Efficient Deployment Design of Wireless Charging Electric Tram System with Battery Management Policy

sustainability

Article Eﬃcient Deployment Design of Wireless Charging Electric Tram System with Battery Management Policy

Young Dae Ko 1 and Yonghui Oh 2,* 1 Department of Hotel and Tourism Management, College of Hospitality and Tourism, Sejong University, 209, Neungdong-ro, Gwangjin-gu, Seoul 05006, Korea; [email protected] 2 Department of Industrial and Management Engineering, Daejin University, Pocheon 11159, Korea * Correspondence: [email protected]; Tel.: +82-31-539-2006

Received: 4 March 2020; Accepted: 3 April 2020; Published: 6 April 2020

Abstract: As an alternative to the environmental pollution problem of transportation means, the application of electric tram is considered in urban areas. However, due to the aesthetic problems occurs by the electric supply line for an electric tram, the wireless charging electric tram may be regarded as an alternative. It can be supplied electricity wirelessly from the wireless charging infrastructure installed on the railways even while moving. For a successful application, it is important to install and operate the overall systems with minimum investment cost. In this study, a mathematical model-based optimization technique, one of the methods of operations research, is adopted to derive the decision-making elements such as capacity and management of battery and allocation of the wireless charging infrastructure. Numerical example shows the optimal capacity and management of battery for a wireless charging electric tram and the ideal installation locations of the wireless charging infrastructures.

Keywords: mathematical model; wireless charging; battery capacity; battery management; wireless charging infrastructure; regenerative braking

1. Introduction In order to prevent environmental pollution, electric transportation is considered as an alternative to the existing internal combustion engine transportation. There are various types of electric transportation such as electric cars, electric trains, electric motorcycles, electric bicycles, and so on. Above all, electric trams are considered as eco-friendly transportation in urban areas [1]. Electric trams have the advantage of emitting less environmentally harmful compounds while using electricity as an energy source, but there are also some disadvantages too. First, the electric supply line on electric trams is not aesthetically good, and high-height vehicles at an intersection can threaten safety. In addition, the maintenance cost of the electric supply line is relatively expensive, and the tunnel excavation for the electric supply line area requires an additional cost. Moreover, due to the electric supply line, it is impossible to apply various types of trams such as double deck trains, or duplex type trains for both passenger and cargo. To overcome these disadvantages, a wireless charging electric tram has been proposed as an eco-friendly transportation system in urban areas [2]. Unlike conventional electric trams, a wireless charging electric tram can be powered remotely from wireless charging infrastructure on the railway and can store the remaining electricity in the battery. In addition, if a wireless charging electric tram is located on a railway with a wireless charging infrastructure, electricity can be supplied either during a stop or in operation. This makes it possible to design an entire system with a smaller battery than a pure battery-powered electric tram [3]. That is, if the wireless charging technology is applied to the electric tram, the wireless charging infrastructure is installed in the railway to overcome the disadvantage caused by the electric supply line of the existing

Sustainability 2020, 12, 2920; doi:10.3390/su12072920 www.mdpi.com/journal/sustainability Sustainability 20202020, 1122, x 2920 FOR PEER REVIEW 2 of 11 infrastructure is installed in the railway to overcome the disadvantage caused by the electric supply electric tram. In addition, it can be operated with a smaller battery than a pure battery-powered electric line of the existing electric tram. In addition, it can be operated with a smaller battery than a pure tram, so that the entire system can be installed with a relatively low cost. battery-powered electric tram, so that the entire system can be installed with a relatively low cost. The conceptual structure of the wireless charging electric tram is shown in Figure1. The wireless The conceptual structure of the wireless charging electric tram is shown in Figure 1. The wireless charging infrastructure consists of a wireless pick-up device and a power transmitter. The power charging infrastructure consists of a wireless pick-up device and a power transmitter. The power transmitter is installed between the railway lines and supplies electric power to the wireless pick-up transmitter is installed between the railway lines and supplies electric power to the wireless pick-up device wirelessly through electromagnetic induction. The supplied electricity is used to operate the device wirelessly through electromagnetic induction. The supplied electricity is used to operate the wireless charging electric tram, and the remaining electricity is stored in the battery. wireless charging electric tram, and the remaining electricity is stored in the battery.

Figure 1. ConceptualConceptual structure structure of wireless charging electric tram tram..

There is a trade-otrade-offff relationship between the battery capacity of the wireless charging electric tram and the installation installation length of the the wireless wireless charging infrastructure. If the the battery battery capacity capacity is large large enough, the wireless charging electric tram will be like a pure battery-poweredbattery-powered electric tram. In this case, it is not necessary to install a wireless charging infrastructure at all. On the other hand, if the battery capacity of the electric tram is zero, zero, a wireless wireless charging infrastructure must be installed on all railways. ThisThis isis the the same same situation situation as conventional as conventional electric electric trams withtrams electric with supplyelectric lines. supply Therefore, lines. Therefore,in order to in operate order to a wirelessoperate a charging wireless electriccharging tram electric system tram with system minimum with minimum investment investment cost, it is cost,necessary it is necessary to derive optimalto derive battery optimal capacity battery and capacity installation and lengthinstallation of wireless length charging of wireless infrastructure. charging infrastructure.In this study, operations research, a scientific decision-making technique, is applied to determine the optimalIn this study, capacity operations and management research, a scientific of a battery decision for a-making wireless technique, charging is electric applied tram to determine and the thelocation optimal and capacity length of and a wireless management charging of infrastructure. a battery for Amonga wireless the variouscharging techniques electric tram of operations and the locationresearch, and a mathematical length of a wireless model-based charging optimization infrastructure. technique Among is usedthe various to derive techniques the decision of operations variables research,by modeling a mathematical the goal as themodel objective-based function optimization and the technique various is conditions used to derive of the the problem decision situation variables as bythe modeling constraint the equations. goal as the objective function and the various conditions of the problem situation as the constraintThis paper equations. is organized as follows. In Section2, related previous studies are announced as the literatureThis paper review. is organized The description as follows. of In proposed Section 2, problem related andprevious overall studies procedure are announced are explained as the in literatureSection3. Thereview. development The description of a mathematical of proposed model problem and theand numerical overall procedure examples are are presentedexplained inin SectionSections 3.4 andThe5 development, respectively. of Finally, a mathematical findings andmodel insights and the from numerical this research examples are provided are presented during in Sectionconcluding 4 and remarks Section in 5, Section respectively.6. Finally, findings and insights from this research are provided during concluding remarks in Section 6. 2. Literature Review 2. LiteraThisture study Review deals with the efficient system design of a wireless charging electric tram using wirelessThis power study transmissiondeals with the technology efficient system to replace design existing of a electric wireless trams charging with electricelectric supply tram using lines. wirelessThe first power theoretical transmission foundation technology of wireless to replace power existing transmission electric technology trams with waselectric from supply Maxwell’s lines. Theequation first bytheoretical Maxwell foundation in 1862. Shinohara of wireless [4] introducedpower transmission the technology technology development was from and Maxwell’s research equationprogress sinceby Maxwell Maxwell’s in 1862. equation Shinohara in his research. [4] introduced In recent the research technology by Lu development et al. [5], it was and mentioned research progress since Maxwell’s equation in his research. In recent research by Lu et al. [5], it was mentioned Sustainability 2020, 12, 2920 3 of 11 that wireless power transmission technology can be categorized as non-radiative coupling-based charging and radiative RF(radio frequency)-based charging. In addition, non-radiative coupling-based charging consists of three technique such as inductive coupling [6], magnetic coupling [7] and capacitive coupling [8], while radiative RF-based charging [9] is divided between a directive RF power beamforming technique and a nondirective RF power transfer technique. Since this study is not a technical aspect research, a reference related to wireless power transmission technology is addressed at this part. The wireless power transmission technology was first applied in the field of electric vehicles rather than other means of transportation. As the world gets more interested in finding a method that can reduce CO2, people’s effort to develop the eco-friendly technology is getting bigger too. Between various eco-friendly resources, electric vehicles with wireless power transmission attract attention [10]. Therefore, there are researches to improve the power receiver technology [11], plans to set wireless charging infrastructure [12], or locate wireless charging lanes for vehicles that can maximize recharged electricity while maintaining small road congestion [13]. However, in order to apply wireless power transmission technology to transportation, it is necessary to transmit a large amount of electric power with high efficiency through a relatively large air-gap. Huh et al. presented a new inductive power transfer system (IPTS) for electric cars with a large air-gap and narrow rail width. They tested the efficiency of their proposed power transfer technology from 10 cm to 20 cm of air-gap and announced that maximum efficiency is 74% at 27 kW output [14]. Wang et al. described the theoretical and practical design issues associated with inductive power transfer systems, and verified the developed theory using a practical electric vehicle battery charger. They proposed a new approach to the design of the main resonant circuit, and the proposed method minimized the deviation of the design expectation due to phase or frequency shift [15]. Huang et al. proposed a hands-free inductive power transmission system for charging batteries in electric vehicles. They explained how to design a power regulator that can guarantee a high efficiency and continuous power flow even though the distance between the bottom of the vehicle and the charge pad may vary depending on the vehicle type [16]. The studies of wireless power transmission technology applied to electric trams are as follows. Fujii and Mizuma [17] analytically studied the characteristics of new electromagnetic devices with propulsion and non-contact power collection capabilities for future wireless trams. The devices they designed operate as linear motors or linear transformers, using finite element method (FEM) and special integral equations method (IEM) for analysis. Lee et al. [18] proposed wireless power transfer (WPT) as a way to effectively solve the energy supply problem of electric railway (ER). To develop such systems, design optimization has been described as a solution that optimizes objective functions (e.g., system mass, transfer efficiency and air-gap) while satisfying constraints such as electromagnetic field (EMF), magnetic saturation and induction. In this paper, an optimization framework for railway WPT system was developed by connecting optimization module and electromagnetic commercial software. In addition, because estimating the SOC (state of charge) of a battery is one of the important techniques in wireless charging electric trams, Miyamoto et al. [19,20] performed investigations about that subject. The above studies are related to the wireless power transmission technology applied to transportation. For the common use of such advanced technologies in society, it is necessary to study their management aspects, such as construction of systems with minimum investment cost as well as research on technology. However, research on the management aspect of wireless charging transportation has been rarely performed. Though dealing with general electric vehicles, Li [21] reviewed the worldwide development of battery-electric buses from medium-sized vehicles (e.g., 6.7 m) to large vehicles (e.g., 11 m) and described the charging method from low-speed charging mode (e.g., 6 h) to fast charging mode (e.g., 10 min). In addition, he reviewed the worldwide operations of battery-electric buses from real operation cases such as the early 1980s in Denver, Colorado and the early 1990s in Santa Barbara, California, and from less than 20 vehicles in a transit agency to more than 1000 vehicles. Giménez-Gaydou et al. [22] conducted a study on a method for determining the location of charging station for a battery electric vehicle (BEV) in an urban area. This approach addressed not Sustainability 2020, 12, 2920 4 of 11 only an innovative type of location-allocation model, but also BEV charging needs, charging coverage and adoption potential. Ko and Jang [3] dealt with the optimal system design of wireless charging electric vehicle. They developed a mathematical model to derive optimal battery capacity and the length andSustainability location 2020, of12, x power FOR PEER transmitter REVIEW for On-Line Electric Vehicle, which is developed4 of by11 Korea Advancedcharging Institute coverage of Science and adopti andon Technology potential. Ko (KAIST). and Jang [3] In dealt addition, with the Ko optimal et al. [ 23system] presented design of di fferent way to generatewireless charging an optimal electric design vehicle. of They wireless developed charging a mathematical electric vehicle model withto derive non-linear optimal battery cost function. They proposedcapacity and a mathematical the length and model location with of thepower concept transmitter of segments for On-Line for allElectric operation Vehicle routes, which and is adopt geneticdeveloped algorithm by to Korea calculate Advanced the Institute efficient of solution. Science and Though Technology the (KAIST). above two In addition, studies Ko dealt et al. with the decision[23 of] presented battery capacity different andway deploymentto generate an ofoptimal wireless design charging of wireless infrastructure, charging electric they vehicle did notwith consider non-linear cost function. They proposed a mathematical model with the concept of segments for all regenerative braking nor discuss battery management. There is no research on management aspects of operation routes and adopt genetic algorithm to calculate the efficient solution. Though the above wirelesstwo charging studies electricdealt with trams the withindecision our of knowledge.battery capacity and deployment of wireless charging infrastructure, they did not consider regenerative braking nor discuss battery management. There is 3. Problemno research Description on management aspects of wireless charging electric trams within our knowledge.

3.1. Problem3. Problem Statement Description

In3.1. this Problem study, Statement the optimal system design of wireless charging electric tram is developed to determine the capacity and management of battery capacity and to allocate the wireless charging In this study, the optimal system design of wireless charging electric tram is developed to infrastructure.determine As the shown capacity in and Figure management2, it is assumed of battery that capacity a railway and to isallocate divided the wireless as segment charging level with certaininfrastructure. length, l, and As each shown station in Figure is located 2, it is assumed at speciﬁc that point.a railway Then, is divided if the asith segment segment level is with decided to allocatecertain the wireless length, l,charging and each station infrastructure, is located at then specificl length point. of Then, it can if the be i assignedth segment inis decided the ith to segment. The wirelessallocate charging the wireless electric charging tram infrastructure, can be supplied then l length the electricity of it can be assigned wirelessly in the when ith segment it is operating. The on that segment.wireless Therefore,charging electric the allocation tram can be position supplied ofthe wireless electricity charging wirelessly infrastructure when it is operating should on that be decided segment. Therefore, the allocation position of wireless charging infrastructure should be decided through a mathematical model. through a mathematical model.

FigureFigure 2. The 2. The concept concept of of railway railway for for allocationallocation of of wireless wireless chargi chargingng infrastructure infrastructure.. In this example, wireless charging infrastructure consists of both inverter and inductive cable. In this example, wireless charging infrastructure consists of both inverter and inductive cable. The inverter receives the electricity and sends it to the inductive cable while the inductive cable The inverterreceives receives the electricity the electricity and sends and the sends electricity it to theto the inductive wireless cablepick-up while device the under inductive the wireless cable receives the electricitycharging and electric sends tram the using electricity electromagnetic to the induction. wireless At pick-up this time, device a series under of inductive the wireless cables can charging electricbe tram powered using by electromagnetic one inverter. However, induction. if the At inductive this time, cable a seriesis not connected, of inductive each cables inductiv cane cable be powered by onerequires inverter. a different However, inverter. if the inductive cable is not connected, each inductive cable requires a different inverter.As mentioned earlier, battery capacity and wireless charging infrastructure have a trade-off relationship. Battery capacity which is installed on a wireless charging electric tram should be derived Asconsidering mentioned the earlier, allocation battery decision capacity of wireless and charging wireless infrastructure. charging infrastructure In addition, even have if athe trade-o ff relationship.maximum Battery capacity capacity of the battery which is determined, is installed the on actual a wireless available charging battery capacity electric is limited tram should as be derivedshown considering in Figure the3, considering allocation the decision life of the of battery. wireless Therefore, charging suppose infrastructure. that the maximum In addition, capacity even if the maximumof battery capacity is decided of as the Icapa battery, then the is actual determined, battery utilization the actual area available is between battery Imin and capacity Imax [20,24 is]. As limited as shown ina result, Figure the3 ,maximum considering battery the capacity life of theshould battery. be determined Therefore, considering suppose all that those the situations. maximum capacity of battery is decided as Icapa, then the actual battery utilization area is between Imin and Imax [20,24]. As a result, the maximum battery capacity should be determined considering all those situations. This study deals with not only battery capacity but also battery management. The battery management policy also affects a significant impact on the entire system [21,25]. In addition, unlike previous studies, regenerative braking is considered when calculating the variations in battery charging level. That is, regardless of the wireless charging infrastructure, the battery charging level can increase by regenerative braking. However, the battery charging level can only be changed between Imin and Imax, and even if the electric power is supplied by the regenerative braking and the wireless charging, the battery charging level cannot exceed Imax. In this case, the supplied electricity cannot be Sustainability 2020, 12, x FOR PEER REVIEW 5 of 11

Sustainability 2020, 12, 2920 5 of 11 charged, and it is lost. Therefore, when the wireless charging electric tram starts to operate in the ﬁrst station, it is best to determine the target battery charging level, Itarget, as the optimal value between Imin and Imax. Then, it can prevent the loss of the electricity supplied by regenerative braking and wireless charging. Sustainability 2020, 12, x FOR PEER REVIEW 5 of 11

Figure 3. The concept of actual battery utilization area and target charging level.

This study deals with not only battery capacity but also battery management. The battery management policy also affects a significant impact on the entire system [21,25]. In addition, unlike previous studies, regenerative braking is considered when calculating the variations in battery charging level. That is, regardless of the wireless charging infrastructure, the battery charging level can increase by regenerative braking. However, the battery charging level can only be changed between Imin and Imax, and even if the electric power is supplied by the regenerative braking and the wireless charging, the battery charging level cannot exceed Imax. In this case, the supplied electricity cannot be charged, and it is lost. Therefore, when the wireless charging electric tram starts to operate

in the first station, it is best to determine the target battery charging level, Itarget, as the optimal value betweenFigure IminFigure and 3. I maxThe3. .The Then, concept concept it can of of prevent actual actual battery batterythe loss utilization of the electricity area area and and supplied target target charging by charging regenerative level level.. braking and wireless charging. 3.2. OverallThis Procedure study deals with not only battery capacity but also battery management. The battery management3.2. Overall policy Procedure also affects a significant impact on the entire system [21,25]. In addition, unlike The overall procedure to derive an optimal system design of wireless charging electric tram is previous studies, regenerative braking is considered when calculating the variations in battery shown in FigureThe overall4. procedure to derive an optimal system design of wireless charging electric tram is chargingshown level. in Figure That 4. is, regardless of the wireless charging infrastructure, the battery charging level can increase by regenerative braking. However, the battery charging level can only be changed between Imin and Imax, and even if the electric power is supplied by the regenerative braking and the wireless charging, the battery charging level cannot exceed Imax. In this case, the supplied electricity cannot be charged, and it is lost. Therefore, when the wireless charging electric tram starts to operate in the first station, it is best to determine the target battery charging level, Itarget, as the optimal value between Imin and Imax. Then, it can prevent the loss of the electricity supplied by regenerative braking and wireless charging. FigureFigure 4. Overall 4. Overall procedure procedure for for an an optimal optimal systemsystem design design of ofwireless wireless charging charging electric electric tram. tram.

3.2.1.3.2. Data DataOverall Collection Collection Procedure TheFirst, overall it is procedurenecessary to to collect derive the an physical optimal data system of the designwireless of charging wireless electric charging tram ,electric such as tramthe is First, it is necessary to collect the physical data of the wireless charging electric tram, such as the shownweight in Figure of the 4.tram, the acceleration and deceleration tendency, the air resistance and so on. In weight ofaddition, the tram, it is thealso accelerationnecessary to get and data deceleration on the length, tendency, gradient and the inter air resistance-station distance and soof the on. route In addition, it is alsoon necessary which the wireless to get data charging on the electric length, tram gradient will be operated. and inter-station Although it is distance not covered of thein this route study, on which the wirelessthe numb charginger of passengers electric tram can be will considered be operated. as additional Although data it to is be not collected covered in the in this future. study, the number of passengers can be considered as additional data to be collected in the future. Battery Consumption Calculation 3.2.2. BatteryBased Consumption on the collected Calculation data, the values for the power consumed in each segment, the power supplied through the regenerative braking in each segment and the power charged when the wireless Based on the collected data, the values for the power consumed in each segment, the power chargingFigure infrastructure 4. Overall procedure is installed for an in optimal each segmentsystem design should of wirelessbe calcu charginglated by electric considering tram. the suppliedcircumstance through the of regenerativewireless charging braking electric in tram each insegment operation and. For themore power detailed charged calculations, when please the wireless chargingDatarefer Collection infrastructure to Jong and Chang is installed’s work in [22 each,26]. segment should be calculated by considering the circumstance of wireless charging electric tram in operation. For more detailed calculations, please refer to Jong and OptimalFirst, it Systemis necessary Design to collect the physical data of the wireless charging electric tram, such as the Chang’sweight work of the [22 ,tram,26]. the acceleration and deceleration tendency, the air resistance and so on. In addition, it is also necessary to get data on the length, gradient and inter-station distance of the route 3.2.3. Optimal System Design on which the wireless charging electric tram will be operated. Although it is not covered in this study, theThe numb optimaler of passengers system can design be considered of the as wireless additional charging data to be electriccollected tramin the future. is derived from the mathematical model-based optimization method which is one of the techniques of operations research.Battery Then, Consumption the values Calculation of decision variables such as maximum capacity, target charging level of battery andBased allocation on the collected of wireless data, charging the values infrastructure for the power can consumed be obtained. in each This segment, is covered the inpower detail in Sectionsupplied4. through the regenerative braking in each segment and the power charged when the wireless charging infrastructure is installed in each segment should be calculated by considering the circumstance of wireless charging electric tram in operation. For more detailed calculations, please refer to Jong and Chang’s work [22,26].

Optimal System Design Sustainability 2020, 12, 2920 6 of 11

3.2.4. Real Application Finally, it is enough to operate the wireless charging electric tram system with the value of the derived decision variable. The existing decision variables can be corrected and supplemented in consideration of issues occurring during operation.

4. Mathematical Model

4.1. Notation To develop a mathematical model, the following variables are defined. Index i : Set of segments; overall route is divided by I number of segments (i = 1,2, 3 ... , I) Decision variables Icapa : Maximum capacity of battery installed in wireless charging electric tram [kWh] Itarget : Target battery charging level before operation at first station [kWh] kinverter(i) : 0–1 binary decision variable; if the inverter is allocated in ith segment, then value of 1, otherwise, value of 0 kcable(i) : 0–1 binary decision variable; if the inductive cable is allocated in ith segment, then value of 1, otherwise, value of 0 Variables ninverter : Total number of inverters applied in overall system [unit] ncable : Total length of inductive cable applied in overall system [meter] Imax : Upper limit of battery utilization area regarding maximum battery capacity [kWh] Imin : Lower limit of battery utilization area regarding maximum battery capacity [kWh] I (0) : Initial battery charging level before operation at first station [kWh] I(i) Battery charging level after passing ith segment [kWh] Input parameters ntram : Total number of wireless charging electric trams in overall system [unit] cbattery : Battery cost per unit kWh [$/kWh] cinverter : Unit inverter cost [$/unit] ccable : Inductive cable cost per unit length [$/meter] αmax : Ratio of upper limit of battery utilization area regarding maximum battery capacity αmin : Ratio of lower limit of battery utilization area regarding maximum battery capacity kcable(0) : Initial value for allocation of inductive cable, which is set as 0 s(i) : Electricity supply by wireless charging in ith segment [kWh] r(i) : Electricity supply by regenerative braking in ith segment [kWh] l(i) : Length of ith segment [meter]

4.2. Model Formulation

Minimize ntram c Icapa + n c + n c , (1) · battery · inverter · inverter cable · cable subject to Imax = αmax Icapa, (2) · I = α Icapa, (3) min min· I Itarget Imax, (4) min ≤ ≤ Itarget = I(0), (5) I(i 1) d(i) + s(i) k (i) + r(i) I(i), i = 1, ... , I, (6) − − · cable ≥ I I(i) Imax, i = 1, ... , I, (7) min ≤ ≤ k (i) k (i 1) k (i), i = 1, ... , I, (8) cable − cable − ≤ inverter Sustainability 2020, 12, x FOR PEER REVIEW 7 of 11 Sustainability 2020, 12, 2920 7 of 11

( 1) ( ) + ( ) ( ) + ( ) ( ), = 1, . . . , , (6) k (0) = 0, (9) (cable) , = 1, . . . , 𝐼𝐼 𝑖𝑖 − − 𝑑𝑑 𝑖𝑖 𝑠𝑠 𝑖𝑖 ⋅ 𝑘𝑘𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑖𝑖 𝑟𝑟 𝑖𝑖 ≥ 𝐼𝐼 𝑖𝑖 , 𝑖𝑖 𝐼𝐼 (7) XI ( ) 𝑚𝑚𝑚𝑚𝑚𝑚 ( 1)𝑚𝑚𝑚𝑚𝑚𝑚 inverter( ), = 1, . . . , , (8) 𝐼𝐼 ncable≤ =𝐼𝐼 𝑖𝑖 ≤l(𝐼𝐼i) kcable𝑖𝑖 (i),𝐼𝐼 (10) (0·) = 0 𝑘𝑘𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑖𝑖 − 𝑘𝑘𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑖𝑖 i−=1 ≤ 𝑘𝑘 , 𝑖𝑖 𝑖𝑖 𝐼𝐼 (9) I =𝑘𝑘𝑐𝑐𝑐𝑐𝑐𝑐X𝑐𝑐𝑐𝑐 ( ) ( ), (10) n = k (i), (11) inverter 𝐼𝐼 inverter 𝑛𝑛𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ∑=i=𝑖𝑖=11 𝑙𝑙 𝑖𝑖 ⋅ 𝑘𝑘𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐(𝑖𝑖), (11) kinverter(i)(, k)cable, 𝐼𝐼(i) ( )0, 1{0,,1} (12) 𝑛𝑛𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ∑𝑖𝑖=1 𝑘𝑘∈𝑖𝑖𝑖𝑖𝑖𝑖{ 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖} 𝑖𝑖 , (12) I , I , are are positive positive real real numbers, numbers, (13) capa target𝑘𝑘𝑖𝑖𝑖𝑖𝑖𝑖target𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑖𝑖 𝑘𝑘𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑖𝑖 ∈ (13) The purpose purpose of of this this problem problem is𝐼𝐼𝑐𝑐 𝑐𝑐development𝑐𝑐 is𝑐𝑐 𝐼𝐼 development of an ofoptimal an optimal system systemdesign for design wireless for charging wireless chargingelectric vehicle electric with vehicle minimum with minimum investment investment cost. Therefore, cost. Therefore,the objective the function objective of function the proposed of the proposedmathematical mathematical model, Equation model, (1), Equation is sum (1),of the is sumcosts ofsuch the as costs battery such capacity, as battery number capacity, of inverter numbers ofand inverters length of and inductive length ofcable. inductive Equation cable.s (2) Equationsand (3) are (2) ab andout battery (3) are aboututilization battery area utilization regarding area the regardingmaximum thebattery maximum capacity. battery Equation capacity. (4) Equationis for the (4)target is for battery the target charging battery level charging at initial level operation at initial operationand should and be shouldset between be set betweenits actual its battery actual utilization battery utilization area while area E whilequation Equation (5) means (5) meansthat initial that initialbattery battery charging charging level is level has the is has same the value same with value target with battery target batterycharging charging level. Equation level. Equationss (6) and (7) (6) andare for (7) the are forbattery the batterycharging charging level variation level variation during during the operation the operation of wireless of wireless charging charging electric electric tram. tram.Battery Battery charging charging level in level passing in passing by ith segment by ith segment is affected is by aﬀ ectedbattery by consumption, battery consumption, wireless charging wireless chargingand regenerative and regenerative braking in braking ith segment. in ith segment.Equations Equations (8) and (9) (8) are and developed (9) are developed to describe to describethe location the locationof each ofinverter each inverter which whichshould should be applied be applied in this in thissystem system by byconsidering considering the the number number of of separate inductive cables. Eq Equationuation (10) is about the calculation of length of installed inductive cables while EquationEquation (11) is for counting the number of applied inverters. The r remainingemaining E Equationsquations (12) and (13) address the decision variables.variables.

5. Numerical Example

5.1. System Paramet Parametersers In Korea,Korea, because because the the Pangyo Pangyo area area in Gyeonggi in Gyeonggi province province recently recently has attracted has manyattracted IT companies many IT andcompanies start-ups, and tra startﬃc-ups, demand traffic is demand tending is to tend increaseing to inincrease the urban in the area. urban In area. order In to order meet to the meet tra ﬃthec demands,traffic demands, one considered one considered alternative alternative is to operate is to operate electric elect tramsric in trams Pangyo in Pangyo area. This area. study This tried study to designtried to adesign wireless a wireless rechargeable rechargeable electric electric tram system tram system with minimum with minimum investment investment cost, assuming cost, assuming that a wirelessthat a wireless rechargeable rechargeable electric electric tram is tram installed is installed and operated and operated in this in area this as area shown as shown in Figure in 5Figure. 5.

Figure 5. Pangyo area considered to install the wireless charging electric tram system.system.

The system parameters related to the wireless charging electric tram and wireless charging infrastructure assumed in this numerical example are shown in Table 1. Sustainability 2020, 12, 2920 8 of 11

The system parameters related to the wireless charging electric tram and wireless charging infrastructure assumed in this numerical example are shown in Table1.

Table 1. System parameters.

Notation Meaning Value

Ntram Number of wireless charging electric tram [unit] 5 cbattery Battery cost per unit kWh [$/kWh] $50,000 cinverter Unit inverter cost [$/unit] $5000 ccable Inductive cable cost per unit length [$/meter] $200 αmax Ratio of upper limit of battery utilization area 0.8 αmin Ratio of lower limit of battery utilization area 0.2 l(i) Length of ith segment [meter] 20

Due to the limitations of the paper, data on the amount of electricity consumption, the amount of regenerative braking in each segment and the amount of wireless charging electricity when there is a wireless charging facility are not mentioned. However, it should be noted that the acceleration, deceleration and maximum speed are set as 1 m/s2, 1 m/s2 and 20 m/s, respectively. − 5.2. Computational Result To perform the computational experiment with the proposed mathematical model and given system parameters, Cplex, a well-known optimal solution generation software, was applied. It is guaranteed to derive optimal solution for mathematical models with a linear programming type, used both in industry and in academia [19,23]. The mathematical model consisted of objective function and constraint equations. On the way to derive the value of the objective function, various constraints reflect the actual circumstance of the problem. Moreover, the devised mathematical model is called out as a mixed integer programming model. Since the model consisted of linear equations, the optimal value can be derived. Therefore, with the adequate mathematical model and proper parameters, the program can derive optimal result through a single execution. The numerical result was derived as shown in Table2. The optimal battery capacity was set as 3.2389 kWh while the overall electricity consumption at one round trip of total route described in Figure5 considering the provided electricity by regenerative braking is 12.5041 kWh. Supposing that a decision maker introduces a pure battery-powered electric tram system instead of a wireless charging electric tram, it is also necessary to calculate the required battery capacity. It can be calculated assuming no wireless charging infrastructure can be installed on all railways; the required battery capacity is then 21.9392 kWh. In other words, the required battery capacity can be reduced to 14.76% by introducing a wireless charging electric tram. Of course, the additional cost of wireless charging infrastructure is required, but the utility of the wireless charging electric tram system can be confirmed considering the fact that the battery itself is an important environmental pollutant. In addition, target battery charging level before operation at first station was calculated as 1.7997 kWh when the upper limit of battery utilization area is 2.5911 kWh. In the previous study, it was assumed that the amount of battery charging level at the starting point is always regarded as maximum level. However, in this study, the initial battery charging level was reduced to 69.46% of maximum level by applying battery management. Therefore, more than 30% of the potential electricity is saved over the entire battery capacity in case of intuitive full charge. Moreover, there were eight separate wireless charging infrastructures on overall railways. That is, the total number of inverters was eight while the total length of inductive cables is 1380 m. The inductive cable was allocated between 0 m and 420 m, between 580 m and 680 m, between 960 m and 1040 m, between 1340 m and 1400 m, between 1640 m and 1720 m, between 1960 m and 2040 m, between 2320 m and 2400 m, and between 2680 m and 3160 m as well. All of the wireless charging infrastructures were allocated near the stations; the relative location of each station was 20 m, 640 m, 1020 m, 1380 m, Sustainability 2020, 12, 2920 9 of 11

1700 m, 2020 m, 2380 m, 2760 m, and 3380 m. This is because the speed of a wireless charging electric Sustainability 2020, 12, x FOR PEER REVIEW 9 of 11 tram is relatively low near the station, so it can receive more electricity through wireless charging. In addition, target battery charging level before operation at first station was calculated as 1.7997 kWh when the upper limit of batteryTable 2. utilizationThe result of area numerical is 2.5911 example. kWh. In the previous study, it was assumed that the amount of batteryContent charging level at the starting point Value is always regarded as maximum level. However, in this study, the initial battery charging level was reduced to 69.46% of Total investment cost $1,125,725 maximum level by applyingThe optimal battery battery management. capacity Therefore, more 3.2389than 30% kWh of the potential electricity is Targetsaved batteryover the charging entire level battery before capacity operation in atcase ﬁrst of station intuitive full1.7997 charge. kWh Moreover, there were eigTotalht numberseparate of wireless inverters charging infrastructures 8on units overall railways. That is, the total number of invertersTotal length was of eight inductive while cable the total length of inductive 1380 cables m is 1380 m. The Location of 1st inductive cable 0 m–420 m inductive cable was allocated between 0 m and 420 m, between 580 m and 680 m, between 960 m and Location of 2nd inductive cable 580 m–680 m 1040 m, between 1340 mLocation and 140 of0 3rdm, inductivebetween cable1640 m and 1720 m, between 960 m–1040 196 m0 m and 2040 m, between 2320 m and 240Location0 m, and of between 4th inductive 2680 cable m and 3160 m as well. 1340 All m–1400of the wireless m charging infrastructures were allocatedLocation near of the 5th inductivestations; cablethe relative location of 1640each m–1720station mwas 20 m, 640 m, 1020 m, 1380 m, 1700 m, 202Location0 m, 238 of 6th0 m inductive, 2760 m cable, and 3380 m. This is because 1960 m–2040 the speed m of a wireless Location of 7th inductive cable 2320 m–2400 m charging electric tram isLocation relatively of 8thlow inductive near the cable station, so it can receive 2680 m–3160more electricity m through wireless charging. The variation of battery charging level is depicted in Figure 6. Since the maximum battery capacityThe variationwas 3.2389 of kWh, battery the charging upper and level the is depictedlower limitations in Figure 6of. Sincebattery the utili maximumzation area battery were capacity 2.5911 waskWh 3.2389 and 0.6477 kWh, kWh, the upper respectively. and the It lowercan be limitations confirmed ofthat battery the battery utilization charging area level were varied 2.5911 within kWh andthat 0.6477range. kWh,For all respectively. of the above It situations, can be conﬁrmed the total that investment the battery cost charging of the numerical level varied example within thatwas range.derived For to all$ 1,125,725. of the above situations, the total investment cost of the numerical example was derived to $1,125,725.

Figure 6. Battery charging level variation.variation.

6. Concluding Remarks There are are many many attempts attempts to introduce to introduce and operate and operate electric electric trams in trams certain in areas certain as an areas alternative as an alternativemeans of transportation means of transportation considering consideringenvironmental environmental pollution. In pollution. this study, In the this efficient study, deployment the efficient deploymentdesign of the design wireless of the wirelesscharging charging electric electrictram system tram system which which can can maximize maximize the the environmental advantage of the electric electric tram tram has has been been particularly particularly studied. studied. The The wireless wireless charging charging electric electric tram tram is an is aninnovative, innovative, new new-style-style electric electric tram tram which which can can be be supplied supplied electricity electricity wirelessly wirelessly from from the wireless charging infrastructureinfrastructure installed installed on on railways railways even even though though it is moving. it is moving. Therefore, Therefore, the wireless the chargingwireless electriccharging tram, electric which tram, can which overcome can overcome various various disadvantages disadvantages caused caused by the by electric the electric supply supply line ofline a conventionalof a conventional electric electric tram tram and reduce and reduce the high the battery high battery cost of cost a pure of battery-powereda pure battery-powered type electric type tram,electric has tram, received has received attention attention as a new as transportation a new transportation means in means an urban in an area. urban area. Though wireless charging electric trams have many advantages, eefficientfficient design of the entireentire system toto minimize minimize the the total total investment investment cost cost is required is required for successful for successful application. application. For that, For the that, optimal the decisionoptimal aboutdecision the about maximum the maximum battery capacity battery and capacity the allocation and the of wirelessallocation charging of wireless infrastructure charging infrastructure to minimize the investment cost was investigated. In addition, regenerative braking was considered to reflect the accurate electrical flow in the system, and battery management about the initial battery charging level was also investigated for additional electric efficiency. A Sustainability 2020, 12, 2920 10 of 11 to minimize the investment cost was investigated. In addition, regenerative braking was considered to reflect the accurate electrical flow in the system, and battery management about the initial battery charging level was also investigated for additional electric efficiency. A mathematical model-based optimization technique was adopted to treat those decision-making elements, and Cplex was applied to derive an optimal solution for those decision-making elements. Through the numerical example, the total investment cost was calculated with the information of decision-making elements such as maximum battery capacity, initial battery charging level, number of inverters and location of inductive cables. By applying the wireless charging electric tram in the Pangyo area described in Figure5, it can be confirmed that maximum battery capacity was reduced by 14.76% compared to the pure battery-powered electric tram, and initial battery charging level was also decreased by 69.46% with battery management. For transportation to be operated well, the infrastructure should come first. Especially when it comes to the new technology, a deliberate decision should be made. As can be seen in the results of this research, the battery capacity can be different due to the location of inductive cable and inverters. Since the battery cost is expensive, this research can provide a stable and cost-efficient way to set the infrastructure for an electric tram. However, there can exist various other transportation that consider adopting the wireless charging system. In those cases, more constraints that can reflect certain transportation environments should be devised. As a further study, various transportation environments and operation policies will be considered. Since there are lots of transportations with different policies, the needed infrastructure for wireless charging electric trams can also be different. For example, there exists public transportation with both normal operation that passes every station, and express operation that bypasses certain designated stations. In this case, diverse constraints should be made. By reflecting the different operation policy of transportation, the practicality of the following research to be done might increase.

Author Contributions: Y.D.K. defined the concept and topic of this study, and designed, performed and analyzed the mathematical experiments. Y.O. investigated the previous studies and reviewed the overall manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by the MSIP (Ministry of Science, ICT & Future Planning), Korea, under the National Program for Excellence in SW) (2015–0-00938) supervised by the IITP (Institute for Information & communications Technology Planning & Evaluation). Conflicts of Interest: The authors declare no conflict of interest.

References

1. Costa, A.; Fernandes, R. Urban public transport in Europe: Technology diﬀusion and market organisation. Transp. Res. Part A Policy Pract. 2012, 46, 269–284. 2. Cho, D.; Jung, G.; Yoon, U.; Lee, B. Development & implementation of electric tram system with wireless charging technology. ICT Express 2015, 1, 34–38. 3. Ko, Y.D.; Jang, Y.J. The optimal system design of the online electric vehicle utilizing wireless power transmission technology. IEEE Trans. Intell. Transp. Syst. 2013, 14, 1255–1265. [CrossRef] 4. Shinohara, N. Power without wires. IEEE Microw. Mag. 2011, 12, S64–S73. [CrossRef] 5. Lu, X.; Wang, P.; Niyato, D.; Kim, D.I.; Han, Z. Wireless charging technologies: Fundamentals, standards, and network applications. IEEE Commun. Surv. Tutor. 2016, 18, 1413–1452. [CrossRef] 6. Waﬀenschmidt, E.; Staring, T. Limitation of inductive power transfer for consumer applications. In Proceeding of the 13th European Conference on Power Electronics and Applications, Barcelona, Spain, 8–10 September 2009; pp. 1–10. 7. Cannon, B.L.; Hoburg, J.F.; Stancil, D.D.; Goldstein, S.C. Magnetic resonant coupling as a potential means for wireless power transfer to multiple small receivers. IEEE Trans. Power Electron. 2009, 24, 1819–1825. [CrossRef] 8. Kline, M.; Izyumin, I.; Boser, B.; Sanders, S. Capacitive power transfer for contactless charging. In Proceedings of the 2011 Twenty-Sixth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Fort Worth, TX, USA, 6–11 March 2011; pp. 1398–1404. Sustainability 2020, 12, 2920 11 of 11

9. Jabbar, H.; Song, Y.S.; Jeong, T.T. RF energy harvesting system and circuits for charging of mobile devices. IEEE Trans. Power Electron. 2010, 56, 247–253. [CrossRef] 10. Machura, P.; Li, Q. A critical review on wireless charging for electric vehicles. Renew. Sust. Energy Rev. 2019, 104, 209–234. [CrossRef] 11. Shi, B.; Yang, F.; Wang, S.; Ouyang, M. Eﬃciency Improvement of Wireless Charging System Based on Active Power Source in Receiver. IEEE Access 2019, 7, 98136–98143. [CrossRef] 12. Bi, Z.; Keoleian, G.A.; Lin, Z.; Moore, M.R.; Chen, K.; Song, L.; Zhao, Z. Life cycle assessment and tempo-spatial optimization of deploying dynamic wireless charging technology for electric cars. Transp. Res. Part C Emerg. Technol. 2019, 100, 53–67. [CrossRef] 13. He, J.; Yang, H.; Tang, T.Q.; Huang, H.J. Optimal deployment of wireless charging lanes considering their adverse eﬀect on road capacity. Transp. Res. Part C Emerg. Technol. 2020, 111, 171–184. [CrossRef] 14. Huh, J.; Lee, S.; Park, C.; Cho, G.H.; Rim, C.T. High performance inductive power transfer system with narrow rail width for on-line electric vehicles. In Proceedings of the 2010 IEEE Energy Conversion Congress and Exposition (ECCE), Atlanta, GA, USA, 12–16 September 2010; pp. 647–651. 15. Wang, C.S.; Stielau, O.H.; Covic, G.A. Design considerations for a contactless electric vehicle battery charger. IEEE Trans. Ind. Electron. 2005, 52, 1308–1314. [CrossRef] 16. Huang, C.Y.; Boys, J.T.; Covic, G.A.; Budhia, M. Practical considerations for designing IPT system for EV battery charging. In Proceedings of the 2009 IEEE Vehicle Power and Propulsion Conference, Dearborn, MI, USA, 7–10 September 2009; pp. 402–407. 17. Fujii, N.; Mizuma, T. Analytical study of special linear motor-transformer for wireless tram. In Proceedings of the 2008 IEEE Industry Applications Society Annual Meeting, Edmonton, AB, Canada, 5–9 October 2008; pp. 1–7. 18. Lee, S.B.; Ahn, S.; Lee, J.H.; Jang, I.G. Optimization of the wireless power transfer system in an electric railway. In Proceedings of the 2014 IEEE Wireless Power Transfer Conference (WPTC), Jeju, Korea, 8–9 May 2014; pp. 158–161. 19. Miyamoto, H.; Morimoto, M.; Morita, K. On-line SOC estimation of battery for wireless tram car. In Proceedings of the 7th International Conference on Power Electronics and Drive Systems, Bangkok, Thailand, 27–30 November 2007; pp. 83–89. 20. Miyamoto, H.; Morimoto, M.; Morita, K. Online SOC estimation of battery for wireless tramcar. Electr. Eng. Jpn. 2014, 186, 83–89. [CrossRef] 21. Li, J.Q. Battery-electric transit bus developments and operations: A review. Int. J. Sustain. Transp. 2016, 10, 157–169. [CrossRef] 22. Giménez-Gaydou, D.A.; Ribeiro, A.S.; Gutiérrez, J.; Antunes, A.P. Optimal location of battery electric vehicle charging stations in urban areas: A new approach. Int J. Sustain. Transp. 2014, 10, 393–405. [CrossRef] 23. Ko, Y.D.; Jang, Y.J.; Lee, M.S. The optimal economic design of the wireless powered intelligent transportation system using genetic algorithm considering nonlinear cost function. Comput. Ind. Eng. 2015, 89, 67–79. [CrossRef] 24. Oh, Y.K.; Kwak, J.H.; Lee, H.Y. The SOC Management Strategy of Battery System for Propulsion in Wireless Low Floor System. In Proceedings of the KSR Conference; Korean Society for Railway: Jeju, Korea, 2011; pp. 2329–2335.

25. Plötz, P.; Funke, S.Á.; Jochem, P. The impact of daily and annual driving on fuel economy and CO2 emissions of plug-in hybrid electric vehicles. Transp. Res. Part A Policy Pract. 2018, 118, 331–340. [CrossRef] 26. Jong, J.C.; Chang, E.F. Models for estimating energy consumption of electric trains. J. East Asia Soc. Transp. Stud. 2005, 6, 278–291.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).