Voltage regulation in constrained distribution networks by coordinating electric vehicle charging based on hierarchical ADMM

The charging coordination of large-scale electric vehicles (EVs) for avoiding the voltages at some nodes to drop below feasible ranges in distribution networks, which is formulated as a class of optimisation problems with a certain class of coupled constraints, is studied. Then the alternating direction method of multipliers (ADMM) is introduced to obtain the optimal charging strategies. However, due to the non-separable property of the objective function which includes a non-linear term of the total charging power of EV populations, it is difficult to decentralise the update step of the charging strategy in the ADMM method. Consequently, a novel decentralised hierarchical method is proposed by further developing an iterative update of best responses of individual EVs at each iteration step of the proposed ADMM method, such that individual EVs can implement the coordination behaviours locally and simultaneously without sharing any other private information except the charging power. Furthermore, the proposed approach does not require the objective function to be continuously differentiable. The convergence and optimality of the proposed method are verified and some numerical simulations are studied to illustrate the developed results.