Decentralized PEV Control Based on a Subgradient Method for Mixed-Integer Programming Problems

In this paper, a subgradient method for solving mixed-integer linear programming problems is tailored and used to control in a distributed, and hence scalable way, the recharging process of a fleet of plug-in electric vehicles (PEVs). This makes possible to scale the problem to large PEV fleets, in a privacy-preserving fashion, something that cannot be done when relying on centralized optimization-based methods. A key challenge to face is given by the fact that the mathematical formulation of the PEV charging problem includes both real (i.e., continuous) and integer (in particular, Boolean) variables. This complicates significantly the mathematical theory, compared to the case in which all the involved variables are real. The PEV charging power is realistically modelled as a semi-continuous variable (while most of the works model it as a on/off variable), and the goal is to recharge the PEVs according to the user charging preferences, while letting the aggregated PEV power track a given power reference. Simulation results are discussed and possible directions for future research are outlined.