# Derivation and Generation of Path-Based Valid Inequalities for Transmission Expansion Planning

## TL;DR

This paper introduces a novel method for transmission expansion planning that uses path-based valid inequalities to tighten problem formulations, reducing computational effort and improving solution efficiency.

## Contribution

It proposes a new algorithm that automatically derives and applies path-based valid inequalities, enhancing the efficiency of solving large-scale transmission expansion problems.

## Key findings

- Significant reduction in computation time for large systems
- Effective tightening of the feasible region with new inequalities
- Successful application to IEEE and Polish power systems

## Abstract

This paper seeks to solve the long-term transmission expansion planning problem more effectively by reducing the solution search space and the computational effort. The proposed methodology finds and adds cutting planes based on structural insights about bus angle-differences along paths. Several theorems are proposed which show the validity of these cutting planes onto the underlying mathematical formulations. The path-based bus angle-difference constraints, which tighten the relaxed feasible region, are used in combination with branch-and-bound to find lower bounds on the optimal investment of the transmission expansion planning problem. This work also creates an algorithm that automates the process of finding and applying the discussed valid inequalities, resulting in significantly reduced testing and computation time. The algorithm is implemented in Python, using the solver CPLEX to add constraints and solve the transmission expansion problem. This paper uses two different-sized systems to illustrate the effectiveness of the proposed framework: a modified IEEE 118-bus system and the Polish 2383-bus system.