Mixed-Integer Linear Programming Approaches for Tree Partitioning of Power Networks

In transmission networks, power flows and network topology are deeply intertwined due to power flow physics. Recent literature shows that a specific more hierarchical network structure can effectively inhibit the propagation of line failures across the entire system. In particular, a novel approach named <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tree partitioning</i> has been proposed, which seeks to bolster the robustness of power networks through strategic alterations in network topology, accomplished via targeted line-switching actions. Several tree-partitioning problem formulations have been proposed by considering different objectives, among which power flow disruption and network congestion. Furthermore, various heuristic methods based on a two-stage and recursive approach have been proposed. The present work provides a general framework for tree-partitioning problems based on mixed-integer linear programming (MILP). In particular, we present a novel MILP formulation to optimally solve tree-partitioning problems and also propose a two-stage heuristic based on MILP. We perform extensive numerical experiments to solve two tree-partitioning problem variants, demonstrating the excellent performance of our solution methods. Lastly, through exhaustive cascading failure simulations, we compare the effectiveness of various tree-partitioning strategies and show that, on average, they can achieve a substantial reduction in lost load compared to the original topologies.