Derivation and generation of path-based valid inequalities for transmission expansion planning

This paper seeks to solve the long-term transmission expansion planning problem in power systems more effectively by reducing solution search space and computational effort. The proposed methodology finds adds cutting planes based on structural insights about bus angle differences along paths. Two lemmas a theorem are which formally establish validity of these onto underlying mathematical formulations. These path-based difference constraints, tighten relaxed feasible region, used combination with branch-and-bound find lower bounds optimal investment problem. work also creates an algorithm that automates process finding applying most effective valid inequalities, resulting significantly reduced testing time. is implemented Python, using Gurobi add constraints exact DCOPF-based uses two different-sized illustrate effectiveness framework: GOC 500-bus system modified Polish 2383-bus system.