Distributionally Robust Whole-Process Restoration of Power Systems with Photovoltaic–Battery Energy Storage Stations and Flexible Loads

Restoring a bulk power system after a blackout involves black start, network reconfiguration and load restoration, usually optimized in sequence; renewable stations used as early sources add an output uncertainty that the schedule must anticipate. This paper formulates the three stages jointly for systems with photovoltaic–battery energy storage (PV-BESS) stations as a two-stage distributionally robust model with an L1/L∞ ambiguity set. Each PV scenario is checked on its own network, with the actual station output, redispatch of synchronized units and costly load shedding, while cranking power must be delivered in every scenario; as this recourse is linear, the model has an exact single-level mixed-integer linear reformulation. Energization propagates from black-start sources, a linearized AC model enforces voltage and reactive limits, and a frequency-security limit bounds each load pickup. On the IEEE 118-bus system, every schedule passes an AC optimal power flow, whereas a DC-only schedule has no AC operating point at eight of 22 steps. Over three independent test years, plans relying on three stations fail on 1–3% of days, all darker than every clustered scenario; retaining the darkest observed day makes the distributionally robust plan always executable at 1.5% more outage loss, against 8.6% for robust optimization.