Optimal charging of vehicle-to-grid fleets via PDE aggregation techniques

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 a centrally located fleet of identical PEVs that are distributed to and collected from drivers. The fleet also provides regulation services to the grid, contracted a priori. We develop a partial differential equation (PDE)- based technique for aggregating large populations of PEVs. In particular, the model is a set of two first-order hyperbolic PDEs coupled with an ODE in time. PDE methods are of particular interest, since they provide an elegant modeling paradigm with a broad array of analysis and control design tools. The control design task is to minimize the cost of PEV charging, subject to supplying PEVs to drivers with sufficient charge and supplying the requested power to the grid. We examine this control design on a simulated case study, and analyze sensitivity to a variety of assumptions and parameter selections.