Mixed-integer linear programming approaches for tree partitioning of power networks

TL;DR

The paper tackles mitigating cascading failures in transmission networks by refining topology through targeted line switching to create a tree-like partitioning that localizes disturbances. It builds a unified MILP framework that can solve variants focused on minimizing post-switching power-flow disruption or network congestion, and it couples this with a two-stage heuristic (Tree Partition Identification followed by Optimal Line Switching) to scale to larger networks. Across extensive experiments and cascading failure simulations, the authors demonstrate that tree partitioning can substantially reduce lost load compared to the original network, with the exact MILP yielding higher-quality solutions and the two-stage approach offering faster results. The work provides a practical, scalable optimization toolbox for topology-based resilience design and establishes a foundation for future extensions to AC power flow models and more detailed operational constraints.

Abstract

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 tree partitioning 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.

Figures (4)

• Figure 1: Tree partitioning of the IEEE-73 network with provable line failure localization properties. The three clusters connected in a tree-like manner have been obtained by switching off only three transmission lines (in red).
• Figure 2: (a) A graph $G$ with colors representing a partition $\mathcal{P}$ into three clusters. (b) The reduced graph $G_\mathcal{P}$ that corresponds to the partition in (a).
• Figure 3: Illustration of the two-stage approach. (a) A power network $G$ with three generator groups. (b) A 3-partition $\mathcal{P}$ respecting the generator coherency constraints. (c) A tree partition $\mathcal{P}$ of $G^\mathcal{E}$, where the red lines $\mathcal{E}$ are switched off.
• Figure 4: Average lost loss (as % of initial network load) during cascading failure simulations. Results compare the original network against four tree-partitioned networks: power flow disruption (PFD) and network congestion (NC), each solved with single-stage (1-ST) and two-stage (2-ST) approaches.