New relay-based ESC optimizes grid-forming inverter control in real-time

Grid-forming (GFM) inverters are critical for stabilizing power systems with high penetration of inverter-based resources (IBRs). However, their transient performance hinges on careful tuning of control parameters—especially the active power–frequency droop coefficient—which creates inherent trade-offs among damping, settling time, rate of change of frequency (RoCoF), and frequency nadirs. In a new paper on arXiv (2605.14161), researchers Kyung-Bin Kwon, Min Gyung Yu, Sayak Mukherjee, and Timothy I. Salsbury present a relay-based Extremum Seeking Control (ESC) framework that dynamically optimizes the droop gain in real time.

The approach defines a multi-objective cost function that captures conflicting performance goals: oscillation energy, frequency nadir, RoCoF, and post-disturbance settling behavior. The team proves that the cost function is convex with respect to the droop parameter, justifying gradient-based optimization. Using numerical simulations on a modified IEEE 68-bus system, they show the ESC algorithm can track the time-varying optimal droop coefficient as network conditions change—without requiring an analytical model of the grid. This adaptive, model-free method promises more robust and near-optimal transient behavior for GFM inverters under dynamic grid conditions.