Scalable Iterative Algorithm for Solving Optimal Transmission Switching with De-energization

TL;DR

This work tackles Optimal Transmission Switching with De-energization (OTSD) in subtransmission networks under $N{-}1$ contingencies, where de-energizing parts of the grid may be preferable to avoid thermal violations. It introduces a new MILP formulation that represents post-contingency connectivity without requiring extra binary variables for every possible de-energized state, and couples this with a fast iterative heuristic that targets the most constraining contingencies and local regions via a security-analysis-based search and violation reduction. The key contributions are (i) a scalable OTSD MILP arising from a novel representation of energization constraints, (ii) a fast, practical solver-lean heuristic that often yields feasible, high-quality solutions orders of magnitude faster than solving the full MIP, and (iii) extensive computational results on grids up to a few hundred buses showing the heuristic frequently attains (near) optimal solutions while dramatically reducing computation time. The practical impact is a viable planning and operation tool for TSOs to safely manage congestion and security constraints with de-energization, extending feasible operating space and enabling integration into higher-level optimization programs. Overall, the paper demonstrates a concrete path toward exact OTSD solutions on moderate-scale networks and provides a robust, fast heuristic that significantly improves operational decision support for subtransmission systems.

Abstract

Transmission System Operators routinely use transmission switching as a tool to manage congestion and ensure system security. Motivated by sub-transmission operations at RTE, this paper considers the Optimal Transmission Switching with De-energization (OTSD), which captures potential loss of connectivity (and therefore localized blackout) following loss of transmission elements. While directly relevant to real-life operations, this problem has received very little attention in the literature. The paper proposes a new mixed-integer linear programming formulation for OTSD that represents post-contingency loss of connectivity without requiring additional binary variables. This new formulation provides the foundation for a fast, iterative heuristic algorithm. Computational experiments confirms that state-of-the-art optimization solvers struggle to solve the extensive formulation of OTSD, often failing to find even trivial solutions within reasonable time. In contrast, numerical results demonstrate the efficiency of the proposed heuristic, which finds high-quality feasible solutions 100-1000x faster than using Gurobi.

Figures (2)

• Figure 1: Fast feasible solution finder heuristic. The algorithm terminates when the security analysis with configuration $\mathbf{\bar{v}}_i$ finds no contingency causing violation. Otherwise, the main loop continues, adding the most constraining contingency to the subset $\mathcal{C}_i$. Reduce violations step minimizes the violation; if zero is reached, $\mathbf{\Tilde{v}}_i$ is feasible, otherwise, the inner loop indexed by $j$ expands the set of switchable branches. Finally, unnecessary openings are removed, yielding the resulting configuration $\mathbf{\bar{v}}_i$.
• Figure 2: The $\textbf{Hop}(e,l)$ returns a set of branches composed of the branches separated from the origin branch $e$ by paths of length lower or equal to $l$.

Theorems & Definitions (4)

• Theorem 1
• proof
• Theorem 2
• proof