Accurate Small-Signal Terminal Characteristic Model and SISO Stability Analysis Approach for Parallel Grid-Forming Inverters in Islanded Microgrids

Abstract

This article derives a small-signal terminal characteristic model for the grid-forming inverter with droop-control in the synchronous reference ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -) frame, accurately covering the dynamics of the power controller, the voltage and current control loops, and all circuit components, where a new set of terminal characteristics is proposed to characterize the small-signal dynamics of fundamental frequency introduced by the fundamental frequency-active power droop scheme. Based on the terminal characteristics of individual inverters, the stability of parallel grid-forming inverters can be predicted by the generalized Nyquist criterion. Furthermore, to simplify the stability analysis process and reduce calculation complexity, a single-input single-output (SISO) stability analysis approach is proposed by exploring the interaction among the droop-control of parallel inverters through analyzing mathematical feature of the proposed terminal characteristic model of individual inverters as well as the return ratio of the parallel inverters, which uses <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d-d</i> channel element of system return ratio matrix and Nyquist criterion to predict the stability. Finally, simulation and experimental results validate the effectiveness of the proposed small-signal model and SISO stability analysis approach.