PDE Modeling and Control of Electric Vehicle Fleets for Ancillary Services: A Discrete Charging Case

This paper examines modeling and control of a large population of grid-connected plug-in electric vehicles (PEVs). PEV populations can be leveraged to provide valuable grid services when managed via model-based control. However, such grid services cannot sacrifice a PEV's primary purpose-mobility. We consider an aggregator, which can control a fleet of PEVs with three possible charging rates: charging at a constant rate, discharging at a constant rate or idle. We develop a system of coupled partial differential equations for aggregating large populations of PEVs and transform its discretized version into a state space representation. We propose a linear quadratic regulator to track a power signal that provides load following services. We investigate the sensitivity of controller parameters, different bidding strategies and their impact on the performance of the provided balancing service. We examine this control design on a simulated case study and analyze sensitivity to a variety of assumptions and parameter selections.