A Graph-Based Iterative Strategy for Solving the All-Line Transmission Switching Problem

TL;DR

The paper tackles the all-line DC-OTS problem by addressing the weak MILP relaxations induced by large big-$M$ constants. It introduces a graph-theoretic tightening procedure that derives tighter bounds $M_l$ via a relaxed longest-path problem, and an iterative heuristic that warm-starts the MILP solver with high-quality feasible solutions to accelerate convergence. The two strategies are synergistic and validated on the IEEE 118-bus network under 100 demand scenarios, demonstrating substantial reductions in solution time and unsolved instances compared with baseline methods. This approach enhances the scalability and practical applicability of OTS in power systems with high renewable integration.

Abstract

The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M constants that lead to weak relaxations and significant computational challenges, particularly when all lines are switchable. In this paper, we propose a two-fold approach: first, using graph theory to derive tighter big-M values by solving a relaxed longest path problem; second, introducing an iterative algorithm that incorporates a heuristic version of the switching problem to efficiently generate low-cost feasible solutions, thereby accelerating the search for optimal solutions in the integer optimization solver. Numerical results on the 118-bus network show that the proposed methodology significantly reduces the computational burden compared to conventional approaches.

Figures (4)

• Figure 1: Counterexample for methodology proposed in moulin2010transmission.
• Figure 2: Illustrative example for determining $M_{l_1}$ using the naive approach.
• Figure 3: Illustrative example for determining $M_{l_1}$ using different approaches.
• Figure 4: Comparison of the number of problems solved over time.