Stochastic Black Start Resource Allocation to Enable Dynamic Formation of Networked Microgrids and DER-aided Restoration

Extended outages in distributed systems (DSs) dominated by distributed energy resources (DERs) require innovative strategies to efficiently and securely deploy black start (BS) resources. To address the need, this paper proposes a two-stage stochastic resource allocation method within synchronizing dynamic microgrids (MGs) for black start (SDMG-BS), enabling risk-averse and adaptive restoration across various scenarios while ensuring frequency security. Virtual synchronous generator (VSG)-controlled grid-forming inverters (GFMIs) equipped with primary frequency governors (PFGs) are modeled as BS resources. Their frequency response is characterized by three transient indices, which are deployed as frequency dynamic constraints on load pick-up events to ensure frequency stability during the BS process. SDMG-BS framework facilitates location-independent synchronization among restored MGs and with the transmission grid (TG) with the help of smart switches (SSWs). The model incorporates scenario-based stochastic programming to address multi-source uncertainties, including season-dependent operational conditions and unpredictable TG outage durations, ensuring a resilient allocation plan. The proposed approach is validated on a modified IEEE 123-node feeder with three study cases designed across sixteen uncertainty scenarios.