Socially optimal electric driving range of plug-in hybrid electric vehicles

This study determines the optimal electric driving range of plug-in hybrid electric vehicles (PHEVs) that minimizes the daily cost borne by the society when using this technology. An optimization framework is developed and applied to datasets representing the US market. Results indicate that the optimal range is 16 miles with an average social cost of $3.19 per day when exclusively charging at home, compared to $3.27 per day of driving a conventional vehicle. The optimal range is found to be sensitive to the cost of battery packs and the price of gasoline. When workplace charging is available, the optimal electric driving range surprisingly increases from 16 to 22 miles, as larger batteries would allow drivers to better take advantage of the charging opportunities to achieve longer electrified travel distances, yielding social cost savings. If workplace charging is available, the optimal density is to deploy a workplace charger for every 3.66 vehicles. Moreover, the diversification of the battery size, i.e., introducing a pair and triple of electric driving ranges to the market, could further decrease the average societal cost per PHEV by 7.45% and 11.5% respectively.     

Network equilibrium models with battery electric vehicles

The limited driving ranges, the scarcity of recharging stations and potentially long battery recharging or swapping time inevitably affect route choices of drivers of battery electric vehicles (BEVs). When traveling between their origins and destinations, this paper assumes that BEV drivers select routes and decide battery recharging plans to minimize their trip times or costs while making sure to complete their trips without running out of charge. With different considerations of flow dependency of energy consumption of BEVs and recharging time, three mathematical models are formulated to describe the resulting network equilibrium flow distributions on regional or metropolitan road networks. Solution algorithms are proposed to solve these models efficiently. Numerical examples are presented to demonstrate the models and solution algorithms.     

Deploying public charging stations for electric vehicles on urban road networks

This paper explores how to optimally locate public charging stations for electric vehicles on a road network, considering drivers’ spontaneous adjustments and interactions of travel and recharging decisions. The proposed approach captures the interdependency of different trips conducted by the same driver by examining the complete tour of the driver. Given the limited driving range and recharging needs of battery electric vehicles, drivers of electric vehicles are assumed to simultaneously determine tour paths and recharging plans to minimize their travel and recharging time while guaranteeing not running out of charge before completing their tours. Moreover, different initial states of charge of batteries and risk-taking attitudes of drivers toward the uncertainty of energy consumption are considered. The resulting multi-class network equilibrium flow pattern is described by a mathematical program, which is solved by an iterative procedure. Based on the proposed equilibrium framework, the charging station location problem is then formulated as a bi-level mathematical program and solved by a genetic-algorithm-based procedure. Numerical examples are presented to demonstrate the models and provide insights on public charging infrastructure deployment and behaviors of electric vehicles.     

Optimal recharging strategies for electric vehicle fleets with duration constraints

Electrical vehicles (EVs) have become a popular green transportation means recently because they have lower energy consumption costs and produce less pollution. The success of EVs relies on technologies to extend their driving range, which can be achieved by the good deployment of EV recharging stations. This paper considers a special EV network composed of fixed routes for an EV fleet, where each EV moves along its own cyclic tour of depots. By setting up a recharging station on a depot, an EV can recharge its battery for no longer than a pre-specified duration constraint. We seek an optimal deployment of recharging stations and an optimal recharging schedule for each EV such that all EVs can continue their tours in the planning horizon with minimum total costs. To solve this difficult location problem, we first propose a mixed integer program (MIP) formulation and then derive four new valid inequalities to shorten the solution time. Eight MIP models, which were created by adding different combinations of the four valid inequalities to the basic model, have been implemented to test their individual effectiveness and synergy over twelve randomly generated EV networks. Valuable managerial insights into the usage of valid inequalities and the relations between the battery capacity and the total costs, number of recharging facilities to be installed, and running time are analyzed.     

Electric vehicle tour planning

This study extends the orienteering problem with time windows by considering electric vehicles (EV) with limited range. The model can simulate the change in the battery’s state of charge at each point along the routes, and thus can be used to solve the problem of EV tourist trip design with time windows. A land-sea integrated network for Penghu low-carbon islands was tested, and then the optimal green trip designs are obtained using a heuristic method. Some unique properties of the model are also discussed, as well as a number of management or planning implications.