Boundary Observer Design for Fleets of Plug-in Electric Vehicles in Bidirectional Charging Stations

Abstract

In this paper, we consider the problem of estimating the density profiles of fleets of Plug-in Electric Vehicles (PEVs) in charging stations. We put the focus on the case of bidirectional exchange of energy between the grid and PEVs i.e. both vehicle-to-grid (V2G) and grid-to-vehicle (G2V) modes are considered. In both modes, the energy exchange is assimilated to a transfer phenomenon that is modeled by using a first-order hyperbolic partial differential equation (PDE). We design a boundary observer that provides online estimates of charge/discharge density profiles along the spatial domain. The observer is designed based on the system PDE model. It only makes use of boundary measurements and involves measurement injection in the boundary equation. The exponential convergence of the observer is proved using a suitable Lyapunov functional. Simulation results are provided that highlight the satisfactory observer performances.