Optimal Restoration Planning for Low-Inertia Distribution Systems Using Grid-Forming Distributed Energy Resources

Abstract

The increasing penetration of converter-based distributed energy resources (DERs) introduces critical frequency stability challenges during post-contingency islanded operation. Conventional restoration planning models neglect rate-of-change-of-frequency (ROCOF) and frequency nadir limits, producing islanded configurations that are electrically feasible but could be dynamically unstable. A two-stage stochastic mixed-integer linear programming model is proposed for restoration planning in low-inertia distribution systems, jointly optimizing DER siting and sizing, grid-forming capability enablement, microgrid formation, and post-contingency load restoration under uncertainty. Frequency security is enforced through analytical surrogates derived from the swing equation, embedded directly into the optimization. Applied to the IEEE 33-bus system, the proposed model eliminates all frequency violations observed in the baseline, where ROCOF values exceed the admissible limit by more than six times in 22% of scenario-fault pairs, at a 5.7% increase in total expected cost. Sensitivity analysis confirms robustness against variations in virtual inertia and droop parameters.