A Markov Chain Approach for Cascade Size Analysis in Power Grids based on Community Structures in Interaction Graphs

Cascading failures in power grids are high impact societal and economical phenomena. Local interactions among the components of the system and interactions at-distance, based on the physics of electricity, as well as various stochastic and interdependent parameters and factors (from within and outside of the power systems) contribute to the complexity of these phenomena. As such, predicting the size and path of cascading failures, when triggered, are challenging and interesting research problems. In recent years, interaction graphs, which help in capturing the underlying interactions and influences among the components during cascading failures, are proposed towards simplifying the modeling and analysis of cascades. In this paper, a Markov chain model is designed based on the community structures embedded in the data-driven graphs of interactions for power grids. This model exploits the properties of community structures in interactions to enable the probabilistic analysis of cascade sizes in power grids.