Comparison of Impedance Model and Amplitude–Phase Model for Power- Electronics-Based Power System

Recently power electronics devices have been widely used in power systems, and the dynamical behavior of the power system has been changing with their increasing penetration. Now we are confronting some serious emergent risks of oscillation instability, which are quite different from those in the traditional power system dynamics. Some small-signal stability methods have been developed, including impedance analysis and amplitude-phase analysis, and it is highly desirable to study their relations. The impedance model and amplitude-phase model are based on the same primitive linearized system, but from the perspective of different input-output relations; voltage versus current for the impedance model, and (imbalanced) active and reactive powers versus voltage phase and amplitude for the amplitude-phase model. In this paper, we deduce, in a rigorous mathematical manner, that the amplitude-phase model and the impedance model are equivalent, in terms of the stability of the whole closed-loop system. Furthermore, a voltage-source converter (VSC) model within the dc-link voltage control timescale (around the frequency range of 1-10 Hz) is numerically studied to verify the validity. Clearly, this paper establishes a solid bridge between the two methods, which is expected to be helpful for researchers to understand the complicated dynamical behavior of power-electronics-based power system.