FU Yongsheng()， LEI Ming( )， GAO Leilei()， ZHOU Gang( )

1 College of Electroric Information Engineering, Xi’an Technological University， Xi’an 710021， China 2 Shaanxi Yanchang Petroleum Anyuan Chemical Co.， Ltd.， Shenmu 719300， China

Abstract： There are lots of factors that can influence the wireless charging efficiency in practice， such as misalignment and air-gap difference， which can also change all the charging parameters. To figure out the relationship between those facts and system， this paper presents a serial-parallel compensated (SPC) topology for electric vehicle/plug-in hybrid electric vehicle(EV/PHEV) wireless charger and provides all the parameters changing with corresponding curves. An ANSYS model is built to extract the coupling coefficient of coils. When the system is works at constant output power， the scan frequency process can be applied to wireless power transfer(WPT) and get the resonant frequency. In this way, it could determine the best frequency for system to achieve zero voltage switching status and force the system to hit the maximum transmission efficiency. Then frequency tracking control(FTC) is used to obtain the highest system efficiency. In the paper， the designed system is rated at 500 W with 15 cm air-gap， the overall efficiency is 92%. At the end， the paper also gives the consideration on how to improve the system efficiency.

Key words： wireless power transfer (WPT)； zero voltage switching； frequency tracking control(FTC)； electric vehicle/plug-in hybrid electric vehicle(EV/PHEV)

Introduction

Wireless charging technology， also known as wireless power transfer(WPT)， has many applications in electronics products such as mobile device and automobile chargers[1-2]. Compared with conductive power transfer(usually by plug-in)， WPT is more convenient， weather proof， and electric shock protected[3-4]. The earliest occurrence of WPT concept is attributed to the engineer Nikola Tesla. In 1900 and 1914， Tesla published two patents for wirelessly transmitting electrical energy[5]. A great progress was made by WiTricity， which gained attention from all over the world. They managed to transmit 60 W with an efficiency of around 40% over a distance of 2 m， between two coils with 50 cm diameters. However， there is still more research work which needs to be done to further boost the efficiency， reduce the cost， increase misalignment tolerance， and shrink the size of WPT chargers[6-9]，e.g. receiving coils， four basic compensation topologies labeled as series-series(SS)， series-parallel(SP)， parallel-series(PS) and parallel-parallel(PP) are widely adopted[10]， here the first S or P represents the capacitor in series or parallel with the transmitter coil and the second S or P stands for capacitor in series or parallel with the receiver coil. In Ref.[11]， the results showed that SS and SP topologies were more suitable for high power transmission， but the way how to realize soft switching to reduce the switching loss was not considered. In Ref.[12]， it indicated that SS compensation topology seemed to be the best one， because the system could work at a frequency independent of coupling coefficient and load. However， PP topology was adopted in their work because parallel compensated transmitter could provide a large current and parallel compensated receiver and the current source characteristic which was more suitable for battery charging[13]. In this situation， the system working at resonant frequency is necessary. However， the resonant condition will change as well as coupling coefficient and load condition change[14]. The SS topology， there are two resonant frequencies， which are totally depended on coupling coefficient[15]. This is similar to bifurcation phenomena[16]， which brings difficulties to controller design. Based on the four topologies above， there are two methods to adjust the output power， voltage-regulating model and frequency-regulating model[17]. For the frequency-regulating model， which changes switching frequency with changeless input voltage， has a good characteristic that changing rate of output power is small. The voltage-regulating model， which changes switching frequency at the constant input voltage， and the switching frequency is a little bit higher than resonant frequency.

In this study, the coil air-gap between the primary(power transmitter) and secondary(power receiver) is 15 cm， particularly for electric vehicles(EV). Finite element analysis(FEA) is applied to obtaining the coil self-inductance and mutual-inductance. By changing the input voltage and switching frequency， the system equivalent impedance will also vary， thereby generate different output power. In order to decrease the vehicle weight， the design in this paper has no iron core. Experimental results showed a 500 W wireless charger to charge the on-board 48 V batteries with more than 90% efficiency. This paper also discusses the potential to boost the transmission efficiency through serial-parallel compensation(SPC) circuit.

1 Theoretical Analysis of the SPC System

The SPC resonant topology is shown in Fig. 1(a).CpandLpare the primary-side resonant capacitor and inductor， respectively.CsandLsare the secondary-side resonant capacitor and inductor， respectively.Mis the coupling coefficient betweenLpandLs. The equivalent T-type circuit is shown in Fig. 1(b)， and the turn ratio is 1∶1. The input is a direct current(DC) voltage source. The gate signals ofQ1-Q4are all pulse width modulation(PWM) signals with 50% duty cycle.L1andL2are primary and secondary leakage inductances， respectively.Lmis the mutual inductance. The equivalent model is shown in Fig. 1(c), the input is altemating current (AC).R1andR2are primary and secondary coil internal resistances， respectively.RLis the equivalent load resistance.CpandCsare primary-side and secondary-side resonant capacitors， respectively.

(a) SPC topology

(b) SPC topology with equivalent transformer T model

(c) SPC topology equivalent circuit

The expression of the primary side impedance(Z1)， secondary side impedance(Z2)， can be derived in Eqs.(1)-(4).

(1)

Z2=R2+jωLS+

[(R3/jωC2)/(R3+1/jωC2)]，

(2)

Xm=ω·Lm，

(3)

Zm=j·Xm.

(4)

Meanwhile，

(5)

(6)

(7)

Assuming that the input power and load power arePinandPout， Eqs.(8) and(9) can be derived as

(8)

(9)

The system transmission efficiency can be expressed as Eq.(10).

(10)

According to Eq.(10)， when we choose the capacitors of primary and secondary side as Eqs.(11) and(12)， the maximum transmission efficiency can be achieved.

(11)

(12)

2 Coil Coupling Model and Circuit Simulation

In this study， the spiral wound model is shown in Fig. 2(a). The wire diameter is 5 mm. The distance between each loop is 0.5 mm. The center-to-center air gap between the primary and secondary coils is maintained at 15 cm. The secondary-side coil， which is installed on the EV chassis， has a radius of 40 cm. And the radius is the same for the primary coil， which is located on the ground. The simulation result of the coil inductance obtained from Ansys/Maxwell， indicates that the mutual inductance is 358.66 μH and the self-inductance is 1 304.90 μH， the coupling coefficient is 27.486%. Figure 2(a) shows the practical coils model. Figure 2(b) shows the flux distribution. Figures 2(c) and 2(e) show the 3D view of the coupling coefficient at the different air-gap and misalignment and the magnetic field intensity distribution.

(a) Practical coils model

(b) Flux distribution

(c) 3D coupling coefficient vs. misalignment and airgap

(d) Magnetic field intensity distribution of coupling coil

With the coils parameters deployed， the next step is to select the resonant capacitors. From Eqs.(12) and(14)， the resonant capacitances of primary and secondary side were chosen as 6.9 nF and 6.4 nF， respectively. Then the circuit equivalent impedance and phase angle curvevs. the switching frequency can be obtained in Fig. 3， where the solid line represents the system impedance and the dash line refers to system phase. In order to maintain the zero-voltage switching(ZVS)， any switching frequencyfshigher than 57 kHz is preferred at 0 cm misalignment.

Fig. 3 Overall impedance and phase vs. switching frequency

The other system simulation model and results are shown in Figs.4(a)-4(c). When charging a 48 V battery pack，R5andR6are primary and secondary coil internal resistances， which are 400 mΩ in total.

(a) LTspice simulation model

(b) H-Bridge waveform

(c) Charging current waveform

3 Simulation and Experimental Results

In order to keep the WPT system working in the ZVS state，the switching frequency should be higher than resonant frequency. Figure 5 shows the wireless power transfer system configuration of frequency tracking control.

(a) Schematic diagram of frequency tracking control

(b) Current detection circuit

(c) Simulation result of current detection circuit

As shown in Fig. 5(a)， the aim of frequency tracking control is that has same phase between PWM signal and primary side current. Hence， the digital signal of primary side current is necessary， the corresponding current detection circuit and simulation results are shown in Figs. 5(b) and 5(c)， respectively. The frequency tracking control algorithm flowchart and primary side current detection schematic are shown in Fig. 6, the simulation model has been built by field programnable gate array(FPGA).

In Fig. 6(a)，kmaxandkminare upper and lower limits of switching frequency， respectively. In this paper，kmax=85 kHz andkmin=50 kHz，kis the frequency diving coefficient. Channel A(ChA) and channel B(ChB) are input port of PWM and primary side current. The PWM signal is generated by Wave_o port. As shown in Fig. 6(c)， the switching frequency is changing with the different misalignment of coils. Hence， simulation result indicates the frequency tracking control system works well. Figure 7 shows the test bench， and a frequency tracking control close loop control is adopted by ATERL EP4CE10F17C8 circuit. The secondary side of the system uses SiC Schottky diodes. Table 1 lists the system parameters.

Table 1 Test parameters of WPT

(a) Frequency tracking algorithm flowchart

(b) FPGA simulation model of frequency tracking control

(c) FPGA simulation result of frequency tracking control algorithm

The experimental data indicate 90% overall system efficiency from DC/DC input to the battery terminals. Figures 6(b)- 6(e) show the waveforms of each part at normal condition. In Fig. 6(b)， the H-bridge output voltage(100 V) and the primary-coil current waveform(5 A) show that the system is working on ZVS.

Fig. 7 WPT test bench

(a) Gate waveforms (b) H-bridge waveforms

(c) Voltage and current waveforms of secondary side (d) Voltage and current waveforms of load

Fig. 8 Experimental results at normal condition

In the practice， the primary side coil will be installed underground， and the secondary side coil will embed in EV. Figure 9 shows the possible coils position in the practice， Figs. 9(a) and 9(b) indicate an EV with lower chassis and higher chassis which is compared with the 15 cm gap， respectively. Figure 9(d) shows a misalignment case which is because of the different parking skill and complex terrains. There will be angles between primary side coil and secondary side coil， as shown in Fig. 9(d).

(a) Lower chassis EV (b) Higher chassis EV

(c) Misalignment case (d) Tilt one side coil

All of the possible coil position as shown in Fig. 9 can significantly affect the charging efficiency. Base on the frequency tracking algorithm that is adopted by FPGA， the experimental waveforms in the case of 4 types possible coils position are shown in Fig. 10.

(a) Tilt primary side coil from

0° to 30° (b) Higher chassis EV

(c) Lower chassis EV (d) Misalignment x=15 cm

Because of the misalignment and different EV chassis， the coupling coefficient will be changed as shown in Fig. 10(c)， which will make output power and system efficiency change as well. But due to the FTC applied in the system， the waveforms indicate a constant output power with different switching frequency as shown in Fig. 10. The overall system transfers keeps 482 W charging power with 92% efficiency.

4 Conclusions

The paper designed an SPC wireless charging system for EV， analyzed and calculated the resonant capacitors for primary side and secondary side. In the practice， the coupling coefficient will be change because of different misalignment and air-gap， and result in the transmission efficiency of the WPT variation. The reason is that the mutual inductance and leakage inductance will also change as well as the difference of misalignment and air-gap. The switching frequency deviates from the original resonant frequency and the new resonant frequency changes along with the misalignment and air-gap. So the FTC method using WPT will be the better candidate. Scanning resonant frequency go through all the charging process， and chang the switching frequency close to it， and the system efficiency will be maintained at the desired value. The paper applied the FTC and adopted by FPGA， a 500 W charger with more than 90% system efficiency is achieved at variational switching frequency， meanwhile the system works on ZVS. The experimental and simulation that verified the FTC can keep WPT working on a constant output power and efficiency.