Multi-Scenario Analysis of Hopf Oscillator-Controlled Inverter in Islanded Systems Based on Optimal Numerical Integration Methods

In this paper, a grid-forming (GFM) inverter control method based on the Hopf oscillator is proposed, using voltage amplitude and frequency as inputs to generate a limit cycle with voltage amplitude as the radius and angular frequency as the rotational speed. In power systems, the accuracy of voltage and frequency is crucial. The paper compares numerical solutions from the Runge-Kutta and the Euler methods to derive the optimal solution for the Hopf oscillator's nonlinear oscillation equation. By comparing and analyzing the numerical solutions of the Runge-Kutta method and Euler method, the optimal solution for the nonlinear oscillation equation of the Hopf oscillator is obtained. On this basis, an islanding experiment is then conducted to verify the dynamic stability of the GFM inverter based on the Hopf oscillator control under multi-scenario conditions.