Virtual Admittance Based Modeling and Stability Analysis of Grid-Forming Inverter under Clark Transformation

Grid-forming inverter plays a pivotal role as the increase of the capacity of renewable energy. Existing literature tends to use small signal modeling method to linearize the inner control loop including the voltage loop and current loop in dq coordinate with proportional integral controller, which is complicated. To simplify the analysis, this article chooses to use virtual admittance control strategy from the perspective of αβ coordinate. By using such method, the inner control loop can be strictly regarded as a linear system. Moreover, this article uses classical control theory by simplifying the control diagram step by step, with the help of the Bode diagram, the critical value of the virtual admittance can be located based on the stability analysis. Simulation results and Bode diagram verify the accuracy of the modeling method and the impact from the outer power loop to the system is discussed under different grid condition, revealing that the stability of the system is more likely to be affected by the outer power loop under weak grid condition.