The production, distribution, storage, and use of electrical energy are undergoing significant changes. Demand and production patterns are being altered radically by the advent of ​“smart grids,” renewable generation, hybrid electric vehicles, and storage technologies. The mathematical descriptions of such systems raise numerous challenges, ranging from multiple spatial and temporal variables to uncertainty in future operating conditions. To address these challenges, we will develop, analyze, and integrate predictive models of system behavior, new optimization-based sampling approaches, and new analysis methods and scalable algorithms that can exploit the rich mathematical structure