# A Maximum Transfer Efficiency Tracking Method for Dynamic Wireless Charging Systems of Electric Vehicles

Authors: Nguyen Kien Trung; Nguyen Thi Diep
Journal: Journal of Electrical and Computer Engineering
 (2021)

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## Abstract

This paper proposes a new control method to improve transfer efficiency for dynamic wireless charging systems of electric vehicles (EVs). In the charging process, the equivalent impedance in the receiving side varies according to the state of charge of the battery system that reduces the transfer efficiency. An impedance control circuit is constructed on the receiving side to track the optimization impedance that transfer efficiency is maximized. However, the optimization impedance depends on the coupling coefficient. Therefore, in this paper, the coupling coefficient, which varies according to the EVs position, is online estimated only from the receiving side. A 1.5 kW dynamic wireless charging system prototype is built in the laboratory environment. In experiment results, the greatest transfer efficiency obtains 94.14% when the EVs move in aligned on the charging lane. Furthermore, the proposed control method improves by 6% on the transfer efficiency in the case of 30% misalignment when the transfer efficiency obtains 91%.


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## Body

## 1. Introduction

Recently, electric vehicles (EVs) are considered as a green solution to reduce the air pollution problem in big cities in the world. However, the use of EVs is still limited due to the charging infrastructure. The wire charging system is inconvenient [1–3]. Based on the wireless power transfer (WPT) technology, the wireless charging system promises a convenient charging solution for EVs [4, 5]. Wireless charging systems for EVs are classified into two categories: static wireless charging (SWC) and dynamic wireless charging (DWC). The SWC system has been rapidly developed in the last decade, some commercial products have appeared in the market [2]. However, the big battery capacity and the static charging requirement still are the disadvantages [3]. In the DWC systems, the EVs can be continuously charged while moving. The driving range of the EV can be extended, and a smaller battery pack can be used to reduce the vehicle weight as well as the vehicle cost [3–5]. Now, the dynamic wireless charging system is an attractive research topic. Scientists almost focus on efficiency improvement and high-power charging system design [6–10].The transfer efficiency of WPT systems depends on the coils design, compensation circuit design, operating frequency, and load impedance [1]. However, with a certain DWC system, the coils, the compensation circuits, and the operating frequency are fixed. Then, the impedance matching control is very important to obtain high transfer efficiency. The impedance matching can be done by tuning the compensation circuit [11–15], by using DC/DC converter [16–18], and by controlling the input power to track the maximum efficiency point [19–23]. However, all the research considers the optimal load is a constant value suitable for the SWC system. In the DWC systems, the receiving coil is moving, then the coupling coefficient is changing, and the optimal load value is not constant [24–29]. Therefore, to realize the impedance matching control, the optimal load must be identified previously. In other words, the continuous estimation of the coupling coefficient is needed.The coupling coefficient estimation has been done by some researchers. References [25–28] present a real-time coupling coefficient estimation method applying for a dynamic charging system. Only the secondary side parameters are needed to measure. However, measuring the RMS value of alternating current takes error in the discontinuous current mode. The coupling coefficient can be estimated using the DC side measurement parameters [25, 29]. However, their studies consider a simple dynamic charging system where there is only one transmitting coil and one receiving coil. Furthermore, the analysis and results are done only in the case when the receiving coil moves in the center of the transmitting coil. Reference [30] shows a coupling coefficient identification method by switching the compensation capacitors. However, the estimation equations require the information of the resonant currents on primary and secondary sides, which will increase the difficulty in practice.This paper proposes a maximum transfer efficiency method in the DWC system through the compensation circuit design and optimal impedance load tracking control. The coupling system includes three transmitting coils and one receiving coil. The coupling coefficient is estimated by measuring only the DC parameters on the receiving side. Firstly, the coupling coefficient of the DWC system is analyzed. Secondly, the double-sided LCC compensation circuit is designed to obtain maximum efficiency. Thirdly, the optimal load is calculated through the estimation coupling coefficients from the secondary side. Finally, an impedance controller is proposed to track the optimal load impedance based on a DC/DC converter.The control concept and the stability analysis are provided, and its effectiveness is verified by simulation and experiments. The experiment results show that when the EV moves along the charging lane with no misalignment, the transfer efficiency of over 94.14% is obtained. Moreover, when the EV moves in a 30% misalignment from the center of the transmitting coil, the transfer efficiency could improve by 6% by applying the proposed control method.


## 2. The Theoretical Basis for Maximum Transfer Efficiency Tracking Method

### 2.1. System Structure

Figure1 shows the structure of the proposed DWC of EVs, which consists of the primary side on the road and the secondary side attached to the EV. The input DC voltage is inverted to an 85 kHz AC voltage by a voltage source type full-bridge inverter. The power is transferred from the primary side to the secondary side through the magnetic coupling system. Then, the obtained AC voltage on the receiving coil is rectified to DC voltage and through DC/DC converters supply to the EV.Figure 1
Structure diagram of the designed DWC system.On the primary side, one transmitting modular includes three transmitting coils powered by a single inverter to reduce the number of the inverter. And each transmitter coil is compensated individually by its LCC compensation circuit. Several modules are placed continuously on the road which is called the DWC lane. On the secondary side, the receiving coil is mounted under the EV chassis to receive the energy from the charging lane. On this side, the LCC compensation circuit is also used. A single-phase diode rectifier and a boost converter are used to track the optimal impedance from the secondary side. After that, a DC-DC converter is used to control the battery charging process.


### 2.2. Analysis of the System’s Coupling Coefficient Characteristics

In this system, the magnetic coupler is designed by finite element analysis (FEA) simulation to reduce power pulsation [31]. The magnetic coupler is designed with three layers: the first layer is rectangular unipolar coils. The second layer is the ferrite bars; it is used to conduct the magnetic field and strengthen the magnetic connection between the transmitting coils and the receiving coil. The third layer is an aluminum shield, which protects the magnetic field from leaking into the environment. Each transmitting modular consists of three unipolar coils (T1, T2, T3) placed side by side to reduce the power pulsation. The dimension of each transmitting coil and receiving coil is 400 mm × 400 mm × 42 mm and 500 mm × 400 mm × 42 mm, respectively, in which each coil has 10 turns. The air gap distance between the transmitting coils and receiving coil is 150 mm. The structure of the magnetic coupler is shown in Figure 2.Figure 2
Magnetic coupler structure.When the receiver moves on the DWC lane, the receiver displacement according tox-direction is defined as dr, which is zero when the receiver is centered on the first transmitter (T1). The receiver lateral misalignment according to y-direction is defined as lm, which is zero when the receiver is straight with the transmitters.The FEA simulation result of the coupling coefficients when the receiver moves on the DWC lane is shown in Figure3 (solid lines). The total coupling coefficient between the receiving coil and transmitting coils is defined as kr. When the receiver moves along the DWC lane according to the x-direction and lateral misalignment in 3 cases, lm = 0 mm, lm = 40 mm, lm = 60 mm, the average coefficient coupling is equal to 0.14, 0.111, and 0.078, respectively. This result shows that when lateral misalignment increases, the total coupling coefficient decreases.Figure 3
Simulation and estimation result of the total coupling coefficient.The FEA simulation results of the self-inductance and mutual-inductance values of the transmitters and receiver are shown in Table1. The total mutual-inductance of transmitter Ti (i = 1, 2, 3) with other transmitters is defined as Mi. Li; Lr is self-inductance of the transmitting coils and receiving coil.Table 1
The self-inductance and mutual-inductance values of the transmitters and receiver.
ParameterValue (μH)ParameterValue (μH)Li (i = 1, 2, 3)102M112.474Lr120M220.903M312.474


### 2.3. Optimal Load Conditions to Maximize Transfer Efficiency

In this system, the LCC compensation circuit is designed for both the transmitting and receiving sides [29]. The LCC compensation circuit has many advantages such as high efficiency with both heavy and light loads and resonant frequency regardless of the coupling coefficient and load [8, 10]. The LCC compensation circuit is designed with consideration of the self-coupled of the transmitting coils together [31]. The resonant frequency of the coupling system is designed the same as the switching frequency of the inverter. The primary side compensation circuits are used to reduce the volt-ampere rating of the power converter and help achieve soft switching of power switches on the high-frequency inverter. The secondary side compensation circuit is used to enhance power transfer capability.The equivalent circuit of the coupling system is shown in Figure4, where all of the circuits from the diode rectifier to the battery on the secondary side are considered equivalent impedance (RL). Then, the transfer efficiency can be calculated as follows [31]:(1)η=RLIr2RLIr2+RrILr2+R1IL12+R2IL22+R3IL32=RLRL2.Rr/ω2Lfr23+kr2QiQr/kr2QiQr+RL1+6/kr2QiQr+3ω2Lfr2/Rr1/kr2QiQr,where Qi = ωLi/Ri, Qr = ωLr/Rr is the quality factor of the transmitting coils and receiving coil. Equation (1) shows that, with a designed system, the transfer efficiency depends on the coupling coefficient (kr), switching frequency (fsw), and equivalent impedance (RL). Then, the optimal load for maximum transfer efficiency can be obtained as(2)ηmax=kr2QiQr3+3+kr2QiQr2,(3)RL.opt=ω2Lfr2Rr33+kr2QiQr,where RL.opt is called optimal impedance. Equations (2) and (3) show that the maximum transfer is only achieved when the equivalent impedance is equal to the optimal impedance value. Equation (2) is used to evaluate and estimate the theoretical maximum transfer efficiency shown in Figure 5. When kr = 0.14 and the quality factor Qi = 429, Qr = 458, the maximum theoretical transfer efficiency is about 94.6%.Figure 4
Equivalent circuit of the coupling system.Figure 5
Maximum theoretical transfer efficiency characteristic withkr = 0.14.The parameter values of the compensation circuit are determined according to three conditions: the relationship of the resonant circuit, the output power, and the optimal load. The parameter values for a 1.5 kW dynamic charging system are shown in Table2 [31].Table 2
System and compensation circuit parameter.
ParameterValueParameterValueParameterValueP01.5 kWLr120μHC395 nFUDC310 VRr0.14 ΩLfr28.9μHLi102μHLfi52.6µHCfr120.9 nFRi0.13 ΩCfi66.5 nFCr38.5 nFUb400 VC193.7 nFkr0.14fsw85 kHzC2123.2 nFIn a WPT system, the transfer efficiency depends on the value of load impedance and coupling coefficient. Therefore, it is necessary to consider the effect of these parameters on transfer efficiency. Figure6(a) shows frequency characteristics of the transfer efficiency when equivalent impedance (RL) increases from 10 Ω to 150 Ω and the receiver position dr is 0 mm, lm is 0 mm. The results show that transfer efficiency is the largest in the case of optimal impedance (RL = RL.opt = 53.3 Ω). The maximum transfer efficiency is 94.6% and transfer efficiency is high in the frequency range 83 kHz to 89 kHz. At other values of load impedance, the efficiency drops and drops rapidly in the vicinity of 85 kHz. Figure 6(b) shows frequency characteristics of the transfer efficiency when the receiver is the lateral misalignment and the value of load resistance is optimal load according to equation (3). The results show that the transfer efficiency is the largest in the case of no lateral misalignment (lm = 0 mm). When the lateral misalignment increases, the transfer efficiency decreases.Figure 6
Frequency characteristics of the transfer efficiency. (a)lm = 0 mm and RL is variation. (b) lm is variation and RL = RL.opt.
(a)(b)Thus, in DWC systems, the transfer efficiency only reaches the maximum value at one load impedance value, known as the optimal impedance. However, the equivalent impedance (RL) will be changed due to the state of charge of the EV battery system. Furthermore, the optimum impedance value depends on the position of the receiver. Therefore, optimal impedance control is necessary to achieve maximum transfer efficiency in the DWC systems.


## 2.1. System Structure

Figure1 shows the structure of the proposed DWC of EVs, which consists of the primary side on the road and the secondary side attached to the EV. The input DC voltage is inverted to an 85 kHz AC voltage by a voltage source type full-bridge inverter. The power is transferred from the primary side to the secondary side through the magnetic coupling system. Then, the obtained AC voltage on the receiving coil is rectified to DC voltage and through DC/DC converters supply to the EV.Figure 1
Structure diagram of the designed DWC system.On the primary side, one transmitting modular includes three transmitting coils powered by a single inverter to reduce the number of the inverter. And each transmitter coil is compensated individually by its LCC compensation circuit. Several modules are placed continuously on the road which is called the DWC lane. On the secondary side, the receiving coil is mounted under the EV chassis to receive the energy from the charging lane. On this side, the LCC compensation circuit is also used. A single-phase diode rectifier and a boost converter are used to track the optimal impedance from the secondary side. After that, a DC-DC converter is used to control the battery charging process.


## 2.2. Analysis of the System’s Coupling Coefficient Characteristics

In this system, the magnetic coupler is designed by finite element analysis (FEA) simulation to reduce power pulsation [31]. The magnetic coupler is designed with three layers: the first layer is rectangular unipolar coils. The second layer is the ferrite bars; it is used to conduct the magnetic field and strengthen the magnetic connection between the transmitting coils and the receiving coil. The third layer is an aluminum shield, which protects the magnetic field from leaking into the environment. Each transmitting modular consists of three unipolar coils (T1, T2, T3) placed side by side to reduce the power pulsation. The dimension of each transmitting coil and receiving coil is 400 mm × 400 mm × 42 mm and 500 mm × 400 mm × 42 mm, respectively, in which each coil has 10 turns. The air gap distance between the transmitting coils and receiving coil is 150 mm. The structure of the magnetic coupler is shown in Figure 2.Figure 2
Magnetic coupler structure.When the receiver moves on the DWC lane, the receiver displacement according tox-direction is defined as dr, which is zero when the receiver is centered on the first transmitter (T1). The receiver lateral misalignment according to y-direction is defined as lm, which is zero when the receiver is straight with the transmitters.The FEA simulation result of the coupling coefficients when the receiver moves on the DWC lane is shown in Figure3 (solid lines). The total coupling coefficient between the receiving coil and transmitting coils is defined as kr. When the receiver moves along the DWC lane according to the x-direction and lateral misalignment in 3 cases, lm = 0 mm, lm = 40 mm, lm = 60 mm, the average coefficient coupling is equal to 0.14, 0.111, and 0.078, respectively. This result shows that when lateral misalignment increases, the total coupling coefficient decreases.Figure 3
Simulation and estimation result of the total coupling coefficient.The FEA simulation results of the self-inductance and mutual-inductance values of the transmitters and receiver are shown in Table1. The total mutual-inductance of transmitter Ti (i = 1, 2, 3) with other transmitters is defined as Mi. Li; Lr is self-inductance of the transmitting coils and receiving coil.Table 1
The self-inductance and mutual-inductance values of the transmitters and receiver.
ParameterValue (μH)ParameterValue (μH)Li (i = 1, 2, 3)102M112.474Lr120M220.903M312.474


## 2.3. Optimal Load Conditions to Maximize Transfer Efficiency

In this system, the LCC compensation circuit is designed for both the transmitting and receiving sides [29]. The LCC compensation circuit has many advantages such as high efficiency with both heavy and light loads and resonant frequency regardless of the coupling coefficient and load [8, 10]. The LCC compensation circuit is designed with consideration of the self-coupled of the transmitting coils together [31]. The resonant frequency of the coupling system is designed the same as the switching frequency of the inverter. The primary side compensation circuits are used to reduce the volt-ampere rating of the power converter and help achieve soft switching of power switches on the high-frequency inverter. The secondary side compensation circuit is used to enhance power transfer capability.The equivalent circuit of the coupling system is shown in Figure4, where all of the circuits from the diode rectifier to the battery on the secondary side are considered equivalent impedance (RL). Then, the transfer efficiency can be calculated as follows [31]:(1)η=RLIr2RLIr2+RrILr2+R1IL12+R2IL22+R3IL32=RLRL2.Rr/ω2Lfr23+kr2QiQr/kr2QiQr+RL1+6/kr2QiQr+3ω2Lfr2/Rr1/kr2QiQr,where Qi = ωLi/Ri, Qr = ωLr/Rr is the quality factor of the transmitting coils and receiving coil. Equation (1) shows that, with a designed system, the transfer efficiency depends on the coupling coefficient (kr), switching frequency (fsw), and equivalent impedance (RL). Then, the optimal load for maximum transfer efficiency can be obtained as(2)ηmax=kr2QiQr3+3+kr2QiQr2,(3)RL.opt=ω2Lfr2Rr33+kr2QiQr,where RL.opt is called optimal impedance. Equations (2) and (3) show that the maximum transfer is only achieved when the equivalent impedance is equal to the optimal impedance value. Equation (2) is used to evaluate and estimate the theoretical maximum transfer efficiency shown in Figure 5. When kr = 0.14 and the quality factor Qi = 429, Qr = 458, the maximum theoretical transfer efficiency is about 94.6%.Figure 4
Equivalent circuit of the coupling system.Figure 5
Maximum theoretical transfer efficiency characteristic withkr = 0.14.The parameter values of the compensation circuit are determined according to three conditions: the relationship of the resonant circuit, the output power, and the optimal load. The parameter values for a 1.5 kW dynamic charging system are shown in Table2 [31].Table 2
System and compensation circuit parameter.
ParameterValueParameterValueParameterValueP01.5 kWLr120μHC395 nFUDC310 VRr0.14 ΩLfr28.9μHLi102μHLfi52.6µHCfr120.9 nFRi0.13 ΩCfi66.5 nFCr38.5 nFUb400 VC193.7 nFkr0.14fsw85 kHzC2123.2 nFIn a WPT system, the transfer efficiency depends on the value of load impedance and coupling coefficient. Therefore, it is necessary to consider the effect of these parameters on transfer efficiency. Figure6(a) shows frequency characteristics of the transfer efficiency when equivalent impedance (RL) increases from 10 Ω to 150 Ω and the receiver position dr is 0 mm, lm is 0 mm. The results show that transfer efficiency is the largest in the case of optimal impedance (RL = RL.opt = 53.3 Ω). The maximum transfer efficiency is 94.6% and transfer efficiency is high in the frequency range 83 kHz to 89 kHz. At other values of load impedance, the efficiency drops and drops rapidly in the vicinity of 85 kHz. Figure 6(b) shows frequency characteristics of the transfer efficiency when the receiver is the lateral misalignment and the value of load resistance is optimal load according to equation (3). The results show that the transfer efficiency is the largest in the case of no lateral misalignment (lm = 0 mm). When the lateral misalignment increases, the transfer efficiency decreases.Figure 6
Frequency characteristics of the transfer efficiency. (a)lm = 0 mm and RL is variation. (b) lm is variation and RL = RL.opt.
(a)(b)Thus, in DWC systems, the transfer efficiency only reaches the maximum value at one load impedance value, known as the optimal impedance. However, the equivalent impedance (RL) will be changed due to the state of charge of the EV battery system. Furthermore, the optimum impedance value depends on the position of the receiver. Therefore, optimal impedance control is necessary to achieve maximum transfer efficiency in the DWC systems.


## 3. Estimate Optimal Load and Proposed Secondary Side Control

### 3.1. Estimation Coupling Coefficients from the Secondary Side

Analysis in Section2.2 has shown that, in the DWC system, the coupling coefficient changes when the EVs move. Then, the optimal impedance to obtain maximum transfer efficiency also varies according to equation (3). Therefore, to realize the impedance matching control, the coupling coefficient must be estimated previously.The coupling coefficient is estimated using only information from the receiving side proposed in this paper. From the equivalent circuit, as shown in Figure4, in the resonant condition, the current on the transmitting coils will be the same, and it can be calculated as follows [29]:(4)IL1=IL2=IL3=ILi=−UAB1/jωCfi=−jωCfiUAB.On the receiving side, the relationship among the parameters is(5)jωLr+Rr+1jωCrILr+1jωCfrICfr=jωMrILi,jωLfr+RLIr=1jωCfrICfr,ICfr=ILr−Ir.From equations (4) and (5), if the value UAB is constant, the coupling coefficient can be estimated as(6)kr=LfrUABLiLrRrωLfrUab+ωLfrIr,where UAB is the RMS value of the output voltage of the full-bridge inverter and Uab and Ir are the voltage and the current of equivalent load RL.However, the RMS current and voltage measurement will take error in the case of the nonsinusoidal or discontinuous current mode. Therefore, instead of measuring the RMS value, the output voltage (ULe) and current (ILe) in the DC side of the diode rectifier are measured to estimate the coupling coefficient:(7)kr=22LfrπUABLiLrRrωLfrULe+8ωLfrπ2ILe.And then, according to equation (3), the optimal load is calculated.


### 3.2. Analysis of the Proposed Secondary Side Control

On the receiving side, a boost converter is used in impedance control as shown in Figure7. The equivalent input resistance is seen in the rectifier, which is regulated by the duty cycle D of the boost converter [17]. The power losses of the Boost converter are ignored to simplify the analysis. Based on the power balance between input and output of the converter, the relationship between equivalent load is shown as follows:(8)RL=8π2RL.e,(9)RL.e=1−D2RL.eq.Figure 7
Closed-loop control block diagram.Combining equation (3) with equation (8),(10)RL.e.opt=8π2ω2Lfr2Rr33+kr2QiQr,where RL, RL.e, RL.eq are equivalent load impedance values seen from the input of the full-bridge rectifier, boost converter, and DC/DC converter to load, respectively.Thus, for the maximum transfer efficiency, instead of controllingRL value according to RL.opt value in equation (3), it is possible to adjust RL.e value according to RL.e.opt value in equation (10). From equations (9) and (10) through adjusting D, RL.e is regulated to RL.e.opt; then, the transfer efficiency is maximum.Figure7 shows the control diagram of the proposed DWC system. Since the transmitting side is considered as working individually, on the receiving side, ULe and ILe are measured. The total coupling coefficient is estimated by equation (7), the optimal load is calculated by equation (10) and feedback to the optimal load impedance controller.


## 3.1. Estimation Coupling Coefficients from the Secondary Side

Analysis in Section2.2 has shown that, in the DWC system, the coupling coefficient changes when the EVs move. Then, the optimal impedance to obtain maximum transfer efficiency also varies according to equation (3). Therefore, to realize the impedance matching control, the coupling coefficient must be estimated previously.The coupling coefficient is estimated using only information from the receiving side proposed in this paper. From the equivalent circuit, as shown in Figure4, in the resonant condition, the current on the transmitting coils will be the same, and it can be calculated as follows [29]:(4)IL1=IL2=IL3=ILi=−UAB1/jωCfi=−jωCfiUAB.On the receiving side, the relationship among the parameters is(5)jωLr+Rr+1jωCrILr+1jωCfrICfr=jωMrILi,jωLfr+RLIr=1jωCfrICfr,ICfr=ILr−Ir.From equations (4) and (5), if the value UAB is constant, the coupling coefficient can be estimated as(6)kr=LfrUABLiLrRrωLfrUab+ωLfrIr,where UAB is the RMS value of the output voltage of the full-bridge inverter and Uab and Ir are the voltage and the current of equivalent load RL.However, the RMS current and voltage measurement will take error in the case of the nonsinusoidal or discontinuous current mode. Therefore, instead of measuring the RMS value, the output voltage (ULe) and current (ILe) in the DC side of the diode rectifier are measured to estimate the coupling coefficient:(7)kr=22LfrπUABLiLrRrωLfrULe+8ωLfrπ2ILe.And then, according to equation (3), the optimal load is calculated.


## 3.2. Analysis of the Proposed Secondary Side Control

On the receiving side, a boost converter is used in impedance control as shown in Figure7. The equivalent input resistance is seen in the rectifier, which is regulated by the duty cycle D of the boost converter [17]. The power losses of the Boost converter are ignored to simplify the analysis. Based on the power balance between input and output of the converter, the relationship between equivalent load is shown as follows:(8)RL=8π2RL.e,(9)RL.e=1−D2RL.eq.Figure 7
Closed-loop control block diagram.Combining equation (3) with equation (8),(10)RL.e.opt=8π2ω2Lfr2Rr33+kr2QiQr,where RL, RL.e, RL.eq are equivalent load impedance values seen from the input of the full-bridge rectifier, boost converter, and DC/DC converter to load, respectively.Thus, for the maximum transfer efficiency, instead of controllingRL value according to RL.opt value in equation (3), it is possible to adjust RL.e value according to RL.e.opt value in equation (10). From equations (9) and (10) through adjusting D, RL.e is regulated to RL.e.opt; then, the transfer efficiency is maximum.Figure7 shows the control diagram of the proposed DWC system. Since the transmitting side is considered as working individually, on the receiving side, ULe and ILe are measured. The total coupling coefficient is estimated by equation (7), the optimal load is calculated by equation (10) and feedback to the optimal load impedance controller.


## 4. Simulation and Experiment Results

To verify the proposed DWC system, a circuit simulation is performed where the topology is shown in Figure1, and the parameters are shown in Tables 1 and 2. The transmitting coils are fixed in place, while the receiving coil is moving along the charging lane.The estimation results of the total coupling coefficient are shown in Figure3 (dot lines). The estimation errors of the coupling coefficient are less than 5%.The load response simulation results according to the preset value are shown in Figure8, and the maximum response time is 0.007 s when the EV runs at a speed less than 40 km/h. This result shows that the optimal load controller responds to the system DWC requirements.Figure 8
Simulation results of load impedance response according to a preset value.As shown in Figure9, an experimental setup in the laboratory environment has been built to verify the proposed control method. A 1.5 kW output power dynamic charging system is demonstrated. The coils and compensation circuit parameters as shown in Table 2. The stranded wire and ferrite are used to design the magnetic coupler. The polypropylene film capacitors are used to their low losses and high current bearing capability at high frequency. For the full-bridge inverter and boost converter, SIC C3M0280090D is used to obtain low switching power loss. The DWC system works at 85 kHz according to the SEA J2954 standard. The input DC voltage is fixed at 310 V, and the DC/DC converter and battery are replaced by a resistor with the resistance value changing from 10 Ω to 250 Ω.Figure 9
The DWC system experimental setup.The experiment results in Figure10 verify the LCC compensation circuit design and the impedance matching control ability of the boost converter. Figure 10(a) shows that all switching devices in the 85 kHz inverter on the transmitting side obtain the ZVS condition thanks to the LCC compensation circuit design. Figure 10(b) shows the equivalent impedance RLe which is calculated from the measured voltage ULe and current ILe at the DC side of the diode rectifier in the receiving side. The results verify the impedance control ability of the boost converter. The equivalent impedance is kept at 65.7 Ω when the load resistance changes from 10 Ω to 275 Ω.Figure 10
Experiment result at 0 mm position with no lateral misalignment. (a) Output voltage and output current of 85 kHz inverter. (b) The measurement result of equivalent impedanceRLe.
(a)(b)Figure11 shows transfer efficiency characteristics according to receiver position and equivalent impedance in case of no impedance control. The experiment is performed when dr = 0 mm, lm changes from 0 mm to 60 mm, and RLe increases from 10 Ω to 275 Ω. As a result, when lm = 0 mm, the maximum transfer efficiency is 94.5% with the load impedance value of 65.7 Ω. In the case of lm = 40 mm and lm = 60 mm, the maximum transfer efficiency is 93% and 91%, with the load impedance value of 83 Ω and 118 Ω, respectively. The results show that the optimal impedance value varies with receiver position. When the impedance is not controlled, the efficiency decreases when the load impedance value is different from the optimal impedance value.Figure 11
Transfer efficiency characteristic according to receiver position and equivalent impedance (RL).Figure12 shows the experiment transfer efficiency results in other cases. In case 1 (blue line), the receiver moves lateral misalignment according to the y-direction by 30% (lm = 60 mm). The equivalent load impedance is kept as the designed value (RLe.opt = 65.7 Ω), without the optimal load estimation. In this case, the coupling coefficient is decreased, and then the load is designed to a value that is not the optimal one. Therefore, the transfer efficiency is reduced to 85%. In case 2 (red line), the receiver moves lateral misalignment according to y-direction by 30% (lm = 60 mm). The optimal impedance is estimated and updated according to the receiver position. Then, the equivalent impedance is controlled by tracking to the new optimal impedance. In this case, the transfer efficiency increases up to over 91%. Thus, when performing the optimal load-tracking control, the transfer efficiency is improved by 6% compared to the fixed optimum load impedance control. In case 3 (orange line) and case 4 (black line), the receiver moves lateral misalignment according to the y-direction by 20% and 0% (lm = 40 mm and 0 mm), respectively. Equivalent impedance is controlled by tracking the optimal impedance. The transfer efficiency is 93.2% and 94.14%, respectively. This result shows that when the optimal impedance tracking control is applied, the transfer efficiency is significantly improved.Figure 12
The transfer efficiency characteristics.The experimental results of the system efficiency from the DC input of the primary inverter to the DC output on theRLe load behind the secondary boost converter are shown in Figure 13. In case the receiver moves along the DWC lane and has lateral misalignment according to y-direction 0%, 20%, 30% (lm = 0 mm; lm = 40 mm; lm = 60 mm), the system efficiency average is achieved as 80.7%, 79%, and 77%, respectively.Figure 13
The system efficiency characteristics.


## 5. Conclusions

This paper proposes a maximum transfer efficiency tracking method in the DWC system of EVs. The proposed method can track the optimal impedance on the receiving side without any communication with the transmitting side to improve the transfer efficiency and stability in the dynamic charging system. This paper has not mentioned the charging process such as constant current charging and constant voltage charging. These issues will be addressed in future studies.



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