Refining bridge-block decompositions through two-stage and recursive tree partitioning

In transmission networks power flows and network topology are deeply intertwined due to power flow physics. Recent literature shows that specific network substructures named bridge-blocks prevent line failures from propagating globally. A two-stage and recursive tree partitioning approach have been proposed to create more bridge-blocks in transmission networks, improving their robustness against cascading line failures. In this paper we consider the problem of refining the bridge-block decomposition of a given power network with minimal impact on the maximum congestion. We propose two new solution methods, depending on the preferred power flow model. More specifically, (i) we introduce a novel MILP-based approach that uses the DC approximation to solve more efficiently the second-stage optimization problem of the two-stage approach and (ii) we show how the existing recursive approach can be extended to work with AC power flows, drastically improving the running times when compared to the pre-existing AC-based two-stage method.