Stability Analysis of a Single-Phase Active Power Decoupling Converter Based on Discrete Harmonic State Space Model

A digitally controlled single-phase active power decoupling converter is a continuous-discrete hybrid system with nonlinear time-periodic (NTP) nature, thus the conventional linear time-invariant (LTI) model cannot accurately describe the system’s dynamic behavior. This article presents a discrete harmonic state space (DHSS) modeling method to analyze the small-signal stability of a digitally controlled single-phase current source converter (SCSC) with an active power decoupling circuit (APDC). The proposed model retains the switching details, and it has the potentiality to accurately describe the high-frequency dynamics. Moreover, the DHSS model not only transforms the NTP system into an LTI system but also includes harmonic interaction dynamics. Furthermore, an LTI Toeplitz matrix is developed to analyze the oscillation phenomenon and system stability, and the stability boundaries of system parameters are obtained based on the eigenvalues loci. Finally, the physical experimental results validate the correctness of the theory analysis.