Decentralized control of plug-in electric vehicles under driving uncertainty

Plug-in electric vehicles (PEVs) can be considered flexible loads, as the time when they are charged can be shifted to a certain extent without impacting the drivers´ mobility. An aggregator coordinating these flexible resources aims to minimize the costs of charging, subject to individual PEV constraints, imposed by battery and charging infrastructure characteristics, as well as driving patterns. Since driving behavior cannot be perfectly forecasted, this problem is stochastic. In this paper, we propose a decentralized control algorithm to coordinate charging, based on the Alternating Direction Method of Multipliers (ADMM). In this setup, the aggregator and PEVs find the global solution by individually solving local optimization problems. The solution is found iteratively, whereby information between the PEVs and the aggregator is exchanged at each iteration. When the objective function of the charging optimization problem and the PEV constraints are convex, the algorithm converges to the global optimum. To take driving behavior uncertainty into account, the scheme considers several scenarios of driving patterns for each vehicle. A receding time horizon optimization is used, whereby at each new stage the representation of the fleet is updated with new scenarios consistent with the current observations. The local optimization problems, which can be solved very fast, could be solved in parallel for each PEV and scenario using decentralized computing, making the approach suitable for large-scale problems. A numerical example shows how this method can be applied to flatten the system load.