Stability Analysis of Digital-Controlled Single-Phase Inverter with Synchronous Reference Frame Voltage Control

Stability analysis of single-phase power converters controlled in stationary reference frame is now mature and well developed, by using either linear or nonlinear methods. However, for the single-phase converters with synchronous reference frame (SRF) control loops, little work has been done on the evaluation of the nonlinear approaches for stability analysis. In this paper, the stability of a digital-controlled single-phase voltage-source inverter (VSI) with SRF voltage control loop is investigated from the perspective of nonlinear system. The analysis is based on the discrete-time model defined by the stroboscopic map, which is derived using the state-space averaging (SSA) technique. Furthermore, two different nonlinear analysis methods, the Jacobian matrix method and the Lyapunov exponent method, are adopted to analyze the fast-scale stability and the slow-scale stability of the pulsewidth-modulated (PWM) inverter under variations of control parameters; hence, the stability regions can be obtained. The theoretical results indicate that, for the established stroboscopic models, the Jacobian matrix method and the Lyapunov exponent method are mathematically equivalent, which means that the fast-scale stability and the slow-scale stability of the studied single-phase VSI are consistent, especially under linear load conditions. Experimental results under resistive load, inductive-resistive load, and diode rectifier load conditions are presented to support the theoretical results, which also proves that the discrete-time model plus the Jacobian matrix method or the Lyapunov exponent method is capable to investigate the stability of a converter with SRF control loops accurately.