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

TL;DR

The paper introduces a Dynamic Phasor (DP) modeling framework to analyze grid-forming converters (GFCs) connected to series-compensated lines under unbalanced faults, enabling linear-time-invariant analysis and eigen-decomposition for root-cause analysis and control design. The GFC is modeled in the rotating $dq$-frame with DP orders $k=0,\pm2$ while the network is represented in the $pnz$-frame with $k=\pm1$, and current-limiting strategies are integrated. It demonstrates close agreement with EMT simulations, identifies a poorly damped mode that arises with higher series compensation, and shows that reducing the droop coefficient $d_{pc}$ is an effective damping method validated by EMT results. The framework provides a scalable, analyzable alternative to EMT for planning and control design in grids with high inverter-based resource penetration. Practical impact includes improved root-cause analysis and damping control for GFCs in series-compensated grids.

Abstract

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.

Figures (11)

• Figure 1: Single-line diagram of the simulated system.
• Figure 2: Proposed DP-based modeling framework showing interface between GFC and transmission network model.
• Figure 3: (a) Droop control and (b) outer voltage control loop.
• Figure 4: (a) Inner current and voltage control loops and (b) filter.
• Figure 5: Current limiting strategy in DP framework.