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.     

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.     

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.     

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.     

Optimal deployment of charging lanes for electric vehicles in transportation networks

Given the rapid development of charging-while-driving technology, we envision that charging lanes for electric vehicles can be deployed in regional or even urban road networks in the future and thus attempt to optimize their deployment in this paper. We first develop a new user equilibrium model to describe the equilibrium flow distribution across a road network where charging lanes are deployed. Drivers of electric vehicles, when traveling between their origins and destinations, are assumed to select routes and decide battery recharging plans to minimize their trip times while ensuring to complete their trips without running out of charge. The battery recharging plan will dictate which charging lane to use, how long to charge and at what speed to operate an electric vehicle. The speed will affect the amount of energy recharged as well as travel time. With the established user equilibrium conditions, we further formulate the deployment of charging lanes as a mathematical program with complementarity constraints. Both the network equilibrium and design models are solved by effective solution algorithms and demonstrated with numerical examples.     

Gas anxiety and the charging choices of plug-in hybrid electric vehicle drivers

Plug-in hybrid electric vehicles (PHEVs) can provide many of the benefits of battery electric vehicles (BEVs), such as reduced petroleum consumption and greenhouse gas emissions, without the “range anxiety” that can accompany driving a vehicle with limited range when there are few charging opportunities. However, evidence indicates that PHEVs are often plugged in more frequently than BEVs in practice. This is somewhat paradoxical: drivers for whom plugging in is optional tend to do so more frequently than those for whom it is necessary. This has led to the coining of a new term – “gas anxiety” – to describe the apparent desire of PHEV drivers to avoid using gasoline. In this paper, we analyze the variables influencing the charging choices of PHEV owners, testing whether drivers express preferences consistent with the concept of gas anxiety. We analyze data collected in a web-based stated preference survey using a latent class logit model. The results reveal two classes of decision-making patterns among the survey respondents: (1) those who weight the cost of gasoline and the cost of recharging approximately equally (the cost-minimizing class), and (2) those who weight the cost gasoline more heavily than the cost of recharging (the gas anxiety class). Respondents in the gas anxiety class expressed a willingness to recharge at a charging station even when doing so would cost approximately four times as much as the cost of the gasoline avoided. While the gas anxiety class represents the majority of our sample, more recent PHEV adopters are more likely to be in the cost-minimizing class. Looking forward, this suggests that public charging station operators may need to price charging competitively with gasoline on a per-mile basis to attract PHEV owners.     

Optimum routing of battery electric vehicles: Insights using empirical data and microsimulation

This study investigates the energy consumption impact of route selection on battery electric vehicles (BEVs) using empirical second-by-second Global Positioning System (GPS) commute data and traffic micro-simulation data. Drivers typically choose routes that reduce travel time and therefore travel cost. However, BEVs’ limited driving range makes energy efficient route selection of particular concern to BEV drivers. In addition, BEVs’ regenerative braking systems allow for the recovery of energy while braking, which is affected by route choices. State-of-the-art BEV energy consumption models consider a simplified constant regenerative braking energy efficiency or average speed dependent regenerative braking factors. To overcome these limitations, this study adopted a microscopic BEV energy consumption model, which captures the effect of transient behavior on BEV energy consumption and recovery while braking in a congested network. The study found that BEVs and conventional internal combustion engine vehicles (ICEVs) had different fuel/energy-optimized traffic assignments, suggesting that different routings be recommended for electric vehicles. For the specific case study, simulation results indicate that a faster route could actually increase BEV energy consumption, and that significant energy savings were observed when BEVs utilized a longer travel time route because energy is regenerated. Finally, the study found that regenerated energy was greatly affected by facility types and congestion levels and also BEVs’ energy efficiency could be significantly influenced by regenerated energy.     

To save money or to save time: Intelligent routing design for plug-in hybrid electric vehicle

Electric vehicles (EVs) are promising alternative to conventional vehicles, due to their low fuel cost and low emissions. As a subset of EVs, plug-in hybrid electric vehicles (PHEVs) backup batteries with combustion engines, and thus have a longer traveling range than battery electric vehicles (BEVs). However, the energy cost of a PHEV is higher than a BEV because the gasoline price is higher than the electricity price. Hence, choosing a route with more charging opportunities may result in less fuel cost than the shortest route. Different with the traditional shortest-path and shortest-time routing methods, we propose a new routing choice with the lowest fuel cost for PHEV drivers. Existing algorithms for gasoline vehicles cannot be applied because they never considered the regenerative braking which may result in negative energy consumption on some road segments. Existing algorithms for BEVs are not competent too because PHEVs have two power sources. Thus, even if along the same route, different options of power source will lead to different energy consumption. This paper proposes a cost-optimal algorithm (COA) to deal with the challenges. The proposed algorithm is evaluated using real-world maps and data. The results show that there is a trade-off between traveling cost and time consumed when driving PHEVs. It is also observed that the average detour rate caused by COA is less than 14%. Significantly, the algorithm averagely saves more than 48% energy cost compared to the shortest-time routing.     

Battery capacity design for electric vehicles considering the diversity of daily vehicles miles traveled

In this paper, we study battery capacity design for battery electric vehicles (BEVs). The core of such design problems is to find a good tradeoff between minimizing the capacity to reduce financial costs of drivers and increasing the capacity to satisfy daily travel demands. The major difficulty of such design problems lies in modeling the diversity of daily travel demands. Based on massive trip records of taxi drivers in Beijing, we find that the daily vehicle miles traveled (DVMT) of a driver (e.g., a taxi driver) may change significantly in different days. This investigation triggers us to propose a mixture distribution model to describe the diversity in DVMT for various driver in different days, rather than the widely employed single distribution model. To demonstrate the merit of this new model, we consider value-at-risk and mean-variance battery capacity design problems for BEV, with respect to conventional single and new mixture distribution models of DVMT. Testing results indicate that the mixture distribution model better leads to better solutions to satisfy various drivers.     

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.     

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.     

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.     

Consumer preferences for battery electric vehicles: A choice experimental survey in China

To accelerate the diffusion of battery electric vehicles (BEVs), consumer preferences for different products and policy attributes must be determined. Although previous studies have investigated consumer preferences for some product attributes, including purchase price, operation cost, driving range, and charging time, limited studies have discussed the broader aspects of product attributes, such as battery warranty and depreciation rate. Moreover, market-oriented incentives, including the personal carbon trading (PCT) scheme and the tradable driving credits (TDC) scheme, can theoretically be effective alternatives to expensive purchase subsidies. However, there is a lack of empirical evidence that confirms the influence of these two schemes on BEV adoption. To fill these gaps, we conducted a stated preference choice experimental survey in China and investigated the effect of product attributes, existing policy incentives, and two emerging market-oriented incentives on BEV adoption. Our results reveal that along with the main product attributes, battery warranty has a significant positive effect on inducing mainstream consumers to adopt BEVs while no preference difference occurs among existing policy incentives after purchase subsidies are abolished. For young consumers, almost all incentives that reduce the operation cost (e.g., PCT) or increase convenience (e.g., TDC) can increase their adoption of BEVs. These findings can provide important implications for the government with regard to designing novel incentives and promoting BEV adoption.     

Trends in life cycle greenhouse gas emissions of future light duty electric vehicles

The majority of previous studies examining life cycle greenhouse gas (LCGHG) emissions of battery electric vehicles (BEVs) have focused on efficiency-oriented vehicle designs with limited battery capacities. However, two dominant trends in the US BEV market make these studies increasingly obsolete: sales show significant increases in battery capacity and attendant range and are increasingly dominated by large luxury or high-performance vehicles. In addition, an era of new use and ownership models may mean significant changes to vehicle utilization, and the carbon intensity of electricity is expected to decrease. Thus, the question is whether these trends significantly alter our expectations of future BEV LCGHG emissions.To answer this question, three archetypal vehicle designs for the year 2025 along with scenarios for increased range and different use models are simulated in an LCGHG model: an efficiency-oriented compact vehicle; a high performance luxury sedan; and a luxury sport utility vehicle. While production emissions are less than 10% of LCGHG emissions for today’s gasoline vehicles, they account for about 40% for a BEV, and as much as two-thirds of a future BEV operated on a primarily renewable grid. Larger battery systems and low utilization do not outweigh expected reductions in emissions from electricity used for vehicle charging. These trends could be exacerbated by increasing BEV market shares for larger vehicles. However, larger battery systems could reduce per-mile emissions of BEVs in high mileage applications, like on-demand ride sharing or shared vehicle fleets, meaning that trends in use patterns may countervail those in BEV design.     

An empirical assessment of the feasibility of battery electric vehicles for day-to-day driving

Driven by sustainability objectives, Australia like many nations in the developed world, is considering the option of battery electric vehicles (BEVs) as an alternative to conventional internal combustion engine vehicles (ICEVs). In addition to issues of capital and running costs, crucial questions remain over the specifications of such vehicles, particularly the required driving range, recharge time, re-charging infrastructure, performance, and other attributes that will be of importance to consumers. With this in mind, this paper assesses (hypothetically) the extent to which current car travel needs could be met by BEVs for a sample of motorists in Sydney assuming a home-based charging set-up, which is likely to be the primary option for early adopters of the technology. The approach uses five weeks of driving data recorded by GPS technology and builds up home-home tours to assess the distances between (in effect) charging possibilities. An energy consumption model based on characteristics of the vehicle, and the speeds recorded by the GPS is adapted to determine the charge used, while a battery recharge function is used to determine charging times based on the current battery level. Among the most pertinent findings are that over the five weeks, (i) BEVs with a range as low as 60 km and a simple home-charge set-up would be able to accommodate well over 90% of day-to-day driving, (ii) however the incidence of tours requiring out-of-home charging increases markedly for vehicles below 24 kWh (170 km range), (iii) recharge time in itself has little impact on the feasibility of BEVs because vehicles spend the majority of their time parked and (iv) effective range can be dramatically impacted by both how a vehicle is driven and use of electrical auxiliaries, and (v) while unsuitable for long, high-speed journeys without some external re-charging options, BEVs appear particularly suited for the majority of day-to-day city driving in big cities where average journey speeds of 34 km/h are close to optimal in terms of maximising vehicle range. The paper has implications for both policy-makers and auto manufacturers in breaking down some of the (perceived) barriers to greater uptake of BEVs in the future.     

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.     

Investigating barriers for plug-in electric vehicle deployment in fleets

Commercial vehicle fleets constitute a favourable entry for plug-in electric vehicles (PEVs) into the road transport system. During an extensive demonstration project, with 500 PEVs operating in 100 public and private enterprises, 40 battery electric vehicle (BEV) users were invited to focus group discussions. The focus groups allowed the users to discuss their actual experiences of operating BEVs and thereby provide a greater understanding of the operating conditions experienced by BEV users in different organisations. Based on the discussions, this paper focus on operational barriers, rather than traditional technical or economical barriers. The findings complemented earlier data collected from the demonstration project and further explained the recorded driving and charging behaviour. The conditions to adopt the BEVs vary between the users, and this in turn can relate to organisational conditions. Given a favourable introduction, users adopt and accept the technology. The paper contributes with new findings regarding implementation of BEVs in commercial vehicle fleets and provides an in-depth understanding of the operational barriers that public or private enterprises face when introducing BEVs in their vehicle fleets.     

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.     

A consumer-oriented total cost of ownership model for different vehicle types in Germany

In Germany, market penetration by alternative powertrains has been generally processing at a slow pace. Therefore, reaching the 2020 target of one million registered electric vehicles (EVs) is a major challenge. We analyze the German market by advancing and refining existing consumer-oriented total cost of ownership (TCO_C) models and demonstrate the validity of our model by comparing the cost-efficiency of EVs and internal combustion engine vehicles (ICEVs) including the battery resale value for second use and second life. The TCO_C model was calculated for the ten most frequently registered battery electric vehicles (BEVs) and hybrid electric vehicles (HEVs) and compared with ICEVs in the same vehicle segments. The results are further validated through applying three typical annual mileage driver profiles and by Monte Carlo simulations under various scenarios. Results reveal that only a few BEVs and HEVs are economical without subsidies when compared with ICEVs in all considered scenarios. The subsidies only barely change the results. The mini and the medium vehicle segment remain uneconomical in all tested scenarios. Overall, we conclude that subsidies support the competitiveness of BEVs, but fail to lead to favorable TCO_C within several vehicle segments and several tested annual mileages.     

Will subsidies drive electric vehicle adoption? Measuring consumer preferences in the U.S. and China

We model consumer preferences for conventional, hybrid electric, plug-in hybrid electric (PHEV), and battery electric (BEV) vehicle technologies in China and the U.S. using data from choice-based conjoint surveys fielded in 2012–2013 in both countries. We find that with the combined bundle of attributes offered by vehicles available today, gasoline vehicles continue in both countries to be most attractive to consumers, and American respondents have significantly lower relative willingness-to-pay for BEV technology than Chinese respondents. While U.S. and Chinese subsidies are similar, favoring vehicles with larger battery packs, differences in consumer preferences lead to different outcomes. Our results suggest that with or without each country’s 2012–2013 subsidies, Chinese consumers are willing to adopt today’s BEVs and mid-range PHEVs at similar rates relative to their respective gasoline counterparts, whereas American consumers prefer low-range PHEVs despite subsidies. This implies potential for earlier BEV adoption in China, given adequate supply. While there are clear national security benefits for adoption of BEVs in China, the local and global social impact is unclear: With higher electricity generation emissions in China, a transition to BEVs may reduce oil consumption at the expense of increased air pollution and/or greenhouse gas emissions. On the other hand, demand from China could increase global incentives for electric vehicle technology development with the potential to reduce emissions in countries where electricity generation is associated with lower emissions.