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.     

Deployment of stationary and dynamic charging infrastructure for electric vehicles along traffic corridors

As charging-while-driving (CWD) technology advances, charging lanes can be deployed in the near future to charge electric vehicles (EVs) while in motion. Since charging lanes will be costly to deploy, this paper investigates the deployment of two types of charging facilities, namely charging lanes and charging stations, along a long traffic corridor to explore the competitiveness of charging lanes. Given the charging infrastructure supply, i.e., the number of charging stations, the number of chargers installed at each station, the length of charging lanes, and the charging prices at charging stations and lanes, we analyze the charging-facility-choice equilibrium of EVs. We then discuss the optimal deployment of charging infrastructure considering either the public or private provision. In the former, a government agency builds and operates both charging lanes and stations to minimize social cost, while in the latter, charging lanes and stations are assumed to be built and operated by two competing private companies to maximize their own profits. Numerical experiments based on currently available empirical data suggest that charging lanes are competitive in both cases for attracting drivers and generating revenue.     

Dynamic charging infrastructure deployment for plug-in hybrid electric trucks

Inspired by the rapid development of charging-while-driving (CWD) technology, plans are ongoing in government agencies worldwide for the development of electrified road freight transportation systems through the deployment of dynamic charging lanes. This en route method for the charging of plug-in hybrid electric trucks is expected to supplement the more conventional charging technique, thus enabling significant reduction in fossil fuel consumption and pollutant emission from road freight transportation. In this study, we investigated the optimal deployment of dynamic charging lanes for plug-in hybrid electric trucks. First, we developed a multi-class multi-criteria user equilibrium model of the route choice behaviors of truck and passenger car drivers and the resultant equilibrium flow distributions. Considering that the developed user equilibrium model may have non-unique flow distributions, a robust deployment of dynamic charging lanes that optimizes the system performance under the worst-case flow distributions was targeted. The problem was formulated as a generalized semi-infinite min-max program, and a heuristic algorithm for solving it was proposed. This paper includes numerical examples that were used to demonstrate the application of the developed models and solution algorithms.     

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.     

Integrated planning of static and dynamic charging infrastructure for electric vehicles

This paper investigates the optimal deployment of static and dynamic charging infrastructure considering the interdependency between transportation and power networks. Static infrastructure means plug-in charging stations, while the dynamic counterpart refers to electrified roads or charging lanes enabled by charging-while-driving technology. A network equilibrium model is first developed to capture the interactions among battery electric vehicles’ (BEVs) route choices, charging plans, and the prices of electricity. A mixed-integer bi-level program is then formulated to determine the deployment plan of charging infrastructure to minimize the total social cost of the coupled networks. Numerical examples are provided to demonstrate travel and charging plans of BEV drivers and the competitiveness of static and dynamic charging infrastructure. The numerical results on three networks suggest that (1) for individual BEV drivers, the choice between using charging lanes and charging stations is more sensitive to parameters including value of travel time, service fee markup, and battery size, but less sensitive to the charging rates and travel demand; (2) deploying more charging lanes is favorable for transportation networks with sparser topology while more charging stations can be more preferable for those denser networks.     

A cost-competitiveness analysis of charging infrastructure for electric bus operations

This study investigates the cost competitiveness of different types of charging infrastructure, including charging stations, charging lanes (via charging-while-driving technologies) and battery swapping stations, in support of an electric public transit system. To this end, we first establish mathematical models to investigate the optimal deployment of various charging facilities along the transit line and determine the optimal size of the electric bus fleet, as well as their batteries, to minimize total infrastructure and fleet costs while guaranteeing service frequency and satisfying the charging needs of the transit system. We then conduct an empirical analysis utilizing available real-world data. The results suggest that: (1) the service frequency, circulation length, and operating speed of a transit system may have a great impact on the cost competitiveness of different charging infrastructure; (2) charging lanes enabled by currently available inductive wireless charging technology are cost competitive for most of the existing bus rapid transit corridors; (3) swapping stations can yield a lower total cost than charging lanes and charging stations for transit systems with high operating speed and low service frequency; (4) charging stations are cost competitive only for transit systems with very low service frequency and short circulation; and (5) the key to making charging lanes more competitive for transit systems with low service frequency and high operating speed is to reduce their unit-length construction cost or enhance their charging power.     

Optimal deployment of autonomous vehicle lanes with endogenous market penetration

This paper develops a mathematical approach to optimize a time-dependent deployment plan of autonomous vehicle (AV) lanes on a transportation network with heterogeneous traffic stream consisting of both conventional vehicles (CVs) and AVs, so as to minimize the social cost and promote the adoption of AVs. Specifically, AV lanes are exclusive lanes that can only be utilized by AVs, and the deployment plan specifies when, where, and how many AV lanes to be deployed. We first present a multi-class network equilibrium model to describe the flow distributions of both CVs and AVs, given the presence of AV lanes in the network. Considering that the net benefit (e.g., reduced travel cost) derived from the deployment of AV lanes will further promote the AV adoption, we proceed to apply a diffusion model to forecast the evolution of AV market penetration. With the equilibrium model and diffusion model, a time-dependent deployment model is then formulated, which can be solved by an efficient solution algorithm. Lastly, numerical examples based on the south Florida network are presented to demonstrate the proposed models.     

Routing aspects of electric vehicle drivers and their effects on network performance

This study investigates the routing aspects of battery electric vehicle (BEV) drivers and their effects on the overall traffic network performance. BEVs have unique characteristics such as range limitation, long battery recharging time, and recuperation of energy lost during the deceleration phase if equipped with regenerative braking system (RBS). In addition, the energy consumption rate per unit distance traveled is lower at moderate speed than at higher speed. This raises two interesting questions: (i) whether these characteristics of BEVs will lead to different route selection compared to conventional internal combustion engine vehicles (ICEVs), and (ii) whether such route selection implications of BEVs will affect the network performance. With the increasing market penetration of BEVs, these questions are becoming more important. This study formulates a multi-class dynamic user equilibrium (MCDUE) model to determine the equilibrium flows for mixed traffic consisting of BEVs and ICEVs. A simulation-based solution procedure is proposed for the MCDUE model. In the MCDUE model, BEVs select routes to minimize the generalized cost which includes route travel time, energy related costs and range anxiety cost, and ICEVs to minimize route travel time. Results from numerical experiments illustrate that BEV drivers select routes with lower speed to conserve and recuperate battery energy while ICEV drivers select shortest travel time routes. They also illustrate that the differences in route choice behavior of BEV and ICEV drivers can synergistically lead to reduction in total travel time and the network performance towards system optimum under certain conditions.     

Charge timing choice behavior of battery electric vehicle users

This paper aims to examine choice behavior in respect of the time at which battery electric vehicle users charge their vehicles. The focus is on normal charging after the last trip of the day, and the alternatives presented are no charging, charging immediately after arrival, nighttime charging, and charging at other times. A mixed logit model with unobserved heterogeneity is applied to panel data extracted from a two-year field trial on battery electric vehicle usage in Japan. Estimation results, obtained using separate models for commercial and private vehicles, suggest that state of charge, interval in days before the next travel day, and vehicle-kilometers to be traveled on the next travel day are the main predictors for whether a user charges the vehicle or not, that the experience of fast charging negatively affects normal charging, and that users tend to charge during the nighttime in the latter half of the trial. On the other hand, the probability of normal charging after the last trip of a working day is increased for commercial vehicles, while is decreased for private vehicles. Commercial vehicles tend not to be charged when they arrival during the nighttime, while private vehicles tend to be charged immediately. Further, the correlations of nighttime charging with charging immediately and charging at other times reveal that it may be possible to encourage charging during off-peak hours to lessen the load on the electricity grid. This finding is supported by the high variance for the alternative of nighttime charging.     

Predicting market potential and environmental benefits of deploying electric taxis in Nanjing,China

This paper investigates the market potential and environmental benefits of replacing internal combustion engine (ICE) vehicles with battery electric vehicles (BEVs) in the taxi fleet in Nanjing, China. Vehicle trajectory data collected by onboard global positioning system (GPS) units are used to study the travel patterns of taxis. The impacts of charger power, charging infrastructure coverage, and taxi apps on the feasibility of electric taxis are quantified, considering taxi drivers’ recharging behavior and operating activities. It is found that (1) depending on the charger power and coverage, 19% (with AC Level 2 chargers and 20% charger network coverage) to 56% (with DC chargers and 100% charger network coverage) of the ICE vehicles can be replaced by electric taxis without driving pattern changes; (2) by using taxi apps to find nearby passengers and charging stations, drivers could utilize the empty cruising time to charge the battery, which may increase the acceptance of BEVs by up to 82.6% compared to the scenario without taxi apps; and (3) tailpipe emissions in urban areas could be significantly reduced with taxi electrification: a mixed taxi fleet with 46% compressed-natural-gas-powered (CNG) and 54% electricity-powered vehicles can reduce the tailpipe emissions by 48% in comparison with the fleet of 100% CNG taxis.     

Statistical assessment of EV usage potential from user’s perspective considering rapid-charging technology

The aim of the German Government is the licensing of one million electric vehicles (EV) in Germany until 2020. However, the number of battery electric vehicles (EVs) today still is just above 25,000. There are several reasons for deciding against an EV, but especially low battery ranges as well as too long perceived charging duration inhibit the usage of an EV. To eliminate the negative influence of these two reasons on the decision to purchase an EV, a novel charging technology is established. The rapid-charging technology enables the user to recharge the battery to 80% of its state of charge (SOC) within 20–30 min. For the examination of the technology’s impact from (potential) user’s perspective, users and nonusers of battery electric vehicles were questioned about the perceived additional value of public rapid-charging infrastructure by taking into account different trip purposes and running comparisons to regular charging options. The results show an increased perceived value especially for trips with leisure purpose, considering their share of all trip purposes in Germany, according to the MiD 2008. In order to increase the number of licensed EVs in Germany, the study’s results also suggest further dissemination of information on rapid charging which might influence the perceived usefulness of the technology and consequentially the perceived usefulness of an EV.     

Stochastic frontier analysis of excess access to mid-trip battery electric vehicle fast charging

This study aims to explore how factors including charging infrastructure and battery technology associate the way people currently charge their battery electric vehicles, as well as to explore whether good use of battery capacity can be encouraged. Using a stochastic frontier model applied to panel data obtained in a field trial on battery electric vehicle usage in Japan, the remaining charge when mid-trip fast charging begins is treated as a dependent variable. The estimation results obtained using four models, for commercial and private vehicles, respectively, on working and non-working days, show that remaining charge is associated with number of charging stations, familiarity with charging stations, usage of air-conditioning or heater, battery capacity, number of trips, Vehicle Miles of Travel, paid charging. However, the associated factors are not identical for the four models. In general, EVs with high-capacity batteries are initiated at higher remaining charge, and so are the mid-trip fast charging events in the latter period of this trial. The estimation results also show that there are great opportunities to encourage more efficient charging behavior. It appears that the stochastic frontier modeling method is an effective way to model the remaining charge at which fast-charging should be initiated, since it incorporates trip and vehicle characteristics into the estimation process to some extent.     

Public charging infrastructure for plug-in electric vehicles: What is it worth?

Lack of charging infrastructure is an important barrier to the growth of the plug-in electric vehicle (PEV) market. Public charging infrastructure has tangible and intangible value, such as reducing range anxiety or building confidence in the future of the PEV market. Quantifying the value of public charging infrastructure can inform analysis of investment decisions and can help predict the impact of charging infrastructure on future PEV sales. Estimates of willingness to pay (WTP) based on stated preference surveys are limited by consumers’ lack of familiarity with PEVs. As an alternative, we focus on quantifying the tangible value of public PEV chargers in terms of their ability to displace gasoline use for PHEVs and to enable additional electric (e−) vehicle miles for BEVs, thereby mitigating the limitations of shorter range and longer recharging time. Simulation studies provide data that can be used to quantify e-miles enabled by public chargers and the value of additional e-miles can be inferred from econometric estimates of WTP for increased vehicle range. Functions are synthesized that estimate the WTP for public charging infrastructure by plug-in hybrid and battery electric vehicles, conditional on vehicle range, annual vehicle travel, pre-existing charging infrastructure, energy prices, vehicle efficiency, and household income. A case study based on California’s public charging network in 2017 indicates that, to the purchaser of a new BEV with a 100-mile range and home recharging, existing public fast chargers are worth about $1500 for intraregional travel, and fast chargers along intercity routes are valued at over $6500.     

Network user equilibrium of battery electric vehicles considering flow-dependent electricity consumption

This paper addresses the equilibrium traffic assignment problem involving battery electric vehicles (BEVs) with flow-dependent electricity consumption. Due to the limited driving range and the costly/time-consuming recharging process required by current BEVs, as well as the scarce availability of battery charging/swapping stations, BEV drivers usually experience fear that their batteries may run out of power en route. Therefore, when choosing routes, BEV drivers not only try to minimize their travel costs, but also have to consider the feasibility of their routes. Moreover, considering the potential impact of traffic congestion on the electricity consumption of BEVs, the feasibility of routes may be determined endogenously rather than exogenously. A set of user equilibrium (UE) conditions from the literature is first presented to describe the route choice behaviors of BEV drivers considering flow-dependent electricity consumption. The UE conditions are then formulated as a nonlinear complementarity model. The model is further formulated as a variational inequality (VI) model and is solved using an iterative solution procedure. Numerical examples are provided to demonstrate the proposed models and solution algorithms. Discussions of how to evaluate and improve the system performance with non-unique link flow distribution are offered. A robust congestion pricing model is formulated to obtain a pricing scheme that minimizes the system travel cost under the worst-case tolled flow distribution. Finally, a further extension of the mathematical formulation for the UE conditions is provided.     

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.     

An optimal location choice model for recreation-oriented scooter recharge stations

To minimize air pollution from scooters in Taiwan, the government has promoted electric scooters. However, their range limits these vehicles and the establishment of recharge facilities is important for fostering their use. Short distance recreational trips are the most common use for electric scooters, because their limited. Locating recharging stations is thus important if their use is to be widened. A model is developed and the locations of recharging stations determined using an integer program with a case study offering validation. Sensitivity analyses is performed seeking the minimum recharge time and the length of stay at each site. It is found that the speedy charge method for recharging the battery would significantly reduce the number of recharge stations.     

Agent-based modelling for assessing hybrid and electric cars deployment policies in Luxembourg and Lorraine

Electric mobility is often presented as a way to tackle the environmental issues associated with individual mobility, provided that electric vehicles are adopted by drivers on a mass scale. In this paper, we propose an agent-based model (ABM) aiming at modelling the deployment of these vehicles. ABM is particularly indicated when modelling complex systems whose final results are the combination of the interactions between individuals and their environment and when the agents have partial information to take their decisions. We selected Luxembourg and its French neighbouring region, Lorraine, as the case study for our model, to test Luxembourg’s ambitious objective of deploying 40,000 electric vehicles by the year 2020. Model results show that the number of battery powered electric vehicles in Luxembourg (including vehicles from Lorraine’s commuters crossing the border every day) could be between 2000 and 21,000. A high number of commercial vehicles in Luxembourg, as well as an unlikely deployment in the neighbouring Belgium and Germany would therefore be required to meet the deployment objective. However, the deployment of plug-in hybrid vehicles could reach 60,000 cars by the end of 2020. To achieve this number, the deployment of charging points seems to be the more effective policy, along with actions aiming at increasing public awareness and acceptance of electric vehicles. The interest in using the ABM also lies in the identification of the main individuals’ characteristics affecting the deployment of electric vehicles (household size, commuting distances, etc.), which further support the setting of public policies.     

Partial recharge strategies for the electric vehicle routing problem with time windows

The Electric Vehicle Routing Problem with Time Windows (EVRPTW) is an extension to the well-known Vehicle Routing Problem with Time Windows (VRPTW) where the fleet consists of electric vehicles (EVs). Since EVs have limited driving range due to their battery capacities they may need to visit recharging stations while servicing the customers along their route. The recharging may take place at any battery level and after the recharging the battery is assumed to be full. In this paper, we relax the full recharge restriction and allow partial recharging (EVRPTW-PR), which is more practical in the real world due to shorter recharging duration. We formulate this problem as a 0–1 mixed integer linear program and develop an Adaptive Large Neighborhood Search (ALNS) algorithm to solve it efficiently. We apply several removal and insertion mechanisms by selecting them dynamically and adaptively based on their past performances, including new mechanisms specifically designed for EVRPTW and EVRPTW-PR. These new mechanisms include the removal of the stations independently or along with the preceding or succeeding customers and the insertion of the stations with determining the charge amount based on the recharging decisions. We test the performance of ALNS by using benchmark instances from the recent literature. The computational results show that the proposed method is effective in finding high quality solutions and the partial recharging option may significantly improve the routing decisions.     

Dynamic charging-while-driving systems for freight delivery services with electric vehicles: Traffic and energy modelling

This paper presents a research on traffic modelling developed for assessing traffic and energy performance of electric systems installed along roads for dynamic charging-while-driving (CWD) of fully electric vehicles (FEVs).The logic adopted by the developed traffic model is derived from a particular simulation scenario of electric charging: a freight distribution service operated using medium-sized vans. In this case, the CWD service is used to recover the state of charge of the FEV batteries to shortly start with further activities after arrival at the depot.The CWD system is assumed to be implemented in a multilane ring road with several intermediate on-ramp entrances, where the slowest lane is reserved for the dynamic charging of authorized electric vehicles. A specific traffic model is developed and implemented based on a mesoscopic approach, where energy requirements and charging opportunities affect driving and traffic behaviours. Overtaking manoeuvres as well as new entries in the CWD lane of vehicles that need to charge are modelled according to a cooperative driving system, which manages adequate time gaps between consecutive vehicles. Finally, a speed control strategy is simulated at a defined node to create an empty time-space slot in the CWD lane, by delaying the arriving vehicles. This simulated control, implemented to allow maintenance operations for CWD that may require clearing a charging zone for a short time slot, could also be applied to facilitate on-ramp merging manoeuvres.     

Assessing the cost-optimal mileage of medium-duty electric vehicles with a numeric simulation approach

Electric freight vehicles have the potential to mitigate local urban road freight transport emissions, but their numbers are still insignificant. Logistics companies often consider electric vehicles as too costly compared to vehicles powered by combustion engines. Research within the body of the current literature suggests that increasing the driven mileage can enhance the competitiveness of electric freight vehicles. In this paper we develop a numeric simulation approach to analyze the cost-optimal balance between a high utilization of medium-duty electric vehicles – which often have low operational costs – and the common requirement that their batteries will need expensive replacements. Our work relies on empirical findings of the real-world energy consumption from a large German field test with medium-duty electric vehicles. Our results suggest that increasing the range to the technical maximum by intermediate (quick) charging and multi-shift usage is not the most cost-efficient strategy in every case. A low daily mileage is more cost-efficient at high energy prices or consumptions, relative to diesel prices or consumptions, or if the battery is not safeguarded by a long warranty. In practical applications our model may help companies to choose the most suitable electric vehicle for the application purpose or the optimal trip length from a given set of options. For policymakers, our analysis provides insights on the relevant parameters that may either reduce the cost gap at lower daily mileages, or increase the utilization of medium-duty electric vehicles, in order to abate the negative impact of urban road freight transport on the environment.