Multi-Objective Black-Start Planning for Distribution Networks with Grid-Forming Storage: A Control-Constrained NSGA-III Framework

The increasing frequency of climate- and cyber-induced blackouts in modern distribution networks calls for restoration strategies that are both resilient and control-aware. Traditional black-start schemes, based on predefined energization sequences from synchronous machines, are inadequate for inverter-dominated grids characterized by high penetration of distributed energy resources and limited system inertia. This paper proposes a novel multi-layered black-start planning framework that explicitly incorporates the dynamic capabilities and operational constraints of grid-forming energy storage systems (GFESs). The approach formulates a multi-objective optimization problem solved via the Non-Dominated Sorting Genetic Algorithm III (NSGA-III), jointly minimizing total restoration time, voltage–frequency deviations, and maximizing early-stage load recovery. A graph-theoretic partitioning module identifies restoration subgrids based on topological cohesion, critical load density, and GFES proximity, enabling localized energization and autonomous island formation. Restoration path planning is embedded as a mixed-integer constraint layer, enforcing synchronization stability, surge current thresholds, voltage drop limits, and dispatch-dependent GFES constraints such as SoC evolution and droop-based frequency support. The model is evaluated on a modified IEEE 123-bus system with five distributed GFES units under multiple blackout scenarios. Simulation results show that the proposed method achieves up to 31% faster restoration and 46% higher voltage compliance compared to MILP and heuristic baselines, while maintaining strict adherence to dynamic safety constraints. The framework yields a diverse Pareto frontier of feasible restoration strategies and provides actionable insights into the coordination of distributed grid-forming resources for decentralized black-start planning. These results demonstrate that control-aware, partition-driven optimization is essential for scalable, safe, and fast restoration in the next generation of resilient power systems.