Risk measures for power failures in transmission systems.

We present a novel framework for evaluating the risk of failures in power transmission systems. We use the concept of systemic risk measures from the financial mathematics literature with models of power system failures in order to quantify the risk of the entire power system for design and comparative purposes. The proposed risk measures provide the collection of capacity vectors for the components in the system that lead to acceptable outcomes. Keys to the formulation of our measures of risk are two elements: a model of system behavior that provides the (distribution of) outcomes based on component capacities and an acceptability criterion that determines whether a (random) outcome is acceptable from an aggregated point of view. We examine the effects of altering the line capacities on energy not served under a variety of networks, flow manipulation methods, load shedding schemes, and load profiles using Monte Carlo simulations. Our results provide a quantitative comparison of the performance of these schemes, measured by the required line capacity. These results provide more complete descriptions of the risks of power failures than the previous, one-dimensional metrics.

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