Boundary–Node Coordinated Operation for Restoration Areas Considering Electric Vehicle-Embedded Soft Open Points

After a severe outage occurs, restoring a distribution network can take from several hours to days, making the secure and stable operation of restoration areas (RAs) critical. During a post-disaster partitioned operation, asymmetric controllable distributed generator (CDG) regulation capacity, non-controllable distributed generator (NDG) fluctuation risks, and concentrated high-value loads cause significant inter-area power imbalances. Soft open points bridge this resource gap by integrating electric vehicle charging directly into soft open points via vehicle-to-grid (V2G) technology; the resulting electric vehicle-embedded soft open points (EV-SOPs) acquire storage-like energy transfer capability. This paper proposes a boundary–node coordinated optimization strategy for post-disaster RA operation, which integrates CDGs, NDGs, smart switches, and EV-SOPs. Firstly, the boundary dynamic updating model with a multi-homogeneity indicator—load importance, NDG fluctuation risk, and CDG flexibility—enables adaptive resource allocation. Secondly, the optimal operational model of RA is formulated considering the various characteristics of facilities and topology constraints. Thirdly, EV-SOP uncertainties in response reliability, discharge power, and energy capacity are characterized by Bernoulli, log-normal, and truncated normal distributions, reformulated into a tractable mixed-integer quadratically constrained programming via chance-constraint interval linear transformation, and solved by a sequential weight-based priority search with hot-start strategy. Case studies on the IEEE 123-bus system verify the effectiveness of the proposed method. Specifically, the dynamic boundary strategy reduces the comprehensive weighted index by up to 29.10%; physical feasibility truncation reduces EV-driven load loss from 3.2073 MW to 3.1038 MW; and the sequential weight-based priority search with hot-start strategy achieves a cone constraint satisfaction measure of 9.3175 × 10−7, confirming robust convergence.