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.     

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.     

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.     

Within-day recharge of plug-in hybrid electric vehicles: Energy impact of public charging infrastructure

This paper examines the role of public charging infrastructure in increasing the share of driving on electricity that plug-in hybrid electric vehicles might exhibit, thus reducing their gasoline consumption. Vehicle activity data obtained from a global positioning system tracked household travel survey in Austin, Texas, is used to estimate gasoline and electricity consumptions of plug-in hybrid electric vehicles. Drivers’ within-day recharging behavior, constrained by travel activities and public charger availability, is modeled. It is found that public charging offers greater fuel savings for hybrid electric vehicles s equipped with smaller batteries, by encouraging within-day recharge, and providing an extensive public charging service is expected to reduce plug-in hybrid electric vehicles gasoline consumption by more than 30% and energy cost by 10%, compared to the scenario of home charging only.     

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.     

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.     

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.     

Optimal deployment of public charging stations for plug-in hybrid electric vehicles

This paper develops an equilibrium modeling framework that captures the interactions among availability of public charging opportunities, prices of electricity, and destination and route choices of plug-in hybrid electric vehicles (PHEVs) at regional transportation and power transmission networks coupled by PHEVs. The modeling framework is then applied to determine an optimal allocation of a given number of public charging stations among metropolitan areas in the region to maximize social welfare associated with the coupled networks. The allocation model is formulated as a mathematical program with complementarity constraints, and is solved by an active-set algorithm. Numerical examples are presented to demonstrate the models and offer insights on the equilibrium of the coupled transportation and power networks, and optimally allocating resource for public charging infrastructure.     

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.     

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.     

Path-constrained traffic assignment: A trip chain analysis under range anxiety

This paper proposes and analyzes a distance-constrained traffic assignment problem with trip chains embedded in equilibrium network flows. The purpose of studying this problem is to develop an appropriate modeling tool for characterizing traffic flow patterns in emerging transportation networks that serve a massive adoption of plug-in electric vehicles. This need arises from the facts that electric vehicles suffer from the “range anxiety” issue caused by the unavailability or insufficiency of public electricity-charging infrastructures and the far-below-expectation battery capacity. It is suggested that if range anxiety makes any impact on travel behaviors, it more likely occurs on the trip chain level rather than the trip level, where a trip chain here is defined as a series of trips between two possible charging opportunities (Tamor et al., 2013). The focus of this paper is thus given to the development of the modeling and solution methods for the proposed traffic assignment problem. In this modeling paradigm, given that trip chains are the basic modeling unit for individual decision making, any traveler’s combined travel route and activity location choices under the distance limit results in a distance-constrained, node-sequenced shortest path problem. A cascading labeling algorithm is developed for this shortest path problem and embedded into a linear approximation framework for equilibrium network solutions. The numerical result derived from an illustrative example clearly shows the mechanism and magnitude of the distance limit and trip chain settings in reshaping network flows from the simple case characterized merely by user equilibrium.     

Modeling the charging and route choice behavior of BEV drivers

Due to the limited cruising range of battery electric vehicle (BEV), BEV drivers show obvious difference in travel behavior from gasoline vehicle (GV) drivers. To analyze BEV drivers’ charging and route choice behaviors, and extract the differences between BEV and GV drivers’ travel behavior, two multinomial logit-based and two nested logit-based models are proposed in this study based on a stated preference survey. The nested structure consists of two levels: the upper level represents the charging decision, and the lower level shows the route choices corresponding to the charging and no-charging situations respectively. The estimated results demonstrate that the nested structure is more appropriate than the multinomial structure. Meanwhile, it is observed that the initial state of charge (SOC) at origin of BEV is the most important factor that affects the decision of charging or not, and the SOC at destination becomes an important impact factor affecting BEV drivers’ route choice behavior. As for the route choice behavior when BEV has charging demand, the charging station attributes such as charging time and charging station’s location have significant influences on BEV drivers’ decision-making process. The results also show that BEV drivers incline to choose the routes with charging station having less charging time, being closer to origin and consistent with travel direction. Finally, based on the proposed models, a series of numerical analysis has been conducted to verify the effect of range anxiety on BEV charging and route choice behavior and to reveal the variation of comfortable initial SOC at origin with travel distance. Meanwhile, the effects of charging time and distance from origin to charging station also have been discussed.     

Simulation of electric vehicle driver behaviour in road transport and electric power networks

The integration of electric vehicles (EVs) will affect both electricity and transport systems and research is needed on finding possible ways to make a smooth transition to the electrification of the road transport. To fully understand the EV integration consequences, the behaviour of the EV drivers and its impact on these two systems should be studied. This paper describes an integrated simulation-based approach, modelling the EV and its interactions in both road transport and electric power systems. The main components of both systems have been considered, and the EV driver behaviour was modelled using a multi-agent simulation platform. Considering a fleet of 1000 EV agents, two behavioural profiles were studied (Unaware/Aware) to model EV driver behaviour. The two behavioural profiles represent the EV driver in different stages of EV adoption starting with Unaware EV drivers when the public acceptance of EVs is limited, and developing to Aware EV drivers as the electrification of road transport is promoted in an overall context. The EV agents were modelled to follow a realistic activity-based trip pattern, and the impact of EV driver behaviour was simulated on a road transport and electricity grid. It was found that the EV agents’ behaviour has direct and indirect impact on both the road transport network and the electricity grid, affecting the traffic of the roads, the stress of the distribution network and the utilization of the charging infrastructure.     

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.     

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.     

Optimizing charging station locations for urban taxi providers

Recently, electric vehicles are gaining importance which helps to reduce dependency on oil, increases energy efficiency of transportation, reduces carbon emissions and noise, and avoids tail pipe emissions. Because of short daily driving distances, high mileage, and intermediate waiting time, fossil-fuelled taxi vehicles are ideal candidates for being replaced by battery electric vehicles (BEVs). Moreover, taxi BEVs would increase visibility of electric mobility and therefore encourage others to purchase an electric vehicle. Prior to replacing conventional taxis with BEVs, a suitable charging infrastructure has to be established. This infrastructure consists of a sufficiently dense network of charging stations taking into account the lower driving ranges of BEVs.In this case study we propose a decision support system for placing charging stations in order to satisfy the charging demand of electric taxi vehicles. Operational taxi data from about 800 vehicles is used to identify and estimate the charging demand for electric taxis based on frequent origins and destinations of trips. Next, a variant of the maximal covering location problem is formulated and solved to satisfy as much charging demand as possible with a limited number of charging stations. Already existing fast charging locations are considered in the optimization problem. In this work, we focus on finding regions in which charging stations should be placed rather than exact locations. The exact location within an area is identified in a post-optimization phase (e.g., by authorities), where environmental conditions are considered, e.g., the capacity of the power network, availability of space, and legal issues.Our approach is implemented in the city of Vienna, Austria, in the course of an applied research project that has been conducted in 2014. Local authorities, power network operators, representatives of taxi driver guilds as well as a radio taxi provider participated in the project and identified exact locations for charging stations based on our decision support system.     

Analysis of plug-in hybrid electric vehicles’ utility factors using GPS-based longitudinal travel data

The benefit of using a PHEV comes from its ability to substitute gasoline with electricity in operation. Defined as the proportion of distance traveled in the electric mode, the utility factor (UF) depends mostly on the battery capacity, but also on many other factors, such as travel pattern and recharging pattern. Conventionally, the UFs are calculated based on the daily vehicle miles traveled (DVMT) by assuming motorists leave home in the morning with a full battery, and no charge occurs before returning home in the evening. Such an assumption, however, ignores the impact of the heterogeneity in both travel and charging behavior, such as going back home more than once in a day, the impact of available charging time, and the price of gasoline and electricity. Moreover, the conventional UFs are based on the National Household Travel Survey (NHTS) data, which are one-day travel data of each sample vehicle. A motorist’s daily travel distance variation is ignored. This paper employs the GPS-based longitudinal travel data (covering 3–18 months) collected from 403 vehicles in the Seattle metropolitan area to investigate how such travel and charging behavior affects UFs. To do this, for each vehicle, we organized trips to a series of home and work related tours. The UFs based on the DVMT are found close to those based on home-to-home tours. On the other hand, it is seen that the workplace charge opportunities significantly increase UFs if the CD range is no more than 40 miles.     

A geometry-based algorithm to provide guidance for electric vehicle charging

Electric vehicles (EVs) have been regarded as effective options for solving the environmental and energy problems in the field of transportation. However, given the limited driving range and insufficient charging stations, searching and selecting charging stations is an important issue for EV drivers during trips. A smart charging service should be developed to help address the charging issue of EV drivers, and a practical algorithm for charging guidance is required to realise it. This study aims to design a geometry-based algorithm for charging guidance that can be effectively applied in the smart charging service. Geographic research findings and geometric approaches are applied to design the algorithm. The algorithm is practical because it is based on the information from drivers’ charging requests, and its total number of calculations is significantly less than that of the conventional shortest-first algorithm. The algorithm is effective because it considers the consistency of direction trend between the charging route and the destination in addition to the travel distance, which conforms to the travel demands of EV drivers. Moreover, simulation examples are presented to demonstrate the proposed algorithm. Results of the proposed algorithm are compared with those of the other two algorithms, which show that the proposed algorithm can obtain a better selection of charging stations for EV drivers from the perspective of entire travel chains and take a shorter computational time.     

Optimization of incentive polices for plug-in electric vehicles

High purchase prices and the lack of supporting infrastructure are major hurdles to the adoption of plug-in electric vehicles (PEVs). It is widely recognized that the government could help break these barriers through incentive policies, such as offering rebates to PEV buyers or funding charging stations. The objective of this paper is to propose a modeling framework that can optimize the design of such incentive policies. The proposed model characterizes the impact of the incentives on the dynamic evolution of PEV market penetration over a discrete set of time intervals, by integrating a simplified consumer vehicle choice model and a macroscopic travel and charging model. The optimization problem is formulated as a nonlinear and non-convex mathematical program and solved by a specialized steepest descent direction algorithm. We show that, under mild regularity conditions, the KKT conditions of the proposed model are necessary for local optimum. Results of numerical experiments indicate that the proposed algorithm is able to obtain satisfactory local optimal policies quickly. These optimal policies consistently outperform the alternative policies that mimic the state-of-the-practice by a large margin, in terms of both the total savings in social costs and the market share of PEVs. Importantly, the optimal policy always sets the investment priority on building charging stations. In contrast, providing purchase rebates, which is widely used in current practice, is found to be less effective.     

Analysis of the effect of charging needs on battery electric vehicle drivers’ route choice behaviour: A case study in the Netherlands

Electric travelling appears to dominate the transport sector in the near future due to the needed transition from internal combustion vehicles (ICV) towards Electric Vehicles (EV) to tackle urban pollution. Given this trend, investigation of the EV drivers’ travel behaviour is of great importance to stakeholders including planners and policymakers, for example in order to locate charging stations. This research explores the Battery Electric Vehicle (BEV) drivers route choice and charging preferences through a Stated Preference (SP) survey. Collecting data from 505 EV drivers in the Netherlands, we report the results of estimating a Mixed Logit (ML) model for those choices. Respondents were requested to choose a route among six alternatives: freeways, arterial ways, and local streets with and without fast charging. Our findings suggest that the classic route attributes (travel time and travel cost), vehicle-related variables (state-of-charge at the origin and destination) and charging characteristics (availability of a slow charging point at the destination, fast charging duration, waiting time in the queue of a fast-charging station) can influence the BEV drivers route choice and charging behaviour significantly. When the state-of-charge (SOC) at the origin is high and a slow charger at the destination is available, routes without fast charging are likely to be preferred. Moreover, local streets (associated with slow speeds and less energy consumption) could be preferred if the SOC at the destination is expected to be low while arterial ways might be selected when a driver must recharge his/her car during the trip via fast charging.