Reduced-Order Transfer Function Model of the Droop-Controlled Inverter via Jordan Continued-Fraction Expansion

This article proposes a reduced-order small-signal closed-loop transfer function model based on Jordan continued-fraction expansion to assess the dynamic characteristics of the droop-controlled inverter and provide the preprocessing method for the real-time simulation of power systems. Firstly, dynamic phasors, time delay and zero-order hold are embedded into the small-signal model at the same time, then the closed-loop transfer function of the droop-controlled inverter is built. Compared with the existing closed-loop transfer function approaches, the accuracy of the built transfer function model is dramatically enhanced. Meanwhile, the inner cascaded voltage/current controller parameters are also designed. In order to directly obtain and preserve the maximum overshoot and settling time, which are main features to evaluate the system input-output dynamic response characteristics, the reduced second order closed-loop transfer function is proposed through the continued-fraction expansion regarding arbitrary points on the real frequency axis. Therein, this second order closed-loop transfer function with dynamic response of the original inverter is reduced to the lowest order. Furthermore, combined with the impedance-based approach, the proposed stability assessment approach is utilized to analyze the stability of the microgrid with multiple converters. Finally, simulations and experimental results demonstrate the convenience and accuracy of the proposed approach.