A frequency-secured load pickup strategy for black-start restoration in IBR-rich distribution systems under dynamic microgrid formation

In recent years, renewable energy sources have been integrated into power grids at scale through grid-tie inverters. While these inverter-based resources (IBRs) reduce system inertia and pose challenges to frequency security, they also present opportunities for frequency support through effective control mechanisms. Traditional black-start restoration strategies relying on synchronous generators are no longer suitable for IBR-rich distribution systems. To address this challenge, this paper proposes a novel frequency-secured load pickup strategy that leverages dynamic microgrid (MG) formation to aggregate frequency support from IBRs. Grid-forming inverter-based resources provide parallel black-start services, forming boundary-dynamic MGs that progressively expand by restoring loads and connecting lines. To ensure frequency security during MG formation, key frequency indicators—including the rate of change of frequency, frequency nadir, and steady-state frequency—are employed to assess whether IBRs can manage power imbalances resulting from load pickup and renewable energy uncertainties. The flexibility of dynamic MGs facilitates operations such as merging, splitting, and reconfiguring, enabling IBRs to support neighboring MGs and maintain overall frequency stability. This problem is reformulated as a mixed-integer quadratically constrained quadratic program and solved using partial-relaxed rolling horizon optimization to reduce computational complexity. The effectiveness of the proposed strategy is validated on the IEEE-33 and IEEE-123 node test feeders.