Contract-based approach to provide electric vehicles with charging service in heterogeneous networks

Abstract

Recently, mobile charging stations (MCSs) have attracted more attentions compared with fixed charging stations (FCSs). Electric vehicles (EVs) can be easily provided with charging service through MCSs. However, most of existing approaches cannot be properly used to design the optimal pricing strategy for MCSs, leading to the inefficiency of power in MCSs. Thus, it is necessary to study new incentive mechanisms to improve MCSs’ profits. In this paper, we propose a contract-based scheme to maximize MCSs’ profits in the heterogeneous networks. Considering the power trading between EV users and MCSs, we develop the utility function with EV users’ types. Aiming to maximize MCSs’ profits, we formulate this problem as an optimization problem under the complete and incomplete information of EV users, respectively. Through the theoretical analysis, we prove the existence of optimal contract items, which also ensure the feasibility of EV users. Then optimal solutions can be achieved based on our proposed algorithm. Numerical and simulation results validate the effectiveness of our proposal.

Introduction

WITH rapid mobile technologies, electric vehicles (EVs) as a significant transportation option have attracted a lot of attentions and been widely applied in some countries, considering their advantages on higher power efficiency, lower gas emissions and fuel consumption cost [1], [2], [3], [4], [5], [6], [7]. The related report showed that the total number of the world’s EV sales had reached 774 thousand with 15.7 billion dollars in 2016, which rose up to 40% in sales compared with that in 2015 [8]. It can be predicted that the EV sales will achieve about 310 thousand with 24.3 billion dollars in 2025, and more and more fuel vehicles will be replaced in future [9], [10], [11].

Fixed charging stations (FCSs) have been recognized as a beneficially and conveniently available solution to charge EV [12], [13], [14]. However, much more payment and waiting time are needed for charging service [15]. Considering FCSs’ deficiencies, mobile charging stations (MCSs) are studied and designed [16], [17], [18], [19]. It brings some advantages: (1) It is convenient for EV users to buy the power when they need the charging service. (2) EV users will spend less amount of power on the way to MCS, compared with FCS [20]. (3) It can mitigate the peak-to-average ratio of power grid during peak hours. At the same time, it brings new challenges for MCS: (1) It needs to study how MCS efficiently makes the optimal decisions on power supply for EV users, considering the quality of service (QoS) in the heterogeneous networks. (2) Aiming to maximize MCS’s profits, a new pricing strategy should be designed, given the total amount of power supply in MCS.

Since MCS’s profits mainly depend on EV users’ charging service, more power may be supplied to EV users. In order to design an optimal strategy for charging service, some pricing plans have recently been studied [21], [22], [23]. The popular approach is the application of the game theory to formulate the charging power scheduling problem as an optimization problem with the optimal solution. However, the optimal strategy will be updated, based on the various requirements of EV users in power demand and payment, which increases the computation and overhead in the game-theoretical approach. Heuristic algorithms and dynamic programming are developed to search for the optimal solutions in [24], [25], respectively, while much more complicated computation is also needed. Another promising approach attracting much more attention is the contract theory [26], [27], [28], [29], [30]. Through this incentive approach, optimal contract items will be designed and offered to EV users with various types based on their requirements. Compared with approaches mentioned above, the optimal strategy in the contract mechanism will be obtained easily, in which the computations of time and payment are much lower. In this paper, we further study how to decide the optimal charging strategy offered by MCS through the contract-based approach in the heterogeneous networks, which is different from the existing works. To maximize its profits, the proposed strategy is used to stimulate more EV users to buy charging service from MCS.

Our contributions in this paper are summarized as follows:

• We design a novel network scheme in the heterogeneous networks, where the contract theory is adopted to design the optimal strategy with maximum profits of MCS. Specially, we develop the utility function based on the relationship between MCS and EV users, where MCS as the power supplier offers the power-price contract to EV users.

• Considering different requirements, EV users are characterized into different types. In order to improve MCS’s profits, the power distribution problem is formulated as an optimization problem under the complete and incomplete information of EV users, respectively.

• Through the theoretical analysis, the existence of the optimal contract items is proved, which also ensure the feasibility of EV users. Then, based on our proposed algorithm, the optimal solutions can be achieved to maximize MCS’s profits. Our simulation results validate the effectiveness of the proposal, which benefits both EV users and MCS.

The rest of the paper is organized as follows. Section 2 presents a brief overview of the related work. The system model is developed in Section 3. We design the utility function to describe the charging problem, and propose a contract-based scheme in Section 4. Section 5 presents the analysis of the contract-based scheme. Meanwhile, the iterative search algorithm is proposed to achieve the optimal solution of the proposal. After the theoretical study, simulation results and related analysis of our approach are shown in Section 6. Finally, conclusions are provided in Section 7.