Analytical characterization of grid-forming converter response time under voltage sags

Abstract

The response time of grid-forming (GFM) converters under grid disturbances is a critical metric that reflects how fast GFM capabilities can be delivered. In this letter, the analytical expression for the response time under voltage sags is derived using the geometric singular perturbation method. It is revealed that the response speed is naturally faster in weaker grids, and for a wide range of grid conditions, the response time under voltage sags has an inherent minimum limit of a quarter of the fundamental cycle, i.e., 5 ms at 50 Hz. Increasing the voltage-loop integral gain <i>kᵢᵥ</i> approaches this limit, but an excessively large <i>kᵢᵥ</i> induces small-signal instability. Hence, a transient reactive current augmentation strategy is proposed to approach and even break the limit while ensuring stability. Moreover, it is derived that current-limiting control reduces the response time. Therefore, the analytical response time constitutes an upper bound on the practical response time with current limiting. The findings suggest potential refinements to grid code requirements for GFM converter response time. The results are validated by hardware-in-the-loop testing.