A Topological Sorting Approach to Identify Coherent Cut-Sets Within Power Grids

Abstract

This paper proposes a new technique to identify sets of branches that form heavily loaded and potentially vulnerable flowgates within power grids. To this end, a directed acyclic graph is used to model the instantaneous state of power grids. One of the advantages of directed acyclic graphs is they allow the identification of where power flows are coherent e.g where power flows in a uniform direction along a set of branches that partition the network into two islands. This paper uses topological sorts to identify many sets of branches having this property. Definitions are provided for two new concepts, termed coherent cut-sets and coherent crack-sets, which are particular sets of branches extracted from a specific topological sort. Notably, there are numerous possible topological sorts for a directed acyclic graph and calculating distinctive topological sorts is challenging. In this paper a novel optimization algorithm is proposed to find multiple, diverse topological sorts each of which implies many cut-sets. The effectiveness of the proposed methods for enhancing grid observability and situational awareness is demonstrated using two standard test networks.