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.     

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.     

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.     

Siting charging stations for electric vehicle adoption in shared autonomous fleets

The transportation sector is undergoing three revolutions: shared mobility, autonomous driving, and electrification. When planning the charging infrastructure for electric vehicles, it is critical to consider the potential interactions and synergies among these three emerging systems. This study proposes a framework to optimize charging infrastructure development for increasing electric vehicle (EV) adoption in systems with different levels of autonomous vehicle adoption and ride sharing participation. The proposed model also accounts for the pre-existing charging infrastructure, vehicle queuing at the charging stations, and the trade-offs between building new charging stations and expanding existing ones with more charging ports.Using New York City (NYC) taxis as a case study, we evaluated the optimum charging station configurations for three EV adoption pathways. The pathways include EV adoption in a 1) traditional fleet (non-autonomous vehicles without ride sharing), 2) future fleet (fully autonomous vehicles with ride sharing), and 3) switch-over from traditional to future fleet. Our results show that, EV adoption in a traditional fleet requires charging infrastructure with fewer stations that each has more charging ports, compared to the future fleet which benefits from having more scattered charging stations. Charging will only reduce the service level by 2% for a future fleet with 100% EV adoption. EV adoption can reduce CO₂ emissions of NYC taxis by up to 861 Tones/day for the future fleet and 1100 Tones/day for the traditional fleet.     

Dynamic operations and pricing of electric unmanned aerial vehicle systems and power networks

The emergence of electric unmanned aerial vehicle (E-UAV) technologies, albeit somewhat futuristic, is anticipated to pose similar challenges to the system operation as those of electric vehicles (EVs). Notably, the charging of EVs en-route at charging stations has been recognized as a significant type of flexible load for power systems, which often imposes non-negligible impacts on the power system operator’s decisions on electricity prices. Meanwhile, the charging cost based on charging time and price is part of the trip cost for the users, which can affect the spatio-temporal assignment of E-UAV traffic to charging stations. This paper aims at investigating joint operations of coupled power and electric aviation transportation systems that are associated with en-route charging of E-UAVs in a centrally controlled and yet dynamic setting, i.e., with time-varying travel demand and power system base load. Dynamic E-UAV charging assignment is used as a tool to smooth the power system load. A joint pricing scheme is proposed and a cost minimization problem is formulated to achieve system optimality for such coupled systems. Numerical experiments are performed to test the proposed pricing scheme and demonstrate the benefits of the framework for joint operations.     

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.     

Design framework of large-scale one-way electric vehicle sharing systems: A continuum approximation model

This paper proposes a Continuum Approximation (CA) model for design of a one-way Electrical Vehicle (EV) sharing system that serves a metropolitan area. This model determines the optimal EV sharing station locations and the corresponding EV fleet sizes to minimize the comprehensive system cost, including station construction investment, vehicle charging, transportation and vehicle balancing, under stochastic and dynamic trip demands. This is a very complex problem due to the NP-hard nature of location design, the large number of individual users, and the stochasticity and dynamics of generated trips. Further, the considerable charging time required by EVs distinguishes this problem from traditional car sharing problems where a vehicle is immediately available for pickup after being dropped at a station. We find that the CA approach can overcome these modeling challenges by decomposing the studied area into a number of small neighborhoods that each can be approximated by an Infinite Homogeneous Plane (IHP). We find that the system cost of an IHP is a unimodal function of the station service area size and can be efficiently solved in a sub-linear time by the bisection algorithm. Then integrating the solutions of all IHPs yields an approximate solution to the original heterogeneous area. With numerical experiments, we show that the CA solution is able to estimate the total system cost of the discrete counterpart solution efficiently with good accuracy, even for large-scale heterogeneous problems. This implies that the proposed CA approach is capable of providing a near-optimum solution to the comprehensive design of a practical large-scale EV sharing system. With this model, we also conduct sensitivity analysis to reveal insights into how cost components and system design vary with key parameter values. As far as the author’s knowledge, this study is the first work that addresses design of an EV sharing system considering both longer-term location and fleet size planning and daily vehicle operations. The proposed CA model also extends the CA methodology literature from traditional location problems with stationary demand, single-facility based service to EV sharing problems considering dynamic demands, OD trips, and nonlinear vehicle charging times.     

Optimal design of electric vehicle public charging system in an urban network for Greenhouse Gas Emission and cost minimization

In this paper, we address the optimization problem of allocation of Electric Vehicle (EV) public fast charging stations over an urban grid network. The objective is to minimize Greenhouse Gas Emissions (GHG) under multiple constraints including a limited agency budget, accessibility of charging stations in every possible charging request and charging demands during peak hours. Additionally, we address bi-criteria problems to consider user costs as the second objective. A convex parsimonious model that depends on relatively few assumptions and input parameters is proposed and it is shown to be useful for obtaining conceptual insights for high-level planning. In a parametric study using a hypothetical urban network model generated based on realistic parameters, we show that GHG emissions decrease with agency budget, and that the reductions vary depending on multiple factors related to EV market and EV technologies. The optimal solutions found from the bi-criteria problems are shown to be close to the solution minimizing GHG emissions only, meaning that the emission minimizing policy can also minimize user costs.     

Forecasting electricity demand of electric vehicles by analyzing consumers’ charging patterns

The spread of electric vehicles (EVs) and their increasing demand for electricity has placed a greater burden on electricity generation and the power grid. In particular, the problem of whether to expand the electricity power stations and distribution facilities due to the construction of EV charging stations is emerging as an immediate issue. To effectively meet the demand for additional electricity while ensuring the stability of the power grid, there is a need to accurately predict the charging demands for EVs. Therefore, this study estimates the changes in electricity charging demand based on consumer preferences for EVs, charging time of day, and types of electric vehicle supply equipment (EVSE) and elucidates the matters to be considered for constructing EV infrastructure. The results show that consumers mainly preferred charging during the evening. However, when we considered different types of EVSEs (public and private) in the analysis, people preferred to charge at public EVSEs during the day. During peak load time, people tended to prefer charging using fast public EVSEs, which shows that consumers considered the tradeoffs between the full charge time and the price for charging. Based on these findings, this study provides key political implications for policy makers to consider in taking preemptive measures to adjust the electricity supply infrastructure.     

Electric vehicle charging station locations: Elastic demand,station congestion,and network equilibrium

Battery-only electric vehicles (BEVs) generally offer better air quality through lowered emissions, along with energy savings and security. The issue of long-duration battery charging makes charging-station placement and design key for BEV adoption rates. This work uses genetic algorithms to identify profit-maximizing station placement and design details, with applications that reflect the costs of installing, operating, and maintaining service equipment, including land acquisition. Fast electric vehicle charging stations (EVCSs) are placed across a congested city's network subject to stochastic demand for charging under a user-equilibrium traffic assignment. BEV users’ station choices consider endogenously determined travel times and on-site charging queues. The model allows for congested-travel and congested-station feedback into travelers’ route choices under elastic demand and BEV owners’ station choices, as well as charging price elasticity for BEV charging users.Boston-network results suggest that EVCSs should locate mostly along major highways, which may be a common finding for other metro settings. If 10% of current EV owners seek to charge en route, a user fee of $6 for a 30-min charging session is not enough for station profitability under a 5-year time horizon in this region. However, $10 per BEV charging delivers a 5-year profit of $0.82 million, and 11 cords across 3 stations are enough to accommodate a near-term charging demand in this Boston-area application. Shorter charging sessions, higher fees, and/or allowing for more cords per site also increase profits generally, everything else constant. Power-grid and station upgrades should keep pace with demand, to maximize profits over time, and avoid on-site congestion.     

Incorporating institutional and spatial factors in the selection of the optimal locations of public electric vehicle charging facilities: A case study of Beijing,China

In this paper, we present a case study on planning the locations of public electric vehicle (EV) charging stations in Beijing, China. Our objectives are to incorporate the local constraints of supply and demand on public EV charging stations into facility location models and to compare the optimal locations from three different location models. On the supply side, we analyse the institutional and spatial constraints in public charging infrastructure construction to select the potential sites. On the demand side, interviews with stakeholders are conducted and the ranking-type Delphi method is used when estimating the EV demand with aggregate data from municipal statistical yearbooks and the national census. With the estimated EV demand, we compare three classic facility location models – the set covering model, the maximal covering location model, and the p-median model – and we aim to provide policy-makers with a comprehensive analysis to better understand the effectiveness of these traditional models for locating EV charging facilities. Our results show that the p-median solutions are more effective than the other two models in the sense that the charging stations are closer to the communities with higher EV demand, and, therefore, the majority of EV users have more convenient access to the charging facilities. From the experiments of comparing only the p-median and the maximal covering location models, our results suggest that (1) the p-median model outperforms the maximal covering location model in terms of satisfying the other’s objective, and (2) when the number of charging stations to be built is large, or when minor change is required, the solutions to both models are more stable as p increases.     

Energy impact evaluation for eco-routing and charging of autonomous electric vehicle fleet: Ambient temperature consideration

This paper studies the heterogeneous energy cost and charging demand impact of autonomous electric vehicle (EV) fleet under different ambient temperature. A data-driven method is introduced to formulate a two-dimensional grid stochastic energy consumption model for electric vehicles. The energy consumption model aids in analyzing EV energy cost and describing uncertainties under variable average vehicle trip speed and ambient temperature conditions. An integrated eco-routing and optimal charging decision making framework is designed to improve the capability of autonomous EV’s trip level energy management in a shared fleet. The decision making process helps to find minimum energy cost routes with consideration of charging strategies and travel time requirements. By taking advantage of derived models and technologies, comprehensive case studies are performed on a data-driven simulated transportation network in New York City. Detailed results show us the heterogeneous energy impact and charging demand under different ambient temperature. By giving the same travel demand and charging station information, under the low and high ambient temperature within each month, there exist more than 20% difference of overall energy cost and 60% difference of charging demand. All studies will help to construct sustainable infrastructure for autonomous EV fleet trip level energy management in real world applications.     

The design of electric vehicle charging network

The promotion of Electric Vehicles (EVs) has become a key measure of the governments in their attempt to reduce greenhouse gas emissions. However, range anxiety is a big barrier for drivers to choose EVs over traditional vehicles. Installing more charging stations in appropriate locations can relieve EV drivers’ range anxiety. To determine the locations of public charging stations, we propose two optimization models for two different charging modes - fast and slow charging, which aim at minimizing the total cost while satisfying certain coverage goal. Instead of using discrete points, we use geometric objects to represent charging demands. Importantly, to resolve the partial coverage problem (PCP) for networks, we extend the polygon overlay method to split the demands on the road network. After applying the models to Greater Toronto and Hamilton Area (GTHA) and to Downtown Toronto, we show that the proposed models are practical and effective in determining the locations of charging stations. Moreover, they can eliminate PCP and provide much more accurate results than the complementary partial coverage method (CP).     

A corridor-centric approach to planning electric vehicle charging infrastructure

The transition to electric vehicles (EV) faces two major barriers. On one hand, EV batteries are still expensive and limited by range, owing to the lack of technology breakthrough. On the other hand, the underdeveloped supporting infrastructure, particularly the lack of fast refueling facilities, makes EVs unsuitable for medium and long distance travel. The primary purpose of this study is to better understand these hurdles and to develop strategies to overcome them. To this end, a conceptual optimization model is proposed to analyze travel by EVs along a long corridor. The objective of the model is to select the battery size and charging capacity (in terms of both the charging power at each station and the number of stations needed along the corridor) to meet a given level of service in such a way that the total social cost is minimized. Two extensions of the base model are also considered. The first relaxes the assumption that the charging power at the stations is a continuous variable. The second variant considers battery swapping as an alternative to charging. Our analysis suggests that (1) the current paradigm of charging facility development that focuses on level 2 charging delivers poor level of service for long distance travel; (2) the level 3 charging method is necessary not only to achieve a reasonable level of service, but also to minimize the social cost; (3) investing on battery technology to reduce battery cost is likely to have larger impacts on reducing the charging cost; and (4) battery swapping promises high level of service, but it may not be socially optimal for a modest level of service, especially when the costs of constructing swapping and charging stations are close.     

Model and a solution algorithm for the dynamic resource allocation problem for large-scale transportation network evacuation

Allocating movable resources dynamically enables evacuation management agencies to improve evacuation system performance in both the spatial and temporal dimensions. This study proposes a mixed integer linear program (MILP) model to address the dynamic resource allocation problem for transportation evacuation planning on large-scale networks. The proposed model is built on the earliest arrival flow formulation that significantly reduces problem size. A set of binary variables, specifically, the beginning and the ending time of resource allocation at a location, enable a strong formulation with tight constraints. A solution algorithm is developed to solve for an optimal solution on large-scale network applications by adopting Benders decomposition. In this algorithm, the MILP model is decomposed into two sub-problems. The first sub-problem, called the restricted master problem, identifies a feasible dynamic resource allocation plan. The second sub-problem, called the auxiliary problem, models dynamic traffic assignment in the evacuation network given a resource allocation plan. A numerical study is performed on the Dallas–Fort Worth network. The results show that the Benders decomposition algorithm can solve an optimal solution efficiently on a large-scale network.     

Determining the optimal electric vehicle DC-charging infrastructure for Western Australia

Take-up rates of electric vehicles (EV) are increasing and are predicted to accelerate rapidly. Public EV charging networks will be required to support future EV fleets. If unplanned, public charging networks are highly likely to be suboptimal. Planners need to understand and plan for future EV charging infrastructure requirements, particularly public DC fast charging networks, as both the upfront investment costs and the consequences of misallocation are high. However, the task of determining the optimal locations and allocations (types and numbers) of public EV charging infrastructure is complicated as it requires knowledge of many variables. These include EV driver behaviors, driving patterns, predicting evolutionary changes in EV and EV charging technologies, future EV take-up rates, and what investment may or may not occur in the absence of government funding support.     

Market dynamics and indirect network effects in electric vehicle diffusion

The diffusion of electric vehicles (EVs) is studied in a two-sided market framework consisting of EVs on the one side and EV charging stations (EVCSs) on the other. A sequential game is introduced as a model for the interactions between an EVCS investor and EV consumers. A consumer chooses to purchase an EV or a conventional gasoline alternative based on the upfront costs of purchase, the future operating costs, and the availability of charging stations. The investor, on the other hand, maximizes his profit by deciding whether to build charging facilities at a set of potential EVCS sites or to defer his investments.The solution of the sequential game characterizes the EV-EVCS market equilibrium. The market solution is compared with that of a social planner who invests in EVCSs with the goal of maximizing the social welfare. It is shown that the market solution underinvests EVCSs, leading to slower EV diffusion. The effects of subsidies for EV purchase and EVCSs are also considered.     

Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations

Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). This paper first proposes a new time-discretized multi-commodity network flow model for the VRPPDTW based on the integration of vehicles’ carrying states within space–time transportation networks, so as to allow a joint optimization of passenger-to-vehicle assignment and turn-by-turn routing in congested transportation networks. Our three-dimensional state–space–time network construct is able to comprehensively enumerate possible transportation states at any given time along vehicle space–time paths, and further allows a forward dynamic programming solution algorithm to solve the single vehicle VRPPDTW problem. By utilizing a Lagrangian relaxation approach, the primal multi-vehicle routing problem is decomposed to a sequence of single vehicle routing sub-problems, with Lagrangian multipliers for individual passengers’ requests being updated by sub-gradient-based algorithms. We further discuss a number of search space reduction strategies and test our algorithms, implemented through a specialized program in C++, on medium-scale and large-scale transportation networks, namely the Chicago sketch and Phoenix regional networks.     

Infrastructure planning for fast charging stations in a competitive market

Most existing studies on EV charging infrastructure planning take a central planner’s perspective, by assuming that investment decision on charging facilities can be controlled by a single decision entity. In this paper, we establish modeling and computational methods to support business-driven EV charging infrastructure investment planning problem, where the infrastructure system is shaped by collective actions of multiple decision entities who do not necessarily coordinate with each other. A network-based multi-agent optimization modeling framework is developed to simultaneously capture the selfish behaviors of individual investors and travelers and their interactions over a network structure. To overcome computational difficulty imposed by non-convexity of the problem, we rely on recent theoretical development on variational convergence of bivariate functions to design a solution algorithm with analysis on its convergence properties. Numerical experiments are implemented to study the performance of proposed method and draw practical insights.     

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.