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.     

Anticipating plug-in hybrid vehicle energy impacts in California: Constructing consumer-informed recharge profiles

Plug-in hybrid electric vehicles (PHEVs) can be powered by gasoline, grid electricity, or both. To explore potential PHEV energy impacts, a three-part survey instrument collected data from new vehicle buyers in California. We combine the available information to estimate the electricity and gasoline use under three recharging scenarios. Results suggest that the use of PHEV vehicles could halve gasoline use relative to conventional vehicles. Using three scenarios to represent plausible conditions on PHEV drivers’ recharge patterns (immediate and unconstrained, universal workplace access, and off-peak only), tradeoffs are described between the magnitude and timing of PHEV electricity use. PHEV electricity use could be increased through policies supporting non-home recharge opportunities, but this increase occurs during daytime hours and could contribute to peak electricity demand. Deferring all recharging to off-peak hours could eliminate all additions to daytime electricity demand from PHEVs, although less electricity is used and less gasoline displaced.     

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.     

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.     

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.     

A range-restricted recharging station coverage model for drone delivery service planning

Unmanned Aerial Vehicles (UAVs) are attracting significant interest for delivery service of small packages in urban areas. The limited flight range of electric drones powered by batteries or fuel cells requires refueling or recharging stations for extending coverage to a wider area. To develop such service, optimization methods are needed for designing a network of station locations and delivery routes. Unlike ground-transportation modes, however, UAVs do not follow a fixed network but rather can fly directly through continuous space. But, paths must avoid barriers and other obstacles. In this paper, we propose a new location model to support spatially configuring a system of recharging stations for commercial drone delivery service, drawing on literature from planar-space routing, range-restricted flow-refueling location, and maximal coverage location. We present a mixed-integer programming formulation and an efficient heuristic algorithm, along with results for a large case study of Phoenix, AZ to demonstrate the effectiveness and efficiency of the model.     

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.     

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.     

Site selection for EVCS in Istanbul by GIS and multi-criteria decision-making

Considering the depletion of fossil fuels and the environmental impact of transport, reducing the use of such fuels is a globally accepted priority. Thus, when moving towards alternative energy types, the first will undoubtedly be electrical energy. In order to accelerate and contribute to this process, electric vehicles (EV) must be preferred over conventional motor vehicles. However, there are various problems associated with the use of EVs, such as range and recharge status. Optimal planning of electric vehicle charging stations (EVCS) is a solution to these problems. For this purpose, parameters affecting EVCS locations have been determined in the paper. Considering these parameters and the current EVCS locations, the most suitable alternative EVCS locations were identified using Geographical Information Systems (GIS). Both the current and alternative EVCS locations were evaluated by Analytic Hierarchy Process (AHP), Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE), and VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) from multi-criteria decision-making (MCDM) methods. The results show that, in Istanbul, the southeast of the European side and the southwest of the Anatolian side were most suitable for EVCS.     

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.     

Adapting interactive stated response techniques to a self-completion survey

We report here on how we adapted Interactive Stated Response Methods to use in a self-completion survey of 454 California households to measure the market for electric vehicles in California. Electric vehicles are a novel product and have many features unfamiliar to consumers, in particular their home recharging capability and limited range. Reflexive techniques were designed to draw households into a deeper exploration of the lifestyle implications of electric vehicles than can be done in more typical self-completion surveys, and to stimulate key decision processes previously observed in detailed gaming interviews with 51 households. Reflexive self-completion techniques provide a middle course between typical large sample quantitative surveys and small sample, detailed gaming interviews. One of the benefits of the more intensive techniques was that participants reported finding the surveys interesting and return rates were high for a self-completion approach – over sixty percent. We review previous transportation and sociological methods which inspired our design, describe the design goals and features of our research, and summarize research results pertinent to testing the validity of our approach.     

Stakeholders interests,expectations, and strategies regarding the development and implementation of electric vehicles: The case of the Netherlands

In this paper, we study the strategies of the most relevant stakeholders with regard to the development and commercialization of electric vehicles (EVs) and their recharging infrastructure. Building on the perspective of socio-technical transitions, we relate the strategies of stakeholders to their current and future interests, as well as to their expectations with regard to EVs. Our analysis is based on a series of 38 semi-structured interviews with representatives of a variety of stakeholders in the Netherlands.EVs pose both opportunities and threats to various stakeholders. They therefore participate in the development of the emerging EV system, primarily in order to learn about the potential positive and negative impacts of these systems on their interests and, ultimately, to be able to grasp the opportunities and mitigate the threats. In other words, the expectations, interests, and resulting strategies of stakeholders relate to and depend upon the specific configuration of the emerging socio-technical system for electric mobility. We identify six potential conflicts of interest: the division of tasks within a public recharging infrastructure; the allocation of charging spots; the ways in which charging behavior can be influenced; the role of fast-charging, technical standards for charging equipment; and supportive policies for full-electric and plug-in hybrid vehicles.In general, the stakeholders do not seem overly concerned about either short-term returns on investments or long-term negative impacts. In this regard, the early phase of the transition can be understood as a relatively carefree phase. In order to continue the development of the emerging EV system and to keep it on the right track, however, for the foreseeable future, supportive policies will be necessary in order to provide a stable and reliable basis for further market expansion.     

Charging infrastructure demands of shared-use autonomous electric vehicles in urban areas

Ride-hailing is a clear initial market for autonomous electric vehicles (AEVs) because it features high vehicle utilization levels and strong incentive to cut down labor costs. An extensive and reliable network of recharging infrastructure is the prerequisite to launch a lucrative AEV ride-hailing fleet. Hence, it is necessary to estimate the charging infrastructure demands for an AEV fleet in advance. This study proposes a charging system planning framework for a shared-use AEV fleet providing ride-hailing services in urban area. We first adopt an agent-based simulation model, called BEAM, to describe the complex behaviors of both passengers and transportation systems in urban cities. BEAM simulates the driving, parking and charging behaviors of the AEV fleet with range constraints and identifies times and locations of their charging demands. Then, based on BEAM simulation outputs, we adopt a hybrid algorithm to site and size charging stations to satisfy the charging demands subject to quality of service requirements. Based on the proposed framework, we estimate the charging infrastructure demands and calculate the corresponding economics and carbon emission impacts of electrifying a ride-hailing AEV fleet in the San Francisco Bay Area. We also investigate the impacts of various AEV and charging system parameters, e.g., fleet size, vehicle battery capacity and rated power of chargers, on the ride-hailing system’s overall costs.     

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.     

Fast-charging station choice behavior among battery electric vehicle users

This study explores how battery electric vehicle users choose where to fast-charge their vehicles from a set of charging stations, as well as the distance by which they are generally willing to detour for fast-charging. The focus is on fast-charging events during trips that include just one fast-charge between origin and destination in Kanagawa Prefecture, Japan. Mixed logit models with and without a threshold effect for detour distance are applied to panel data extracted from a two-year field trial on battery electric vehicle usage in Japan. Findings from the mixed logit model with threshold show that private users are generally willing to detour up to about 1750 m on working days and 750 m on non-working days, while the distance is 500 m for commercial users on both working and non-working days. Users in general prefer to charge at stations requiring a shorter detour and use chargers located at gas stations, and are significantly affected by the remaining charge. Commercial users prefer to charge at stations encountered earlier along their paths, while only private users traveling on working days show such preference and they turn to prefer the stations encountered later when choosing a station in peak hours. Only private users traveling on working days show a strong preference for free charging. Commercial users tend to pay for charging at a station within 500 m detour distance. The fast charging station choice behavior is heterogeneous among users. These findings provide a basis for early planning of a public fast charging infrastructure.     

Determining locations of charging stations for electric taxis using taxi operation data

The adequate provision of charging infrastructure is critical for the effective deployment of electric taxis. This study attempts to locate charging stations for electric taxis reflecting real-world taxi travel patterns identified from taxis equipped with digital tachographs. Data for one week are processed in order to estimate their charge demand. The estimated temporal distribution of charge demand indicates that it varies day-by-day and hour-by-hour. The maximum set covering model is applied for determining the locations of charging stations. The results show that the pre-specified service distance and service coverage rate (defined by the proportion of total demand served) can be critical factors for determining the number and location of charging stations. These factors should be carefully specified by considering the tradeoff between operational efficiency of charging facilities and user convenience.     

Joint deployment of charging stations and photovoltaic power plants for electric vehicles

The focus of this study is to jointly design charging stations and photovoltaic (PV) power plants with time-dependent charging fee, to improve the management of the coupled transportation and power systems. We first propose an efficient and extended label-setting algorithm to solve the EV joint routing and charging problem that considers recharging amount choices at different stations and loop movement cases. Then, a variational inequality problem is formulated to model the equilibrium of EV traffic on transportation networks, and an optimal power flow model is proposed to model the power network flow with PV power plants and optimally serve the EV charging requirements. Based on the above models for describing system states, we then formulate a model to simultaneously design charging stations, PV plants, and time-dependent charging fee. A surrogate-based optimization (SBO) algorithm is adopted to solve the model. Numerical examples demonstrate that the proposed SBO algorithm performs well. Additionally, important insights concerning the infrastructure design and price management of the coupled transportation and power networks are derived accordingly.     

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.