Xie and Huang 1 An Optimal Deployment of Wireless ...

Xie and Huang

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An Optimal Deployment of Wireless Charging Lane for Electric Vehicles on Highway Corridors Fei Xie Postdoctoral Research Associate 865-946-1353 Center for Transportation Analysis Oak Ridge National Laboratory Knoxville, TN 37931 Email: [email protected] Yongxi Huang (corresponding author) Assistant Professor 864-656-3661 Glenn Department of Civil Engineering Clemson University Clemson, SC 29634 Email: [email protected]

Submitted August 01, 2015 Words (excluding references): 4,909+7 figures+1 tables=6,909 words Number of References: 35

This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan(http://energy.gov/downloads/doe-publicaccess-plan

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ABSTRACT We propose an integrated modeling framework to optimally locate wireless charging facilities along a highway corridor to provide sufficient in-motion charging. The integrated model consists of a master, Infrastructure Planning Model that determines best locations with integrated two sub-models that explicitly capture energy consumption and charging and the interactions between electric vehicle and wireless charging technologies, geometrics of highway corridors, speed, and auxiliary system. The model is implemented in an illustrative case study of a highway corridor of Interstate 5 in Oregon. We found that the cost of establishing the charging lane is sensitive and increases with the speed to achieve. Through sensitivity analyses, we gain better understanding on the extent of impacts of geometric characteristics of highways and battery capacity on the charging lane design.

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INTRODUCTION Electric Vehicle (EV) has been rapidly growing and becoming a vital alternative to the conventionally fueled vehicles. The latest report shows that the Plug-in EVs (including both the Plug-in hybrid EVs and Battery EVs) has made up about 1% of the total car sales of 2014 (1). EVs provide a plausible way to achieve independence of oil imports, reduction in emissions, and enhancement of renewable energy mix for power production. Like many other emerging technologies, EV technology comes with a price. In addition to the high upfront cost of owning an EV, which can be largely compensated by federal and local tax incentives for now, one of the major obstacles is the limited distance that EVs can perform per charge due to the limited battery capacity, compared to the conventional internal combustion engine (ICE) vehicles (2, 3). This so-called “range anxiety” limitation has been in call for strategic deployment of charging infrastructure on transportation networks. It has been an acutely discussed topic in the research communities of transportation and geographic spatial study (4-7). It is widely believed that EVs are particularly useful for short-distance daily commute trips with ample access to charging at home and/or workplace (8), but may be ill-suited for long-distance trips (9) without sufficient charging in place along major highway corridors. In recognition of the barriers, a great deal of research efforts have been primarily focused on the locations of charging stations, especially to enable long-distance trips for electric vehicles or to more generalized alternative fueled vehicles (AFVs)(6, 7, 10). The most widely considered charging solutions include the three different levels of charging technologies, namely level 1, level 2 and direct current (DC) fast charging, which are all stationary and consume 8-9 hours, 3-4 hours, and 20 minutes, respectively, to fully recharge a typical EV, e.g., Nissan Leaf (11). These charging considerations are for different land-use types. For example, level 1 and 2 charging solutions are suitable for “destination” type of places, where vehicles need to park for a substantial period of time while DC fast charging method, due to substantially reduced charging time, can potentially work in a similar way as current ubiquitous gas refueling stations and provide “pass-through” kind of service. However, in reality, the 15-20 minute charging time by fast charging (12) is still way longer than the target of five-minute recharge time, set by the Department of Energy (13) and it may be more practical as an auxiliary service to places like coffee shop, restaurant, etc. Another possible charging solution that had ever been considered is through swapping batteries at designated battery swapping stations (14, 15), which however has been criticized for the obstacle in standardizing batteries across various vehicle models and difficulty in making batteries removable and thus demonstrated to be unsuccessful in US market (16). An emerging charging technology is wireless charging. Distinct from the afore-described charging solutions, by which drivers need to drive to charging stations for charging, wireless charging instead provides non-stop, in-motion charging supported by embedded wireless charging pads (17). However, the success of this new technology is in face of several challenges. For example, study (17) indicates the power transmitted wireless could potentially harm human health and high power transmission in short period of time may overload power distribution systems. In addition, charging efficiency is mainly in inverse to travel speed. A higher travel speed, compared to a lower speed, reduces the time traversing a segment of road, and thereby leads to less power transmitted from the wireless charger to vehicles. As a result, more wireless charging pads or a longer “charging lane” needs to be installed. On the other hand, it is unlikely to lower a speed limit as highways are responsible for providing high mobility for travelers. This speed-cost tradeoff is of the major concern in the planning of wireless charging infrastructure system.

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Prior research studies on optimization of a wireless charging system can be generally classified into two schools. The first school of studies is focused on the advancement of vehicle wireless charging technology (18-21). The other school of studies tackles charging infrastructure systems. Similar to prior studies focused on the locational decisions for alternative fueling stations (AFS) (4-7), these studies primarily take into account the spatial relations between chargers and vehicles on transportation networks while seeking the most cost-effective solutions (22, 23) or maximum social welfare through smart pricing scheme (24). Our study extends the modeling scope to incorporate other critical factors closely related to the wireless charging efficiency, including speed, geometric characteristics of highway corridors, and interactions with EV technologies, into our developed optimization framework for the best distribution of wireless charging facilities along a highway corridor. Our study will contribute to the research community of charging infrastructure planning and management. To the best of our knowledge, this study is at first to explicitly integrate the external factors, in addition to EV technology, into an optimization framework for a wireless charging infrastructure system. In particular, the framework determines the best locations for placing wireless charging facilities while achieving a desired speed. The model also explicitly accounts for the constraints of EV technology and geometric characteristics of highway corridors of study. The optimization framework consists of a master problem and two sub-problems. The master problem is presented by an Infrastructure Planning Model, which comprises of two conflicting objectives: minimizing the capital cost of establishing the wireless charging infrastructure system while maximizing the desired travel speed. The model assures that EVs can complete a trip while charging in-motion. The energy consumption and charging that are directly associated with the state-of-charge (SOC) of EVs are explicitly captured in the Energy Consumption and the Energy Charging sub-models, respectively and are provided to the master model as inputs. Note that the energy consumption/charging are in nonlinear relationship to speed. This integrated model is a multi-objective, mixed integer, non-linear program, which are computationally challenging. Thanks to a special structure of the integrated model, we adopt the brutal force method to partition the problem to a set of single-objective, mixed integer programs that are tractable by solvers like CPLEX. The model is demonstrated by using a section of Interstate 5 in Oregon with sensitivity analysis of the impacts of relevant factors on strategies of charging infrastructure deployment. Note that as a preliminary study, the model presented in this paper is only for a highway corridor and the effects of networked highway systems have not been addressed yet, which is our ongoing research effort. The rest of the paper is organized as follows. We present the mathematical formulations of the Infrastructural Planning Model and two vehicle sub-models in the section of methods. The experimental case study of Oregon is followed with discussions of results and sensitivity analyses. The remarks of this study and future work will be briefly described in the last section.

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METHODS

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We develop an optimization model to strategically locate wireless charging facilities along a highway corridor such that drivers can charge their EVs “on the go”. We adopted the concept of “charging lane” (18), which is a dedicated lane for deploying wireless charging facilities. Users use the charging lane for a fee in similar way of High Occupancy Toll (HOT) lane, although the HOT lane builds on the mechanism of congestion pricing for the road congestion mitigations. This study tends to explore the economic feasibility of wireless charging as an alternative

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solution to the current stationary charging technology and to study interactions between relevant factors in planning the infrastructure. The goal is to find minimum-cost location strategy subject to the constraints inherent with EV and wireless charging technologies, geometric features of highways, and auxiliary systems (e.g., air conditioning). These factors may differ significantly across geographic regions and technology scopes. In particular, the geometric characteristics of highway corridors (i.e., vertical slopes) can even vary substantially between different locations even within a corridor, which makes the planning of wireless charging more complex than stationary charging infrastructure. It is thus desirable to derive a generalizable formulation that can accurately capture these factors. To account for the heterogeneity of highway geometry within one corridor, a charging lane is partitioned into sufficiently N small segments such that each of them is homogenous in term of geometric features (i.e., vertical grades). Let Li be the length (mile) of a segment i (i = 1,...,N)

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and  i be the vertical grade (in angle degree) of that segment. Note that both length and vertical grades may vary between segments along a highway corridor. We consider a corridor with multiple entries (origins) r  O and exits (destinations) s  D . Let O  {1..N} , D  {2..N  1} ,

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and all origin-destination pairs (r , s)  T  O  D r  s .

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Assume that an EV leaves an origin r  O with the SOC of brO (KWh) and arrives at a

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destination s  D with an expected SOC of bsD (KWh) that is the amount of energy reserved onboard (e.g., a certain percentage of battery capacity) for further exploration before being able to find a charging source in the city. We also require that at any segment of the road, the SOC has to be within a range between b Min and b Max , both in KWh. We define a continuous variable Bi ,rs

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as the SOC at the beginning of a segment i  r,..., s , for trip (r , s)  T . For example, Br ,rs is the

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SOC of an EV at origin r  O and it equals brO . Note that Bs ,rs defines the SOC at destination

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s  D and is thus not less than bsD . Please see Figure 1 as an illustration. As the charging lane is exclusive in a highway corridor, it is reasonable to assume that the effects of traffic congestion are negligible for the charging lane. However, we do recognize that dedicated charging lanes suppress other lanes for conventionally fueled vehicles and may cause congestions. Such negative impacts will be carefully addressed in the future study. Although the drivers’ driving habits can substantially impact the power transmitted from wireless charging facility to the on-board battery, it is extremely difficult to formulate such relationship in a closed-form mathematical model. We assume that drivers will drive at the desired speed (i.e., speed limit) to simplify the modeling in this study.

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SOC at beginning of segment i

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Figure 1. Segmentation of a charging lane with example vertical profile. We would like to use a simple example to demonstrate how wireless charging lane works. Assume that there is a fully charged EV with battery capacity of 30 KWh traverses a charging lane. Without loss of generality, the lane has only three segments and we assume that the profile of power consumption and charging over each segment is known. For example, it consumes 10, 10 and 20 KWh to complete the segments #1, 2 and 3, respectively and a wireless charger can provide up to 40 KWh energy when an EV transverses a segment. With this setup, it is clear that the EV is not able to complete the entire trip with the battery of 30 KWh and it has to charge somewhere prior to destination. In this example, the wireless charger can be placed in segment #2 or #3 if both segments are equally costly to install the charger. However, in a more realistic modeling environment, the profile of energy consumption and charging is not available as simple as numerical values, which may need to be derived mathematically to describe the relationships between speed, geometric feature of roadways, and EV and charging technologies. In addition, the cost of installing wireless charger can also vary with segments, which makes the locations become cost dependent, although in general the model may not be able to guarantee a unique solution of locating chargers on highway corridors. Our developed integrated modeling framework is presented as follows. The master, Infrastructure Planning Model, determines the optimal charging facility layout and the desired speed, subject to energy-conservation constraints (i.e., the SOC of an EV at any point of highway corridor is a result of energy consumed and charged) and the requirement of completing a trip. The profile of energy consumption and charging are supplied by the sub-models, namely the Energy Consumption Model and Energy Charging Model. The structure of integrated modeling framework is described by the diagram in Figure 2.

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Input Electric Vehicle Technology

Integrated Model Energy Consumption Model

Highway Geometric

Driving Environment

Infrastructure Model

Energy Charging Model

Output Wireless Charging Facility Location

Desired Speed

Wireless Charging Technology

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Figure 2. Roadway map and grade profile.

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Master model: Infrastructure Planning Model

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The Infrastructure Planning Model is a bi-objective model, which seeks compromised decisions between cost-effectiveness and operational efficiency. The cost objective in (1) is to minimize the total capital cost of establishing the charging lane. Z i is a binary variable indicating if a

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wireless charger is placed in segment i  1,..., N and Ci is a parameter denoting the cost of installing a wireless charging facility in segment i. Note that the operation and maintenance costs are not included in the model, mainly because such costs are not yet clear and dependent on actual usage of the charging lane, such as the coordination between the pavement management team with the power sector, the level of personnel training, and utilities’ detailed power systems planning (25). The efficiency objective in (2) is to find a desired speed V that can possibly be achieved under external constraints (e.g., SOC within certain range). Note that the desired speed V can be defined as a continuous variable from a mathematical viewpoint. While in the context of transportation engineering, it may be more realistic to define it as an integer variable within a range of 25 to 65 miles per hour (mph) by a constant increment of 5 mph. Note that 65 mph is speed limit on most highways. The complete model is presented in (1)-(9). Note that this model is primarily applicable for deploying charging lane on only a highway corridor and an extension to a network of highway system is a study undertaken. Minimize

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Ci  Zi

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Maximize V 22 23

(2)

Subject to: Br ,rs  brO

(r , s)  T

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Bs ,rs  bsD

(r , s)  T

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b Min  Bi ,rs  b Max

i  r ,..., s , (r , s)  T

(5)

i  r ,..., s  1 , (r , s)  T

(6)

Bi1,rs  minBi ,rs  fi Li ,i ,V   gi Li ,V  Zi , b M ax

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Zi 0,1

i  1,..., N

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(8) i  r ,..., s , (r , s)  T

Bi ,rs  0 1 2 3 4 5 6 7 8

(7)

(9)

Where, fi Li ,i ,V  and gi  Li ,V  in (6) are the amounts of energy consumed and charged, respectively in each segment i  r ,..., s , (r , s)  T . Constraints (3) and (4) are boundary conditions at origins and destinations, respectively. Constraint set (5) imposes the limits of the SOC in any segment of highway corridor. Constraint (6) is the energy conservation constraint for each segment i  r ,..., s  1 , (r , s)  T . When an EV traverses a segment i , it consumes fi Li ,i ,V  the amount of energy and absorbs gi  Li ,V 

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amount of energy if a wireless charging facility is in place in segment i . The resulting SOC Bi1,rs cannot exceed the limit b Max . Note that the functions fi Li ,i ,V  and gi  Li ,V  are nonlinear to speed V and dependent on several other technical inputs, which are explicitly formulated in the two vehicle sub-models. Constraints (7)-(9) are binary and non-negativity constraints.

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Sub-model I: Vehicle Energy Consumption Model

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The Vehicle Energy Consumption Model aims to calculate the energy consumption fi Li ,i ,V 

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for each segment i  1,..., N , in recognition of the interrelationships between vehicle speed, vertical grade, and properties of electric vehicles. Let Pi be the output power (watt) generated by

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the electric motor and ti be the travel time (second) across segment i  1,..., N . Then, the

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equation fi Li ,i ,V   Pi ti holds with the unit in joules. Given the design speed V and segment

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length Li , the average travel time can be calculated as ti  Li / V . According to (18, 26), the

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output power Pi is balanced by three major energy consumptions to operate EV, due to motor

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operation Pi Motor , travel resistance PiTravel , and auxiliary systems Pi Aux . The Pi Motor and PiTravel are defined in equalities (10)-(11), respectively. The Pi Aux relates to auxiliary systems (e.g., radio, lights, horn, and air conditioning) and is a parameter adopted from report (27).

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Pi

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PiTravel V  Fi

(11)

Fi  kV 2  f rl mg  mg sini

(12)

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Fi V

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 total resistance (variable, in N)  the desired speed (variable, in m/s)  the resistance of motor (parameter, in Ω)

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 the radius of tire (parameter, in meter)  the product of armature constant and magnetic flux (parameter, in V s)  vehicle mass (parameter, in kilogram)  g-force (parameter, in m/s2)  vertical grade (parameter, in degree)

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Both Pi Motor and PiTravel depend on the total resistance Fi , which can be further partitioned

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into three parts, as shown in (12), aerodynamic kV 2 , rolling f rl mg and grade resistances

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mg sini . The total energy consumption fi Li ,i ,V  is the sum of the three components as expressed in (13). 2 r  R 2 L fi  Li ,i ,V    2 kV 2  f rl mg  mg sini  V kV 2  f rl mg  mg sini   Pi Aux  i K V

(13)

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Sub-model II: Vehicle Energy Charging Model

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The Vehicle Energy Charging Model aims to calculate the amount of energy charging gi  Li ,V 

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for each segment i  1,..., N . The amount of energy charged to an EV mainly depends on the time traversing a segment with (18). Let Q be the input power (watt) transmitted from the charging facility. With the travel time ti (seconds) in segment i  1,..., N , the total charged

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energy equals Q ti and ti  Li / V . Let  be the charging efficiency (%), a percentage of the

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actual received energy by EVs. The gi  Li ,V  is calculated by (14), which is inverse to speed V.

gi  Li ,V   Q

Li V

(14)

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Solution Methods for the Integrated Model

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The integrated model is a multi-objective mixed integer non-linear program. Multi-objective problems are notoriously difficult to solve and many solution methods can result in Pareto-front solutions, such as ε-constraint method, weighted-sum method, and goal programming method (28). However, this study presents a more challenging multi-objective mixed integer non-linear problem, and it is extremely difficult to identify a complete Pareto-efficient set of optimal solutions for a mixed integer non-linear problem. However, the model offers a unique structure, in which the set of desired speed V belongs to a small discrete set as defined in (8). This unique structure assures that the enumeration based brutal force method is acceptable and the entire optimization problem can be partitioned into a set of single objective mixed integer programs by evaluating a discrete set of desire speeds, (i.e., objective (2) is relaxed). The resulting singleobjective problem can be efficiently solved by commercial solvers, e.g., CPLEX.

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CASE STUDY OF I-5 INTERSTATE HIGHWAY IN OREGON

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The model is demonstrated by using the I-5 Interstate Highway in Oregon, which is of our interest due to Oregon’s stewardship in environment, green living, and aggressive strategies on encouraging mass adoption of EVs. For example, through collaborations with seven other states, Oregon has a Multi-State Zero Emission Vehicle (ZEV) Action Plan which sets an aggressive target to put 3.3 million ZEVs (including EVs) by 2025 in the eight states (29).

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Data inputs

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We pick the milepost of 228 of interstate 5 as the starting point, which is near the city of Corvallis and the milepost of 299 as the ending point, which is the exit to the city of Portland. The 71 miles’ highway section is the corridor of our study scope and the map of the corridor is highlighted in Figure 3(a). Note that only one direction (northbound) of the highway is considered. The deployment of charging facilities or the design of charging lane in other direction can be similarly conducted. We assume that one single-lane as the charging lane that will be constructed adjacent to the existing corridor so that the vertical slope of the charging lane will be identical to the existing highway geometric profile, which is publically available from the Oregon State Highway Inventory Report (30). In the case study, we set a resolution by one-mile segment and evenly partition the studied highway corridor into 71 segments. The vertical grades vary substantially between -5.0% and 3.8% along the 71-mile corridor, as shown in Figure 3(b).

Vertical Slope (%)

5% 3% 1%

-1% 1

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-3% -5%

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Segments

(a) Roadway Map (b) Roadway grade profile Figure 3. Geographical information of selected corridor. Table 1 summarizes critical technical inputs for the model. The minimum battery SOC b is set to be 20% of the battery capacity b Max to maintain battery’s lifespan and quality (31). It is assumed that EV leaves origins with full battery (i.e., brO = b Max , r  O ) and by a conservative standard, 50% of the battery is reserved at destinations for urban exploration needs (i.e., bsD =0.5 b Max , s  D ). Since all segments in the case study have identical length of one mile, Min

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the capital cost of establishing wireless chargers is assumed to be identical for all segments and is about $380,000 per one mile according to the report (32). TABLE 1a. Summary of Critical Technical Inputs Technical items Value Max 24 Battery capacityb, b (KWh) Min Max 4.8 Minimum battery SOC, b  0.2b (KWh) c Vehicle mass , m (kg) 1,266 c Aerodynamic resistance coefficient , k (kg/m) 1.3 c 0.006 Rolling resistance coefficient , f rl (dimensionless) Resistance of motorc, r (Ω) 0.11 b Product of armature constant and magnetic flux , K (V s) 10.08 Tire radiusc, R (meter) 0.5 Aux d 0.5 Auxiliary power , Pi (KW) Charging rate of charging facilitiese, Q (KW) Power transfer efficiencye,  (%)

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a. b. c. d. e.

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This study only considers a single charging technology and single battery size Battery capacity of Nissan Leaf is adopted (33). Adopted from (26). Energy use of air conditioning and heating systems when outside temperature is 110 °F and desired vehicle temperature is 84 °F (27). On-line Electric Vehicle technology (32).

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Results and Analysis

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The model was coded in Java and solved by solver CPLEX 12.6. This subsection presents the results of baseline case study, followed by sensitivity analyses on the impacts of critical factors on the infrastructure planning strategies.

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Baseline Results The baseline results are based on the data described in the section of data inputs and are for a trip traversing the whole 71-mile stretch of Interstate 5. We solve the model by adopting a complete range of desired speed from 25 to 65 mph with an increment of 5 mph. The resulting numbers of segments installed with wireless chargers are plotted in Figure 4 in response to different speeds. A higher desired speed requires more segments of charging facilities to be deployed or a longer charging lane. Note also that for gaining the same increment in speed (e.g., 20 mph), a much longer charging lane and higher cost is expected when the desired speed wants to stay relatively high. For example, the system requires 12 (= 13-1) additional segments to be installed with wireless charger versus 40 (=53-13) of them when speed increases from 25 to 45 mph compared to the speed increasing from 45 to 65 mph. That is equivalent to $15.2 million difference. It is a result of combined effects of both energy consumption and charging. According to the Energy Consumption Model (13), the aerodynamic resistance kV 2 has polynomial growth with the speed V and thus energy consumption rate rises with speed. On the other hand, according to the Energy Charging Model (14), a higher speed reduces the travel time and thus the charging time is shorter, resulting in lower power transmitted.

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# of Segments with Charging Facilities

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Figure 4 Relationship between charging facility layouts and design speed. Figure 5 plots the SOCs, cumulative energy consumption and charge of electric vehicles along the entire corridor at different speeds, taking three representative speeds of 25, 45, and 65 mph. The figure provides a close-up look of the impact of different speed on EV operations. For example, with the full capacity of battery at 24 KWh at the beginning of a trip, the cumulative energy consumed for completing the entire trip of 71 miles is 13 KWh when the speed is at lowest 25 mph (see Figure 5(a)) while rising to 77 KWh when the speed is at highest 65 mph (see Figure 5(c)). The curve of cumulative energy charge in the figure also implies the segments that wireless chargers are deployed. For example, positive slopes indicate that wireless chargers are placed while flat portions indicate that there is no charging. Note that in Figure 5(a) one segment (i.e., segment #8) is installed with wireless charger when the desired speed is 25 mph, although the on-board battery with the capacity of 24 KWh is sufficient to cover the trip (i.e., consumes 13 KWh in total). This is due to the assumption of 50% battery reserved at destination. For a higher speed, the on-board battery does not suffice and requires charging on the way. The locations of placing wireless chargers may not be unique while the minimum number of chargers is. The baseline results are based the farthest origin-destination (O-D) pair on the corridor. Other pairs on this corridor can also be taken into account by the model. The results indicate that although the minimum number of segments to install wireless chargers will remain, the locations of placing those chargers can be different.

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(c) Speed = 65 mph Figure 5 State of charge, energy consumption and energy charge by design speed levels. Sensitivity Analyses We conduct a set of sensitivity analyses on the vertical slope and vehicle battery capacity, both of which may directly impact the strategies on deploying the charging lane. Vertical Slope: We apply two types of changes on the vertical grade. The first type changes the steepness of vertical slopes. In particular, two cases are considered – flatter slope by multiplying by 0.5 labeled as “0.5X” and steeper slope by multiplying by 2 labeled as “2X”. For example, if the current slope of a segment is +2%, then the resulting flatter slope is +1% and steeper slop is +4%. The second type adds additional grades to the slopes, which results in a profile with overall increased vertical slopes. For example, adding “+0.5%” to the current slope of +2% yields a new slope of +2.5%. In this study, we only consider a small range of additions: “+0.5%” and “+1%” and apply them to all segments of the highway corridor. The resulting new charging lanes in terms of number of segments installed with wireless charger are plotted in Figure 6, in which three different representative speeds are considered and different bars correspond to different scenarios of vertical slope changes. The baseline results are also included for comparisons.

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The results indicate that scenarios “0.5X” and “2X” have negligible impacts on the deployment of charging lane. This may be due to the fact that a steeper uphill segment, though temporally yielding higher energy consumption, can be compensated by a steeper downhill segment. However, the second type of slope change by adding “+0.5%” and “+1%” leads to a substantially longer charging lane and this effect is even amplified with higher speeds. This is mainly due to the constant increase in the grade resistance mg sini in (12).

# of Segments with Charging Facilities

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Baseline slope

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"0.5X": 0.5 times baseline slope

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"+0.5%": Baseline slope + 0.5%

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45 mph Speed

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Figure 6 Impacts of vertical slopes. Battery Capacity: The battery capacity has long been considered as a dominating factor for operating EV. The capacities can vary significantly with vehicle models. For example, Chevrolet Volt, a plug-in hybrid vehicle, has a small on-board battery with a capacity of 16.5 KWh (34) while Tesla Model S features a substantially larger battery with a capacity of 60 KWh (35). We are interested in understanding to what extent the battery sizes will impact the design of the charging lane. In this sensitivity analysis, we test the two other battery capacities: 16.5 KWh and 65 KWh. The results are represented by bars in Figure 7, in comparison with the baseline results. The figure shows that a larger battery sizes can shorten a charging lane because a higher capacity reserves more onboard power to run, vice versa. The effect can be remarkable. For example, when a 60KWh battery is used instead of 24 KWh, the charging lane can be shortened by 28% (=(54-39)/54), which is equivalent to cost reduction by $5.7 million when speed is at 65mph,. When speed is at 45mph, the charging lane can be even less than a quarter of the original length (i.e., 3/13).

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# of Segments with Charging Facilities

60 Baseline 24 KWh battery capacity 50

56

54

16.5 KWh battery capacity 39

60 KWh battery capacity

40 30 20

13

15

10 2

1

3

0

0 25 mph

1 2 3 4

45 mph Speed

65 mph

Figure 7 Impacts of battery capacity. CONCLUSIONS

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An integrated modeling framework was developed to optimally locate wireless charging facility along highway corridor. The integrated model comprises of a master, Infrastructure Planning Model and two sub-models, the Energy Consumption Model and Energy Charging Model. The integrated model is a multi-objective, mixed integer, non-linear program, which takes into account EV and wireless charging technologies, highway geometries, and auxiliary systems. Due to the inherent special model structure, we partitioned the model into multiple single-objective problems through enumerating possible speeds. The single-objective problem is a mixed integer program and solved by the commercial solver CPLEX. The integrated model was implemented in an illustrative case study of establishing a charging lane on Interstate 5 in Oregon. The results indicate that the cost of the charging lane increases rapidly with speed. The sensitivity analyses on the two critical factors - vertical grade and battery capacity help us understand the extent of impacts on charging lane design. This paper presents a preliminary study on wireless charging infrastructure planning and hopefully will trigger more research interests in this community. There are several immediate extensions to enrich the context of the work. First, it is important to investigate how actual traffic flows will impact the energy transmissions between chargers and EVs and how to incorporate such effects in charging lane planning. Second, as an emerging technology, it is unrealistic to have the entire charging infrastructure in place at all once. Instead, the network should be expanded over time in response to the growth of EV adoptions. Incorporations of such dynamics into a multistage decision making framework is challenging in terms of both modeling and solution. Last, charging lane suppresses the space for conventional vehicles and such negative impacts should also be carefully addressed as a societal equity issue.

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ACKNOWLEDGEMENT

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We are grateful to Dr. Joachim Taiber and his research team from International Center for Automotive Research (ICAR) of Clemson University for technical discussions and data support.

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The first author also acknowledges that the majority of research was conducted while the he was attending the Clemson University as well as acknowledges the Oak Ridge National Laboratory’s postdoctoral education and self-development support for completing this manuscript.

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