Reserve Provision from Electric Vehicles: Aggregate Boundaries and Stochastic Model Predictive Control

Controlled charging of electric vehicles, EVs, is a major potential source of flexibility to facilitate the integration of variable renewable energy and reduce the need for stationary energy storage. To offer system services from EVs, fleet aggregators must address the uncertainty of individual driving and charging behaviour. This paper introduces a means of forecasting the service volume available from EVs by considering several EV batteries as one conceptual battery with aggregate power and energy boundaries. This avoids the impossible task of predicting individual driving behaviour by taking advantage of the law of large numbers. The forecastability of the boundaries is demonstrated in a multiple linear regression model which achieves an $R^2$ of 0.7 for a fleet of 1,000 EVs. A two-stage stochastic model predictive control algorithm is used to schedule reserve services on a day-ahead basis addressing risk trade-offs by including Conditional Value-at-Risk in the objective function. A case study with 1.2 million domestic EV charge records from Great Britain shows that increasing fleet size improves prediction accuracy, thereby increasing reserve revenues and decreasing effective charging costs. For fleet sizes of 400 or above, charging cost reductions plateau at 60\%, with an average of 1.8kW of reserve provided per vehicle.