The Sweet Spot of Bound Tightening for Topology Optimization

TL;DR

This paper introduces a topology-aware bound tightening method for power system topology optimization, balancing computational effort and bound tightness by selectively relaxing switching variables based on network structure.

Contribution

It proposes a novel topology-aware bound tightening approach that improves bound quality without excessive computational costs in power system optimization.

Findings

Selective relaxation of switching variables enhances bound tightness.

The method achieves a good trade-off between computational effort and solution quality.

Experimental results on IEEE 118-bus system validate the approach.

Abstract

Topology optimization has emerged as a powerful and increasingly relevant strategy for enhancing the flexibility and efficiency of power system operations. However, solving these problems is computationally demanding due to their combinatorial nature and the use of big-M formulations. Optimization-based bound tightening (OBBT) is a well-known strategy to improve the solution of mixed-integer linear programs (MILPs) by computing tighter bounds for continuous variables. Yet, existing OBBT approaches in topology optimization typically relax all switching decisions in the bounding subproblems, leading to excessively loose feasible regions and limited bound improvements. In this work, we propose a topology-aware bound tightening method that uses network structure to determine which switching variables to relax. Through extensive computational experiments on the IEEE 118-bus system, we find that keeping a small subset of switching variables as binary, while relaxing the rest, strikes a sweet spot between the computational effort required to solve the bounding problems and the tightness of the resulting bounds.