Model Predictive Black Start for Dynamic Formation of DER-Led Microgrids with Inrush Current Impacts

Black start (BS) of the distribution system (DS) with high penetration of distributed energy resources (DERs) requires advanced control frameworks to ensure secure and efficient restoration. This paper proposes a model predictive black start (MPBS) framework that captures the mutual interaction between switching decisions and physical feasibility to generate restoration sequences. Short-term forecasts of DER output, load demand, and transmission grid (TG) availability are incorporated within a receding-horizon control structure to construct cranking paths. To evaluate decision-dependent feasibility, an analytical inrush current estimation method is developed based on dynamically formed microgrid (MG) nodal impedance matrices under worst-case (WC) switching conditions. To mitigate excessive inrush current and prevent protection misoperations, a structural preventive mechanism is introduced, combining an emergency operation–inspired voltage reduction strategy with a switch-blocking function executed in a hierarchical manner. The proposed inrush model is validated against electromagnetic transient (EMT) simulations in PowerFactory with estimation accuracies exceeding 90%. Case studies on IEEE and EPRI networks demonstrate that the proposed MPBS framework effectively prevents fuse and recloser misoperations, reduces DER energy consumption, and improves load restoration efficiency during DER-led BS processes.