General Rules of Using Bode Plots for Impedance-Based Stability Analysis

The impedance-based stability analysis method has been widely utilized to assess the stability of power electronics-based systems, since it can regard subsystems as “black boxes” without the prior knowledge on their internal parameters. The Bode plot serves as an intuitive and practical tool to assess the impedance interaction, and the resulted oscillation frequency is generally identified as the intersection frequency of the impedance-magnitude responses where the impedance-phase difference is out of 180°. However, this prediction only applies to certain cases, since the direction of the Nyquist trajectory is overlooked, corresponding to the derivatives of magnitude and phase response with respect to the frequency on Bode plots, which may result in failure predictions of the system stability. In this paper, a rigorous mapping between Nyquist plots and Bode plots is presented, and the general rules of using Bode plots for the impedance-based stability analysis are proposed, considering the magnitude and phase derivatives at the crossover frequencies. Simulations and experimental tests on a grid-tied inverter system validate the correctness of the theoretical analysis.