Flow Refueling Location Model Research Articles

Effect of uncertainties on siting and sizing of charging stations and renewable energy resources: A modified capacitated flow-refueling location model

Fast-charging stations (FCSs) are critical charging infrastructures for electric vehicles (EVs) that can impose a significant load demand on the distribution network. Therefore, one of the original challenges in the development of EVs is the optimal allocation of FCSs considering the goals and limitations of both transportation and distribution networks. This paper proposes a model for locating FCSs and renewable energy resources (RESs) taking into account the EVs behavior as well as a wide range of affecting factors, including the uncertainty associated with the RESs, EVs arrival rate, and state of charge (SoC), different driving ranges, and all-shortest and deviation paths. The proposed model minimizes the costs of installing FCSs and RESs and substation expansion and maximizes the traffic flow captured by the FCSs. For this purpose, first, the modeling of the uncertainties of RESs and the capacitated diversion flow-refueling location model based on expanded networks (CDFRLM-EN) is introduced to cover the charging demand of EVs on the transportation network. Then the problem of locating FCSs and RESs is formulated based on the mixed-integer linear programming (MILP) model. The proposed framework is implemented on a 14-bus distribution test system coupled with a 25-node transportation network. The results show that the presence of RESs, diversion paths, and the uncertainty associated with the arrival state of charge and the driving range differences influence the location and size of FCSs, the investment cost, and the EVs’ satisfaction.

Planning of Hydrogen Refueling Stations in Urban Setting While Considering Hydrogen Redistribution

Electrified transportation systems and renewable energy resources have been recognized as effective environmental-friendly technologies against global warming contributed by greenhouse gas (GHG). Remarkably, hydrogen fuel cell-powered electric vehicles can outperform battery-powered electric vehicles largely in the sense of the driving range and the refueling time. However, both of them require a better coordination of infrastructure system and renewable energy resources to achieve a significant reduction of GHG emissions. This article aims to maximize the long-term profitability for the planning model of hydrogen refueling stations, where the capacitated flow refueling location model is leveraged for maximal traffic flow coverage. Furthermore, we discuss various real-world constraints, such as traffic network constraints, distribution network constraints, hydrogen balance constraints, and energy constraints for electric vehicles, to make the planning model more practical. By considering the uncertainty of the short-term refueling demand across the city, an approach for geographically redistributing hydrogen among the stations is also presented where the minimal cost of redistribution is modeled by one-commodity pickup-and-delivery traveling salesman problem. A real-life case study of Western Sydney is adopted to testify the efficiency of the planning model under current and future cost levels. Finally, a numerical simulation is utilized to demonstrate the validity of the hydrogen redistribution method.

Electric Vehicle Charging Facility Planning Based on Flow Demand—A Case Study

The location of electric vehicle charging facilities is of great significance in promoting the use of electric vehicles. Most existing electric vehicle location models, including the flow refueling location model (FRLM) and its flexible reformulation (FRFRLM), are based on flow demand. At present, these models cannot effectively deal with large-scale traffic networks within a limited time, and there has been little comparison of their relative benefits and limitations. Additionally, there have been few evaluations of the actual construction and location of charging facilities in cities. This paper describes an algorithm that can solve the large-scale transportation network problem within a reasonable time. Using this algorithm, the FRLM and FRFRLM models are compared in a case study focused on Jiading District, Shanghai, China, which provides some direction for the future development of flow demand models. Finally, to evaluate the actual construction of urban charging facilities, this paper presents an algorithm that can map the actual charging facilities to the transportation network, and compares the actual construction situation with the model output. This enables a comprehensive evaluation of the actual construction of charging facilities and provides guidance for future construction.

Allocation of RESs and PEV Fast-Charging Station on Coupled Transportation and Distribution Networks

Utilization of plug-in electric vehicles (PEVs) in the world is increasing, causing researchers to pay more attention to issues related to PEV fast-charging stations (FCSs). Since PEV FCSs are used simultaneously by a large number of PEVs, they can cause negative effects on electrical networks, including increased losses and voltage deviations. Therefore, optimal siting and sizing of these stations to decrease their negative effects on electrical networks is one of the main challenges in the extensive use of PEVs. In this paper, optimal location and capacity of FCSs and renewable energy sources (RES) are simultaneously determined, while deviation paths and uncertainties of RESs are considered. For this purpose, first a capacitated deviation flow refueling location model (CDFRLM) is proposed to cover the charging demand for PEVs on the transport network. Then, the desired problem is modeled based on the mixed-integer linear programming (MILP), which can be solved using commercially available softwares. The proposed model is implemented on 14-bus and 33-bus distribution test systems which are coupled with a 25-node transportation network. The results show that considering the volatile RES and deviation paths in the problem will affect the location and capacity of charging stations, investment costs, and coverage rates of vehicles charging.

Locating electric vehicle charging stations under uncertain battery energy status and power consumption

Fostering the adoption of electric vehicles (EVs) by private drivers requires the development of a wide network of fast charging stations in which drivers traveling long-distance trips will be able to easily recharge their battery within a few minutes. However, due to their high installation costs, the number of stations that can actually be deployed with the available investment budget is strongly limited. It is thus necessary to carefully choose their location so that the charging demand satisfaction is maximized. This leads to the formulation of a facility location problem known as the flow refueling location problem (FRLP). In this paper, we study the FRLP and seek to take into account uncertainties on the vehicle driving range in the problem modeling. We propose to relax several modeling assumptions previously used in the literature to handle this problem. First, we allow the power consumption on a road segment to depend on the crossing direction. Second, we take into account uncertainties related to the energy available in the battery after recharging at a station as well as uncertainties related to the power consumption on each portion of the road network. Finally, we consider statistical dependencies between the stochastic power consumption on different arcs of the network.We focus on the chance-constrained flow refueling location model, which seeks to maximize the number of drivers for whom the probability of running out of fuel when carrying out their trip is below a certain threshold. To solve the resulting stochastic optimization problem, we propose to use a solution approach based on a partial sample approximation of the stochastic parameters and compare its performance with the one of a previously published approach based on Bonferroni’s inequality. We carry out numerical experiments on a set of medium-size randomly generated and real life instances. Our results show that the proposed partial sample approximation approach outperforms the Bonferroni approach in terms of solution quality and gives station locations which provide a significantly improved demand coverage in practice.

Planning PEV Fast-Charging Stations Using Data-Driven Distributionally Robust Optimization Approach Based on ϕ-Divergence

Plug-in electric vehicles are widely acknowledged as an effective tool for numerous environmental and economic concerns. In this article, a novel model for the planning of fast-charging stations is established based on a data-driven distributionally robust optimization approach, which aims to minimize the expected planning cost for both transportation network and distribution network. φ-divergence, a statistical measure, is utilized to establish the serviceability constraints. On the other hand, a modified capacitated flow refueling location model is employed to develop the location constraints. In addition, ac power flow constraints are developed to model the operation of DN with the penetrations of PEVs. Finally, a case study is illustrated to validate the proposed planning model.

Robust chance-constrained programming approach for the planning of fast-charging stations in electrified transportation networks

In this paper, a bi-level programming model is established to address the planning issues of fast-charging stations in electrified transportation networks with the consideration of uncertain charging demands. The capacitated flow refueling location model is considered in the upper level to minimize the planning cost of fast-charging stations while the traffic assignment model is utilized in the lower level to determine the spatial and temporal distribution of plug-in electric vehicle flows over entire transportation networks. Such bi-level model unveils the inherent relationship among charging demands, electrical demands and the spatial and temporal distribution of plug-in electric vehicle flows. Robust chance constraints are formulated to characterize the service abilities of fast-charging stations under distribution-free uncertain charging demands, where the ambiguity set is constructed to estimate the potential values of the uncertainties based on their moment-based information, such that the robust chance constraints can exactly be reduced to mixed integer linear constraints. By introducing new variables, the bi-level model is then reformulated into a single-level mixed integer second-order cone programming model so as to be solved via off-the-shelf solvers, which guarantee the optimality of the solution. A case study is conducted to illustrate the effectiveness of the proposed planning model, which reveals three critical factors that significantly impact the planning outcomes.

Location Optimization of Electric Vehicle Mobile Charging Stations Considering Multi-Period Stochastic User Equilibrium

This study researches the dynamical location optimization problem of a mobile charging station (MCS) powered by a LiFePO 4 battery to meet charging demand of electric vehicles (EVs). In city suburbs, a large public charging tower is deployed to provide recharging services for MCS. The EV’s driver can reserve a real-time off-street charging service on the MCS through a vehicular communication network. This study formulates a multi-period nonlinear flow-refueling location model (MNFRLM) to optimize the location of the MCS based on a network designed by Nguyen and Dupuis (1984). The study transforms the MNFRLM model into a linear integer programming model using a linearization algorithm, and obtains global solution via the NEOS cloud CPLEX solver. Numerical experiments are presented to demonstrate the model and its solution algorithm.

A multi-scale framework for fuel station location: From highways to street intersections

Electric drive vehicles (plug-in electric vehicle or hydrogen fuel cell vehicles) have been promoted by governments to foster a more sustainable transportation future. Wider adoption of these vehicles, however, depends on the availability of a convenient and reliable refueling/recharging infrastructure. This paper introduces a path-based, multi-scale, scenario-planning modeling framework for locating a system of alternative-fuel stations. The approach builds on (1) the Flow Refueling Location Model (FRLM), which assumes that drivers stop along their origin-destination routes to refuel, and checks explicitly whether round trips can be completed without running out of fuel, and (2) the Freeway Traffic Capture Method (FTCM), which assesses the degree to which drivers can conveniently reach sites on the local street network near freeway intersections. This paper extends the FTCM to handle cases involving clusters of nearby freeway intersections, which is a limitation of its previous specification. Then, the cluster-based FTCM (CFTCM) is integrated with the FRLM and the DFRLM (FRLM with Deviations) to better conduct detailed geographic optimization of this multi-scale location planning problem. The main contribution of this research is the introduction of a framework that combines multi-scale planning methods to more effectively inform the early development stage of hydrogen refueling infrastructure planning. The proposed multi-scale modeling framework is applied to the Hartford, Connecticut region, which is one of the next areas targeted for fuel-cell vehicle (FCV) market and infrastructure expansion in the United States. This method is generalizable to other regions or other types of fast-fueling alternative fuel vehicles.

How many fast-charging stations do we need along European highways?

For a successful market take-up of plug-in electric vehicles, fast-charging stations along the highway network play a significant role. This paper provides results from a first study on estimating the minimum number of fast-charging stations along the European highway network of selected countries (i.e., France, Germany, the Benelux countries, Switzerland, Austria, Denmark, the Czech Republic, and Poland) and gives an estimate on their future profitability. The combination of a comprehensive dataset of passenger car trips in Europe and an efficient arc-cover-path-cover flow-refueling location model allows generating results for such a comprehensive transnational highway network for the first time. Besides the minimum number of required fast-charging stations which results from the applied flow-refueling location model (FRLM), an estimation of their profitability as well as some country-specific results are also identified. According to these results the operation of fast-charging stations along the highway will be attractive in 2030 because the number of customers per day and their willingness to pay for a charge is high compared to inner-city charging stations. Their location-specific workloads as well as revenues differ significantly and a careful selection of locations is decisive for their economic operation.

The Location of Electric Vehicle Charging Stations based on FRLM with Robust Optimization

It is very important for the application of artificial intelligence to accurately and quickly help the electric vehicles to find matching charging facilities. The site selection for electric vehicle charging station (EVCS) is a new field of artificial intelligence application, using artificial intelligence to analyze the current complex urban electric vehicle driving path, and then determining the location of charging stations. This paper proposes a novel hybrid model to decide the location of EVCS. First of all, this paper carries out the flow-refueling location model (FRLM) based on path requirement to determine the site selection of EVCS. Secondly, robust optimization algorithm is used to resolve the location model considering the uncertainty of charging demand. Then, queuing theory, which takes the charging load as a constraint in the location model, is integrated into the model. Last, but not the least, a case is conducted to verify the validity of the proposed model when dealing with location problem. As a result of the above analysis, it is effective to apply robust optimization algorithm and to determine the location of EVCSs effectively when charging demand generated on the path is uncertain. At the same time, queuing theory can help to determine the optimal number of EVCSs effectively, and reduce the cost of building EVCSs.

Optimizing Number and Locations of Alternative-Fuel Stations Using a Multi-Criteria Approach

The transition to alternative fuels is obligatory due to the finite amount of available fossil fuels and their rising prices. However, the transition cannot be done unless enough infrastructure exists. A very important infrastructure is the fueling station. As establishing alternative-fuel stations is expensive, the problem of finding the optimal number and locations of initial alternative-fuel stations emerges and it is investigated in this paper. A mixed-integer linear programming (MILP) formulation is proposed to minimize the costs using net present value (NPV) technique. The proposed formulation considers the criteria of the two most common models in the literature for such a problem, namely P-median model and flow refueling location model (FRLM). A decision support system is developed for the users to be able to control the parameter values and run different scenarios. For case study purposes, the method is used to find the optimal number and locations of the alternative-fuel stations in the city of Chicago. Some data wrangling techniques are used to overcome the inability of the method to solve very large-scale problems.

Optimal locations of U.S. fast charging stations for long-distance trip completion by battery electric vehicles

Due to environmental and energy challenges, promoting battery electric vehicles (BEVs) is a popular policy for many countries. However, a lack of fast recharging infrastructure and limitations on BEV range limit their purchase and use. It is important to have a well-designed charging station network, so this paper uses U.S. long-distance travel data to place charging stations with the objective of maximizing long-distance trip completions. Each scenario assumes a certain number of charging stations—from 50 to 250, across the U.S., and an all-electric-range (AER) of 60–250 miles (97–402 km). The problem is formulated as a mixed integer program, and a modified flow-refueling location model (FRLM) is solved via a branch-and-bound algorithm. Results reveal that the 60-mile-AER percentage varies between 31% and 65%, as one increases station count from 50 stations to 250 stations. At least 100 mile-range (161 km) BEVs appear needed, to avoid long-distance-trip issues for the great majority of U.S. households. This research also provides an effective method to decide the number and locations of fast charging stations for different conditions, to enable better planning and more sustainable transportation systems.

Benders-and-Price approach for electric vehicle charging station location problem under probabilistic travel range

This paper investigates the optimal locations for refueling stations for electric vehicles. Electric vehicles have been successfully introduced into the market. However, their use seems to be limited to urban transport since recharging facilities are readily available only near home and work. Planning recharging infrastructure for electric vehicles is highly relevant because this will enable longer trips, including inter-state travel which requires multiple battery charges. Among various models to determine optimal locations of recharging stations, a flow refueling location model (FRLM) is considered in this study. It determines locations for recharging stations to maximize the flow that can travel between origin and destination pairs by refueling at built facilities. FRLM is extended by introducing a probabilistic consideration of the travel range which might vary depending on various factors including road conditions. We develop a mixed integer nonlinear programming formulation and propose a Benders-and-Price algorithm by combining the Benders decomposition and column generation to solve the proposed formulation. The proposed algorithm is validated using extensive computational experiments on two transport networks, including a real-life Texas highway network.

A Second-Order Cone Programming Model for Planning PEV Fast-Charging Stations

This paper studies siting and sizing of plug-in electric vehicle (PEV) fast-charging stations on coupled transportation and power networks. We develop a closed-form service rate model of highway PEV charging stations' service abilities, which considers heterogeneous PEV driving ranges and charging demands.We utilize a modified capacitated flow refueling location model (CFRLM) to explicitly capture time-varying PEV charging demands on the transportation network under driving range constraints. We explore extra constraints of the CFRLM to enhance model accuracy and computational efficiency.We then propose a stochastic mixed-integer second order cone programming (SOCP) model for PEV fast-charging station planning. The model considers the transportation network constraints of CFRLM and the power network constraints with AC power flow. Numerical experiments are conducted to illustrate the effectiveness of the proposed method.

A threshold covering flow-based location model to build a critical mass of alternative-fuel stations

To facilitate the transition to alternative-fuel vehicles (AFVs), researchers have developed models for optimally locating an initial refueling infrastructure for AFVs with limited driving range. Recently, clustering of stations has emerged as a strategy to encourage consumers to purchase AFVs by building a critical mass of stations. Clustering approaches, however, have focused on serving demands represented as nodes or arcs rather than origin-destination (O-D) trips. This study proposes a Threshold Coverage extension to the original Flow Refueling Location Model that focuses on the percentage of a zone's O-D trips that can be successfully completed given a typical driving range and location of stations. It is motivated by the idea that drivers in an area will not purchase an AFV unless a critical mass of the trips they regularly make can be completed. Therefore, the new model optimally locates p refueling stations on a network to maximize the sum of weighted demand of covered origin zones, where “covered” means that the zone exceeds a specified threshold percentage of their total outbound round trips that are refuelable. The model is tested on networks for Orlando and the state of Florida. As the threshold percentage is raised, fewer zones can surpass the threshold. Covered nodes increasingly cluster together, as do stations for serving their O-D flows. The model's policy implementation will provide managerial insights for some key concerns of the industry, such as geographic equity vs. critical mass, from a new perspective.

Efficient and equitable transnational infrastructure planning for natural gas trucking in the European Union

The European Union relies on oil for over 90% of its transportation fuels. To reduce this dependency, the EU is developing an integrated market for compressed (CNG) and liquefied (LNG) natural gas as alternatives to diesel for long-haul trucking. This paper develops a modeling approach for optimizing a subsidized European network of LNG truck stops based on the flow-refueling location model (FRLM). The FRLM locates stations to cover the maximum flow volume of origin–destination trips on their shortest paths. The FRLM explicitly accounts for the need for multiple refueling stops to serve long-distance trips given a user-specified vehicle driving range. In this paper, the FRLM maximizes covered flows in terms of ton-kilometers (tkm) rather than tons because tkm are proportional to the amount of diesel that can be replaced by LNG and the associated difference in carbon emissions. Nevertheless, despite the fact that maximizing covered tkm prioritizes longer shipments, the basic FRLM clusters all new stations in Germany, which has the densest concentration of flows. For subsidized stations promoting pan-European trucking, concentrating new stations in a few countries may not be politically desirable. We therefore introduce and compare several new side constraints for producing a more equitable distribution of covered flows across EU members, including transnational corridor constraints that require connectivity between different countries and partial country coverage constraints that require a minimum percentage coverage threshold in each country. The country coverage constraints show the most promise for offering decision-makers distinct alternatives for a network of alternative-fuel stations across countries.

Optimizing the allocation of fast charging infrastructure along the German autobahn

The allocation of fast charging stations is a severe investment for the future mobility system with electric vehicles. The allocation of the first charging stations influences the profitability of all other fast charging stations and should therefore be perfectly arranged. Hence, we applied and extended the flow-refueling location model (FRLM) developed by Capar et al. (Eur J Oper Res 227(1):142–151, 2013) to the German autobahn with a focus on the states Baden-Wurttemberg and Bavaria with 595 nodes and 3569 highway km. Our model extension comprehends mainly the inclusion of the access distance for traffic participants to their closest network node. In order to analyze the impact of different vehicle ranges and the desired coverage of flows we defined four scenarios. The results indicate the significance of vehicle range and the desired coverage value. 20 optimally allocated fast charging stations along the highways lead already to a coverage of about 62 % (100 km vehicle range) or even 83 % (150 km vehicle range) of all trips. A complete coverage of trips requires at least 50 (150 km vehicle range), 77 (100 km vehicle range) or even 84 (70 km vehicle range) fast charging stations. The last 30 % coverage leads to a tripling of charging stations. Furthermore, a first estimation of the corresponding surcharge for fixed costs per charging process amounts to about 20 % of the total costs for a charging process.

Multi-period planning for electric car charging station locations: A case of Korean Expressways

Abstract One of the most critical barriers to widespread adoption of electric cars is the lack of charging station infrastructure. Although it is expected that a sufficient number of charging stations will be constructed eventually, due to various practical reasons they may have to be introduced gradually over time. In this paper, we formulate a multi-period optimization model based on a flow-refueling location model for strategic charging station location planning. We also propose two myopic methods and develop a case study based on the real traffic flow data of the Korean Expressway network in 2011. We discuss the performance of the three proposed methods.

A Flexible Reformulation of the Refueling Station Location Problem

Serious environmental and economic problems of using fossil fuels in transportation sections force managers to think of alternative fuels such as hydrogen, ethanol, biodiesel, natural gas, or electricity. Meanwhile, lack of fuel network infrastructures is a major problem, which needs to be investigated considering the number and optimal location of alternative fuel stations. In the literature, two different flow-based demand modeling concepts (the maximum cover and set cover) have been proposed for solving this problem. Because of the huge number of combinations of fuel stations for covering the flow of each path, the models are impractical for the real size problems. In this paper, the flow refueling location model was reformulated and a flexible mixed-integer linear programming model was presented, which was able to obtain an optimal solution much faster than the previous set cover version. The model also could be solved in the maximum cover form in a reasonable time on the large-sized networks.