Estimating the probability of load curtailment in power systems with responsive distributed storage

Controllable electricity loads and storage devices have the potential to significantly and inexpensively increase the operating reliability of power systems, especially in systems with variable, unpredictable generation from renewable sources. However, in cases where a large number of small devices is used for operating reserves, it may be difficult to estimate the available reserve capacity, especially if one desires to minimally impact the end-use function of the devices. To address this issue, we present a probabilistic modeling framework with the specific goal of developing a model of active storage devices, i.e. devices that can both consume and supply electricity to a power system, and to develop bounds on the probability of a load curtailment event based on limited observable characteristics of the devices. The formal analysis in this paper uses asymptotic probability theory to derive bounds for the probability of load curtailment. We expect that this work will form the basis to developing control laws for active device power management as well as for designing reliability-constrained power systems with large active device populations.