Tri-level stochastic optimization for optimal switch placement in distribution systems under distributed generation uncertainty and electric vehicle charging demand

This paper proposes a novel tri‑level stochastic optimization framework for optimal switch placement in distribution systems under distributed generation uncertainty and plug‑in electric vehicle charging demand. Distinct from existing approaches that treat planning and operation separately, the proposed formulation uniquely integrates planning and operational decisions through a hierarchical structure in which the upper level determines the locations of sectionalizing and tie switches, the middle level performs post‑fault network reconfiguration, and the lower level represents worst‑case fault scenarios. A key methodological contribution is the reformulation of this tri‑level model into a single‑level mixed‑integer linear programming problem using Karush‑Kuhn‑Tucker conditions, strong duality, and big‑M linearization, making the solution computationally tractable for realistic networks. The primary innovation of this work is the first‑of‑its‑kind coordinated optimization of switch placement, reliability enhancement, fault restoration, and uncertainty management within a unified framework. Numerical results show that the proposed strategy reduces SAIDI by 53.1%, SAIFI by 36.8%, CAIDI by 25.8%, and ENS by 56.5%, while also lowering total annual cost by 56.5%. In addition, total voltage violation hours decrease by 83.4%, and total distributed generation output increases by 3.2%, indicating improved system reliability and better utilization of local generation resources. The results confirm that the proposed model effectively improves resilience, operational flexibility, and economic performance in active distribution networks.