Derivation of a Small-Signal Harmonic Model for Closed-Loop Power Converters Based on the State-Variable Sensitivity Method

An admittance or impedance matrix of a power converter is highly desirable for harmonic analysis of a power system. However, power converters are inherently nonlinear and time-varying systems. Therefore, a small-signal harmonic model needs to be derived. While there have been many methods to obtain the small-signal models of DC-DC converters, most of these methods cannot be directly applied to AC-DC converters. Moreover, while accurate methods exist for obtaining accurate models of open-loop AC-DC converters, there are few existing methods for obtaining accurate models for closed-loop AC-DC converters. This paper proposes an analytical method for obtaining an accurate small-signal harmonic model for a power converter. The proposed method is based on state-variable sensitivity methods, which have been previously used to derive a transfer function of a DC-DC converter. This paper will show what modifications are required to extend it to derive the small-signal harmonic model of a closed-loop AC-DC converter. A small-signal harmonic model of a closed-loop pulse-width modulated (PWM) voltage source converter (VSC) with synchronous
$dq$
frame current controllers and a dc voltage controller is derived based on the proposed method. The results are in good agreement with large-signal simulations by means of PSCAD/EMTDC.