Equivalent circuit model of grid-forming-converter based power grids: Visualizing control loop interactions on synchronization stability

• Equivalent circuit of GFM-converter system is derived by the analogy-based method, which shows control loop interactions. • Control loop interaction and their impact on small-signal synchronization stability are visualized by equivalent circuits. • It uncovers that AC voltage control brings about negative damping and deteriorates small-signal synchronous stability. • Instructions for improvements of small-signal synchronous stability are given by parameter analyses of AC voltage control. For grid-forming (GFM) converter-based power grids, the impacts of AC voltage control (ACVC) loops on small-signal synchronization stability are rarely discussed in literature. To present the interactions between the synchronization control loop and the ACVC loop in an intuitive and clear approach, this paper establishes the equivalent circuit model of multi-GFM-converter based power systems, and analyzes the impacts of control loop interactions on small-signal synchronization stability. Firstly, the model of multi-GFM converter-based power grids has been established that incorporates the ACVC loop. Then, for the further visualization of control loop interactions, equivalent circuits of the whole systems are derived by the analogy-based method. This analysis allows us to assess the impacts of the ACVC on small-signal synchronization stability. This paper illustrates that ACVC can be equivalently represented as a negative impedance in parallel with the filter inductor. In this case, the ACVC brings about negative damping effects and deteriorates small-signal synchronization stability. Furthermore, the control parameters of the ACVC on small-signal synchronization stability are also quantitatively evaluated. Additionally, interactions between different GFM converters on small-signal synchronization stability are also investigated. Finally, the modified IEEE 10-GFM-converter 39-bus system is built in MATLAB/Simulink platform to validate analyzes and the proposed method.