  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.
