Decentralised optimal vehicle-to-grid coordination with forecast errors

Considering vehicle-to-grid (V2G) coordination schemes, plug-in electric vehicles (PEVs) are expected to be an energy storage system (ESS) to smooth out the fluctuation of the intermittent renewable energy source (RES) and the power load profile. In this study, firstly the optimal coordination of PEVs minimising total costs is shown to possess the valley-fill and peak-shift property for any pair of adjacent instants. Due to the decoupling relationship among the admissible sets of coordination behaviours of all the PEVs in the modelling issue, a decentralised algorithm is proposed by applying the gradient projection method, such that the coordination behaviours of individual PEVs can be updated locally and simultaneously. It is proved that the convergence and optimality of the proposed method are guaranteed in case the step-size parameter of the update procedure is in a certain region, and its performance does not rely on the shape of the net demand trajectory. Furthermore, a receding horizon-based algorithm is presented to account for the forecast errors occurred in the predictions of PEV populations, RES productions and inelastic load profiles. The results developed in this study are demonstrated with numerical simulations and comparisons with other decentralised methods are also provided.