Parameter Optimization of Double LCC MCRWPT System Based on ZVS

: At present, magnetically coupled resonance wireless power transfer (MCRWPT) is the main technology used in electric vehicle wireless power transfer (WPT) due to its advantages of high transmission power and high efﬁciency. The resonant compensation circuit of the system generally adopts the double LCC (DLCC) structure, which has many capacitor and inductor components. Therefore, it is necessary to optimize the circuit parameters to improve the transmission performance of the system. In this study, the DLCC compensation circuit was modeled and analyzed to lay the foundation for parameter optimization. Secondly, the size parameters of the energy transmitting and receiving coil were determined, and the inﬂuence of the change of the primary and secondary compensation inductance on the circuit element stress and output performance was analyzed to determine the optimal compensation inductance value. Thirdly, the realization condition of zero voltage switching (ZVS) was analyzed, the relationship between the input impedance angle of the compensation circuit and the component parameter value was obtained, and a parameter optimization control strategy for realizing ZVS was proposed. Finally, through simulation and experiment, it was concluded that under different power levels, the efﬁciency of the parameter optimization strategy proposed in this study is as high as 91.86%, increasing by about 1%. Therefore, the research undertaken in this study can promote the development of WPT technology and has certain practical signiﬁcance. Z.L.; G.F. R.D.; Z.L. Y.H.; Z.L. Y.H.; G.F., X.L. Y.H.; Z.L. and A.Y.; validation, G.F., S.S. and R.D.; writing—original writing—review G.F.


Introduction
The automobile industry is undergoing a comprehensive energy transition, and developing electric vehicles has become a clear direction for numerous countries, such as China, those of Europe, and the United States [1]. Following the advent of intelligent driving, WPT technology has attracted the close attention of numerous scholars and industry researchers due to its advantages, such as safety, reliability, and convenience [2]. MCRWPT technology adds a resonant compensation network to the transmitting and receiving coils, which solves the problems of high leakage inductance and the low power factor of the system [3]. At present, this approach is the main technology for wireless power supply of electric vehicles.
Improving the energy transmission efficiency of the WPT system of electric vehicles is a major challenge in current research. In the power electronic system, the application of soft switching technology is an effective method to improve the system efficiency and reduce the interference [4,5]. The high-frequency inverter circuit commonly used in the electric vehicle WPT system is a voltage-type full-bridge inverter circuit, whose load is connected with the resonance compensation circuit, which creates the conditions for the realization of the soft switch [6,7].
Due to the high operating frequency of the electric vehicle WPT system, which usually reaches the kHz level, when the compensation network reaches the perfectly resonant state

DLCC MCRWPT System Modeling Analysis
The DLCC MCRWPT system structure and mutual inductance equivalent circuit are shown in Figures 1 and 2. The system includes a high-frequency inverter circuit, a DLCC resonant compensation circuit (magnetically coupled mechanism), and a rectifier filter circuit. U in is the input DC voltage; S 1 , S 2 , S 3 , and S 4 are MOSFETs; L f1 and L f2 are the primary and secondary compensating inductors, respectively; L p and L s are the self-inductance of the transmitting coil and the receiving coil, respectively; M is the mutual inductance, M = k L p L s , where k is the coupling coefficient between L p and L s ; C 1 and C 2 are series compensation capacitors of primary and secondary sides, respectively; and C f1 and C f2 are parallel compensation capacitors of primary and secondary sides, respectively. D 1 , D 2 , D 3 , and D 4 are rectifying diodes; C o represents filtering capacitors of the rectifying circuit; R L is the load; and R eq is the equivalent load on the secondary side, where R eq = 8R L /π 2 . u 1 and u 2 are the input and output voltages of the resonant network, respectively; i f1 and i f2 are the input and output currents of the resonant network, respectively; i p and i s are the transmitting coil and receiving coil currents, respectively.
Energies 2021, 14, x FOR PEER REVIEW 3 of 19 analyzed to determine the optimal compensation inductance value. Thirdly, the realization condition of ZVS is analyzed, the input impedance expression of the compensation circuit is deduced when the component parameter values are changed, the expression of the inverter output current and circuit parameters is established, and the parameter optimization control strategy for realizing ZVS is proposed. Finally, the effectiveness of the control strategy is verified by establishing a Simulink simulation and experimental platforms.

DLCC MCRWPT System Modeling Analysis
The DLCC MCRWPT system structure and mutual inductance equivalent circuit are shown in Figures 1 and 2. The system includes a high-frequency inverter circuit, a DLCC resonant compensation circuit (magnetically coupled mechanism), and a rectifier filter circuit. Uin is the input DC voltage; S1, S2, S3, and S4 are MOSFETs; Lf1 and Lf2 are the primary and secondary compensating inductors, respectively; Lp and Ls are the selfinductance of the transmitting coil and the receiving coil, respectively; M is the mutual inductance, M=k √ , where k is the coupling coefficient between Lp and Ls; C1 and C2 are series compensation capacitors of primary and secondary sides, respectively; and Cf1 and Cf2 are parallel compensation capacitors of primary and secondary sides, respectively. D1, D2, D3, and D4 are rectifying diodes; Co represents filtering capacitors of the rectifying circuit; RL is the load; and Req is the equivalent load on the secondary side, where Req = 8RL/π 2 . u1 and u2 are the input and output voltages of the resonant network, respectively; if1 and if2 are the input and output currents of the resonant network, respectively; ip and is are the transmitting coil and receiving coil currents, respectively.    analyzed to determine the optimal compensation inductance value. Thirdly, the realization condition of ZVS is analyzed, the input impedance expression of the compensation circuit is deduced when the component parameter values are changed, the expression of the inverter output current and circuit parameters is established, and the parameter optimization control strategy for realizing ZVS is proposed. Finally, the effectiveness of the control strategy is verified by establishing a Simulink simulation and experimental platforms.

DLCC MCRWPT System Modeling Analysis
The DLCC MCRWPT system structure and mutual inductance equivalent circuit are shown in Figures 1 and 2. The system includes a high-frequency inverter circuit, a DLCC resonant compensation circuit (magnetically coupled mechanism), and a rectifier filter circuit. Uin is the input DC voltage; S1, S2, S3, and S4 are MOSFETs; Lf1 and Lf2 are the primary and secondary compensating inductors, respectively; Lp and Ls are the selfinductance of the transmitting coil and the receiving coil, respectively; M is the mutual inductance, M=k √ , where k is the coupling coefficient between Lp and Ls; C1 and C2 are series compensation capacitors of primary and secondary sides, respectively; and Cf1 and Cf2 are parallel compensation capacitors of primary and secondary sides, respectively. D1, D2, D3, and D4 are rectifying diodes; Co represents filtering capacitors of the rectifying circuit; RL is the load; and Req is the equivalent load on the secondary side, where Req = 8RL/π 2 . u1 and u2 are the input and output voltages of the resonant network, respectively; if1 and if2 are the input and output currents of the resonant network, respectively; ip and is are the transmitting coil and receiving coil currents, respectively.   Ignoring the parasitic resistances of the capacitor and inductor, and the high-order harmonic components of the voltage of the resonant network, Equation (1) is established according to the mutual inductance equivalent circuit of the system.
The conditions of the full resonance state of the double LCC compensation circuit are as follows: In the above equation, ω 0 is the resonant angular frequency. According to Equations (1)-(3), we can obtain: According to Equation (4), i p and i f2 have independent of the load, and the system has a constant current output characteristic. The output power is as follows: According to Figure 2, the total input impedance Z in , the equivalent impedance Z s of the secondary side, and the reflection impedance Z r converted from the secondary side to the primary side of the DLCC compensation circuit are, respectively: According to the above analysis, it can be concluded that the output characteristics of the DLCC WPT system are mainly related to the parameters of the compensation circuit elements, the coupling coefficient of the transmitting and receiving coils, and the secondary side load. In the following, we optimize the parameters of the system so that the system has a good output characteristic and driving load capacity.

Inductance Parameter Optimization Analysis
In this paper, according to the relevant standards of SAE J2954-2020 and GB/T3877, the magnetically coupled mechanism was selected, as shown in Figure 3, and its 3D model was established based on ANSYS EM.
( 1 (6) According to the above analysis, it can be concluded that the output characteristics of the DLCC WPT system are mainly related to the parameters of the compensation circuit elements, the coupling coefficient of the transmitting and receiving coils, and the secondary side load. In the following, we optimize the parameters of the system so that the system has a good output characteristic and driving load capacity.

Inductance Parameter Optimization Analysis
In this paper, according to the relevant standards of SAE J2954-2020 and GB/T3877, the magnetically coupled mechanism was selected, as shown in Figure 3, and its 3D model was established based on ANSYS EM. In the figure, the orange portion is the energy transfer coil, the black plate represents the ferrite core, and the gray area is the aluminum magnetic shielding layer. The specific geometric parameters of the model are shown in Table 1. In the case that the energy transfer coil is completely aligned (the distance is 20 cm), the simulation results show that the coupling coefficient k is about 0.2. The thickness of the magnetic core 5 In the figure, the orange portion is the energy transfer coil, the black plate represents the ferrite core, and the gray area is the aluminum magnetic shielding layer. The specific geometric parameters of the model are shown in Table 1. In the case that the energy transfer coil is completely aligned (the distance is 20 cm), the simulation results show that the coupling coefficient k is about 0.2.
The parameters of the DLCC line compensation circuit are generally determined as follows: firstly, the output power level is determined, and the L p and L s are set appropriately. Then the maximum coupling coefficient is determined, and the compensation inductance L f1 and L f2 are determined according to Equation (7). Finally, the compensation capacitance is determined according to the resonant condition and the system frequency. The basic parameters of the radio energy transmission system in this paper are shown in Table 2. The thickness of the magnetic core 5 Let L = L f1 = L f2 , L f1 ×L f2 = L 2 ; this indicates that the values of L f1 and L f2 are not unique, and are defined as: In theory, L f1 and L f2 can be reconfigured by changing the value of σ, assuming that the basic parameters of the system are constant and ensuring that L is constant. According to the above analysis, each σ corresponds to a different set of topological parameters. Therefore, the DLCC compensation circuit can be reconfigured by adjusting the value of σ without changing the basic system parameters. Next, the transmission characteristics of the MCRWPT system under different σ conditions are analyzed to determine the optimal value range of σ.

Stress Analysis of DLCC Compensation Circuit Elements
The analysis of the voltage and current stress of the capacitor and the inductor resonant element is a factor that must be considered in compensation circuit design. Excessive voltage and current stress may increase the power loss of the element, affect the energy transmission efficiency of the system, and even damage the equipment. According to Table 2 and Equation (8), five groups of values of circuit elements under different values of σ are shown in Table 3. According to Equations (4) and (8), and in combination with the parameters in Tables 2 and 3, the variation in voltage and current stress of each element of the DLCC compensation circuit with output power under different σ values is plotted, as shown in Figure 4. The current I p flowing through the L p and the I f2 of the compensation circuit are constant and independent of the output power, which also verifies the constant current output characteristic of the DLCC circuit structure. I f1 , I s , I Cf1 , I Cf2 , U s , U Cf1 , U Cf2 , U C2 , and U f1 increase with the increase in output power. Under the same output power condition, I f1 and I f2 do not change with the change in σ, indicating that the value of σ does not affect the input and output current characteristics of the double LCC compensation circuit. I p , I Cf1 , U p , U C1 , U Cf2 , and U f2 decrease gradually with the increase in σ, whereas I s , I Cf2 , U s , U Cf1 , U C2 , and U f1 increase gradually. Relatively speaking, the voltage on C f1 and C f2 does not vary significantly with σ, whereas the voltage on C 1 and C 2 varies considerable with σ; thus, the reasonable choice of σ should be based on the voltage limit of the resonant capacitor. In addition, as the most important component of the MCRWPT system, the magnetically coupling mechanism has a decisive influence on the transmission power and efficiency of the system, and the power loss of this component is an important contributor to the total loss of the system. The loss of the magnetically coupling mechanism is comprised mainly of the coil loss. I p and I s directly determine the size of the coil loss. Therefore, a reasonable choice of the σ value can reduce the power loss. the input and output current characteristics of the double LCC compensation circuit. Ip, ICf1, Up, UC1, UCf2, and Uf2 decrease gradually with the increase in σ, whereas Is, ICf2, Us, UCf1, UC2, and Uf1 increase gradually. Relatively speaking, the voltage on Cf1 and Cf2 does not vary significantly with σ, whereas the voltage on C1 and C2 varies considerable with σ; thus, the reasonable choice of σ should be based on the voltage limit of the resonant capacitor. In addition, as the most important component of the MCRWPT system, the magnetically coupling mechanism has a decisive influence on the transmission power and efficiency of the system, and the power loss of this component is an important contributor to the total loss of the system. The loss of the magnetically coupling mechanism is comprised mainly of the coil loss. Ip and Is directly determine the size of the coil loss. Therefore, a reasonable choice of the σ value can reduce the power loss.

High-Frequency Harmonic Suppression
The voltage waveform of the full-bridge inverter circuit is quantitatively analyzed, and the rectangular wave u1 with the amplitude of Uin is expanded into Fourier series, which can be obtained as follows: As can be seen from Equation (9), the output voltage contains abundant odd harmonics. Although the dual LCC compensation circuit only allows specific resonant frequency components to pass through and has an attenuation effect on the harmonic component, the suppression effect of the high-frequency harmonics is not ideal due to the large number of resonant components in the circuit. Normally, higher harmonics increase switching losses. Because harmonic amplitudes above the fifth order are small, only the fundamental frequencies (85 kHz), the third (255 kHz), and the fifth (425 kHz) are considered. According to the relevant parameters in Tables 2 and 3, the If1 harmonic content under different σ values was simulated in Simulink. As can be seen from Figure  5, with the increase in σ, the harmonic content of current If1 was lower. Therefore, to obtain better harmonic suppression performance, the maximum σ should be used.

High-Frequency Harmonic Suppression
The voltage waveform of the full-bridge inverter circuit is quantitatively analyzed, and the rectangular wave u 1 with the amplitude of U in is expanded into Fourier series, which can be obtained as follows: As can be seen from Equation (9), the output voltage contains abundant odd harmonics. Although the dual LCC compensation circuit only allows specific resonant frequency components to pass through and has an attenuation effect on the harmonic component, the suppression effect of the high-frequency harmonics is not ideal due to the large number of resonant components in the circuit. Normally, higher harmonics increase switching losses. Because harmonic amplitudes above the fifth order are small, only the fundamental frequencies (85 kHz), the third (255 kHz), and the fifth (425 kHz) are considered. According to the relevant parameters in Tables 2 and 3, the I f1 harmonic content under different σ values was simulated in Simulink. As can be seen from Figure 5, with the increase in σ, the harmonic content of current I f1 was lower. Therefore, to obtain better harmonic suppression performance, the maximum σ should be used.

The Realization of ZVS
The MCRWPT system adopts full-bridge inverter. In practical application, to prevent the circuits of the upper and lower bridge arms from appearing directly and to avoid damage to the switching devices, enough dead time should be set for the switches of the upper and lower bridge arms to ensure the normal operation of the circuit when driving the switch tube of the full-bridge inverter. When the system operates in a completely resonant state, that is, the difference between the input voltage and the current is 0, ZVS is difficult to achieve. To realize ZVS, the input impedance of the system must be inductive. From the perspective of parameter optimization design, in this study, we realized the inverter ZVS under a wide range of coupling coefficients and load changes.

The Realization Conditions of ZVS
For the case in which the system realizes ZVS, the waveform diagrams of the inverter drive signal, output voltage, and current are shown in Figure 6, and the commutation process is shown in Figure 7. The process of turning off S1 and S4, and turning on S2 and S3, are analyzed as follows.
Prior to t0, S1 and S4 conduct, and u1 is Uin. At the stage of t0-t1, S1 and S4 are turned off, the inverter output current i f1 passes through the junction capacitance of the switch tube, the junction capacitance of S1 and S4 (Coss) charges, the junction capacitance of S2 and S3 discharges, and u1 shows a linear decreasing trend. At the stage of t1−t2, the junction capacitors of S2 and S3 discharge completely, the voltage at both ends of S2 and S3 drops to zero, the current if1 does not reverse, and the volume diodes of S2 and S3 continue to flow. At the moment of t2, the driving signals of S2 and S3 arrive to realize ZVS. At the stage of t2−t3, if1 reverses, S2 and S3 conduct, and u1 is −Uin. During this process, the dead time td = t2 − t0, during which the current approximately linearly decreases, and the conditions for realizing ZVS of the inverter switch tube, are as follows: (10) where itd is the dead zone ending current and it0 is the shutdown current. When Coss, Uin, and td are determined, the implementation of ZVS is only related to it0 and itd. it0 and itd are essentially the if1, so it can be known from Equation (4) that the size of it0 and itd is related to the system coupling coefficient, load resistance value, and the compensation circuit element parameters. Therefore, in the case of a wide range of coupling coefficients and load resistances, ZVS can be realized by optimizing the component parameters so that it0 and itd always satisfy Equation (10).

The Realization of ZVS
The MCRWPT system adopts full-bridge inverter. In practical application, to prevent the circuits of the upper and lower bridge arms from appearing directly and to avoid damage to the switching devices, enough dead time should be set for the switches of the upper and lower bridge arms to ensure the normal operation of the circuit when driving the switch tube of the full-bridge inverter. When the system operates in a completely resonant state, that is, the difference between the input voltage and the current is 0, ZVS is difficult to achieve. To realize ZVS, the input impedance of the system must be inductive. From the perspective of parameter optimization design, in this study, we realized the inverter ZVS under a wide range of coupling coefficients and load changes.

The Realization Conditions of ZVS
For the case in which the system realizes ZVS, the waveform diagrams of the inverter drive signal, output voltage, and current are shown in Figure 6, and the commutation process is shown in Figure 7. The process of turning off S 1 and S 4 , and turning on S 2 and S 3 , are analyzed as follows.

Design of Dead Time
Setting a reasonable dead time is the key to realizing the ZVS inverter. If the de time setting is too short, a short circuit of the upper and lower bridge arms of the inver will occur; if the parasitic capacitor impulse current is too large, it may burn out MOSFET. If the dead time too long, the inverter cannot realize ZVS and generate impulse current. With the increase in dead time, the output voltage waveform of inverter is worsened, affecting the transmission efficiency of the system. To ensure optimal dead time of the inverter MOSFET to realize ZVS, the parasitic capacitor shou be fully charged and discharged, and another branch MOSFET should be conduct before the end of the reverse parallel diode continuation current. Thus, the dead time should satisfy: where tc is the charge and discharge time of the parasitic capacitor, toff is the MOSFET tu off time, and tD is the diode continuation time.
When the model of the MOSFET is determined, the toff time is determined. T charging and discharging time of the parasitic capacitor, tc, is: Prior to t 0 , S 1 and S 4 conduct, and u 1 is U in . At the stage of t 0 -t 1 , S 1 and S 4 are turned off, the inverter output current i f1 passes through the junction capacitance of the switch tube, the junction capacitance of S 1 and S 4 (C oss ) charges, the junction capacitance of S 2 and S 3 discharges, and u 1 shows a linear decreasing trend. At the stage of t 1 −t 2 , the junction capacitors of S 2 and S 3 discharge completely, the voltage at both ends of S 2 and S 3 drops to zero, the current i f1 does not reverse, and the volume diodes of S 2 and S 3 continue to flow. At the moment of t 2 , the driving signals of S 2 and S 3 arrive to realize ZVS. At the stage of t 2 −t 3 , i f1 reverses, S 2 and S 3 conduct, and u 1 is −U in . During this process, the dead time t d = t 2 − t 0 , during which the current approximately linearly decreases, and the conditions for realizing ZVS of the inverter switch tube, are as follows: where i td is the dead zone ending current and i t0 is the shutdown current. When C oss , U in , and t d are determined, the implementation of ZVS is only related to i t0 and i td . i t0 and i td are essentially the i f1 , so it can be known from Equation (4) that the size of i t0 and i td is related to the system coupling coefficient, load resistance value, and the compensation circuit element parameters. Therefore, in the case of a wide range of coupling coefficients and load resistances, ZVS can be realized by optimizing the component parameters so that i t0 and i td always satisfy Equation (10).

Design of Dead Time
Setting a reasonable dead time is the key to realizing the ZVS inverter. If the dead time setting is too short, a short circuit of the upper and lower bridge arms of the inverter will occur; if the parasitic capacitor impulse current is too large, it may burn out the MOSFET. If the dead time too long, the inverter cannot realize ZVS and generate the impulse current. With the increase in dead time, the output voltage waveform of the inverter is worsened, affecting the transmission efficiency of the system. To ensure the optimal dead time of the inverter MOSFET to realize ZVS, the parasitic capacitor should be fully charged and discharged, and another branch MOSFET should be conducted before the end of the reverse parallel diode continuation current. Thus, the dead time t d should satisfy: where t c is the charge and discharge time of the parasitic capacitor, t off is the MOSFET turn-off time, and t D is the diode continuation time.
When the model of the MOSFET is determined, the t off time is determined. The charging and discharging time of the parasitic capacitor, t c , is: The diode continuation time, t D , is: where T is the one switching period of the inverter. In practical application, considering that the time of the MOSFET turn-on and turn-off is prolonged due to heat, the optimal dead zone time t d should be relatively large.

Analysis of the Influence of Resonant Circuit Parameters on Input Impedance Angle
According to Equation (6), the input impedance expression of the compensation circuit is derived when the parameters of complete resonance and inductance, and capacitance, change: ] where Z r = w 2 M 2 C f2 R eq /L f2 , C 1 ', C f1 ', L f1 ', C 2 ', C f2 ', and L f2 ' are the changed circuit component parameter values. The variation range of the component parameters is set from 0.8 to 1.2. Combined with Tables 2 and 3, and Equation (14), the curve of the circuit input impedance angle, for component parameters under different loads, can be fitted, as shown in Figure 8. It can be seen from Figure 8 that, with the change in component parameters, the circuit input impedance angle changes in inductance, resistance, and capacitance. By contrast, changing the values of C 1 and C 2 has a more obvious effect on the impedance angle. As C 1 and C 2 change from small to large, they have the opposite effect on the impedance angle. However, according to Equation (4), changing C 2 affects the constant current output characteristics of the secondary side. Therefore, ZVS is finally realized by changing the value of parameter C 1 .
circuit input impedance angle with the change in C1 under different coupling coefficients, as shown in Figure 9. According to Figures 8d and 9, when the value of C1 is determined (excluding the ratio of 1), with the increase in the coupling coefficient and the load value, the change in the input impedance angle steadily becomes smaller. Therefore, as long as the value of C1 satisfying ZVS is determined in the case of the maximum coupling coefficient and the maximum load value, ZVS in the full range of coupling coefficients and loads can be realized.   We can take the equivalent resistance R eq = 30 Ω to fit the curve of the change in the circuit input impedance angle with the change in C 1 under different coupling coefficients, as shown in Figure 9. According to Figures 8d and 9, when the value of C 1 is determined (excluding the ratio of 1), with the increase in the coupling coefficient and the load value, the change in the input impedance angle steadily becomes smaller. Therefore, as long as the value of C 1 satisfying ZVS is determined in the case of the maximum coupling coefficient and the maximum load value, ZVS in the full range of coupling coefficients and loads can be realized.
We can take the equivalent resistance Req = 30 Ω to fit the curve of the chang circuit input impedance angle with the change in C1 under different coupling coef as shown in Figure 9. According to Figures 8d and 9, when the value of C1 is dete (excluding the ratio of 1), with the increase in the coupling coefficient and the loa the change in the input impedance angle steadily becomes smaller. Therefore, as the value of C1 satisfying ZVS is determined in the case of the maximum c coefficient and the maximum load value, ZVS in the full range of coupling coe and loads can be realized.   According to Equation (10), the value of i t0 + i td is determined by C oss , U in , and t d . Therefore, the relationship between i t0 , i td , and C 1 needs to be clarified to obtain the optimized value of C 1 . The high-order harmonics of the current i f1 are ignored. The phase difference between the fundamental voltage of the compensation circuit and the input fundamental voltage is defined as α, and the expressions of i t0 and i td are obtained by combining with Equation (1).

Parameters Optimization Control Strategy
According to the analysis in the above section, after optimizing the basic parameters of the WPT system, when the load and coupling coefficient change, the inverter can theoretically be guaranteed to work in the ZVS state at all times. However, due to the progress in the wireless charging process of electric vehicles, the temperature of the magnetically coupled mechanism and compensation circuit will inevitably rise, and the system parameters will change. This will result in interference in the inverter output voltage and the current waveform. Although this change will not have a significant impact on the system, it is likely to change the working state of the inverter ZVS. When the MCRWPT system works normally, the circuit parameters cannot be changed. It can be seen from Equations (10) and (15) Because the output voltage and current of the inverter will not mutate, the dynamic adjustment of the dead zone time does not require a high speed. Thus, the control is carried out by adjusting the dead zone and frequency with a fixed-length step. The MCRWPT system control block diagram and parameter optimization control flow chart are shown in Figures 10 and 11, respectively. difference between the fundamental voltage of the compensation circuit and the fundamental voltage is defined as α, and the expressions of it0 and itd are obtai combining with Equation (1).

Parameters Optimization Control Strategy
According to the analysis in the above section, after optimizing the basic para of the WPT system, when the load and coupling coefficient change, the inver theoretically be guaranteed to work in the ZVS state at all times. However, due progress in the wireless charging process of electric vehicles, the temperature magnetically coupled mechanism and compensation circuit will inevitably rise, a system parameters will change. This will result in interference in the inverter voltage and the current waveform. Although this change will not have a significant on the system, it is likely to change the working state of the inverter ZVS. Wh MCRWPT system works normally, the circuit parameters cannot be changed. It seen from Equations (10)  Because the output voltage and current of the inverter will not mutate, the dy adjustment of the dead zone time does not require a high speed. Thus, the con carried out by adjusting the dead zone and frequency with a fixed-length ste MCRWPT system control block diagram and parameter optimization control flow are shown in Figures 10 and 11, respectively.

Analysis of Simulation Results
According to the stress analysis of the compensating circuit elements and the effect of harmonic suppression, the value of σ is 1.25. The basic parameters of the circuit are obtained from Tables 2 and 3, and the output power level is 7.7 KW. The IMZ120R045M1 MOSFET of Infineon was selected. According to the device manual, the Coss is 1100 pF and the dead zone time is set at 400 ns. From Equation (10), we can obtain it0 + itd > 4.4 A. The high-frequency component of the current is not considered in Equations (15) and (16) in this paper, but the existence of the high-frequency component will inevitably affect the accuracy of the ZVS implementation. A margin can be set to ensure the sum of the current is 6 A. According to the above analysis, as long as the system can realize ZVS at the maximum coupling coefficient and the maximum output voltage, it can guarantee the realization of ZVS at all times. Combined with the above equations, the curves of it0 and itd with C1 were obtained under the conditions of the maximum coupling coefficient (0.2) and the maximum output voltage (450 V), as shown in Figure 12.

Analysis of Simulation Results
According to the stress analysis of the compensating circuit elements and the effect of harmonic suppression, the value of σ is 1.25. The basic parameters of the circuit are obtained from Tables 2 and 3, and the output power level is 7.7 KW. The IMZ120R045M1 MOSFET of Infineon was selected. According to the device manual, the C oss is 1100 pF and the dead zone time is set at 400 ns. From Equation (10), we can obtain i t0 + i td > 4.4 A. The high-frequency component of the current is not considered in Equations (15) and (16) in this paper, but the existence of the high-frequency component will inevitably affect the accuracy of the ZVS implementation. A margin can be set to ensure the sum of the current is 6 A. According to the above analysis, as long as the system can realize ZVS at the maximum coupling coefficient and the maximum output voltage, it can guarantee the realization of ZVS at all times. Combined with the above equations, the curves of i t0 and i td with C 1 were obtained under the conditions of the maximum coupling coefficient (0.2) and the maximum output voltage (450 V), as shown in Figure 12.

Analysis of Simulation Results
According to the stress analysis of the compensating circuit elements and th of harmonic suppression, the value of σ is 1.25. The basic parameters of the cir obtained from Tables 2 and 3, and the output power level is 7.7 KW. The IMZ120 MOSFET of Infineon was selected. According to the device manual, the Coss is 1100 the dead zone time is set at 400 ns. From Equation (10), we can obtain it0 + itd > 4.4 high-frequency component of the current is not considered in Equations (15) and this paper, but the existence of the high-frequency component will inevitably a accuracy of the ZVS implementation. A margin can be set to ensure the sum of the is 6 A. According to the above analysis, as long as the system can realize ZV maximum coupling coefficient and the maximum output voltage, it can guara realization of ZVS at all times. Combined with the above equations, the curves o itd with C1 were obtained under the conditions of the maximum coupling coeffici and the maximum output voltage (450 V), as shown in Figure 12.  As can be seen from the figure, when C 1 ' < 0.99C 1 , i td is always greater than 0; when C 1 ' < 0.92C 1 , i t0 + i td is always greater than 6 A. Therefore, to realize ZVS, the optimal value of C 1 'is 0.92C 1 (141.65 nF).
A simulation circuit was built in Simulink. When k = 0.2 and U o = 450 V, C 1 ' was set to 0.92C 1 , C 1 , and 1.08C 1 . The output voltage and current curves of the inverter and the opening of the MOSFET (taking S 3 as an example) were obtained under the three conditions of realizing ZVS (input impedance is inductive), PRS (input impedance is pure resistance), and capacitive input impedance. The results are shown in Figures 13-15. When the inverter implements ZVS, the voltage u 1 phase leads i f1 . The turn-off current i t0 is 4.84 A, the dead-zone ending current i td is 1.68 A, and the sum of the two is 6.52 A. The MOSFET has good breaking characteristics. When the system is fully resonant, u 1 and i f1 are in phase and the voltage oscillates during the dead time. When the MOSFET cannot achieve ZVS, switching loss occurs. When the input impedance of the system is capacitive, the phase of u 1 lags behind i f1 , and both i t0 and i td are less than zero. When the S 3 drive signal arrives, the voltage at both ends of S 3 is greater than zero, so there is also opening loss in S 3 .
A simulation circuit was built in Simulink. When k = 0.2 and Uo = 450 V, C1' was set to 0.92C1, C1, and 1.08C1. The output voltage and current curves of the inverter and the opening of the MOSFET (taking S3 as an example) were obtained under the three conditions of realizing ZVS (input impedance is inductive), PRS (input impedance is pure resistance), and capacitive input impedance. The results are shown in Figures 13-15. When the inverter implements ZVS, the voltage u1 phase leads if1. The turn-off current it0 is 4.84 A, the dead-zone ending current itd is 1.68 A, and the sum of the two is 6.52 A. The MOSFET has good breaking characteristics. When the system is fully resonant, u1 and if1 are in phase and the voltage oscillates during the dead time. When the MOSFET cannot achieve ZVS, switching loss occurs. When the input impedance of the system is capacitive, the phase of u1 lags behind if1, and both it0 and itd are less than zero. When the S3 drive signal arrives, the voltage at both ends of S3 is greater than zero, so there is also opening loss in S3.  As can be seen from the figure, when C1' < 0.99C1, itd is always greater than 0; when C1' < 0.92C1, it0 + itd is always greater than 6A. Therefore, to realize ZVS, the optimal value of C1'is 0.92C1 (141.65 nF).
A simulation circuit was built in Simulink. When k = 0.2 and Uo = 450 V, C1' was set to 0.92C1, C1, and 1.08C1. The output voltage and current curves of the inverter and the opening of the MOSFET (taking S3 as an example) were obtained under the three conditions of realizing ZVS (input impedance is inductive), PRS (input impedance is pure resistance), and capacitive input impedance. The results are shown in Figures 13-15. When the inverter implements ZVS, the voltage u1 phase leads if1. The turn-off current it0 is 4.84 A, the dead-zone ending current itd is 1.68 A, and the sum of the two is 6.52 A. The MOSFET has good breaking characteristics. When the system is fully resonant, u1 and if1 are in phase and the voltage oscillates during the dead time. When the MOSFET cannot achieve ZVS, switching loss occurs. When the input impedance of the system is capacitive, the phase of u1 lags behind if1, and both it0 and itd are less than zero. When the S3 drive signal arrives, the voltage at both ends of S3 is greater than zero, so there is also opening loss in S3.  As can be seen from the figure, when C1' < 0.99C1, itd is always greater than 0; when C1' < 0.92C1, it0 + itd is always greater than 6A. Therefore, to realize ZVS, the optimal value of C1'is 0.92C1 (141.65 nF).
A simulation circuit was built in Simulink. When k = 0.2 and Uo = 450 V, C1' was set to 0.92C1, C1, and 1.08C1. The output voltage and current curves of the inverter and the opening of the MOSFET (taking S3 as an example) were obtained under the three conditions of realizing ZVS (input impedance is inductive), PRS (input impedance is pure resistance), and capacitive input impedance. The results are shown in Figures 13-15. When the inverter implements ZVS, the voltage u1 phase leads if1. The turn-off current it0 is 4.84 A, the dead-zone ending current itd is 1.68 A, and the sum of the two is 6.52 A. The MOSFET has good breaking characteristics. When the system is fully resonant, u1 and if1 are in phase and the voltage oscillates during the dead time. When the MOSFET cannot achieve ZVS, switching loss occurs. When the input impedance of the system is capacitive, the phase of u1 lags behind if1, and both it0 and itd are less than zero. When the S3 drive signal arrives, the voltage at both ends of S3 is greater than zero, so there is also opening loss in S3.

Analysis of Experimental Results
Under the parameter adjustment control strategy proposed in this paper, the step size of the dead zone time reduction is set as 20 ns, and the step size of the frequency reduction is set as 0.2 kHz. According to the simulation parameters, an experimental platform was constructed, as shown in Figure 16. According to the current flow direction, the system comprised a DC power supply, an inverter controller, a resonant circuit, a magnetically coupled mechanism, a rectifier filter circuit, and an electronic load.

Analysis of Experimental Results
Under the parameter adjustment control strategy proposed in this paper, the step size of the dead zone time reduction is set as 20 ns, and the step size of the frequency reduction is set as 0.2 kHz. According to the simulation parameters, an experimental platform was constructed, as shown in Figure 16. According to the current flow direction, the system comprised a DC power supply, an inverter controller, a resonant circuit, a magnetically coupled mechanism, a rectifier filter circuit, and an electronic load. Under two conditions of the system, i.e., PRS and ZVS, the wireless charging experiment with maximum output power of 7.7 kW was completed. Figure 17 compares the experimental waveforms of PRS and ZVS at different power levels. It was found that the turn-off current and dead-zone ending current in the ZVS state are larger, and the switching performance is better in the dead-zone time. Figure 18 shows the variation curve of the output power and efficiency with the input power of the system under PRS and ZVS conditions. According to the results in the figure, the system efficiency shows an upward trend with the increase in power level. Under the same input power condition, compared with PRS, the system implementing ZVS has higher output power and higher efficiency. Under different power levels, the average efficiency of PRS is 90.87%, and the average efficiency of ZVS is 91.86%, thus indicating an improvement in ZVS efficiency of about 1%. Under two conditions of the system, i.e., PRS and ZVS, the wireless charging experiment with maximum output power of 7.7 kW was completed. Figure 17 compares the experimental waveforms of PRS and ZVS at different power levels. It was found that the turn-off current and dead-zone ending current in the ZVS state are larger, and the switching performance is better in the dead-zone time.   Figure 18 shows the variation curve of the output power and efficiency with the input power of the system under PRS and ZVS conditions. According to the results in the figure, the system efficiency shows an upward trend with the increase in power level. Under the same input power condition, compared with PRS, the system implementing ZVS has higher output power and higher efficiency. Under different power levels, the average efficiency of PRS is 90.87%, and the average efficiency of ZVS is 91.86%, thus indicating an improvement in ZVS efficiency of about 1%.

Conclusions
The MCRWPT system studied in this paper has a high power grade, and the DLCC topology has better anti-migration and power transmission stability. Based on the DLCC Figure 18. Variation in the output power and efficiency of the system with the input power.

Conclusions
The MCRWPT system studied in this paper has a high power grade, and the DLCC topology has better anti-migration and power transmission stability. Based on the DLCC topology, this study proposed a parameter optimization control strategy based on frequency and dead time to improve power transmission efficiency. Without changing the circuit structure, ZVS in a wide range of voltage classes was realized. This method comprehensively considers the influence of parameter changes on the implementation of ZVS, can be simply controlled, and overcomes the shortcomings of the ZVS implementation method, as noted in Section 1.
First, a DLCC equivalent circuit model was established, and the expressions of output voltage, current, and input impedance were derived. Second, five sets of component parameter values were obtained according to the changes in the primary and secondary side compensation inductance values. The suppression effect of the circuit component stress and high-frequency harmonics under different parameters was analyzed, and the optimal compensation inductance value was determined. Third, the realization conditions of ZVS were analyzed, the best dead time of the MOSFET was determined, and the change in the system input impedance angle with different component parameter values was obtained. The relationship between the inverter output current and the capacitor C 1 was established, and the optimal capacitor value was determined through simulation. Finally, a parameter optimization control strategy to achieve ZVS was proposed. Under different output power levels, the average efficiency of the PRS was 90.87%, the average efficiency of ZVS was 91.86%, indicating an increase in efficiency of about 1%. Therefore, the parameter optimization strategy of the DLCC MCRWPT system based on ZVS can reduce the power loss of the MOSFET, effectively improve the charging efficiency, and promote the development of WPT technology. This strategy can be applied to high-power WPT systems, such as robots and electric vehicles, and has certain practical significance.