Design Methodology, Modeling, and Comparative Study of Wireless Power Transfer Systems for Electric Vehicles

Recently, wireless power transfer (WPT) systems have been used as battery chargers for electric vehicles. In a WPT system, the design approach and control strategy have a significant impact on the performance of the wireless power transfer systems in electric vehicle powertrains in terms of efficiency, charging power, charging modes, charging time, etc. A characteristic of different topologies appears depending on whether the compensation capacitor is connected in series or parallel with coils. Therefore, it is necessary to select a suitable compensation topology depending on different applications. Thus, this paper proposes a new design methodology and control system for bidirectional 3.7 kW and 7.7 kW WPTs in light-duty electric vehicles (EVs) operating at both 40 kHz and 85 kHz resonance frequencies. In this paper, the series-series (SS) WPT compensation topology is optimally designed and controlled for grid-to-vehicle (G2V) mode using MATLAB/Simulink. A simulation study is performed for a selected WPT design for G2V mode to ensure its functionality and performance at different power levels. Moreover, the magnetic design of the coils and its parameters are verified by using COMSOL. Finally, experimental results are validated for the WPT system.


Introduction
Electric vehicles (EVs) are considered to be an attractive alternative to conventional vehicles that are mainly based on an internal combustion engine (ICE), especially for reducing greenhouse emissions. In recent years, the commercialization of electric vehicles has significantly grown thanks to recent advances in battery technologies, power electronics interfaces (i.e., inverters, DC/DC converters, on/off-board charging systems), electric motors, and power management control [1]. Nowadays, the number of EVs in circulation increases more and more every year. According to data from the European Automobile Manufacturers' Association (ACEA), during the first nine months of 2015, more than 190,000 plug-in electric and hybrid cars were sold in Europe, with a growth of approximately 95% in comparison with 2014 [2]. However, EVs have some major issues (such as battery cost, battery lifetime, slow charging speed, efficient charging systems, limited energy density, weight, reliability, etc.) that need to be solved. One of the main challenges for EV growth is represented by the lack of adequate infrastructures, such as charging stations [3]. The most frequented areas

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Convenience: eliminating the need for power cables and the effect of the bad weather; • Safety: eliminating the danger of sparking and electrical shock risk; • Reliability: eliminating the components with the greatest possibility of failure in most electronic systems, namely, the power cords and connectors.
In the literature, the WPT system can be divided into stationary wireless charging and dynamic wireless charging [14,15]. With stationary wireless charging, the user simply parks the vehicle over a charging pad mounted on the ground and a corresponding charging pad mounted on the underside of the vehicle picks up the signal and charges the vehicle. The key challenge of WPT technology is that WPT has lower transfer efficiency and lower receiver power compared with conductive charging systems. Generally, the coupling coefficient is proportional to the size of the loosely coupled transformer at a fixed air gap. Most of the current WPT researches focus on the topologies of resonant circuits and the control method for the inverters or converters either in the charger side or in the load side. For the topologies of resonant circuits, two common topologies for the primary and secondary resonant circuits, the series and parallel connected circuits, have been tested in previous works for different applications [16][17][18]. As reported in the literature, there are many different compensation topologies which have been addressed. Each topology has its advantages and drawbacks. The choice has to be made according to the specifications of the application [19][20][21]. Therefore, different compensation networks and the choice of compensation networks are explicated in this section. In [22,23], the authors proposed a general design method that includes the magnetic coupling effect in the primary resonance design for the commonly used resonant topologies. The series-series (SS) compensation topology has been established as a good solution because its resonant circuit can be designed independently of the coupling and load. Moreover, the equivalent electric circuit model with SS compensation is discussed in [24,25]. In [26], the parallel-parallel (PP) compensation topology is the dependence of primary capacitance on load and it can be driven more easily than SS topologies. In [27], the authors studied a series-parallel mixed resonant coupling topology, which has the advantages of the transfer distance being longer than series topology and the transfer efficiency being higher than parallel topology. In [28], the authors proposed a novel compensation circuit called the series parallel-series (SP-S) topology for inductive power transfer (IPT) systems. By designing a proper ratio between the two primary side capacitors, the characteristics of SS and PS are mixed. The results showed that the SP-S topology is suitable for mobile battery chargers, where high misalignment may occur. In this paper, considering the convenience for EV battery charging and practical application, the SS topology was selected for our analysis of compensation topology. The choice of the SS topology allows for the selection of compensation capacitances depending only on the self-inductances, with no relation with the load and the magnetic coupling [25]. Due to these reasons, the SS topology turns out to be convenient for EV battery charging. For the control methods of WPT systems, in [29] they used the standard control concepts: (1) frequency control at fixed duty cycle; (2) duty cycle control at a fixed frequency; and (3) dual control-combine frequency control and duty cycle control. In [30], the authors applied a pulse width modulation (PWM) control method. PWM is most commonly used as a basic modulation. Regarding some research on the charging strategies to determine the location and size of the EVs and photovoltaic (PV) systems, in [31], the authors presented a probabilistic method that accurately verifies the fulfillment of voltage constraints in radial distribution systems (RDSs) with PV systems and EV charging loads. Moreover, the assessment accuracy of the EV and PV interaction in RDSs was improved, which was extended from a weekly assessment to a one-year time period in [32]. In addition, concerning the safe use of EVs, Hernández et al. [33] defined the foundations for the safe, efficient, and smart interconnection of complementary AC and DC sources, which feed bidirectional EV charging stations thanks to a reference DC node. In [34], the authors described a multiterminal DC compact node consisting of voltage-source converters and DC-DC converters as a promising arrangement to feed EV charging stations with renewable power sources.
In this paper, the main objective is to develop a new design approach and control system for a series-series (SS) topology based on 3.7 kW and 7.7 kW WPT systems operating at resonant frequencies of both 40 kHz and 85 kHz to verify their feasibility and performance for light-duty EV applications operating in charging grid-to-vehicle (G2V) mode. The paper is structured as follows: In Section 2, the design optimization approach for the SS topology of the WPT system is presented in detail. In Section 3, this paper presents the optimal sizing of the primary and secondary coils to achieve the maximum coupling coefficient through the proposed design methodology. In Section 4, the magnetic design of the coils is verified by using the COMSOL program. In Section 5, the power electronics converter (PEC) topology and its control strategies for G2V operating modes is presented, which were designed and validated using MATLAB/Simulink. In Section 6, the experimental results are presented to verify the design performance of the WPT system. Section 7 draws the final conclusion of this paper.

Resonant Wireless Power Transfer System
The resonant WPT system consists of magnetically coupled primary and secondary coils as well as power electronics converters (such as AC/DC rectifier, DC/AC inverters) and compensation circuits. Figure 1 shows a general block diagram of the components and power electronics conversion for wireless power transfer from the grid to load. The input AC utility grid power is converted to DC power, and then an inverter converts the DC power into a high-frequency AC power. The high-frequency current in the primary coil generates an alternating magnetic field, which induces an AC voltage on the secondary coil. By resonating with the compensation circuits, the transfer power and efficiency are

WPT System Model for SS Topology
The principle of the design method of the WPT system is in a backward calculation, whereas the design steps are calculated from the battery side to the high-frequency inverter side in the primary side. The bidirectional WPT system of SS-compensated topology is shown in Figure 2. The specific design steps for the SS topology of the WPT system are explained in Section 2.5. An equivalent circuit model of a WPT system with compensation capacitors arranged in an SS topology is shown in Figure 3. For simplification, the equivalent source resistance is neglected. Here, the subscripts "1" and "2" refer to the "primary" and "secondary" coil values of inductor L, resistance R, and capacitance C, respectively. V1 is the source voltage of the primary circuit. RL is the equivalent load resistance. I1 is the source current flowing through the primary coil, and I2 is the load current flowing through the secondary coil. The degree of the coupling between two coils can be expressed with the coupling coefficient k, which has a value ranging from 0 to 1, and is defined by Equation (1).
represents the mutual inductance between the primary and secondary coils.

WPT System Model for SS Topology
The principle of the design method of the WPT system is in a backward calculation, whereas the design steps are calculated from the battery side to the high-frequency inverter side in the primary side. The bidirectional WPT system of SS-compensated topology is shown in Figure 2. The specific design steps for the SS topology of the WPT system are explained in Section 2.5.

WPT System Model for SS Topology
The principle of the design method of the WPT system is in a backward calculation, whereas the design steps are calculated from the battery side to the high-frequency inverter side in the primary side. The bidirectional WPT system of SS-compensated topology is shown in Figure 2. The specific design steps for the SS topology of the WPT system are explained in Section 2.5. An equivalent circuit model of a WPT system with compensation capacitors arranged in an SS topology is shown in Figure 3. For simplification, the equivalent source resistance is neglected. Here, the subscripts "1" and "2" refer to the "primary" and "secondary" coil values of inductor L, resistance R, and capacitance C, respectively. V1 is the source voltage of the primary circuit. RL is the equivalent load resistance. I1 is the source current flowing through the primary coil, and I2 is the load current flowing through the secondary coil. The degree of the coupling between two coils can be expressed with the coupling coefficient k, which has a value ranging from 0 to 1, and is defined by Equation (1).
represents the mutual inductance between the primary and secondary coils. An equivalent circuit model of a WPT system with compensation capacitors arranged in an SS topology is shown in Figure 3. For simplification, the equivalent source resistance is neglected. Here, the subscripts "1" and "2" refer to the "primary" and "secondary" coil values of inductor L, resistance R, and capacitance C, respectively. V 1 is the source voltage of the primary circuit. R L is the equivalent load resistance. I 1 is the source current flowing through the primary coil, and I 2 is the load current flowing through the secondary coil.
The degree of the coupling between two coils can be expressed with the coupling coefficient k, which has a value ranging from 0 to 1, and is defined by Equation (1). M represents the mutual inductance between the primary and secondary coils. The voltage equations in Figure 3 can be written using the mutual inductance, M. ω is the frequency of V 1 . An equivalent circuit model of a WPT system with compensation capacitors arranged in an SS topology is shown in Figure 3. For simplification, the equivalent source resistance is neglected. Here, the subscripts "1" and "2" refer to the "primary" and "secondary" coil values of inductor L, resistance R, and capacitance C, respectively. V1 is the source voltage of the primary circuit. RL is the equivalent load resistance. I1 is the source current flowing through the primary coil, and I2 is the load current flowing through the secondary coil. The degree of the coupling between two coils can be expressed with the coupling coefficient k, which has a value ranging from 0 to 1, and is defined by Equation (1).
represents the mutual inductance between the primary and secondary coils. The resonant frequencies ω 0 at the primary coil and the secondary coil are assumed to be equal to At the perfect resonant frequency ω 0 , Equation (2) can be rewritten as (4).
In Figure 3, the delivered power to the load P L and the transfer efficiency η at the resonant frequency ω 0 can be obtained as follows in Equations (5) and (6) [35]: By defining the quality factor of the primary and secondary coils, Q 1 = ωL 1 /R 1 , Q 2 = ωL 2 /R 2 , so the transferred efficiency Equation (6) replaced by Q 1 and Q 2 can be rewritten in Equation (7): The maximum transmission efficiency η max of the WPT system can be derived as [35] From Equation (8), the maximum efficiency increases as k 2 Q 1 Q 2 increases. It should be noted that the maximum efficiency of a WPT system is limited by the product of the coupling coefficient k and the inductor quality factor Q. Therefore, the foremost design consideration in a WPT system is the attainment of the higher possible Q and k. These two vital parameters are functions of the shape, size, and the relative position of the primary and secondary coils. The main goal in the design of a WPT system is to achieve maximum efficiency and to optimize the power transfer capability according to the operating conditions.
In EV wireless charging applications, the battery is usually connected to the coil through a diode-bridge rectifier or via a controlled converter. The battery could be represented as a resistance where U b and I b are the battery voltage and current, respectively. If the battery is connected to the rectifier directly in an SS-compensated WPT system, the equivalent AC side resistance R L could be calculated by Equation (9). Thus, a battery load could be converted to an equivalent resistive load [36]. Figure 4 shows a rectangular spiral coil with a square cross-section. The basic dimensional parameters of such a spiral are N, w, γ, d xi , and d xo , as depicted in Figure 4, which are the number of turns, cross-sectional width, the spacing between consecutive turns, the inner side length of the spiral, and the outer side length of the spiral, respectively. The outer side length d xo is derived from the other geometrical parameters as

Windings Sizing Calculation
Energies 2018, 11, x FOR PEER REVIEW 6 of 22 be calculated by Equation (9). Thus, a battery load could be converted to an equivalent resistive load [36]. Figure 4 shows a rectangular spiral coil with a square cross-section. The basic dimensional parameters of such a spiral are N, w, ,

Windings Sizing Calculation
, and , as depicted in Figure 4, which are the number of turns, cross-sectional width, the spacing between consecutive turns, the inner side length of the spiral, and the outer side length of the spiral, respectively. The outer side length is derived from the other geometrical parameters as The total length of the spiral can be calculated as

Self and Mutual Inductance Calculation
From Figure 4, the inductance of each coil is obtained with Equation (12), where the number of turns is , the coil resistance is , the coil cross-section area is , and is the equivalent radius of the coil. In addition, = 1 should be used for the primary coil and = 2 for the secondary coil. The total length l tot of the spiral can be calculated as Energies 2018, 11, 1716 7 of 22

Self and Mutual Inductance Calculation
From Figure 4, the inductance of each coil is obtained with Equation (12), where the number of turns is N i , the coil resistance is R i , the coil cross-section area is S i , and r i is the equivalent radius of the coil. In addition, i = 1 should be used for the primary coil and i = 2 for the secondary coil.
where ρ = 1.72 × 10 −8 Ω ·m. The calculation of mutual inductance M is computed using Neumann's formula for a rectangular coil with N 1 and N 2 turns and their equivalent radius. The coupling coefficient k of two magnetically coupled coils is defined by the ratio of the mutual inductance M and the two self-inductances L 1 and L 2 .

Design Steps for the SS Topology WPT System
Step 1: Calculate the AC equivalent load resistance R L : where P bat is the battery charging power and V bat is the battery voltage.
Step 2: Calculate the optimal frequency f 0 [37]: where f 0 is the resonant frequency. R 1 , R 2 is the primary and secondary coil resistance.
Step 3: Calculate the primary capacitance C 1 and secondary capacitance C 2 : Step 4: Calculate the total impedance Z 1 of the equivalent circuit [18]: Energies 2018, 11, 1716 8 of 22 Step 5: Calculate the primary current I 1 and the secondary current I 2 : Step 6: Choose the current density δ and calculate the coils cross-sectional area S i .
Step 7: Calculate the primary capacitance voltage V c1 and secondary capacitance voltage V c2 : Step 8: Calculate the quality factor of the primary coil Q p and secondary coil Q s [38]:

Design Optimization for SS Topology of WPT System
In [37], the authors presented a basic design method using an iterative algorithm for the WPT system. In this paper, a design optimization approach for the SS topology of WPT system was developed with coil dimension optimization using an iterative algorithm. For the desired SS-compensated 3.7 kW and 7.7 kW WPT systems, the design process initiates with an initial geometry, number of turns, cross-sectional area, and the current density of the coils and then an iterative optimization process is applied to fulfill the required power level within the permissible maximum frequency and the geometry of coil. All of these parameters along with the circuit's electrical states and outputs (system currents and voltages) can be iteratively evaluated. In this section, we focus on the optimal design of an SS topology WPT system using an iterative algorithm. From the various results, a WPT design is selected based on the required operation parameters such as needed power and voltage levels and operating (resonance) frequency.

Flow Chart of Coil Sizing Optimization
A flow chart of the WPT system design process is depicted in Figure 5. This design flow process can be applied to different power levels of a WPT system. According to this flow chart, the design process initiates with an initial geometry, number of turns, cross-sectional area, and the current density of the coils and then an iterative process is applied until the fulfillment of the required power level with the permissible maximum frequency and the geometry of coils.

Optimal Parameters and Coil Dimensions
In [37,39,40], only preliminary simulation results were presented. However, there is no optimization method for the dimensions of the primary and secondary coils. In this paper, the design optimization approach for the SS topology of the WPT system is presented. For the 3.7 kW and 7.7 kW WPT systems, the airgap is fixed at 100 mm and the spacing between consecutive turns is fixed at 1 mm when the resonant frequency is at both 40 kHz and 85 kHz. However, the number of turns and the inner dimensions of the primary and secondary coils are variable. The coupling coefficient is calculated by the simulation process using an iterative algorithm, which is a function of the inner dimension of the primary and secondary coils [41].
For the 3.7 kW WPT system, shown in Table 1, the inner dimensions of 250 × 250 mm of the primary and secondary coils was chosen to get the maximum coupling coefficient at the resonant frequency for both 40 kHz and 85 kHz and the number of turns 1 = 23, 2 = 22 when the current density of the coils is 4 A/mm 2 .
For the 7.7 kW WPT system, the inner dimensions of 250 × 250 mm of the primary and secondary coils was chosen to get the maximum coupling coefficient at the resonant frequency for both 40 kHz and 85 kHz and the number of turns 1 = 16, 2 = 15, respectively. The optimal coil dimensions are summarized in Table 1, where the current density of coils is 4 A/mm 2 .

Optimal Parameters and Coil Dimensions
In [37,39,40], only preliminary simulation results were presented. However, there is no optimization method for the dimensions of the primary and secondary coils. In this paper, the design optimization approach for the SS topology of the WPT system is presented. For the 3.7 kW and 7.7 kW WPT systems, the airgap L g is fixed at 100 mm and the spacing between consecutive turns is fixed at 1 mm when the resonant frequency is at both 40 kHz and 85 kHz. However, the number of turns and the inner dimensions of the primary and secondary coils are variable. The coupling coefficient is calculated by the simulation process using an iterative algorithm, which is a function of the inner dimension of the primary and secondary coils [41].
For the 3.7 kW WPT system, shown in Table 1, the inner dimensions of 250 × 250 mm of the primary and secondary coils was chosen to get the maximum coupling coefficient at the resonant frequency for both 40 kHz and 85 kHz and the number of turns N 1 = 23, N 2 = 22 when the current density of the coils is 4 A/mm 2 . For the 7.7 kW WPT system, the inner dimensions of 250 × 250 mm of the primary and secondary coils was chosen to get the maximum coupling coefficient at the resonant frequency for both 40 kHz and 85 kHz and the number of turns N 1 = 16, N 2 = 15, respectively. The optimal coil dimensions are summarized in Table 1, where the current density of coils is 4 A/mm 2 .
The main parameters of the final design process that were used in this simulation study are reported in Table 2. The resistance values R 1 and R 2 represented the primary and secondary resistors, respectively. The design process was analyzed to ensure the optimal parameters of the primary and secondary coils and their dimensions. Design parameters for the 3.7 kW and 7.7 kW WPT systems, which are both operating at 40 kHz and 85 kHz, are shown in Table 2. Table 2. Parameters of SS compensation topology for the 3.7 kW and 7.7 kW WPT systems.

Magnetic Design and Verification of Coils Parameters
The finite element method (FEM) was used to verify the design of the coils. After the CAD models were built by the mechanical design software SOLIDWORKS, FEM computations were implemented by the commercial FEM software COMSOL Multiphysics 5.3a. The verification was implemented with a physics interface, named Magnetic Fields (mf), within the AC/DC module. An infinite element component was used to simulate the infinite far area in the air. Figure 6 shows the CAD model of the WPT system.  The main parameters of the final design process that were used in this simulation study are reported in Table 2. The resistance values 1 and 2 represented the primary and secondary resistors, respectively. The design process was analyzed to ensure the optimal parameters of the primary and secondary coils and their dimensions. Design parameters for the 3.7 kW and 7.7 kW WPT systems, which are both operating at 40 kHz and 85 kHz, are shown in Table 2.

Magnetic Design and Verification of Coils Parameters
The finite element method (FEM) was used to verify the design of the coils. After the CAD models were built by the mechanical design software SOLIDWORKS, FEM computations were implemented by the commercial FEM software COMSOL Multiphysics 5.3a. The verification was implemented with a physics interface, named Magnetic Fields (mf), within the AC/DC module. An infinite element component was used to simulate the infinite far area in the air. Figure 6 shows the CAD model of the WPT system.
The current distribution in the primary coil and magnetic flux lines in the air are illustrated in Figure 7 in 3D, with maximum and minimum values of flux density. In this situation, the coil below is the primary coil. The current in the primary coil is 10 A and the current in the secondary coil is 0. Figure 8 shows a cross-section view of the 3D vision magnetic flux density distribution.   The current distribution in the primary coil and magnetic flux lines in the air are illustrated in Figure 7 in 3D, with maximum and minimum values of flux density. In this situation, the coil below is the primary coil. The current in the primary coil is 10 A and the current in the secondary coil is 0. Figure 8 shows a cross-section view of the 3D vision magnetic flux density distribution.  Two systems were verified. They were the 3.7 kW and 7.7 kW systems, in which the air-gaps in both were 100 mm. Self-inductance and mutual inductance were calculated respectively. Table 3 indicates the verification results between the analytical model and the FEM of the 3.7 kW and 7.7 kW WPT systems. The mutual inductance was related to air-gap between primary and secondary coil. The impact of the air-gap on the 3.7 kW and 7.7 kW systems is illustrated in Figures 9 and 10, respectively. In Figures 9 and 10, the mutual inductance is shown to have declined rapidly when the airgap was increased.   Two systems were verified. They were the 3.7 kW and 7.7 kW systems, in which the air-gaps in both were 100 mm. Self-inductance and mutual inductance were calculated respectively. Table 3 indicates the verification results between the analytical model and the FEM of the 3.7 kW and 7.7 kW WPT systems. The mutual inductance was related to air-gap between primary and secondary coil. The impact of the air-gap on the 3.7 kW and 7.7 kW systems is illustrated in Figures 9 and 10, respectively. In Figures 9 and 10, the mutual inductance is shown to have declined rapidly when the airgap was increased.  Two systems were verified. They were the 3.7 kW and 7.7 kW systems, in which the air-gaps in both were 100 mm. Self-inductance and mutual inductance were calculated respectively. Table 3 indicates the verification results between the analytical model and the FEM of the 3.7 kW and 7.7 kW WPT systems. The mutual inductance was related to air-gap between primary and secondary coil. The impact of the air-gap on the 3.7 kW and 7.7 kW systems is illustrated in Figures 9 and 10, respectively. In Figures 9 and 10, the mutual inductance is shown to have declined rapidly when the airgap was increased.

WPT System Control for Low-Voltage Battery
Starting from the AC supply, an H-Bridge was used for the active rectification of the grid current, which was operated as a single-phase PWM rectifier when performing in the G2V mode. The ensuring DC-link was supplied by the H-Bridge as single-phase inverter, which operated in squarewave mode at a fixed switching frequency, exciting the primary resonant circuit. The output of the secondary resonant circuit was rectified using the reverse conducting diodes of the H-Bridge at the secondary side. An on-board bidirectional DC-DC converter was used to bring the rectified DC-link voltage to a lower battery pack voltage. This DC-DC converter operated as a conventional Buck converter in G2V mode.
At the grid side, a hysteresis current control (HCC) was used as a current controller. The hysteresis band was set considering Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) as power switches, for which the maximum switching frequency lies around 40 kHz or 85 kHz. The amplitude of the voltage reference value was set by DC-link voltage control in order to maintain a constant DC voltage at 400 V. The H-Bridges exciting the primary and secondary resonant circuits were operated in square-wave operation at fixed switching frequencies. The DC-DC converter was controlled by a cascade of an inner inductor current control loop and an outer voltage battery control loop with DC-link voltage stabilization [41]. The control method block diagram is depicted in Figure  11.

Airgap (mm) Mutual inductance (uH)
Analytical model FEM Figure 9. Impact of air-gap on the 3.7 kW system.

WPT System Control for Low-Voltage Battery
Starting from the AC supply, an H-Bridge was used for the active rectification of the grid current, which was operated as a single-phase PWM rectifier when performing in the G2V mode. The ensuring DC-link was supplied by the H-Bridge as single-phase inverter, which operated in squarewave mode at a fixed switching frequency, exciting the primary resonant circuit. The output of the secondary resonant circuit was rectified using the reverse conducting diodes of the H-Bridge at the secondary side. An on-board bidirectional DC-DC converter was used to bring the rectified DC-link voltage to a lower battery pack voltage. This DC-DC converter operated as a conventional Buck converter in G2V mode.
At the grid side, a hysteresis current control (HCC) was used as a current controller. The hysteresis band was set considering Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) as power switches, for which the maximum switching frequency lies around 40 kHz or 85 kHz. The amplitude of the voltage reference value was set by DC-link voltage control in order to maintain a constant DC voltage at 400 V. The H-Bridges exciting the primary and secondary resonant circuits were operated in square-wave operation at fixed switching frequencies. The DC-DC converter was controlled by a cascade of an inner inductor current control loop and an outer voltage battery control loop with DC-link voltage stabilization [41]. The control method block diagram is depicted in Figure  11.

Airgap (mm) Mutual inductance (uH)
Analytical model FEM Figure 10. Impact of air-gap on the 7.7 kW system.

WPT System Control for Low-Voltage Battery
Starting from the AC supply, an H-Bridge was used for the active rectification of the grid current, which was operated as a single-phase PWM rectifier when performing in the G2V mode. The ensuring DC-link was supplied by the H-Bridge as single-phase inverter, which operated in square-wave mode at a fixed switching frequency, exciting the primary resonant circuit. The output of the secondary resonant circuit was rectified using the reverse conducting diodes of the H-Bridge at the secondary side. An on-board bidirectional DC-DC converter was used to bring the rectified DC-link voltage to a lower battery pack voltage. This DC-DC converter operated as a conventional Buck converter in G2V mode.
At the grid side, a hysteresis current control (HCC) was used as a current controller. The hysteresis band was set considering Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) as power switches, for which the maximum switching frequency lies around 40 kHz or 85 kHz. The amplitude of the voltage reference value was set by DC-link voltage control in order to maintain a constant DC voltage at 400 V. The H-Bridges exciting the primary and secondary resonant circuits were operated in square-wave operation at fixed switching frequencies. The DC-DC converter was controlled by  [41]. The control method block diagram is depicted in Figure 11.

Simulation Results for 3.7 kW at 40 kHz
A grid-to-vehicle power transfer system was simulated for the charging of a 200 V lithium-ion battery pack. The charging battery power was set to 3700 W, and the operating frequency was set at 40 kHz. According to Figure 12a, the average battery current of 17.4 A was achieved with a ripple of 0.4 A. As can be seen in Figure 12b, a battery voltage of 212.51 V was given.
Furthermore, as can be seen in Figure 13a, the unity power factor at the grid side was achieved. Regarding the resonant circuit, Figure 13b,c show that both the primary side and secondary sides of the circuit were in resonance.

Simulation Results for 3.7 kW at 40 kHz
A grid-to-vehicle power transfer system was simulated for the charging of a 200 V lithium-ion battery pack. The charging battery power was set to 3700 W, and the operating frequency was set at 40 kHz. According to Figure 12a, the average battery current of 17.4 A was achieved with a ripple of 0.4 A. As can be seen in Figure 12b, a battery voltage of 212.51 V was given.

Simulation Results for 3.7 kW at 85 kHz
A grid-to-vehicle power transfer system was simulated for a battery with the identical specification as above-a 200 V lithium-ion battery pack. The battery charging power was set to 3700 W, whereas the operating frequency was set at 85 kHz. A battery discharging current of 17 A was achieved with a ripple of 8 A, as shown in Figure 14a. Figure 14b demonstrates the battery voltage of 212.5 V.
Furthermore, the unity power factor was achieved, as can be seen in Figure 15a. Regarding the resonant circuit, Figure 15b,c show that both the primary and secondary sides of the circuit were in resonance. Furthermore, as can be seen in Figure 13a, the unity power factor at the grid side was achieved. Regarding the resonant circuit, Figure 13b,c show that both the primary side and secondary sides of the circuit were in resonance.

Simulation Results for 3.7 kW at 85 kHz
A grid-to-vehicle power transfer system was simulated for a battery with the identical specification as above-a 200 V lithium-ion battery pack. The battery charging power was set to 3700 W, whereas the operating frequency was set at 85 kHz. A battery discharging current of 17 A was achieved with a ripple of 8 A, as shown in Figure 14a. Figure 14b demonstrates the battery voltage of

Simulation Results for 3.7 kW at 85 kHz
A grid-to-vehicle power transfer system was simulated for a battery with the identical specification as above-a 200 V lithium-ion battery pack. The battery charging power was set to 3700 W, whereas the operating frequency was set at 85 kHz. A battery discharging current of 17 A was achieved with a ripple of 8 A, as shown in Figure 14a. Figure 14b demonstrates the battery voltage of 212.5 V.

Simulation Results for 7.7 kW at 40 kHz
A grid-to-vehicle power transfer system was simulated for the charging of a 200 V lithium-ion battery pack. The charging power reference was set at 7700 W, while the operating frequency was set at 40 kHz. As shown in Figure 16a, the average battery current of 36 A was achieved with a ripple of 1 A. Figure 16b shows the battery voltage of 212.88 V.
Furthermore, the unity power factor was achieved, as can be seen in Figure 17a. Regarding the resonant circuit, Figure 17b,c demonstrate that both the primary and secondary sides of the circuit were in resonance. Furthermore, the unity power factor was achieved, as can be seen in Figure 15a. Regarding the resonant circuit, Figure 15b,c show that both the primary and secondary sides of the circuit were in resonance.

Simulation Results for 7.7 kW at 40 kHz
A grid-to-vehicle power transfer system was simulated for the charging of a 200 V lithium-ion battery pack. The charging power reference was set at 7700 W, while the operating frequency was set at 40 kHz. As shown in Figure 16a, the average battery current of 36 A was achieved with a ripple of 1 A. Figure 16b shows the battery voltage of 212.88 V.
Furthermore, the unity power factor was achieved, as can be seen in Figure 17a. Regarding the resonant circuit, Figure 17b,c demonstrate that both the primary and secondary sides of the circuit were in resonance.

Simulation Results for 7.7 kW at 40 kHz
A grid-to-vehicle power transfer system was simulated for the charging of a 200 V lithium-ion battery pack. The charging power reference was set at 7700 W, while the operating frequency was set at 40 kHz. As shown in Figure 16a, the average battery current of 36 A was achieved with a ripple of 1 A. Figure 16b shows the battery voltage of 212.88 V.

Simulation Results for 7.7 kW at 85 kHz
A grid-to-vehicle power transfer system was simulated for a battery with a 150 V lithium-ion battery pack. The battery charging power was set at 7700 W, but the operating frequency was set at 85 kHz. Figure 18a shows a battery discharging current of 48 A with a ripple of 6 A. At the battery side, a battery voltage of 159.7 V is shown in Figure 18b.
Furthermore, as can be seen in Figure 19a, the unity power factor was achieved. Regarding the resonant circuit, Figure 19b,c demonstrate that both the primary and secondary sides of the circuit were in resonance. Furthermore, the unity power factor was achieved, as can be seen in Figure 17a. Regarding the resonant circuit, Figure 17b,c demonstrate that both the primary and secondary sides of the circuit were in resonance.

Simulation Results for 7.7 kW at 85 kHz
A grid-to-vehicle power transfer system was simulated for a battery with a 150 V lithium-ion battery pack. The battery charging power was set at 7700 W, but the operating frequency was set at 85 kHz. Figure 18a shows a battery discharging current of 48 A with a ripple of 6 A. At the battery side, a battery voltage of 159.7 V is shown in Figure 18b.
Furthermore, as can be seen in Figure 19a, the unity power factor was achieved. Regarding the resonant circuit, Figure 19b,c demonstrate that both the primary and secondary sides of the circuit were in resonance.

Simulation Results for 7.7 kW at 85 kHz
A grid-to-vehicle power transfer system was simulated for a battery with a 150 V lithium-ion battery pack. The battery charging power was set at 7700 W, but the operating frequency was set at  Figure 18a shows a battery discharging current of 48 A with a ripple of 6 A. At the battery side, a battery voltage of 159.7 V is shown in Figure 18b.

Experimental Validation
To validate the concept of the proposed topology in Figure 20, a prototype of the 3.7 kW WPT system was built and tested in our laboratory, as illustrated in Figure 21. For the experimental testing, the load resistance was adjusted to 8.3 Ω, the switching frequency was set to 37 kHz, while the input single-phase AC voltage from the utility grid was 230 V. Each leg of the H-Bridge was connected with a 1.5 uF snubber capacitor to reduce the spike voltage of SiC MOSFETs. The parameters of the lab measurement and simulation are given in Table 4, and Table 5 shows the components used for the prototype. The 37 kHz switching frequency, which is not the perfect resonance frequency (40 kHz), was experimentally used to minimize the voltage spikes during the SiC MOSFETs switching (at on/off states) and to provide satisfied waveforms of current and voltage in both sides. Meanwhile, it was necessary to consider the efficiency of the WPT system. The main focus was on the realization of the WPT concept and design. Furthermore, as can be seen in Figure 19a, the unity power factor was achieved. Regarding the resonant circuit, Figure 19b,c demonstrate that both the primary and secondary sides of the circuit were in resonance.

Experimental Validation
To validate the concept of the proposed topology in Figure 20, a prototype of the 3.7 kW WPT system was built and tested in our laboratory, as illustrated in Figure 21. For the experimental testing, the load resistance was adjusted to 8.3 Ω, the switching frequency was set to 37 kHz, while the input single-phase AC voltage from the utility grid was 230 V. Each leg of the H-Bridge was connected with a 1.5 uF snubber capacitor to reduce the spike voltage of SiC MOSFETs. The parameters of the lab measurement and simulation are given in Table 4, and Table 5 shows the components used for the prototype. The 37 kHz switching frequency, which is not the perfect resonance frequency (40 kHz), was experimentally used to minimize the voltage spikes during the SiC MOSFETs switching (at on/off states) and to provide satisfied waveforms of current and voltage in both sides. Meanwhile, it was necessary to consider the efficiency of the WPT system. The main focus was on the realization of

Experimental Validation
To validate the concept of the proposed topology in Figure 20, a prototype of the 3.7 kW WPT system was built and tested in our laboratory, as illustrated in Figure 21. For the experimental testing, the load resistance was adjusted to 8.3 Ω, the switching frequency was set to 37 kHz, while the input single-phase AC voltage from the utility grid was 230 V. Each leg of the H-Bridge was connected with a 1.5 uF snubber capacitor to reduce the spike voltage of SiC MOSFETs. The parameters of the lab measurement and simulation are given in Table 4, and Table 5 shows the components used for the prototype. The 37 kHz switching frequency, which is not the perfect resonance frequency (40 kHz), was experimentally used to minimize the voltage spikes during the SiC MOSFETs switching (at on/off states) and to provide satisfied waveforms of current and voltage in both sides. Meanwhile, it was necessary to consider the efficiency of the WPT system. The main focus was on the realization of the WPT concept and design.   Figure 21. Laboratory setup of a 3.7 kW WPT system. Figure 22 shows the waveforms of the primary and secondary sides (voltage and current). The AC input voltage, the current drawn from the grid, the DC load current, and the voltage of the experimental waveforms are provided in Figure 23. The input voltage and current were measured in connection with a single-phase passive rectifier. The WPT experimental efficiency results are shown in Figure 24. It shows the plotted efficiency map for the SiC MOSFETs switches. The efficiency was calculated by measuring both DC input power (the input of the high frequency inverter) and DC output power (load power), as seen in Equation (28).   Figure 21. Laboratory setup of a 3.7 kW WPT system. Figure 22 shows the waveforms of the primary and secondary sides (voltage and current). The AC input voltage, the current drawn from the grid, the DC load current, and the voltage of the experimental waveforms are provided in Figure 23. The input voltage and current were measured in connection with a single-phase passive rectifier. The WPT experimental efficiency results are shown in Figure 24. It shows the plotted efficiency map for the SiC MOSFETs switches. The efficiency was calculated by measuring both DC input power (the input of the high frequency inverter) and DC output power (load power), as seen in Equation (28).   Figure 22 shows the waveforms of the primary and secondary sides (voltage and current).
From the results of Figure 24, it can be seen that the DC/DC efficiency for the lab WPT system was around 91.6% when the output DC power was 3.1 kW and the inverter was used as SiC MOSFETs.   The AC input voltage, the current drawn from the grid, the DC load current, and the voltage of the experimental waveforms are provided in Figure 23. The input voltage and current were measured in connection with a single-phase passive rectifier. The WPT experimental efficiency results are shown in Figure 24. It shows the plotted efficiency map for the SiC MOSFETs switches. The efficiency η was calculated by measuring both DC input power (the input of the high frequency inverter) and DC output power (load power), as seen in Equation (28). η = P out,DC P in,DC (28) From the results of Figure 24, it can be seen that the DC/DC efficiency for the lab WPT system was around 91.6% when the output DC power was 3.1 kW and the inverter was used as SiC MOSFETs.

Conclusions
In this paper, a design optimization approach was proposed for an SS WPT system. A WPT system with SS compensation topology was designed for 3.7 kW and 7.7 kW charging systems, both operating at 40 kHz and 85 kHz resonant frequency with optimized coil sizes and system efficiency. The primary and secondary coil parameters and dimensions were designed using coil optimization. In addition, the primary and secondary coils were designed to have the maximum coupling coefficient and efficiency. In this paper, control systems were developed and used to incorporate the grid-to-vehicle (G2V) operating modes by implementing unidirectional rectifiers/inverters and DC-DC converters. The simulation results and magnetic verification have shown that a WPT system could be efficiently used in light-duty EV applications. Furthermore, A 3.7 kW WPT system prototype was built and implemented in the lab to preliminarily validate the WPT design and performance.