With the intensification of environmental pollution and energy shortage problems, electric vehicles as an alternative fuel vehicle are receiving more and more attention. Compared with traditional fossil fuel vehicles, electric vehicles can significantly reduce the dependence on traditional fuels and greenhouse gas emissions. However, the market share of electric vehicles is still relatively low and the development of electric vehicles is impeded by various limitations, including shortened driving range, lack of charging infrastructure, and long battery recharging period. The construction of additional charging facilities can ease the range anxiety of electric vehicle travelers and promote the development of electric vehicles. Accessibility refers to the ability of users to reach their destinations and complete expected activities. It is an important indicator for evaluating the service quantity of a transportation system. Based on the space-time-electricity accessibility of electric vehicle travelers, this study optimizes the distribution of charging facilities including charging stations and wireless charging segments. Specifically, our research includes the following aspects:
(1) Definition of space-time-electricity accessibility for electric vehicles
Based on the existing space accessibility and space-time accessibility indicators, we extend the electricity dimension and derive a space-time-electricity accessibility indicator. If the electric vehicle traveler can reach the destination from the origin satisfying the travel time budget and battery capacity restrictions, we denote that this origin-destination (OD) pair is space-time-electricity accessible. Otherwise, this OD pair is space-time-electricity inaccessible. To judge the space-time-electricity accessibility, we construct a mathematical programming model in the space-time-electricity network. We use the number of space-time-electricity accessible OD pairs to evaluate the accessibility. More space-time-electricity accessible OD pairs mean better accessibility of electric vehicle travelers in the transportation network.
(2) Accessibility-oriented charging station location optimization
Based on the space-time-electricity accessibility, a multi-commodity network flow model in the space-time-electricity network is constructed for this problem. By dualizing the coupling constraints between location and routing variables to the objective function, the Lagrangian relaxed problem can be decomposed into a series of least-cost path subproblems and a knapsack subproblem. These least-cost path subproblems can be efficiently solved by a time-dependent forward dynamic-programming algorithm and the knapsack problem can be solved by a standard solver (such as Gurobi). At each iteration, Lagrangian multipliers are adjusted by the subgradient optimization method and feasible solutions are generated using a heuristic method. The Lagrangian relaxation-based decomposition method is tested in three transportation networks, and the influence of key parameters is analyzed.
(3) Accessibility-oriented wireless charging segment location optimization
With the development of charging-while-driving techniques, electric vehicles can recharge on the road segments without stopping. Since electric vehicles do not need to spend a long period at fixed stations, dynamic charging infrastructures can significantly improve the mobility and accessibility of electric vehicles. If wireless charging segments are widely applied, the driving range of electric vehicles will be unlimited. For the accessibility-oriented wireless charging segment location problem, a multi-commodity network flow model in the space-time-electricity network and a column-based model are formulated. Based on the column-based model, a column generation-based decomposition approach is developed. At each iteration, a restricted master problem and a set of pricing subproblems should be solved. We design an efficient dynamic-programming algorithm to solve these least-cost path subproblems. In experimental experiments, the characteristics of this problem are analyzed and the performance of the proposed method is tested.
(4) Accessibility-oriented optimization of charging stations and wireless charging segments
Charging stations and wireless charging segments have their own advantages, so it is necessary to jointly optimize the two types of charging facilities. First, a multi-commodity network flow model in the space-time-electricity network is constructed for the joint optimization problem. Based on the augmented Lagrangian relaxation and alternating direction method of multipliers, a problem decomposition framework is proposed for this problem. The standard Lagrangian relaxed problem and the augmented Lagrangian relaxed problem are finally decomposed into several subproblems. By solving a series of simple subproblems, high-quality feasible solutions can be obtained for this problem. In experimental experiments, several key parameters are analyzed including the charging speed, construction budget, travel time budget, and battery capacity.
(5) Wireless charging segment location optimization under fully accessible demand
If wireless charging segments are widely applied in the transportation network, the driving range of electric vehicles will be unlimited by the electricity resources. The difficulty is how to determine the number and distribution of wireless charging segments so that all electric vehicle travelers can complete the trip and the total construction cost is minimal. For this problem, a full cover charging segment location model is formulated in the space-time-electricity network and a path-based model is further achieved. Based on the path-based model, we design a column generation-based decomposition method for this problem. At each iteration, a restricted master problem and a series of pricing subproblems need to be solved. In the experimental experiments, the influence of different parameters on the total construction cost and distribution of wireless charging segments is analyzed.