A Dynamic Phasor Framework for Analysis of Grid-Forming Converter Connected to Series-Compensated Line

A dynamic phasor (DP) framework for time-domain and frequency-domain analyses of grid-forming converters (GFCs) connected to series-compensated transmission lines is proposed. The proposed framework can capture the behavior of GFCs subjected to unbalanced short circuit faults in presence of different current limiting strategies. Moreover, the linearizability and time invariance of this framework allows us to perform eigen decomposition, which is a powerful tool for root-cause analysis and control design. We show that a certain degree of series compensation may result in poorly-damped oscillations in presence of the grid-forming converter. A participation factor analysis using the DP model reveals that the point of interconnection voltage angle is dominant in this mode. Eigenvalue sensitivity analysis of controller parameters shows that reducing the power-frequency droop coefficient is most effective in stabilizing the poorly-damped mode. Detailed validation with electromagnetic transient model demonstrates the accuracy of the proposed framework.