A Probabilistic Model for Cascading Failures in Power Grids Capturing Topological Attributes

Power grids are examples of one of the most complex and interdependent systems. Any initial disturbances in these systems could trigger cascading failures and eventually lead to a complete system blackout. In this paper, we aim to capture the combinations of the initial locations of these disturbances, i.e., the grid topology, to discern various cases of blackouts originating from different combinations of initial transmissionline failures. The analysis is based on using a previously reported generalization of a computationally efficient Markov-chain model that captures the cascading failure dynamics while keeping track of the topological attributes of the failed transmission lines in terms of the power-flow clusters they belong to. In particular, our analysis reveals that initially failed transmission lines originating from high power-flow clusters instigate a larger-size cascade compared to the initially failed lines originating from low power-flow clusters. Moreover, it is also observed that spread-out line failures from either low- or high-power flow clusters adversely impact the cascade propagation more than that caused by line failures from concentrated clusters. These results, in turn, enable us to identify the critical vulnerabilities in the power grid. Finally, the concept of dynamic load-shedding constraint from our earlier work is adopted to include the role of error by human operators during contingencies.