ADMM-Based Coordination of Electric Vehicles in Constrained Distribution Networks Considering Fast Charging and Degradation

Acting as a key to future environmentally friendly transportation systems, electric vehicles (EVs) have attached importance to develop fast charging technologies to accomplish the requirement of vehicle users. However, fast charging behaviors would cause degradations in EVs’ batteries, as well as negative effects like new demand peak and feeder overloads to the connected distribution network, especially when plugging in large scale EVs. Decentralized coordination is encouraged and our goal is to achieve an optimal strategy profile for EVs in a decentralized way considering both the need of fast charging and reducing degradations in batteries and the distribution network. In this article, we innovatively model the EV fast charging problem as an optimization coordination problem subject to the coupled feeder capacity constraints in the distribution network. The need of fast charging is expressed by the total charging time, and the relative tendency to fully charge within the desired time period. We introduce a
$\ell _{0}$
-norm of the charging strategy which is non-convex to represent the total charging time, and apply the
$\ell _{1}$
-norm minimization to approximate the sparse solution of
$\ell _{0}$
-norm minimization. The shorter the charging horizon is the stronger willing of fast charging the user has. The objective of the optimization problem tradeoffs the EVs’ battery degradation cost, the load regulation in the distribution network, the satisfaction of charging and the total charging time, which is non-separable among individual charging behaviors. Even though alternating direction method of multipliers (ADMM) has been widely applied in distributed optimization with separable objective and coupled constraints, its decentralized scheme cannot be applied directly to the underlying non-separable EV charging coordination problem. Hence, a hierarchical algorithm based on ADMM is proposed such that the convergence to the optimal strategies is guaranteed under certain step-size parameter. Furthermore, a receding horizon based algorithm is proposed considering the forecast errors on the base demand and the EV arrival distribution. The results are demonstrated via some simulation results.