A Hierarchical Algorithm for Vehicle-to-Grid Integration under Line Capacity Constraints

This work deals with the coordinated charging/discharging of a population of plug-in electric vehicles (PEVs)under energy efficiency, SOC, battery capacity, and power-line capacity constraints, to minimize energy cost. To address this, we introduce a framework in which the power grid is modeled as an undirected rooted tree, the root of this tree represents the generation/transmission side of the system and the leaves represent PEVs. Due to the several constraints, we are led to a non-convex optimization problem formulation subject to a complementarity constraint. We then show how a relaxed version of the problem can capture a wide set of optimal solutions for the original problem. After this, we propose a hierarchical algorithm for the computation of the PEVs’ charging/discharging profiles based on the relaxed problem formulation. The root generates a control signal based on the price per unit of power according to the demand for each time. Intermediate nodes represent congestible elements on the distribution side (e.g., transformers), which have a bound on the demand they can satisfy. In the proposed algorithm, intermediate nodes modify the control signal according to the difference between the demand they take care of, and its capacity upper bound. PEVs update their charging/discharging strategies according to this pricing signal. A proof of algorithm convergence to the optimizer of the problem is provided. Simulations demonstrate the algorithm performance and convergence rate.