopic mapping model of PWM (Pulse Width Modulation) converter is established and the corresponding dynamics, including bifurcations and chaos is investigated analytically. Taking the switching frequency, controller parameters as the bifurcation parameter, some different dynamic behaviors are identified over a wide range of some specified parameter. Moreover, the bifurcation condition is further verified based on the root locus diagram and Lyapunov exponential spectrum. Second, aiming at deriving the stability regions of PWM converter, the variable substitution approach is utilized to transform the non-autonomous converter model into an autonomous one. Then, the PR (Proportional Resonant) controller is applied to control the grid-side current, which can suppress the chaos and bifurcation in the current loop by increasing the proportional gain. Finally, the experiment results are presented to illustrate the validity of the control scheme.

中文翻译：

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比例谐振控制的级联H桥变换器的分岔分析

摘要 本文研究了PR（比例谐振）控制下的级联H 桥转换器的非线性动力学问题。首先，建立了PWM（脉冲宽度调制）转换器的频闪映射模型，并分析研究了相应的动力学，包括分岔和混沌。以开关频率、控制器参数为分岔参数，在某个指定参数的大范围内识别出一些不同的动态行为。此外，基于根轨迹图和李雅普诺夫指数谱进一步验证了分岔条件。其次，针对PWM变换器稳定区的推导，采用变量代换法将非自治变换器模型转化为自治变换器模型。然后，采用PR（Proportional Resonant）控制器控制网侧电流，通过增加比例增益来抑制电流回路中的混沌和分叉。最后，给出了实验结果来说明控制方案的有效性。