A Partial Augmented Lagrangian Method for Decentralized Electric Vehicle Charging in Capacity-Constrained Distribution Networks

This work deals with decentralized optimization problems where a collection of network agents operate selfishly and individually under a set of coupling constraints among them. This collection of problems are motivated by coordinating electric vehicle (EV) charging in a feeder capacity-constrained distribution network where each EV makes decisions locally to achieve the system's global benefit. First, a centralized scheme is established and admits an optimal coordination behaviour that minimizes the aggregate generation cost and all the EVs' local costs. However, the coupling of the charging behaviours among the EV population brings challenges to the design of the decentralized algorithm, which is expected to converge to the global optimum. A partial augmented Lagrangian method is presented to disperse the coupling constraint by introducing a penalty term. Combined with the gradient projection method, an iterative procedure is designed such that each EV and feeder line update in parallel until satisfying the terminal condition. The convergence can be guaranteed under some certain mild conditions, and the convergence rate to the global optimum is analysed as well. We include some simulation results to demonstrate the performance of the developed results.