An Iterative Transient‐Constrained MILP Model for Black‐Start Restoration Leveraging Grid‐Forming Energy Storage to Enhance Resilience

Large‐scale blackouts, particularly those caused by natural disasters, necessitate efficient black‐start restoration strategies. This paper proposes a black‐start restoration method for power systems considering grid‐forming energy (GFM‐ES) as a black‐start source. First, the control architecture and droop control strategy of GFM‐ES are analysed, highlighting its inherent advantages over grid‐following control in establishing voltage and frequency references during black‐start. Then, a linearised AC power flow‐based mixed‐integer linear programming (MILP) optimisation model is developed, which captures bus voltage magnitudes, time‐sequential restoration decisions, and the Q‐V droop control characteristic of GFM‐ES for autonomous voltage support. An iterative cutting‐plane mechanism is further proposed, where frequency and voltage violations identified by transient simulations are fed back as steady‐state constraints to the MILP model, ensuring that the final restoration plan is dynamically feasible. The model's effectiveness is validated on the IEEE 39‐bus system and a large‐scale provincial grid test case. Results demonstrate that incorporating GFM‐ES significantly accelerates the restoration process, enables earlier and larger‐scale load restoration, substantially increases the total restored energy, and enhances overall system resilience compared to conventional strategies. This work provides an applicable system‐level planning method for utilising GFM‐ES in practical power system black‐start operations.