Due to the nonlinear time-periodic nature, precise impedance modeling of power-converter-based single-phase ac systems is complex. Small-signal modeling for the systems with a fixed operating point is easy, but the extension of the same procedure to the systems with time-periodic trajectory is still challenging. In this article, a recursive single-input single-output (SISO) impedance modeling framework for single-phase rectifiers is presented, which can greatly simplify both the modeling procedure and the resulting impedance model. A general linear-time periodic modeling method is proposed by extending the linear-time invariant modeling method, where frequency-coupling effects are modeled by the transfer function vector rather than the transfer function matrix, so the modeling complexity is reduced. Furthermore, based on the idea of mathematical induction, an analytical and accurate recursive SISO impedance model is derived. The resulting recursive SISO impedance model can characterize the frequency-coupling dynamics of arbitrary order with a low computation burden. Experiments validate the accuracy of the recursive SISO impedance modeling method.

中文翻译：

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单相电压源整流器的递归 SISO 阻抗建模

由于非线性时间周期特性，基于功率转换器的单相交流系统的精确阻抗建模很复杂。具有固定工作点的系统的小信号建模很容易，但将相同的程序扩展到具有时间周期轨迹的系统仍然具有挑战性。在本文中，提出了一种用于单相整流器的递归单输入单输出 (SISO) 阻抗建模框架，它可以大大简化建模过程和生成的阻抗模型。在线性时间不变建模方法的基础上，提出了一种通用的线性时间周期建模方法，通过传递函数向量而不是传递函数矩阵对频率耦合效应进行建模，从而降低了建模复杂度。此外，基于数学归纳法的思想，推导出了一个解析的、精确的递归SISO阻抗模型。由此产生的递归 SISO 阻抗模型可以以较低的计算负担表征任意阶的频率耦合动力学。实验验证了递归 SISO 阻抗建模方法的准确性。