Analysing the Use of Graph Theory to Assess Topological Impacts on Transient Stability

This paper analyses the relationship between system transient stability and network topology by using graph theory and correlation analysis. In an electrical network, changes to system structure have effects on transient stability. It is important to find optimal indicators to represent the topology and transient stability in order to analyse this relationship. In this paper, different graph theory metrics – namely the average node degree and average shortest path length – are selected as candidate topology metrics. A variety of weighting factors are considered including the transmission line reactance, apparent power flow, and reactive power loss. Transient stability is quantified by considering the network critical clearing time and rotor angle difference transient stability index. The correlation between topology and transient stability metrics has been calculated for a wide variety of contingency cases in order to analyse the relationship between topology and stability and to establish which weighted graph metrics have the strongest relationships with the resulting transient stability of the system. Case studies are completed on a four-area network and on the IEEE 39-bus system to demonstrate the proposed method. Topology indices weighted by power flow and power loss have the strongest correlation with transient stability in the small system. In the large system, the relationship is weaker, highlighting the complexities of applying this for the analysis of larger systems.