Vulnerability and Resilience Assessment of Power Systems: From Deterioration to Recovery via a Topological Model based on Graph Theory

Traditionally, vulnerability is the level of degradation caused by failures or disturbances, and resilience is the ability to recover after a high-impact event. This paper presents a topological procedure based on graph theory to evaluate the vulnerability and resilience of power grids. A cascading failures model is developed by eliminating lines both deliberately and randomly, and four restoration strategies inspired by the network approach are proposed. In the two cases, the degradation and recovery of the electrical infrastructure are quantified through four centrality measures. Here, an index called flow-capacity is proposed to measure the level of network overload during the iterative processes. The developed sequential framework was tested on a graph of 600 nodes and 1196 edges built from the 400 kV high-voltage power system in Spain. The conclusions obtained show that the statistical graph indices measure different topological aspects of the network, so it is essential to combine the results to obtain a broader view of the structural behaviour of the infrastructure.