Reliability-Centered Planning with Geographic Graph Constraints for Feeder Routing and Conductor Sizing

Feeder routing and reliability assessment are essential for effective distribution network planning. However, excessively long feeders can lead to increased costs and decreased reliability. To enhance economic and reliability performance, this paper proposes a reliability-centered planning method for feeder routing and sizing. Specifically, a graph-based fictitious power flow model is constructed within the grid graph for feeder routing and conductor sizing. Overlapping feeder routes powered by fictitious flows from multiple sources are designated as line connection points. These feeder routes, constrained by the geographic graph, are interconnected via the line connection points to form a meshed network structure. To meet the requirements of reliability-oriented optimization, the affiliation variables are introduced. Based on the affiliation variables, reliability algebraic formula is allowed to be embedded into the fictitious power flow model to enable the calculation of reliability during the optimization process. By incorporating customized reliability-related constraints in the model, the specific reliability objectives can be achieved. In addition, the non-convex terms in the fictitious power flow model are relaxed into convex forms, and certain variable products are replaced with auxiliary variables, allowing the problem to be solved by an off-the-shelf solver. Finally, the proposed method is tested on two case studies, demonstrating its effectiveness.