Topology-variable-based reliability modeling for optimal smart switch deployment in flexible distribution networks with Scenario-Based parallel progressive hedging algorithm

In flexible distribution networks (FDNs), the placement of smart switches, including circuit breakers (CBs), remote-controlled switches (RCSs), and soft open points (SOPs), substantially impacts fault propagation, isolation, and service restoration, thus influencing system reliability indices. Existing research, however, does not explicitly model the relationship between smart switch placement in FDNs as topological decision variables and these reliability indices. As a result, switch placement and reliability assessment remain an “open-loop” process requiring multiple iterations, which cannot guarantee optimality under reliability constraints or objectives. To address this issue, this paper proposes a topology-variable-based reliability modeling framework for optimizing smart switch placement, which integrates CB, RCS, and SOP, and explicitly links system reliability indices (ASAI, SAIDI, SAIFI, EENS) with smart switch placement decisions. The proposed optimization-based reliability model is developed to capture the synergistic effects of these switches across fault detection (FD), fault isolation (FI), and service restoration (SR) phases, embedding dynamic topology changes and power flow control into a two-stage stochastic mixed-integer programming formulation considering multiple fault scenarios. To solve this complex model efficiently, a scenario-aware element-wise progressive hedging (SEW-PH) algorithm is introduced, leveraging adaptive parameter strategies to decouple multi-scenario computations and accelerate convergence. Case studies reveal that joint deployment of CBs, RCSs, and SOPs in FDNs further enhances reliability indices beyond traditional switch deployment strategy, attributed to SOP’s rapid fault isolation and power flow control—delivering superior cost-effectiveness and comprehensive performance in high-reliability scenarios. Compared to heuristic optimization that fall under open-loop reliability-aware planning frameworks, the proposed close-loop reliability-aware smart switch deployment framework ensures high solving efficiency while improving solution optimality, with the SEW-PH algorithm further accelerating model solving.