On the Dynamics of Transmission Capacity and Load Loss during Cascading Failures in Power Grids

In this paper, a novel analytical model is proposed to predict the average transmission-capacity loss and load loss during a cascading failure as a function of time and their steady state values. Cascading failures in the power grid are described using a Markov-chain approach, in which the state transition probabilities depend on the number and capacities of the failed lines. The transition matrix is characterized parametrically using Monte Carlo simulations of cascading failures in the power grid. The severity of cascading failure is estimated using two metrics: the expected number of transmission-line failures and the amount of load shedding/load loss (inferred from the average transmission capacity loss) in the steady state. These two metrics provide critical information regarding the severity of a cascading failure in a power grid (in terms of both the distribution of blackout sizes and the amounts of load shedding). One of the benefits of this model is that it enables the understanding of the effect of initial failures and of the operating parameters of the power grid on cascading failures.