Recursive SISO Impedance Modeling of Single-Phase Voltage Source Rectifiers

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.