Frequency-aware dynamic microgrid formation for distribution system restoration considering electromechanical transients

The resilience of modern distribution systems increasingly depends on the ability to restore critical loads under low-inertia operating conditions after extreme events. However, most existing restoration models focus primarily on steady-state feasibility and do not explicitly account for transient frequency security during dynamic microgrid formation. To address this issue, this paper proposes a frequency-aware dynamic microgrid formation framework for post-disaster distribution system restoration. The proposed model explicitly embeds the frequency-support dynamics of heterogeneous resources, including distributed generators and energy storage systems, into a multi-period restoration optimization framework via time-discretized frequency-response constraints. This enables co-optimization of topology reconfiguration, load restoration, and resource dispatch while respecting transient frequency-security requirements. To improve computational tractability, a nested solution framework combining alternating optimization (AOP) and the alternating direction method of multipliers (ADMM) is developed. The outer loop updates discrete decisions, while the inner loop coordinates steady-state restoration and transient frequency security under fixed discrete variables. Case studies of a modified 69-bus distribution system show that the proposed method restores 57.7% of the total load within the first three restoration periods while keeping the maximum frequency deviation within 0.5 Hz, demonstrating its effectiveness for rapid load restoration under transient frequency security. In addition, the proposed framework obtains high-quality solutions with substantially improved computational efficiency, converging in 41.3 s for a benchmark 4-period case, whereas the centralized solver requires more than 12 h to obtain only an incumbent feasible solution.