The Impact of Coil Position and Number on Wireless System Performance for Electric Vehicle Recharging

sensors

Article The Impact of Coil Position and Number on Wireless System Performance for Electric Vehicle Recharging

Naoui Mohamed 1 , Flah Aymen 1,* , Zaafouri Issam 1, Mohit Bajaj 2 , Sherif S. M. Ghoneim 3 and Mahrous Ahmed 3

1 Processes, Energy, Environment and Electrical Systems (Code: LR18ES34), National Engineering School of Gabès, University of Gabès, Gabès 6072, Tunisia; [email protected] (N.M.); [email protected] (Z.I.) 2 National Institute of Technology, Delhi 110040, India; [email protected] 3 Department of Electrical Engineering, College of Engineering, Taif University, Taif 21944, Saudi Arabia; [email protected] (S.S.M.G.); [email protected] (M.A.) * Correspondence: ﬂ[email protected]

Abstract: Recently, most transportation systems have used an integrated electrical machine in their traction scheme, resulting in a hybrid electrified vehicle. As a result, an energy source is required to provide the necessary electric power to this traction portion. However, this cannot be efficient without a reliable recharging method and a practical solution. This study discusses the wireless recharge solutions and tests the system’s effectiveness under various external and internal conditions. Moreover, the Maxwell tool is used in this research to provide a complete examination of the coils’ position, size, number, and magnetic flux evolution when the coils are translated. In addition, the mutual inductance for each of these positions is computed to determine the ideal conditions for employing the wireless recharge tool for every charging application. A thorough mathematical analysis is also presented, and Citation: Mohamed, N.; Aymen, F.; the findings clearly demonstrate the relationship between the magnet flux and the various external Issam, Z.; Bajaj, M.; Ghoneim, S.S.M.; Ahmed, M. The Impact of Coil conditions employed in this investigation. Position and Number on Wireless System Performance for Electric Keywords: wireless recharge; electriﬁed transportation; magnet ﬂux; Ansys Maxwell software; Coil’s Vehicle Recharging. Sensors 2021, 21, position; electric vehicle 4343. https://doi.org/10.3390/ s21134343

Academic Editor: Fabio Viola 1. Introduction The area of electric vehicles (EVs) is becoming increasingly relevant in this decade. The Received: 16 May 2021 majority of transportation applications are electrified and employ an electrical powertrain Accepted: 23 June 2021 to supply the necessary mechanical power to these tools [1]. This equipment is often built Published: 25 June 2021 around an electrical machine linked to an electronic converter that regulates the motor speed dependent on the acceleration requirement [2]. There is also a power pack battery Publisher’s Note: MDPI stays neutral within, which serves as the primary energy source in the event of a pure electric car. This with regard to jurisdictional claims in principle energy source must be refilled whenever it is exhausted. Actually, the discharg- published maps and institutional affil- ing curve is determined by various factors, including the acceleration form utilized, the iations. battery’s lifetime, the charging/discharging cycle, the battery temperature, and the initial state of charge when the battery is charged [3,4]. Thus, the major of researchers try finding useful solutions for improving the battery lifetime by minimizing the recharge/discharge number or increasing the vehicle autonomy by reducing the quantity of the consumed Copyright: © 2021 by the authors. power from the main energy source, especially by making the recharge action easier. This Licensee MDPI, Basel, Switzerland. goal was to assist in developing a wireless power transfer (WPT) technology that might This article is an open access article be used to charge an electric vehicle. In this field, the research was not stopped, and more distributed under the terms and than applications and solutions were presented to improve the performances of this kind conditions of the Creative Commons of recharge tool [5]. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ Basing on the conductors’ feedback and the electric car manufacturer’s trends, which 4.0/). is based on the utility and the simplicity of the recharge tool use and how this recharge

Sensors 2021, 21, 4343. https://doi.org/10.3390/s21134343 https://www.mdpi.com/journal/sensors Sensors 2021, 21, 4343 2 of 19

solution can help increasing selling electric vehicle into the world, the WPT principle can be a useful solution [6,7]. But this technology must be more robust and must have a better energetic rentability. The conventional solution is based on only one receiver placed undo the vehicle, and this prototype does not give enough power. This is conducted to search how it is possible integrating two receivers to undo the car and test the efficiency of this solution. This approach cannot be used until testing is performed to determine how the magnetic field influences the two linked coils and what parameters can impact the entire system. The leading technology of the wireless energy transmission between a primary and a secondary coil was firstly proposed by Kurs [8]. This system was found suitable and applicable for electric vehicle recharge applications [9]. Basically, wireless charging was applied for stationary cases, and its efficiency was proved. However, the quantity of transferred energy depends on the coil’s size and inverter performances [10,11]. The coil to coil case was tested in more than a technical review, and the only relation between the number of inductance turns is studied for searching about the efficiency [12]. From the other side, this system was studied by working on the different circuit topologies that can be used to affect the system performances [13]. These studies were searched to improve the versions of this WPT technology, but the possibility of using two receivers’ coils was not tested and mainly studied. Some researchers have investigated the use of more than coil applications for some Biomedical applications [14]. The results showed the importance of this addition and proved some related problems related to the resonance between the coils. This is also discussed by the authors of [15,16]. Moreover, working on the coils form was a severe challenge for researchers. The major of the existing literature was used the rectangular coil to form the main structure, due to its immense power. However, placing two closed receiver coils was found difficult in these versions [17–20]. Actually, the measurement tool of these systems is not very easy, and it needs an initial check for the given performances before starting use. Based on the previous information and by showing the different works of literature, the wireless recharge system has several weaknesses in relation to the coils centralization and then appeared problem in relation to the recharge time or the power losses. Moreover, the standard version, which bases on only one receiver and only one transmitter, has shown a fewer performance in relation to the recharge time for the electrical transportation system, as the electric vehicle. Therefore, studying the possibility of having two coils receiver under an electric vehicle seems essential to test the actual efficiency of this kind of wireless recharge upgrade. Furthermore, as the placement of two coils in serial, can present a problem regarding the mutual flux, the energetic global performances will be affected. This study gives a detailed analysis and discussion regarding these problems and shows what kind of problem can appear. Finally, it recommends using this upgraded version of the wireless recharge solution. This paper provides a comprehensive analysis of coil placement in space and demon- strates what benefits may be obtained if more than one receiver coil is utilized for the same transmitter. This study employed the Maxwell tool to display the magnet flux inside and around the coil and the potentially usable space for energy feedback. The forms of flux vectors from the transmitter to the receivers are shown and explained. This gives information about the movement of flux in the field around the coils. At the end of this analysis, the reader will find useful information for correctly modeling the wireless transmitter and have information about the exigence for using a double coil receiver to face the only one coil receiver. The statics of the utility of the double receiver coils face the only one receiver coil on the electric vehicle autonomy is shown at the end and show the weakness and advantages of each proposal. For having the paper goal, the manuscript is organized as follows. After the introduction section, a general paragraph is implemented, which describes the relationship between the electric vehicle and the wireless recharge method. In the third section, the overall architecture of the principle of the magnetic recharge system is presented. This is Sensors 2021, 21, x FOR PEER REVIEW 3 of 20

showing the different possible topologies. The fourth section shows the mathematical model of the induction charger system and explains the equations used to quantify the final outputted power. The fifth section shows the main objective of this paper. It contains all the analysis results made on the positions of the coils and dimensions. It also contains the needed information about the practice application, which validates the analysis study made with the Maxwell tool. In the end, the conclusion section concludes the paper by resuming the continent and showing future endeavors.

Sensors 2021, 21, 4343 2. Electric Vehicle (EV), Hybrid Electric Vehicle (HEV), and Wireless Recharge 3 of 19 Architectures 2.1. Hybrid and Pure EV in the Literature by showingBasically, the two different models possible of electric topologies. vehicle The exit. fourth The hybrid section version shows theand mathematical the pure ver- modelsion. Figure of the induction1, exposes chargerthese two system different and explainsarchitectures. the equations The combustion used to quantifyengine is thethe ﬁnalonly outputted different block power. from The the ﬁfth pure section electric shows vehicle the main prototype objective in the of thishybrid paper. version. It contains It can allbe theplaced analysis in serial results or in made parallel on with the positions the traction of the system. coils Thus, and dimensions. the nomination It also of containsa parallel theor a needed serial HEV information appears about [21]. the practice application, which validates the analysis study madeBasically, with the Maxwellinside an tool.electric In vehicle, the end, the the initial conclusion pack of section components concludes regroups the paper a source by resumingof energy thebeside continent a battery and system showing connected future endeavors. to the power electronic converter for feeding the main electric motor. The power managing principle is based on a control loop that is 2.placed Electric into Vehicle a high-speed (EV), Hybrid calculator, Electric which Vehicle controls (HEV), all blocks and Wireless inside the vehicle [22]. Recharge Architectures Generally, each of these versions has weaknesses and advantages, and this can be 2.1. Hybrid and Pure EV in the Literature shown in this study [23]. But the main advantage of the pure electric vehicle is the envi- ronmentalBasically, benefit two modelsand the of absence electric of vehicle any gas exit. emission The hybrid problem. version That and advantage the pure version. has en- Figurecouraged1, exposes researchers these to two make different this transport architectures. solution The more combustion efficient, engineand many is the applica- only differenttions, modifications, block from theand pure contributions electric vehicle have appeared. prototype For in theexample, hybrid some version. researchers It can betry placedoptimizing in serial the or size in parallelof the traction with the part, traction improving system. Thus,the battery the nomination technologies, of a parallelor finding or amore serial recharge HEV appears solutions [21]. [24].

BEV

HEV

Battery Electric Electronic ICE Fuel inverter motor

FigureFigure 1. 1.The The architecturearchitecture of of the the EV EV and and the the HEV. HEV.

2.2. TheBasically, Wireless inside Charging an electric System vehicle, the initial pack of components regroups a source of energyAs the beside wireless a battery recharge system solution connected is found to the suitable power for electronic an electric converter vehicle forapplication, feeding thestudying main electric correctly, motor. this Thesystem power is found managing useful principle for knowing is based the on weaknesses a control loop points that and is placedwhat kind into aof high-speed parameters calculator, and variables which can controls affect the all rentability. blocks inside Initially, the vehicle it is mandatory [22]. to knowGenerally, about eachthe overall of these wireless versions recharge has weaknesses system, which and advantages,composes several and this blocks can and be shownhas an inexceptional this study architecture. [23]. But the Figure main 2 advantage shows these of blocs. the pure Basically, electric a vehiclewireless is charging the en- vironmentalsystem regroups benefit one and coil the receiver absence and of one any co gasil transmitter. emission problem. The transmitter That advantage can be found has encouragedin motion for researchers various speeds to make andthis positions, transport and solution the distance more between efficient, the and two many coils appli-is sep- cations,arated by modifications, a vacuum, which and contributions can be variable. have The appeared. transmitter For example,block generates some researchers alternating trymagnetic optimizing flux thewith size high of frequency the traction (HF). part, This improving inverter the contains battery a technologies, filter bloc adaptable or finding for morethe high recharge frequency solutions outputted [24]. signal, called HFX inverter. This magnetic flux is coupled to the receiving coil and converted into electrical energy that can be used to charge a bat- 2.2. The Wireless Charging System tery of EV. As the wireless recharge solution is found suitable for an electric vehicle application, studying correctly, this system is found useful for knowing the weaknesses points and what kind of parameters and variables can affect the rentability. Initially, it is mandatory to know about the overall wireless recharge system, which composes several blocks and has an exceptional architecture. Figure2 shows these blocs. Basically, a wireless charging system regroups one coil receiver and one coil transmitter. The transmitter can be found in motion for various speeds and positions, and the distance between the two coils is separated by a vacuum, which can be variable. The transmitter block generates alternating magnetic flux with high frequency (HF). This inverter contains a filter bloc adaptable for the high frequency outputted signal, called HFX inverter. This magnetic flux is coupled to the receiving coil and converted into electrical energy that can be used to charge a battery of EV. Sensors 2021, 21, x FOR PEER REVIEW 4 of 20

Generally, the basic variable that must be supervised and used for evaluating the performance of the wireless recharge solution. Performance is related to the given electrical power used for charging the battery pack. This depends on the distance between the Sensors 2021, 21, 4343 transmit coil and the receive coil, the amount of energy emitted, according to the positions4 of 19 of the coils [25].

FigureFigure 2. Different 2. Different needed needed blocs blocs for forthe theoverall overall WPT WPT system. system.

3. DifferentGenerally, Topologies the basic variable that must be supervised and used for evaluating the performance of the wireless recharge solution. Performance is related to the given electrical powerFor this used study, for the charging main objective the battery of the pack. wireless This dependscharging on system the distance is related between to vehicle the charging.transmit The coil recharge and the action receive was coil, found the amount depends of energy on various emitted, conditions, according as to thethe positionsbattery stateof of the charge coils [25and]. the type of compensation topology. There are four resonant circuit topologies that could be used in the Induction Power Transfer system. They are named after3. the Different way of Topologiesinserting the resonance capacitors on each side: connection in parallel (P) and/or inFor series this (S). study, Therefore, the main the objective topologi ofes the can wireless be described charging as system follows: is relatedSS, SP, toPS, vehicle and PP. charging.Table 1 regroups The recharge all of these action topologies was found [26,27]. depends The on corresponding various conditions, capacitor as the formula battery in thestate receiver of charge or the and transmitter the type ofcoils compensation can be found topology. differences There in the are compensation four resonant topol- circuit ogies.topologies Table 1, thatgives could all these be used formulas. in the Induction Power Transfer system. They are named after the way of inserting the resonance capacitors on each side: connection in parallel (P) Table 1. Internal parametersand/or of transmitter in series (S).and Therefore,receiver coils the according topologies to the can compensation be described topology as follows: form. SS, SP, PS, and PP. Table1 regroups all of these topologies [ 26,27]. The corresponding capacitor formula in Features Series-Series (SS)the receiverSeries-Parallel or the transmitter (SP) Parallel-Series coils can be found (PS) differences Parallel-Parallel in the compensation (PP) topologies. 1 Table1, gives all these formulas. 1 1 Primary 1 𝑀 Table 1. Internal parameters of transmitter and receiver coils according to the compensation⎛ topology form. ·𝑅 ⎞ 𝑀 𝜔 ·𝑀 𝑀 𝐿 capacitor 𝜔 ·𝐿 𝜔 ·𝐿 − 𝜔 ·𝐿 − 𝜔 · ⎜𝐿 − + ⎟ 𝐿 𝐿 ·𝑅 𝐿 𝑀 Features Series-Series (SS) Series-Parallel (SP) Parallel-Series (PS) Parallel-Parallel𝜔 ·𝐿 − (PP) 𝐿 ⎝ 1 ⎠  4  1 1 1 M ·R2 2 2 4 4 load SecondaryPrimary capacitor 1 2 1 2 M 1 2 ω ·M 1 M2 Ls ω ·LP ω · LP− ω · LP − ω2· L − + Ls LP·Rload  P Ls 2  ω2· L − M capacitor 𝜔 ·𝐿 𝜔 ·𝐿 𝜔 ·𝐿 𝜔 ·𝐿 P Ls

Secondary 𝜔·𝐿 1 1 𝜔·𝐿 1 1 Load 2 𝜔·𝐿 ·𝑄 2 2 𝜔·𝐿 ·𝑄 2 capacitor ω ·Ls ω ·Ls ω ·Ls ω ·Ls 𝑄 𝑄 ω·L ω·L Load Rloads represents the resistanceω·Ls· Qloads on the secondary coil.s ω·Ls·Qs Qs Qs

Rload represents the resistance load on the secondary coil.

4. Modeling of the Wireless Charging System: One or Two Coil Receivers 4.1. Wireless Charging System with a Simple Receiver Coil For the electric vehicle application, the wireless charging system is one of the main processes that transfer the electrical energy to the battery to help to charge and increasing vehicle autonomy. Therefore, the study of this system needs to define all possible parameters and variables that can affect the global performances of this recharge tool. Figure3 illustrates all of these external variables related to the vehicle position face the transmitter coil position. In addition, it shows the case of only one receiver implemented under the vehicle.

Sensors 2021, 21, x FOR PEER REVIEW 5 of 20

Sensors 2021, 21, x FOR PEER REVIEW4. Modeling of the Wireless Charging System: One or Two Coil Receivers 5 of 20

4.1. Wireless Charging System with a Simple Receiver Coil For the electric vehicle application, the wireless charging system is one of the main 4.processes Modeling that of transferthe Wireless the electrical Charging energy System: to the One battery or Two to help Coil to chargeReceivers and increasing 4.1.vehicle Wireless autonomy. Charging Therefore, System with the astudy Simple of Receiverthis system Coil needs to define all possible parameters and variables that can affect the global performances of this recharge tool. Figure 3 For the electric vehicle application, the wireless charging system is one of the main illustrates all of these external variables related to the vehicle position face the transmitter processes that transfer the electrical energy to the battery to help to charge and increasing coil position. In addition, it shows the case of only one receiver implemented under the vehiclevehicle. autonomy. Therefore, the study of this system needs to define all possible parameters andIn this variables phase, thethat selected can affect compensation the global performancestopology is the of SS this model, recharge and then tool. the Figure cor- 3 Sensors 2021, 21, 4343 illustratesresponding all modelof these is externalgiven, as variables shown in related Figure to 4. theThis vehicle is by taken position into face consideration the transmitter5 ofall 19 coilvariable position. parameters In addition, like resistance, it shows localthe case inductances, of only one and receiver mutual inductance.implemented We under note by the vehicle.V1 and V2 the input and output voltages of this IPT [13]. In this phase, the selected compensation topology is the SS model, and then the corresponding model is given, as shown in Figure 4. This is by taken into consideration all variable parameters like resistance, local inductances, and mutual inductance. We note by V1 and V2 the input and output voltages of this IPT [13].

Figure 3. Structure of the inductive power transfer transfer system. system. In this phase, the selected compensation topology is the SS model, and then the corresponding model is given, as shown in Figure4. This is by taken into consideration all variable parameters like resistance, local inductances, and mutual inductance. We note by V1Figureand V 3.2 theStructure input of and the output inductive voltages power of transfer this IPT system. [13].

CPT Transformer

Figure 4. SS compensation topology design with RL load.

CPT Transformer

Figure 4. SS compensation topology design with RL load. Figure 4. SS compensation topology design with RL load.

Firstly, it was indicated that La = Lp − M, and Lb = Ls − M. La, and Lb represent the primary and secondary winding leakage inductances, respectively. In this model, the primary voltage of the coil is noted Vp, which is formed by a sinusoidal voltage source noted V1. Here, RL represents a serial resistive load. It is used to quantify the ﬁnal expression of the global yield value, as shown in Equation (7). Expression (1) shows Sensors 2021, 21, 4343 6 of 19

the power consumption formula if a resistive load is connected, considering the mutual inductance parameter in the function of the primary current [28].

2 ! 2 (ωM) Pwr = Ip. (1) RL

The global impedance of the primary coil can be expressed in Equations (2) and (3). Thus, the corresponding primary current can be evaluated, as seen in Equation (4).

Z1 = X + Y (2)

 (Mω)2  X = j jω(L +M)− +R +R b ω·Cs s L (3)  Y = jω(L + M) − j + R a ω·Cp p

V1 I1 = (4) Z1

The primary and secondary capacitance dimension noted Cp or Cs must be evaluated under a null imaginary part of Z1. The corresponding equation of the related capacitance can then be expressed, as seen in Equation (5).

1 = = Cp CS 2 (5) ω (Lb + M)

The energetic yield of the WPT system can be evaluated if using the Equation (6). The resistance value greatly inﬂuences the yield, as they are supposed to be a real load inside the overall system. Therefore, this expression shows these parameters inside [29].

 → I ·R  s L  η = 2 2 2 → → → Ip ·Rp+ Is ·Rs+ Is ·RL (6)   |Ip|  = Rs+RL |Is| ω·M

Finally, it is concluded that only the reciprocal inductance between the primary and the secondary side coils is connected to the system transmission strength. Therefore, reducing variable parameters makes it easier to study the stability of transmission power and the system efﬁciency given in Equation (7) [10].

R = L η 2 (7) Rp.(Rs+RL) RL + Rs + (ωM)2

RL, in Equation (7), is the secondary side load impedance, R2 and R1 are the secondary and primary sides’ internal impedance, respectively. When the charging system is definite, the load and the internal impedance are constant. It can be concluded that the system efficiency is only related to mutual inductance between the primary and the secondary side coils. The condition for achieving optimal efficiency can be deduced from Equation (7). Rp(Rs+RL) The highest possible efficiency can be achieved if ω2 M2 tends to 0. As a result: q Rp(Rs + RL) ω (8) M In that case, the theoretical maximum efficiency will be, as seen in Equation (9).

RL ηmax = (9) RL + Rs Sensors 2021, 21, x FOR PEER REVIEW 7 of 20

side coils. The condition for achieving optimal efficiency can be deduced from Equation ( ) (7). The highest possible efficiency can be achieved if tends to 0. As a result:

𝑅(𝑅 +𝑅) 𝜔≫ (8) 𝑀 In that case, the theoretical maximum efficiency will be, as seen in Equation (9).

𝑅 (9) 𝜂 = 𝑅 +𝑅

4.2. Wireless Charging System with Multiple Receiver Coils According to the present section, to improve the coupling between the coils, a shield can be used to increase the mutual inductance, noted M, by increasing the magnetic flux between the coils and adding another receiver coil. Figure 5 shows the schematic of the secondary side containing two coil receivers (n = 2), and it presents how much is the zone of the magnetic field according to the positions of the coils. The two receiver coils are normally designed identically, and the total impedance reflected from the receiver part is expressed in Equation (10); n is the number of receiver coils. ∑ 𝑍 =𝑛 (10) Sensors 2021, 21, 4343 The equivalent coupling coefficient is then expressed in Equation (11), 7and of 19 this is equivalent to the reflected impedance of a single identical sensor with an equivalent mutual inductance expressed in Equation (12). 4.2. Wireless Charging System with Multiple Receiver Coils 𝑘 = 𝑛 ·𝑘 According to the present section, to improve √ the coupling between the coils, a shield (11) can be used to increase the mutual inductance,0𝑘1 noted M, by increasing the magnetic ﬂux between the coils and adding another receiver coil. Figure5 shows the schematic of the secondary side containing two coil receivers𝑀 = (n =√ 2),𝑛 ·𝑀 and it presents how much is the zone (12) of the magnetic ﬁeld according to the positions of the coils.

Figure 5.Figure Wireless 5. Wireless power power transfer transfer design design for for two two receiver receiver coils: coils: ( a) highhigh magnetic magnetic field field zone, zone, (b) medium(b) medium magnetic magnetic field field with onewith receiver, one receiver, (c) medium (c) medium magnetic magnetic field field with with two two receivers. receivers.

The two receiver coils are normally designed identically, and the total impedance re- 5. Impactsflected fromof Coil the receiverPosition part and is expressed Receiver in Coil Equation Number (10); n onis thethe number WPT Performance of receiver coils. In this section, the performance of the wireless Power Transfer is evaluated according n ω2 M2 to various external and internal parametersZ = n related to the receiver face, the transmitter(10) ∑ ri Z position, and accordingly to the numberi=1 of coil receivers.s The Ansys Maxwell application is used forThe applied equivalent all of coupling these variable coefficients and is then evaluated expressed the in magnetic Equation field (11), andvalue. this is equivalent to the reflected impedance of a single identical sensor with an equivalent mutual inductance expressed in Equation (12). √ k = n·k n (11) 0 ≤ k ≤ 1

√ Mn = n·M (12)

5. Impacts of Coil Position and Receiver Coil Number on the WPT Performance In this section, the performance of the wireless Power Transfer is evaluated according to various external and internal parameters related to the receiver face, the transmitter position, and accordingly to the number of coil receivers. The Ansys Maxwell application is used for applied all of these variables and evaluated the magnetic ﬁeld value.

5.1. Transmitter/Receiver Coil: Design and Parameters Initially, it is mandatory to design correctly the coils that will be used as receivers and/or transmitters. This is must be adapted to the desired application. In this studied case, the design of the coils must be adaptable to be placed undo the vehicle body. Thus, Table 2 regroups all this information and given what is the dimension of the coils [30,31]. Figure 6 also gives the design applied to Maxwell. After showing these specifications on the coil, it is critical to cite what kind of parameters must be supervised to study the coil coupling factor. For this objective, the coupling coefficient, the mutual inductance, and the coil self-inductance are the factors that will be supervised and discussed. These variables will be studied according to the coil-to-coil relative location, and the coil structural parameters. This study needs complicated mathematical analysis work, and this can be guaranteed by a computational calculation method as the Finite element analysis solution (FEA). Thus, using the Ansys Maxwell tool, a variety of solvers for evaluating the electromagnetic part design can be applied.

Table 2. Coil used specification on maxwell platform.

Designation Used Choice Coil material Copper Polygon Segments 4 Polygon Radius 1 mm Start Helix Radius 20 mm Radius Change 2.05 mm Pitch 0 Sensors 2021, 21, 4343 Turns 108 of 19 Segments Per Tum 36 Right-Handed 1

Table 2. Coil used speciﬁcation on maxwell platform. With Maxwell’s application, this section tries to study the effect of the variation between the coilsDesignation in the vertical position. Thus, it appears Used Choice to the positive or negatively cou- Coil material Copper pling. The resultsPolygon Segmentsshow the analysis of the coupling coefficient 4 and the mutual inductance between thePolygon transmitting Radius and receiving coils. The built 1 mm model can be seen in Figure 7. Figure 6 depictsStart Helix the Radius distribution of magnetic flux density 20 mm in the object field, which is a Radius Change 2.05 mm region with a corePitch near the transmitter’s surface. The magnetic 0 field distribution has symmetric propertiesTurns because the coil structure is strongly 10 symmetrical. Thus, the magnetic Segments Per Tum 36 flux density Right-Handednear the Litz wire is high in this illustration, 1 while it is low near the central field.

FigureFigure 6. Distribution6. Distribution of magnetic of magnetic ﬂux density flux indensity the coil usingin the Ansys coil using Maxwell Ansys software. Maxwell software.

After showing these speciﬁcations on the coil, it is critical to cite what kind of parameters must be supervised to study the coil coupling factor. For this objective, the coupling coefﬁcient, the mutual inductance, and the coil self-inductance are the factors that will be supervised and discussed. These variables will be studied according to the coil-to-coil relative location, and the coil structural parameters. This study needs complicated mathematical analysis work, and this can be guaranteed by a computational calculation method as the Finite element analysis solution (FEA). Thus, using the Ansys Maxwell tool, a variety of solvers for evaluating the electromagnetic part design can be applied. With Maxwell’s application, this section tries to study the effect of the variation between the coils in the vertical position. Thus, it appears to the positive or negatively coupling. The results show the analysis of the coupling coefficient and the mutual inductance between the transmitting and receiving coils. The built model can be seen in Figure7. Figure6 depicts the distribution of magnetic flux density in the object field, which is a region with a core near the transmitter’s surface. The magnetic field distribution has symmetric properties because the coil structure is strongly symmetrical. Thus, the magnetic flux density near the Litz wire is high in this illustration, while it is low near the central field. SensorsSensors 20212021, 21, x21 FOR, 4343 PEER REVIEW 99 of of 19 20

(a)

(b)

(c)

FigureFigure 7. Reference 7. Reference coil coil model model in in Ansys Ansys Maxwell: Maxwell: ( (aa)) identical, identical, ((b)) crisscrossed,crisscrossed, ( c()c) far far apart. apart.

TheThe primary primary and and the the secondary secondary side coil modelsmodels werewere designed designed using using the the Maxwell Maxwell tool.tool. The The distance distance between between the the two-spool two-spool axis axis is variable,variable, andand then, then, the the magnetic magnetic ﬁeld field simulationssimulations were were applied applied for for three three different different cases,cases, asas seenseen inin Figure Figure7. 7. In In the the ﬁrst first case, case, FigureFigure 7a,7a, shows shows the the results results of thethe horizontalhorizontal coil coil offset, offset, which which is is equal equal to to 90%. 90%. In In this this study,study, to to simplify simplify the the analysis analysis of of the the system, system, the WPTWPT consistsconsists of of two two identical identical circulating circulating coils.coils. Figure Figure 88 shows shows the the three three cases ofof coilcoil patternpattern circulating circulating for for a gapa gap equal equal to to 100 100 mm. mm.

SensorsSensors2021, 202121, 4343, 21, x FOR PEER REVIEW 10 of10 20 of 19

p g p g g 0.006

0.005

0.004

0.003

0.002

couplingcoeficient 0.001

0.000

200.00 -0.001 -375.00 -250.00 -125.00 0.00 125.00 250.00 375.00 y_space [mm] (a)

50 45 40 35 30 μH 25 20 15 10

Mutual inductance 5 0 0 0 0 0 0 0 0 0 0 0 -5 90 0 40 -80 -5 -2 10 40 70 0 9 20 5 80 1 -320 -2 -260 -230 -2 -170 -1 -11 1 13 16 1 2 2 2 3 Space between coils center (mm)

(b)

FigureFigure 8. Coil 8. Coil model: model: (a) ( Couplinga) Coupling coefﬁcient coefficient versus versus the thegap gap variation,variation, ( (bb)) mutual mutual inductance inductance vers versusus the the gap gap variation. variation.

TheThe simulation simulation of of thethe corelesscoreless model was was carried carried out out using using the the Ansys Ansys Maxwell Maxwell soft- soft- wareware by by varying varying the the distance distance zz fromfrom 50 to 300 mm. mm. TheThe overall overall measurement measurement results results of of the the coupling coupling coefficient coefficient andand thethe mutualmutual inductanceinduct- forance the variationfor the variation of the of gap the (− gap250/250 (−250/250 mm) mm) are are summarized summarized in in Figure Figure7. 7. The The simulations simula- indicatetions indicate that the that value the of value the coefficientof the coeffici couplingent coupling and the and mutual the mutual inductance inductance decrease de- as crease as the vertical distance between the transmit and receive coils increases. the vertical distance between the transmit and receive coils increases. This implies that a little power is transferred as the distance between coils increases. This implies that a little power is transferred as the distance between coils increases. A weakly coupled coefficient that characterizes this type of system is less than 0.2. A weakly coupled coefficient that characterizes this type of system is less than 0.2. 5.2. One Transmitter and One Receiver Coil: Magnetic Field Zones 5.2. One Transmitter and One Receiver Coil: Magnetic Field Zones The coupling coefficient in Figure 8.a shows the influence of the receiver face on the transmitterThe coupling position. coefficient Even the in two Figure coils8a are shows centralized, the influence and the of coupling the receiver coefficient face on is the transmitterhigh. This position. parameter Even decreases the two even coils the are two centralized, coils center and are theshifted. coupling At 200 coefficient mm the cou- is high. Thispling parameter coefficient decreases will be null. even When the two two circuits coils center have a are mutual shifted. inductance, At 200 mmnoted the M, couplingit can coefficientbe said that will the be two null. elements When are two magnetically circuits have coupled. a mutual This inductance, mutual inductance noted M,parame- it can be saidterthat depends the two on the elements proper primary are magnetically and secondary coupled. inductances This mutual Lp and inductanceLs, respectively. parameter But depends on the proper primary and secondary inductances Lp and Ls, respectively. But their relative position affects too. Mathematically, the mutual inductance M can be expressed, as seen in Equation (13). q M = k Lp Ls (13) Sensors 2021, 21, x FOR PEER REVIEW 11 of 20

Sensors 2021, 21, 4343 11 of 19

their relative position affects too. Mathematically, the mutual inductance M can be expressed, as seen in Equation (13). with k the coupling coefficient in Figure8a. Thus, according to the previous equation, the 𝑀=𝑘𝐿𝐿 (13) mutual inductance variation can be shown in Figure8b. It is clear that the perfect value is alwayswith relatedk the coupling to the coefficient superposition in Figure of 8a. the Thus two, according coils element. to the previous equation, the mutualFigure inductance9 shows thevariation evolution can be ofshown the magneticin Figure 8b. flux It is for clear the that case the ofperfect only value one receiveris and always related to the superposition of the two coils element. one transmitterFigure 9 shows coil. Allthe ofevolution the presented of the magnetic screens flux are for taken the case for of two only different one receiver coil positions. Figureand9 onea shows transmitter that coil. the All two of coilsthe presented center arescreens centralized, are taken for and two it different is clear coil that posi- the magnetic fluxtions. is parallel Figure 9a and shows approximately; that the two coils all thecent yieldser are centralized, are transferred. and it is Onclear the that other the hand, the deviationmagnetic of flux the is magnetic parallel and flux approximately; is clear for theall the cases yields where are transferred. the two coils On the are other not centralized, as seenhand, in the Figure deviation9b. of This the situationmagnetic flux was is clear depicted for the for cases a distancewhere the betweentwo coils are the not two centers centralized, as seen in Figure 9b. This situation was depicted for a distance between the equal to 80 mm. Here, the two coils still have a contact zone, as we do not have over-crossed two centers equal to 80 mm. Here, the two coils still have a contact zone, as we do not the coilhave radius.over-crossed This the is coil why radius. we still This have is why a magneticwe still have zone a magnetic between zone the between two coils.the two coils.

(a)

(b)

FigureFigure 9. 9.Distribution Distribution of of the the flux ﬂux density: density: (a) D( =a )0, D (b =) D 0, = (−b80.) D = −80.

5.3. One Transmitter and Two Receivers Coils: Magnetic Field Zones The two-coil receiver system is studied in this section. Moreover, using Maxwell software, the magnetic field evolution is studied, and this is for different cases related to the two-part positions. The built model consists of one coil transmitter, which has the same previous dimensions, cited in Table2, and the coils receivers, which also have the same performances as the transmitter coil. The distance between the two coils receivers center is 80 mm. As shown in Figure 10a, that the quantity of the magnetic field in the receiver coils is very high as the red color is very concentrated in the centers of the coils. But this is also related to the superposition of the first coil transmitter and two receiver centers. Moreover, Sensors 2021, 21, x FOR PEER REVIEW 12 of 20

5.3. One Transmitter and Two Receivers Coils: Magnetic Field Zones The two-coil receiver system is studied in this section. Moreover, using Maxwell software, the magnetic field evolution is studied, and this is for different cases related to the two-part positions. The built model consists of one coil transmitter, which has the same previous dimensions, cited in Table 2, and the coils receivers, which also have the same performances as the transmitter coil. The distance between the two coils receivers center is 80 mm. As shown in Figure 10a, that the quantity of the magnetic field in the receiver coils is very high as the red color is very concentrated in the centers of the coils. But this is also related to the superposition of the first coil transmitter and two receiver centers. Moreover, it is clear that the mutual magnetic fields are limited between 1.428 tesla as the best value and 1.075 tesla as a minimum value. The form of the magnetic yields is also shown in the same figure, and all yields are parallel. For the previously cited coil specifications, Figure 10b shows that the transferred magnetic field, cannot be assured as the distance between the two centers is high than the diameter of the one coil receiver. Figure 10b shows the results of the distance between the receiver middle and the transmitter middle is 120 mm, proving why the yields cannot be Sensors 2021, 21, 4343 transferred to the receivers. Moreover, in Figure 10b, the concentration of the red color in 12 of 19 the two receivers coils is related to the internal magnetic field that appears between the two receivers coils. However, the color in the transmitter coil is yellow, which means that there is no magnetic field inside. Moreover, the two coils yields do not move from one to it isthe clear other that part; the it mutualis just inside magnetic the same ﬁelds coil. are limited between 1.428 tesla as the best value and 1.075For tesla Figure as 10c, a minimum the case of value. partial The superposition form of the is magnetictested, and yields this is isfor also 40 mm shown as in the sameapplied ﬁgure, spacing and allbetween yields the are transmitter parallel. coil center and the two receivers coils center.

Sensors 2021, 21, x FOR PEER REVIEW 13 of 20

(a) Transmitter coil superposed with the two coils receivers; distance between middles is null

(b) Distance between the receiver middle and the transmitter middle is 120 mm

FigureFigure 10. 10.Distribution Distribution of magnetic flux ﬂux for for two two coils coils receivers receivers case. case.

ForFrom the the previously other side, citedthe coupling coil speciﬁcations, coefficient for the Figure case of 10 twob showsreceivers that coils the is eval- transferred uated, using the given maxwell statistics. Figure 11 shows the corresponding coupling magnetic ﬁeld, cannot be assured as the distance between the two centers is high than the coefficient for each coil proportionally to the transmitter coil position. For example, if the diametercoil transmitter of the one is in coil the receiver.middle of Figure the two 10 receiversb shows coils, the resultsthe magnetic of the coupling distance coeffi- between the cient can be evaluated as 0.0026 for each coil, and the total will be multiplied by two. However, if the coil transmitter is superposed with the first coil receiver, the maximum coupling coefficient touches 0.0058, and it is the same if it is superposed with the left coil receiver. This is different from the case of only one receiver. It is clear that the range of magnetic coefficient for each coil is the same—but as there are two receivers, the total coupling coefficient will be a sum of two elements. For example, if the two receivers center is spaced from the one transmitter coil center by 0.25mm, then the total coupling coefficient is 0.04 and 0.018. The new total coupling coefficient will increase the efficiency of the WPT.

Sensors 2021, 21, 4343 13 of 19

receiver middle and the transmitter middle is 120 mm, proving why the yields cannot be transferred to the receivers. Moreover, in Figure 10b, the concentration of the red color in the two receivers coils is related to the internal magnetic field that appears between the two receivers coils. However, the color in the transmitter coil is yellow, which means that there is no magnetic field inside. Moreover, the two coils yields do not move from one to the other part; it is just inside the same coil. For Figure 10c, the case of partial superposition is tested, and this is for 40 mm as applied spacing between the transmitter coil center and the two receivers coils center. From the other side, the coupling coefficient for the case of two receivers coils is evaluated, using the given maxwell statistics. Figure 11 shows the corresponding coupling coefficient for each coil proportionally to the transmitter coil position. For example, if the coil transmitter is in the middle of the two receivers coils, the magnetic coupling coefficient can be evaluated as 0.0026 for each coil, and the total will be multiplied by two. However, if the coil transmitter is superposed with the first coil receiver, the maximum coupling coefficient touches 0.0058, and it is the same if it is superposed with the left coil receiver. This is different from the case of only one receiver. It is clear that the range of magnetic coefficient for each coil is the same—but as there are two receivers, the total coupling coefficient will be a sum of two elements. For example, if the two receivers center is spaced Sensors 2021, 21, x FOR PEER REVIEWfrom the one transmitter coil center by 0.25mm, then the total coupling coefficient14 of 20 is 0.04 and 0.018. The new total coupling coefficient will increase the efficiency of the WPT.

0.006 second coil center ﬁrst coil center 0.005

second coil receiver curve ﬁrst coil receiver curve 0.004 0.04

0.003

0.002 0.018

coupling coefficeint 0.001

0.000

-0.001 -375.00 -250.00 -125.00 0.00 125.00 250.00 375.00 y_space [mm]

(a)

60 One Coil two coils

H receiver receivers

μ 50

e c

n 40

c u

d 30 n

i 22.5

a 20

t u

M 10

0 0 10 40 70 -80 -50 -20 100 130 160 190 220 250 280 310 340 -320 -290 -260 -230 -200 -170 -140 -110 Space between coils center (mm) (b)

Figure 11.Figure(a) Coupling 11. (a) Coupling coefﬁcient coefficient for each for each receiver receiver coil coil proportionallyproportionally to to the the transmitter transmitter position, position, (b) Mutual (b) Mutual inductance inductance for for only one receiver coil, and the totally mutual inductance for two receivers coil proportionally to the coil transmitter only oneposition. receiver coil, and the totally mutual inductance for two receivers coil proportionally to the coil transmitter position.

Figure 11a shows the mutual inductance evolution according to the only one coil receiver and the case of two coil receivers. Proportionally to the interpretation of the previous results, the total mutual inductance will be bigger when the two coils react to the given magnetic field from the transmitter. This is clear for the case, where the transmitter coil center is in the middle of the two receivers coils. Only one receiver coil will have a mutual inductance equal to 22.5 μH, and the same for the second coil—which gives 45 μH as the total mutual inductance. When the two receiver coils move from the center, the given results demonstrate that the high efficiency of the WPT still exists until 80 mm as a marge of variation. When moving more, the efficiency decreases proportionally and touches zero, when the distance is more than 200 mm. As seen in Figure 8b, the totally mutual inductance is better for the case of two coils receivers. For example, for 110 mm as space between the two centers, the mutual inductance is 40 μH for the case of two receivers and 15 μH for the case of one receiver. On the other hand, this study depicts the possible given power if only one receiver coil is used, and in the case of two receivers, coils were used. Table 3 shows these statistics Sensors 2021, 21, 4343 14 of 19

Figure 11a shows the mutual inductance evolution according to the only one coil receiver and the case of two coil receivers. Proportionally to the interpretation of the previous results, the total mutual inductance will be bigger when the two coils react to the given magnetic field from the transmitter. This is clear for the case, where the transmitter coil center is in the middle of the two receivers coils. Only one receiver coil will have a mutual inductance equal to 22.5 µH, and the same for the second coil—which gives 45 µH as the total mutual inductance. When the two receiver coils move from the center, the given results demonstrate that the high efficiency of the WPT still exists until 80 mm as a marge of variation. When moving more, the efficiency decreases proportionally and touches zero, when the distance is more than 200 mm. As seen in Figure8b, the totally mutual inductance is better for the case of two coils receivers. For example, for 110 mm as space between the two centers, the mutual inductance is 40 µH for the case of two receivers and 15 µH for the case of one receiver. On the other hand, this study depicts the possible given power if only one receiver coil is used, and in the case of two receivers, coils were used. Table3 shows these statistics and resume, the importance of two receiver coils, where it is possible touching 96% of the maximum achieved efficiency. These statistics were depicted for the previously cited coil parameters, as shown in Table2.

Table 3. Power transfer factor for the case of one or two receivers coils.

Distance Power Efﬁciency Max Max Av (mm) Transfer eff pow pow −200 0.3 kw 10% −100 1.9 kw 54% −50 3.6 kw 78% Simple 0 4.9 kw 92% 92% 4.9 kw 2.34 kw receiver coil 50 3.5 kw 77% 100 1.9 kw 54% 200 0.3 kw 10% −300 0.5 kw 12% −250 3.7 79% −200 4.8 87% −100 4.9 88% −50 5.1 kw 96% Multiple 0 5.2 kw 96% 96% 5.1 kw 3.95 kw receiver coils 50 5.2 kw 95% 100 5 kw 90% 200 4.9 kw 88% 250 3.7 kw 79% 300 0.5 kw 12%

Avpow: Average outputted power; Maxe f f : Maximum achievable coil system efﬁciency; Maxpow: Maximum achievable output power.

6. Experimental Validation In this simulation, the prototype operating two coils have two different proper inductances. The ﬁrst coil has an inductance equal to 30 µH, and the second is 21.13 µH. Figure 12 shows a real photo of the prototype, which the necessary measurement tool. The second, larger, coil is the transmitter part, and the second is the receiver part. In this test, the inputted voltage is equal to 35VDC transforms to an alternating voltage of frequency 50 kHz. The applied test simulates a coil placed undo the vehicle and moved into a different position face the transmitter coil. Moreover, the mutual inductance will be evaluated according to the one or two coils receivers mode. Figure 12 shows this prototype. The real dimensions of the coils are summarized in Table4. Sensors 2021, 21, 4343 15 of 19 Sensors 2021, 21, x FOR PEER REVIEW 16 of 20

Sensors 2021, 21, x FOR PEER REVIEW 16 of 20

(a) first and secondary coils not centralized (b) first and secondary coils centralized

FigureFigure 12. 12.Real Real prototypeprototype for the the wireless wireless transfer transfer system. system.

Table 4.TheReal given coils statistics dimensions. validate the obtained results from the Maxwell application. Thus, if concentrating on the coupling coefficient and the mutual inductance, the importance of Coilthe wireless diameter recharge system can be evaluated. 50For cm this practical validation, the best mu- Distancetual inductance between value coil remains constant at approximately 150 cm 45 μH, until 180 mm as a maxi- Widthmum ofdistance winding between “w” centers is shown in Figure 21 cm 13. Whereas, the mutual inductance (a) first and secondaryAveragestarts coilsdecreasing. winding not centralized radius Finally, “r” over 200 mm, ( bthe) first mutual and 14.5 secondaryinductance cm coils comes centralized to zero, and then it Numberis provedFigure of that turns 12. noReal “N” energy prototype will for be the transferred wireless transfer to the 15 Turnssystem.main charge connected to the receiver coils. The given statistics validate the obtained results from the Maxwell application. Thus, The given statistics validate the obtained results from the Maxwell application. Thus, if concentrating on the coupling coefficient and the mutual inductance, the importance of if concentrating on the coupling coefﬁcient and the mutual inductance, the importance of the wireless recharge system can be evaluated. For this practical validation, the best mu- 42.5 thetual wireless inductance recharge value system remains can constant be evaluated. at approximately For this practical 45 μH, validation,until 180 mm the as best a maxi- mutual Two receivers Case inductancemum distance value between remains centers constant is atshown approximately in Figure 13. 45 Whereas,µH, until the 180 mutual mm as inductance a maximum distance between centers is shown in Figure 13. Whereas, the mutual inductance starts (second starts case) decreasing. Finally, over 200 mm, the mutual inductanceOne comes receiver to Case zero, and then it

First and seconddecreasing.is Reecivers proved Finally,that no energy over200 willmm, be transferred the mutual to the inductance main charge comes connected to zero, to the and receiver then it is

e provedcoils. that no energy will be transferred to the main charge connected to the receiver coils.

t (ﬁrst case)

c One coil receiver

l 42.5

u Two receivers Case

t u 3 M (second case) One receiver Case

First and second Reecivers

e 100 mm

t (ﬁrst case)

c One coil receiver

d Distance between transmitter and receiver(s) coil(s) (mm)

t Figure 13. Mutual inductance with one and two receivers. u 3

M 7. One and Two Coils Receivers’ Specifications

To show the specifications100 mm of the case of two coil receivers face the case of only one coil receiver, Table 5 gives five indication factors that can be used to classify the best receiver combination design. Thus, the classification is made based on: The quantity of the Distance between transmitter and receiver(s) coil(s) (mm)

Figure 13. Mutual inductance with one and two receivers. Figure 13. Mutual inductance with one and two receivers.

7. One and Two Coils Receivers’ Specifications To show the specifications of the case of two coil receivers face the case of only one coil receiver, Table 5 gives five indication factors that can be used to classify the best receiver combination design. Thus, the classification is made based on: The quantity of the

Sensors 2021, 21, 4343 16 of 19

7. One and Two Coils Receivers’ Specifications To show the specifications of the case of two coil receivers face the case of only one coil receiver, Table5 gives five indication factors that can be used to classify the best receiver combination design. Thus, the classification is made based on: The quantity of the given power, the quantity of the losses power, the receiver coils additive weight in an electric vehicle, the complexity of the electronic converter, and the possible needed time for a full recharge if using each of these architectures.

Table 5. Speciﬁcations of only one receiver coil and two receiver coils.

Speciﬁcations One Coil Receiver Two Coils Receivers Maximum Quantity of the given current 140 A 280 A Quantity of the losses power 10% of the rated total power 20% of the rated total power Additive weight on the vehicle +10 kg on the vehicle weight +20 kg on the vehicle weight Electronic complexity medium high Needed recharge time in stopped mode * 8 h 6 h Needed recharge time in motion mode *,1 50 h 26 h

*: For 220 volt as input voltage; *,1: For a road totally equipped with a wireless transmitter and for 50 km/h as car speed value; All of these statistics were depicted from these references [10,28,32–35].

8. Conclusions At the conclusion of this study, it is feasible to infer that the wireless power transfer system has been investigated. This is by working on the efficiency of two coils receivers face only one receiver. The significance of this investigation is demonstrated by the magnetic fields sent from the first transmitter coil to the case of one or two utilized receivers. The mutual inductance, the coupling coefficient, and the form of the distributed field are supervised according to the transmitter’s translation face the receiver parts. This is the result of the use of the Maxwell tool and proved by a detailed analytical equation. These results were important, and showed how much energy can extract for each position case. Moreover, this study was validated by an experimental prototype that validates the obtained results from the Maxwell application. All aspects of this study, and the efficiency of electric vehicle autonomy, were discussed in the paper.

Author Contributions: Conceptualization, F.A. and N.M.; Methodology, F.A. and N.M.; Software, N.M. and Z.I.; Vali-dation, F.A.; Formal analysis, F.A. and N.M.; Investigation, F.A. and N.M.; Resources, F.A. and N.M.; Data curation, Z.I.; Writing—Original Draft Preparation, F.A., M.B. and S.S.M.G., M.A. and N.M.; Writing—Review and Editing, F.A., M.B., S.S.M.G., M.A. and N.M.; Visualization. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by TAIF UNIVERSITY RESEARCHERS SUPPORTING PROJECT, grant number “TURSP-2020/146” and “The APC was funded by Mahrous Ahmed”. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors would like to acknowledge the financial support received from Taif University Researchers Supporting Project Number (TURSP-2020/146), Taif University, Taif, Saudi Arabia. Conflicts of Interest: The authors declare no conflict of interest. Sensors 2021, 21, 4343 17 of 19

Abbreviations

IPT Inductive Power Transfer EV Electric Vehicles HEV Hybrid Electric Vehicle HF High-Frequency AFE Active Front End WPT Wireless Power Transfer SWC Static Wireless Charging system FEM Finite Element Method FEA Finite Element Analysis M Mutual inductance (H) ω Oscillation angular frequency (rad/sec) k Coupling coefﬁcient Ls Secondary inductance (H) Lp Primary inductance (H) Zp Primary impedance (Ω) Zs Secondary impedance (Ω) Ip Primary current (A) Is Secondary current (A) Vp Primary voltage (V) Vs Second voltage (V) I1 Source current (A) I2 Load current (A) Cs Secondary capacitance (F) Cp Primary capacitance (F) Ps Secondary power (W) Pp Primary Power (W) La Primary leakage inductance (H) Lb Secondary leakage inductance (H) RL Load (Ω) η The efﬁciency of the power transfer (%) Z1 The global impedance of the primary coil (Ω) V1 Source voltage (V) Rs Secondary resistance (Ω) Rp Primary resistance (Ω) n Number of receiver coils D Distance between the receiver middle and the transmitter middle

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