Dynamic Phasor Modeling and Analysis of Sequence Decomposed Grid-Forming Control under Unbalanced Faults

Stationary frame sequence decomposed Grid-Forming (GFM) control, with power regulation loops and virtual admittance based reference generation for vector current controller, enables flexible and explicit control over nominal and fault transient behavior while retaining GFM nature under both balanced and unbalanced grid fault events. For such systems, one of the positive- and negative-sequence symmetrical components appear as time-varying in a synchronous reference frame aligned with the other, and hence, conventional small-signal modelling methods fail due to time-varying quasi-static steady-state conditions. In this work, a dynamic phasor (DP) model is developed which facilitates linear time-invariant representation of such system enabling analysis and design using frequency domain techniques. This work particularly considers the effect of the power synchronization loop, sequence component extraction (SCE), and dual sequence virtual admittance. The modeling and analysis results are supported by simulations and laboratory experiments.