The Interactive Coupling Between Power Control Loops in Grid-Forming Inverter Based on Spring-Damper Oscillator Model

In grid-forming (GFM) control, the core of simulating synchronous machines lies in the power loop. However, there is limited research analyzing the interactive coupling between the dynamics of the active power synchronization control loop (APSL) and the reactive power voltage control loop (RPVL) in GFM control from a physical perspective. This paper establishes a third-order nonlinear model of the GFM inverter and compares it with the physical model of a two-degree-of-freedom spring-damper oscillator system. This approach derives the fundamental mapping relationship between the small-signal model of the GFM converter and the physical model. The correctness of the analysis is verified through simulations in MATLAB and PLECS. Finally, based on the constructed two-degree-of-freedom spring-damper oscillator model, the interactive coupling phenomenon between the dynamics of the active and reactive output loops is revealed in a more intuitive manner.