Abstract
We develop a strategy, with concepts from Mean Field Games (MFG), to coordinate the charging of a large population of battery electric vehicles (BEVs) in a parking lot powered by solar energy and managed by an aggregator. A yearly parking fee is charged for each BEV irrespective of the amount of energy extracted. The goal is to share the energy available so as to minimize the standard deviation (STD) of the state of charge (SOC) of batteries when the BEVs are leaving the parking lot, while maintaining some fairness and decentralization criteria. The MFG charging laws correspond to the Nash equilibrium induced by quadratic cost functions based on an inverse Nash equilibrium concept and designed to favor the batteries with the lower SOCs upon arrival. While the MFG charging laws are strictly decentralized, they guarantee that a mean of instantaneous charging powers to the BEVs follows a trajectory based on the solar energy forecast for the day. That day ahead forecast is broadcasted to the BEVs which then gauge the necessary SOC upon leaving their home. We illustrate the advantages of the MFG strategy for the case of a typical sunny day and a typical cloudy day when compared to more straightforward strategies: first come first full/serve and equal sharing. The behavior of the charging strategies is contrasted under conditions of random arrivals and random departures of the BEVs in the parking lot.
Highlights
The massive introduction of battery electric vehicles (BEVs) [1,2,3] in modern power systems is bound to have important impacts, positive or negative, depending on the way this novel situation is managed [4]
Our objective in this paper is to propose an algorithm for sharing solar photovoltaic (PV) power amongst homogeneous BEVs parked in a parking lot, or a collection of federated parking lots
The first n1 BEVs connected to their charging stations before 6 a.m. will start charging at 6 a.m., the n2 BEVs connected between 6 a.m. and 6:15 a.m. will start charging at 6:15 a.m., and so on
Summary
The massive introduction of battery electric vehicles (BEVs) [1,2,3] in modern power systems is bound to have important impacts, positive or negative, depending on the way this novel situation is managed [4]. The authors in [20], whose objective is close to ours in this paper, propose a centralized linear programming (LP) algorithm, in a solar powered parking lot of a car-share service to fairly distribute the available solar energy amongst 97 heterogeneous BEVs by favoring those arriving with less charge. They study the case where the SDR is strictly inferior to 1, and that all BEVs are available during the daily charging session of 5 h in the parking lot They demonstrate, by charging a subset of 5 BEVs during each time slot, a reduction of 60%.
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