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We are considering the problem of modelling and observer design for a fleet of Plug-in Electric vehicles (PEVs) in a public station connected to a smart grid. Both charging (Grid-to-Vehicle (G2V)) and discharging (Vehicle-to-Grid (V2G)) are focused on. We first develop models of fleet dynamics in both modes. The models are 1D hyperbolic-type partial differential equations (PDEs), and their well-posed is analysed using the method of characteristics, while their discretisation is performed using the  θ -scheme. Then, we design observers that provide online estimates of the state variable along the PDE domain. The design and the analysis of observers are performed using Volterra integral backstepping transformation. Finally, numerical simulations are provided that confirm the theoretical convergence results in G2V and V2G modes.

PDE-based modelling and observer design for PEV fleets in V2G charging stations