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Calculation and analysis of optimal design for wireless power transfer
Computers and Electrical Engineering 80 (2019) 106470
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Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng
Calculation and analysis of optimal design for wireless power transfer ✩ Jin Xu a,∗, Yuhui Xu b, Qian Zhang a a b
College of Engineering, Nanjing Agricultural University, Nanjing, 210031, China College of Engineering, Virginia Tech, Blacksburg, VA, 24061, United States
a r t i c l e
i n f o
Article history: Received 10 October 2018 Revised 17 September 2019 Accepted 18 September 2019
Keywords: Evaluation function LCCL Wireless charging System performance
a b s t r a c t In this paper, a detailed theoretical analysis, derivation and calculation of the working characteristics of the electric vehicle wireless power transmission system is provided. Firstly, the circuit model of the resonant wireless power transmission is established using the reflection impedance theory. Secondly, the dual LCCL (Inductance capacitance capacitance Inductance) resonant compensation topology is analyzed, and the equations of the output power P and the transmission efficiency η are obtained. Then, the relationships of the output power P and the transmission efficiency η in respect to the mutual inductance M and the coupling coefficient k, as well as the formulas of the mutual inductance M and the coupling coefficient k is analyzed. And a method to realize the optimal design of the planar spiral coupling coil is proposed using the evaluation function. Finally, a prototype of a 3.3 KW WPT (wireless power transform) system was built. Experimental results show that this way is the best. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, wireless power transmission (WPT) is one of the hot research topic in electrical engineering,which has the potential to solve two major pain points for current electric vehicle industry, limited battery endurance and charger shortage. In previous works, several circuit structures with the inductive coupling technique have been proposed for WPT which attempt to transfer a few watts within several centimeters or around one coil diameter [1–5]. Then, circuit structures such as series connection to series connection (SS), series connection to parallel connection (SP), parallel connection to series connection (PS), and parallel connection to parallel connection (PP), in which compensated capacitors are in serious or in shunt with the primary side and secondary side were adopted in WPT [6–9]. The circuit structures are shown in Fig. 1. In this area, the magnetic-coupled resonant-type circuit topology referred to as magnetic-coupled resonant-type wireless power transmission (MCR-WPT) has been studied by scholars at home and abroad. The structure is shown in Fig. 2 [10– 11]. Lp is the primary energy transmitting coil and Ls is the secondary energy receiving coil. The energy contained in the resonant body oscillates freely in the space between the electric field and the magnetic field. Receiving resonators Ls and Cs , which are separated from the resonant body by a certain distance, transmit the electric energy from the primary side to the receiving end by the magnetic coupling between Lp and Ls [12]. ✩ This paper is for regular issues of CAEE. Reviews processed and recommended for publication to the Editor-in-Chief by Associate Editor Dr. Spyros Sioutas. ∗ Corresponding author. E-mail address: [email protected] (J. Xu).
https://doi.org/10.1016/j.compeleceng.2019.106470 0045-7906/© 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. (a) Functional block diagram of the back-EMF based senseless meth-od. (b) Four basic compensation topologies.
Fig. 2. Schematic diagram of MCR-WPT system.
M is the mutual inductance, which indicates the magnetic coupling strength between Lp and Ls . It is obvious that the mutual inductance M determines the energy and efficiency of the system transmission. When the value of the mutual inductance is greater, the efficiency of the system transmission is also higher. However, the mutual inductance M is related to many factors. For the two coaxially placed coils, the radius of each coil, the spacing of the coils, and the number of turns of the coils determine the magnitude of the mutual inductance M. According to Ref. [13], the influence of mutual inductance M on the system performance is analyzed, but there is no specific method for optimizing the mutual inductance and coupling coefficient. From Ref. [14], the formula of M is deduced from the mathematical formula, and the key influencing factors are pointed out, but it did not connect well with engineering practice. It only from the mathematical point to derived single turn coil mutual inductance formula, he did not combine the specific wireless charging system indicators. It need a simple and straightforward basis for judging the engineering design. In the Ref. [15], The magnetic induction of the coil is simulated by software, and the design of the charging coil is carried out on the basis of this. There is no set of specific, convenient and effective coil design. Taking into account the achievements and short comings of previous works, this paper takes the plane spiral coil as an example, derives the calculation formula of M, analyzes the principle of double LCCL resonant circuit, and discusses how to set the radius of the coil, turns and the relative position of the two coils to realize the optimization design of the coupling coil. Finally, the feasibility of the design index is verified by the experimental results in a 3.3KW prototype. This study provides an important guidance for the optimal design of the coupling coil for the magnetically coupled resonance
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Fig. 3. Dual LCCL resonant compensation WPT system topology.
Fig. 4. Equivalent circuit diagram of the LCCL resonant network at the transmitter end.
type wireless power transmission device. Working characteristics analysis of WPT system based on double LCCL resonant network. The topology structure of WPT system based on double LCCL resonant compensation is shown in Fig. 3, where C1 , Lp , Cp and L1 constitutes the LCCL resonant circuit of the emitter; C2 , LS , CS , L2 constitutes a receiving end LCCL resonant compensation circuit; M is the transmitter and receiver mutual inductance [16]. Firstly, this paper introduces about wireless coupling coil. Second, analysis and deduction the resonant network characteristics of transmitter and receiver. Next, the mutual inductance and efficiency of the system are analyzed and deduced. Then, the coupling coefficient of the optimal coupling coil and the evaluation function of the optimal coupling are put forward. In the end, experimental verification of the proposed ideas is carried out by means of experiment. 1.1. Characteristic analysis of LCCL resonant network at the transmitter end The equivalent circuit of the LCCL resonant network is shown in Fig. 4, where L1 is the resonant inductance, C1 is the resonant capacitor, LP is the transmitting coil, and CP is the compensating capacitor. Increasing the CP can also increase the resonant current IP [17] by using a resonant inductor L1 with a relatively small inductance under the same inductance of the transmitting coil LS so as to satisfy the requirements of the high power systems. When the circuit is working properly, L1 resonates with C1 , C1 resonates with the equivalent inductance consisted by LP and CP , both at ω = ω0 , respectively. In order to facilitate the analysis of the working characteristics of the LCCL network, we define the equivalent inductance LP of the transmitting coil and the resonant frequency of ω0 after CS compensation as follows:
jωL p = jωL p +
ω0 =
1 jωC1
(1)
1
(2)
L1C1
The input impedance of the transmitter is:
Z p = j ω L1 +
1 1 // Zre f + jωLP + jωC1 jωCS
= j ω L1 +
1 //(Zre f + jωL p ) jωC1
(3)
where ω is the switching frequency of the inverter, and the Zref is equivalent to the input end of the receiver. Inverter output current I1 is:
I1 =
UIN UIN = ZP jωL1 + jω1C1 //(Zre f + jωL p )
(4)
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Fig. 5. Equivalent circuit diagram of the receiving end LCCL resonant network.
The resonant current IP is:
IP =
UIN j ω L1 +
1 // jωC1
(RP + Zre f + jωL p )
∗
1/ jωC1
1/ jωC1 + (RP + Zre f + jωLP )
(5)
Among them, UIN is the effective value of the output voltage of the inverter. When the inverter switching frequency ω = ω0 = 1/ L1C1 , put it into IP , we have:
IP =
UIN j ω L1
When the circuit is in the resonant state, the resonant current of the transmitting coil is not independent of the load. 1.2. Characteristics analysis of LCCL resonant network at the receiving end The receiving end of LCCL resonant equivalent circuit diagram is shown in Fig. 5, where L2 is a resonant inductor, C2 is a resonant capacitor, LS is a transmitting coil, CS is a compensation capacitor, and RL is the load. Similar to the emission end, L2 and C2 , C2 and the equivalent inductance represented by LS and CS are in the resonance at ω = ω0 . We define the equivalent inductance of the receiving coil LS as:
j ω LS = j ω LS +
1 jωCS
(6)
The equivalent impedance of the receiving end ZS is:
ZS = j ω LS +
1 //( jωL2 + RL ) jωC2
(7)
Combine with the resonance condition, it can be simplified as follows:
ZS =
(ω0 L2 )2
(8)
RL
This shows that the input impedance of the receiving end is pure resistance. According to the reflected impedance theory, the receiver network can be equivalent to impedance of the transmitter, and the function of the transmitter can be equivalent to the effect of the transmitter network to the Zref [18] is:
Zre f =
( ω M )2
(9)
ZS
Load current IL is:
IL =
1/ jωC2 U0 ∗ ZS 1/ jωC2 + jωL2 + RL
(10)
When the system work at the resonance state, ω = ω0 = 1/ L1C1 , we can have new simplification:
IL =
U0 j ω L2
(11)
where U0 is the induction electromotive force of the receiving coil and U0 = jωM∗ IP . In the other words, when the system is in resonant state, the output current is independent of the load, which is very suitable for the application of electric vehicle charger.
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Fig. 6. LCCL system topology of double WPT resonant compensation after correction.
2. Performance index calculation and analysis of WPT system based on double LCCL resonant network In practical applications, the transmission power and efficiency of the system are the important indexes for determining the parameters of the system. Therefore, it is very important to analyze the system power and transmission efficiency. Combining with the engineering practice, the ideal double LCCL resonant WPT network is improved, and the LCCL resonant network topology is obtained, which is shown in Fig. 6. Where RP and RS are the parasitic resistances of the transmitting coil LP and the receiving coil LS . In engineering practice, in order to meet the requirements of high power charging system, transmitting coil LP and receiving coil LS must have relatively large inductance value. If the inductance value is higher, the transfer energy is also higher. At this time LP and LS parasitic resistance should be included in system considerations. In accordance with the above method, the ideal LCCL network at the transmitter input impedance at this time is:
Z p = j ω L1 +
1 //(RP + Zre f + jωL p ) jωC1
(12)
The resonant current of the transmitting coil is:
IP = I1 =
1/ jωC1
1/ jωC1 + (RP + Zre f + jωLP ) UIN
jωL1 + jω1C1 //(RP + Zre f + jωL p )
∗
1/ jωC1
1/ jωC1 + (RP + Zre f + jωLP )
Substituting the resonant conditions ω = ω0 = 1/ L1C1 , it can be simplified as follows:
Zp = IP =
(ωL1 )2
(13)
RP + Zre f Ui j ω L1
(14)
where the Zref is the reflection impedance of the receiving coil and the expression of Zref in the resonant working state can be got by the same system:
Zre f =
(ωM )2 ZS
=
(ωM )2 2 RS + ( ω L2 ) /RL
(15)
System input power PIN is:
UIN 2 RP RS RL + (ωL2 ) + RL (ωM ) UIN 2 UIN 2 PIN = = = Zp (ωL1 )2 /(RP + Zre f ) (ωL1 )2 RS RL + (ωL2 )2 2
2
(16)
System output power POUT is:
POUT = IP 2 Zre f =
UIN 2 RL (ωM )
2
(ωL1 ) RS RL + (ωL2 )2 2
(17)
The system efficiency η is:
η=
PIN RL ( ω M ) = 2 2 POUT RP RS RL + ( ω L2 ) + RL ( ω M ) 2
(18)
Pout, η and the mutual inductance M curves are plotted using Matlab as shown in Figs. 7 and 8. It is not difficult to see from the curve that the greater the mutual inductance M. When the output power of the system is bigger, the transmission
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Fig. 7. Relationship between Pout & η With mutual inductance M.
Fig. 8. Relationship between Pout & η With Load Impendence RL.
efficiency of the system is higher. The larger value of RL, the greater amount of the output power of the system, and the higher transmission efficiency of the system. The relationship between η with frequency is shown in Fig. 9, the car chassis is usually 15 to 30 cm from the ground, so the existing car wireless charging device operating frequency is generally in the tens of kHz can be achieved a very high efficiency. If we continue to improve the frequency, it can further improve the efficiency of the system, but the effect is not particularly obvious. Taking into account the above factors, the experimental device operating frequency is 85 kHz.
3. Optimization design of coupling coil based on mutual inductance M 3.1. Calculation and analysis of coupling M and coupling coefficient K As shown in Fig. 10, choose planar spiral coil as a coupling coil of WPT system. According to the formula of Neumann principle in [19], defining current flowing through the transmitting coil is IP , the magnetic vector potential at any point in the space is:
A=
μ0 4π
lp
I p dl p h
(19)
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Fig. 9. Relationship between η With Frequency.
Fig. 10. Planar spiral coil.
The magnetic flux passing through the receiving coil LS is:
PS =
ls
μ0 A · dls = 4π
lS
lP
The mutual inductance is:
M = MSP = MPS =
SP IP
=
IP dlS h
μo 4π
· dls
=
lS
μo
4π
∗
(20)
GP GS h
(21)
Where GP and GS are the perimeters of the transmitting coil, LS and the receiving coil LS , and the h is the distance between the transmitting coil and the receiving coil, and the μ0 is the vacuum permeability. For the Planar Spiral Coil Wound by High Frequency Liz wire with its outer diameter as R1 , R2 , turns as N1 , N2 and the same wire diameter of D, its mutual inductance is:
M=
μoπ N1 N2 [2R1 − (N1 − 1 )d][2R2 − (N2 − 1 )d] 16h
(22)
Coil inductance can be calculated by empirical formula [20]: 5
L = 2.15 ∗ 10−6 aN 3 ln
8a b
(23)
Where a is the average radius of the plane spiral coil, b is the width of the coil, and N is the number of turns of the coil. The inductance of the planar spiral coil:
L p = 2.15 ∗ 10
−6
R1 −
(N1 − 1 ) 2
5 3
d N1 ln
8 R1 − (N12−1) d N1 d
(24)
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Fig. 11. The curve of coupling coefficient K to α .
Defining the mutual inductance coefficient is:
K=
M
(25)
LP LS
The mutual inductance coefficient of the coil is:
K=
M
LP LS
1
=
π μ0 (N1 N2 ) 6 [2R1 − (N1 − 1 )d][2R2 − (N2 − 1 )d] 3.44∗10−5 h a1 (N1 ) ln 8ca(1N(N)1 ) a2 (N2 ) ln 8ca(2N(N)2 ) 1 2
where, a1 (N1 ) = R1 −
(N1 −1 )d 2
(26)
represents the average radius of the transmitting coil. c(N1 ) = N1 d represents the width of the
transmitting coil. Similarly, a2 (N2 ) = R2 − the width of the transmitting coil.
(N2 −1 )d 2
, represents the average radius of the receiving coil. c(N2 ) = N2 d represents
3.2. The formulation and analysis of evaluation function Since the value of mutual inductance coefficient K is related to many variables, the analysis is very complex and it is difficult to guide the actual design of the coupling coil. For the analysis of multivariable complex systems, constructing the evaluation function is taken as a common method. According to the principle of the evaluation function and the characteristic parameters of the coupled coil model, the parameters in the model studied in this paper are defined as follows: α = R2 / R1 , β = N2 / N1 , γ = h / R2 , the curves of mutual inductance corresponding to α , β and γ are plotted using Mathcad as shown in Figs. 11–13. Defining evaluation index as Qk = αβ /γ , the curve of coil coupling coefficient to Qk can be plotted Using Mathcad as is shown in Fig. 14. In engineering practice, there are usually two principles: 1) γ >0.5. On the one hand, this is to make the transmission distance to meet the requirements of the vehicle chassis height; on the other hand, it is minimizing to the receiving coil area so that the receiving coil can be easily loaded into the space of the car. 2) α and β should be less than 1 in actual design. On the one hand, taking into account the limited space for cars, receiving coil cannot be too large; on the other hand, from the perspective of the electromagnetic coupling mechanism, transmitting coil area should be larger than that of the receiving coil area so as to effectively prevent energy lost due to the shift of the coil. Combined with the above principles and the curves, it can be concluded that when the evaluation index Qk lies in the interval [1.3,2.2], coils have a larger coupling coefficient, and thus better performance of the system. 4. Experimental verification of WPT system based on optimization design of coupling coils According to the above theory, we have set up a set of 3.3KW wireless charging experimental prototype. The electronic device parameters are shown in Table 1, and the experimental prototype hardware structure is shown in Fig. 15.
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Fig. 12. The curve of coupling coefficient K to β .
Fig. 13. The curve of coupling coefficient K to γ .
When the output frequency of the inverter is the resonant frequency and the waveform of the output voltage and current of the inverter are shown in Fig. 16. It can be seen from the figure, the inverter output voltage phase is slightly ahead of the inverter output current phase, and the inverter switch tube is working in (Zero Voltage Switch) ZVS. At the same time, the phase lag is very small, which can be regarded as the same phase of voltage and current. This shows that the inverter only needs to provide active power, when the load is purely resistive. While the input impedance of the transmitter is ZP, which is consistent with the theoretical analysis of the first part. Using the control variable method, taking the input voltage and load impedance as variables respectively in the experiment, the measured data are shown in Table 2. According to the data in the table to make the curve of load current and input voltage as well as the load impedance, which is shown in Figs. 17 and 18. According to the fitting curve, the load current is proportional to the input voltage, which is independent of the load resistance. The WPT system is working as a voltage controlled constant current source, which is consistent with the analysis above. In order to verify the feasibility of the evaluation index, we designed two sets of charging experiments based on different evaluation indexes, and the experimental data are shown in Table 3.
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Fig. 14. The curve of coupling coefficient K to Qk.
Table 1 Experimental parameters of WPT prototype. Parameters
Values
f/kHz L1 /uH C1 /nf LP /uH CP /nf LS /uH CS /nf L2 /uH C2 /nf R1 /cm N1 /turn h/cm
85 140 25 405 13 320 12 32 110 35 18 15 0.857 1 0.5
α β γ
Table 2 Experimental data of output current of WPT prototype. Input voltage UIN (V)
Load impedance ZL ( )
Load current IL (A)
90 100 110 120 130 140 150 150 150 150
1 1 1 1 1 1 1 2 3 4
3.9 4.4 4.9 5.3 5.7 6.1 6.6 6.5 6.5 6.6
According to the data in the table, curves of output power and efficiency under different load impedance of coupling coil group are plotted in Figs. 19 and 20, respectively. By comparing Figs. 17 with 18, we can see that the output power and efficiency of the coupling coil group A is lower than that of the coupling coil group under different load B. That is because the coupling coil group A’s Qk = 1.714 in the above mentioned optimization interval [1.3.2.2], and the coupling coil group B’s Qk = 1.07. It shows that the performance of
J. Xu, Y. Xu and Q. Zhang / Computers and Electrical Engineering 80 (2019) 106470
Fig. 15. WPT experimental device.
Fig. 16. The waveform of operating characteristics of the experimental device.
Fig. 17. Relationship between load current and input voltage.
11
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Fig. 18. Relationship between load current and input voltage.
Fig. 19. Output power curve of coupling coil group under different loads.
Table 3 Experimental data of output performance of WPT system with different coupling coils. Coupling coil group A (QK = 1.714) Load impedance ZLA ( )
Output power PA (W)
Efficiency ηA (%)
4 8 12 16
866.4 1584.0 2324.9 3105.3
84.0 85.5 88.5 90.9
Coupling coil group B (QK = 1.07) Load impedance ZLB ( )
Output power PB (W)
Efficiency η B (%)
4 8 12 16
755.4 1329.6 2052.6 2641.7
74.0 77.1 78.6 80.1
the coupling coil group A performance index is better than the performance of the coupling coil group B. It is proved that the evaluation index mentioned above can realize the optimization design of the coupling coil.
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Fig. 20. Efficiency curve of coupling coils under different loads.
5. Conclusion Mutual inductance and coupling coefficient have great influence on the power and efficiency of magnetic coupled resonant wireless power transmission system. The design of the coupled coil directly determines the performance of the wireless power transmission system. In light of the technological challenges in current research trend of WPT system, this paper puts forward the innovative viewpoints and methods for optimizing the coupling coil combining the state of the art the existing research results in the literature. The contributions of the work can be summarized as and follows: (1) The performance of WPT system with dual LCCL resonant network is analyzed and deduced. (2) According to engineering practice, the ideal double LCCL resonant network is adjusted, and the formula of output power POUT and system efficiency η of the modified WPT system is deduced. (3) The formula of mutual inductance M and coupling coefficient K is deduced for the closely wound spiral coil, and the optimal design of the coil is proposed by using the evaluation index Qk. (4) Using the theory of this paper, a set of 3.3KW car wireless power transfer experimental prototype is designed. The experimental results prove that the optimal design of the coupling coil can be achieved by using the evaluation index Qk, and the performance index of WPT system is improved. In this paper, the method to optimize the design of the coupling coil by using of evaluation indexes to improve the performance system is proposed and verified by the experiment, which has significant value to the development of EV wireless power transfer technology. Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. References [1] Ahson SA, Ilyas M. RFID handbook: applications, technology, security and privacy. Boca Raton, FL: CRC; 2008. [2] Covic GA, Boys JT, Kissin MLG, Lu HG. A three-phase inductive power transfer system for roadway-powered vehicles. IEEE Trans Ind Electron Dec. 2007;54(6):3370–8. [3] Keeling NA, Boys JT, Covic GA. Unity power factor inductive power transfer pick-up for high power applications//2008. In: 34th annual conference of IEEE Industrial Electronics. IEEE; 2008. p. 1039–44. [4] Budhia M, Covic G, Boys J. A new IPT magnetic coupler for electric vehicle charging systems. In: Proc. 36t IEEE IECON; 2010. p. 2487–92. [5] Budhia M, Covic GA, Boys JT. Design and optimisation of magnetic structures for lumped inductive power transfer systems. In: Proc. IEEE ECCE; 2009. p. 2081–8. [6] Zhen NL, Chinga RA, Tseng R. Design and test of a high-power high-efficiency loosely coupled planar wireless power transfer system. IEEE Trans Ind Electron 2009;56(5):1801–12. [7] Zhen NL, Casanova JJ, Maier PH. Method of load/fault detection for loosely coupled planar wireless power transfer system with power delivery tracking. Ind Electron IEEE Trans 2010;57(4):1478–86. [8] Moradewicz AJ, Kazmierkowski MP. Contactless energy transfer system with FPGA-Controlled resonant converter. Ind Electron IEEE Trans 2010;57(9):3181–90.
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[9] Jiang WX, Chin JY, Li Z. Analytical design of conformally invisible cloaks for arbitrarily shaped objects. Phys Rev E Stat Nonlinear Soft Matter Phys 2008;77(6 Pt 2):066607. [10] Yang Y, Xie X, Li G. A combined transmitting coil design for high efficiency WPT of endoscopic capsule. IEEE International Symposium on circuits and systems. IEEE; 2015. [11] Prengel S, Helwig M, Modler N. Lightweight coil for efficient wireless power transfer: optimization of weight and efficiency for WPT coils//. In: Wireless power transfer conference. IEEE; 2014. p. 96–9. [12] Zhongni Z, Jie L, Qingguo S. Research on the development and application of the magnetic resonance radio transmission technology (J). J. Airf Early Warn Coll 2014;28(1):37. [13] Chen L, Liu S, Zhou YC. An optimizable circuit structure for high-efficiency wireless power transfer. Ind Electron IEEE Trans 2013;60(1):339–49. [14] Huangpu G. Two circular coil mutual inductance and coupling coefficient on. J Weinan Teachers Univ 2015(14):24–9 edition. [15] Liu C, Guo Y, Ge S. Characteristics analysis and experimental verification of the double LCL resonant compensation network for electrical vehicles wireless power transfer. Dissertations & Theses - Gradworks; 2015. [16] Jiong Z, Peihuang L, Xiaoming Q. Based on double LCL compensation of contactless power supply system. Trans China Electrotechn Soc 2013;28(10):19–24. [17] Ye X, Hao M. Series voltage compensation type non-contact electric energy transmission converter. Power Electron Technol 2008;42(3):4–6. [18] Wangsness RK. Electromagnetic field. New York: John Wiley & Sons; 1986. p. 278–9. [19] Dill HG. Designing inductors for thin-film applications. Electron Des 1964;17(1):52–60. [20] Hoki K, Kaneko T. Large-scale optimization for evaluation functions with minimax search. J Artif Intell Res 2014;49(49):527–68. Jin Xu received the Ph.D. degrees in electrical engineering from the South East University, Nanjing, China, in 2007. He is currently a Professor in Nanjing Agricultural University. His current research interests include Wireless Power Transformer(WPT), High-frequency switching mode power supply, Control of Buck-Bost DC-DC Converter, soft-switching inverter, high-efficiency power electronics conversions for high power and energy applications. Yuhui Xu is currently working toward the B.S. degree in electrical engineering from the Virginia Polytechnic Institute and State University, Blacksburg, VA, USA. He is a junior student in this school. Since 2017, his research interests include Wireless Power Transformer(WPT), High-frequency switching mode power supply and Control of Buck-Bost DC-DC Converter. Qian Zhang received the B.S. degree from Nanjing Agriculture University, Nanjing, China. He is currently working toward M.S. degree in electrical engineering in Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China. Since 2015, his research interests include soft-switching inverter for renewable energy application, high-efficiency dc/dc converter, and contactless power transfer.
Contents lists available at ScienceDirect
Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng
Calculation and analysis of optimal design for wireless power transfer ✩ Jin Xu a,∗, Yuhui Xu b, Qian Zhang a a b
College of Engineering, Nanjing Agricultural University, Nanjing, 210031, China College of Engineering, Virginia Tech, Blacksburg, VA, 24061, United States
a r t i c l e
i n f o
Article history: Received 10 October 2018 Revised 17 September 2019 Accepted 18 September 2019
Keywords: Evaluation function LCCL Wireless charging System performance
a b s t r a c t In this paper, a detailed theoretical analysis, derivation and calculation of the working characteristics of the electric vehicle wireless power transmission system is provided. Firstly, the circuit model of the resonant wireless power transmission is established using the reflection impedance theory. Secondly, the dual LCCL (Inductance capacitance capacitance Inductance) resonant compensation topology is analyzed, and the equations of the output power P and the transmission efficiency η are obtained. Then, the relationships of the output power P and the transmission efficiency η in respect to the mutual inductance M and the coupling coefficient k, as well as the formulas of the mutual inductance M and the coupling coefficient k is analyzed. And a method to realize the optimal design of the planar spiral coupling coil is proposed using the evaluation function. Finally, a prototype of a 3.3 KW WPT (wireless power transform) system was built. Experimental results show that this way is the best. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, wireless power transmission (WPT) is one of the hot research topic in electrical engineering,which has the potential to solve two major pain points for current electric vehicle industry, limited battery endurance and charger shortage. In previous works, several circuit structures with the inductive coupling technique have been proposed for WPT which attempt to transfer a few watts within several centimeters or around one coil diameter [1–5]. Then, circuit structures such as series connection to series connection (SS), series connection to parallel connection (SP), parallel connection to series connection (PS), and parallel connection to parallel connection (PP), in which compensated capacitors are in serious or in shunt with the primary side and secondary side were adopted in WPT [6–9]. The circuit structures are shown in Fig. 1. In this area, the magnetic-coupled resonant-type circuit topology referred to as magnetic-coupled resonant-type wireless power transmission (MCR-WPT) has been studied by scholars at home and abroad. The structure is shown in Fig. 2 [10– 11]. Lp is the primary energy transmitting coil and Ls is the secondary energy receiving coil. The energy contained in the resonant body oscillates freely in the space between the electric field and the magnetic field. Receiving resonators Ls and Cs , which are separated from the resonant body by a certain distance, transmit the electric energy from the primary side to the receiving end by the magnetic coupling between Lp and Ls [12]. ✩ This paper is for regular issues of CAEE. Reviews processed and recommended for publication to the Editor-in-Chief by Associate Editor Dr. Spyros Sioutas. ∗ Corresponding author. E-mail address: [email protected] (J. Xu).
https://doi.org/10.1016/j.compeleceng.2019.106470 0045-7906/© 2019 Elsevier Ltd. All rights reserved.
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J. Xu, Y. Xu and Q. Zhang / Computers and Electrical Engineering 80 (2019) 106470
Fig. 1. (a) Functional block diagram of the back-EMF based senseless meth-od. (b) Four basic compensation topologies.
Fig. 2. Schematic diagram of MCR-WPT system.
M is the mutual inductance, which indicates the magnetic coupling strength between Lp and Ls . It is obvious that the mutual inductance M determines the energy and efficiency of the system transmission. When the value of the mutual inductance is greater, the efficiency of the system transmission is also higher. However, the mutual inductance M is related to many factors. For the two coaxially placed coils, the radius of each coil, the spacing of the coils, and the number of turns of the coils determine the magnitude of the mutual inductance M. According to Ref. [13], the influence of mutual inductance M on the system performance is analyzed, but there is no specific method for optimizing the mutual inductance and coupling coefficient. From Ref. [14], the formula of M is deduced from the mathematical formula, and the key influencing factors are pointed out, but it did not connect well with engineering practice. It only from the mathematical point to derived single turn coil mutual inductance formula, he did not combine the specific wireless charging system indicators. It need a simple and straightforward basis for judging the engineering design. In the Ref. [15], The magnetic induction of the coil is simulated by software, and the design of the charging coil is carried out on the basis of this. There is no set of specific, convenient and effective coil design. Taking into account the achievements and short comings of previous works, this paper takes the plane spiral coil as an example, derives the calculation formula of M, analyzes the principle of double LCCL resonant circuit, and discusses how to set the radius of the coil, turns and the relative position of the two coils to realize the optimization design of the coupling coil. Finally, the feasibility of the design index is verified by the experimental results in a 3.3KW prototype. This study provides an important guidance for the optimal design of the coupling coil for the magnetically coupled resonance
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Fig. 3. Dual LCCL resonant compensation WPT system topology.
Fig. 4. Equivalent circuit diagram of the LCCL resonant network at the transmitter end.
type wireless power transmission device. Working characteristics analysis of WPT system based on double LCCL resonant network. The topology structure of WPT system based on double LCCL resonant compensation is shown in Fig. 3, where C1 , Lp , Cp and L1 constitutes the LCCL resonant circuit of the emitter; C2 , LS , CS , L2 constitutes a receiving end LCCL resonant compensation circuit; M is the transmitter and receiver mutual inductance [16]. Firstly, this paper introduces about wireless coupling coil. Second, analysis and deduction the resonant network characteristics of transmitter and receiver. Next, the mutual inductance and efficiency of the system are analyzed and deduced. Then, the coupling coefficient of the optimal coupling coil and the evaluation function of the optimal coupling are put forward. In the end, experimental verification of the proposed ideas is carried out by means of experiment. 1.1. Characteristic analysis of LCCL resonant network at the transmitter end The equivalent circuit of the LCCL resonant network is shown in Fig. 4, where L1 is the resonant inductance, C1 is the resonant capacitor, LP is the transmitting coil, and CP is the compensating capacitor. Increasing the CP can also increase the resonant current IP [17] by using a resonant inductor L1 with a relatively small inductance under the same inductance of the transmitting coil LS so as to satisfy the requirements of the high power systems. When the circuit is working properly, L1 resonates with C1 , C1 resonates with the equivalent inductance consisted by LP and CP , both at ω = ω0 , respectively. In order to facilitate the analysis of the working characteristics of the LCCL network, we define the equivalent inductance LP of the transmitting coil and the resonant frequency of ω0 after CS compensation as follows:
jωL p = jωL p +
ω0 =
1 jωC1
(1)
1
(2)
L1C1
The input impedance of the transmitter is:
Z p = j ω L1 +
1 1 // Zre f + jωLP + jωC1 jωCS
= j ω L1 +
1 //(Zre f + jωL p ) jωC1
(3)
where ω is the switching frequency of the inverter, and the Zref is equivalent to the input end of the receiver. Inverter output current I1 is:
I1 =
UIN UIN = ZP jωL1 + jω1C1 //(Zre f + jωL p )
(4)
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J. Xu, Y. Xu and Q. Zhang / Computers and Electrical Engineering 80 (2019) 106470
Fig. 5. Equivalent circuit diagram of the receiving end LCCL resonant network.
The resonant current IP is:
IP =
UIN j ω L1 +
1 // jωC1
(RP + Zre f + jωL p )
∗
1/ jωC1
1/ jωC1 + (RP + Zre f + jωLP )
(5)
Among them, UIN is the effective value of the output voltage of the inverter. When the inverter switching frequency ω = ω0 = 1/ L1C1 , put it into IP , we have:
IP =
UIN j ω L1
When the circuit is in the resonant state, the resonant current of the transmitting coil is not independent of the load. 1.2. Characteristics analysis of LCCL resonant network at the receiving end The receiving end of LCCL resonant equivalent circuit diagram is shown in Fig. 5, where L2 is a resonant inductor, C2 is a resonant capacitor, LS is a transmitting coil, CS is a compensation capacitor, and RL is the load. Similar to the emission end, L2 and C2 , C2 and the equivalent inductance represented by LS and CS are in the resonance at ω = ω0 . We define the equivalent inductance of the receiving coil LS as:
j ω LS = j ω LS +
1 jωCS
(6)
The equivalent impedance of the receiving end ZS is:
ZS = j ω LS +
1 //( jωL2 + RL ) jωC2
(7)
Combine with the resonance condition, it can be simplified as follows:
ZS =
(ω0 L2 )2
(8)
RL
This shows that the input impedance of the receiving end is pure resistance. According to the reflected impedance theory, the receiver network can be equivalent to impedance of the transmitter, and the function of the transmitter can be equivalent to the effect of the transmitter network to the Zref [18] is:
Zre f =
( ω M )2
(9)
ZS
Load current IL is:
IL =
1/ jωC2 U0 ∗ ZS 1/ jωC2 + jωL2 + RL
(10)
When the system work at the resonance state, ω = ω0 = 1/ L1C1 , we can have new simplification:
IL =
U0 j ω L2
(11)
where U0 is the induction electromotive force of the receiving coil and U0 = jωM∗ IP . In the other words, when the system is in resonant state, the output current is independent of the load, which is very suitable for the application of electric vehicle charger.
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Fig. 6. LCCL system topology of double WPT resonant compensation after correction.
2. Performance index calculation and analysis of WPT system based on double LCCL resonant network In practical applications, the transmission power and efficiency of the system are the important indexes for determining the parameters of the system. Therefore, it is very important to analyze the system power and transmission efficiency. Combining with the engineering practice, the ideal double LCCL resonant WPT network is improved, and the LCCL resonant network topology is obtained, which is shown in Fig. 6. Where RP and RS are the parasitic resistances of the transmitting coil LP and the receiving coil LS . In engineering practice, in order to meet the requirements of high power charging system, transmitting coil LP and receiving coil LS must have relatively large inductance value. If the inductance value is higher, the transfer energy is also higher. At this time LP and LS parasitic resistance should be included in system considerations. In accordance with the above method, the ideal LCCL network at the transmitter input impedance at this time is:
Z p = j ω L1 +
1 //(RP + Zre f + jωL p ) jωC1
(12)
The resonant current of the transmitting coil is:
IP = I1 =
1/ jωC1
1/ jωC1 + (RP + Zre f + jωLP ) UIN
jωL1 + jω1C1 //(RP + Zre f + jωL p )
∗
1/ jωC1
1/ jωC1 + (RP + Zre f + jωLP )
Substituting the resonant conditions ω = ω0 = 1/ L1C1 , it can be simplified as follows:
Zp = IP =
(ωL1 )2
(13)
RP + Zre f Ui j ω L1
(14)
where the Zref is the reflection impedance of the receiving coil and the expression of Zref in the resonant working state can be got by the same system:
Zre f =
(ωM )2 ZS
=
(ωM )2 2 RS + ( ω L2 ) /RL
(15)
System input power PIN is:
UIN 2 RP RS RL + (ωL2 ) + RL (ωM ) UIN 2 UIN 2 PIN = = = Zp (ωL1 )2 /(RP + Zre f ) (ωL1 )2 RS RL + (ωL2 )2 2
2
(16)
System output power POUT is:
POUT = IP 2 Zre f =
UIN 2 RL (ωM )
2
(ωL1 ) RS RL + (ωL2 )2 2
(17)
The system efficiency η is:
η=
PIN RL ( ω M ) = 2 2 POUT RP RS RL + ( ω L2 ) + RL ( ω M ) 2
(18)
Pout, η and the mutual inductance M curves are plotted using Matlab as shown in Figs. 7 and 8. It is not difficult to see from the curve that the greater the mutual inductance M. When the output power of the system is bigger, the transmission
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Fig. 7. Relationship between Pout & η With mutual inductance M.
Fig. 8. Relationship between Pout & η With Load Impendence RL.
efficiency of the system is higher. The larger value of RL, the greater amount of the output power of the system, and the higher transmission efficiency of the system. The relationship between η with frequency is shown in Fig. 9, the car chassis is usually 15 to 30 cm from the ground, so the existing car wireless charging device operating frequency is generally in the tens of kHz can be achieved a very high efficiency. If we continue to improve the frequency, it can further improve the efficiency of the system, but the effect is not particularly obvious. Taking into account the above factors, the experimental device operating frequency is 85 kHz.
3. Optimization design of coupling coil based on mutual inductance M 3.1. Calculation and analysis of coupling M and coupling coefficient K As shown in Fig. 10, choose planar spiral coil as a coupling coil of WPT system. According to the formula of Neumann principle in [19], defining current flowing through the transmitting coil is IP , the magnetic vector potential at any point in the space is:
A=
μ0 4π
lp
I p dl p h
(19)
J. Xu, Y. Xu and Q. Zhang / Computers and Electrical Engineering 80 (2019) 106470
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Fig. 9. Relationship between η With Frequency.
Fig. 10. Planar spiral coil.
The magnetic flux passing through the receiving coil LS is:
PS =
ls
μ0 A · dls = 4π
lS
lP
The mutual inductance is:
M = MSP = MPS =
SP IP
=
IP dlS h
μo 4π
· dls
=
lS
μo
4π
∗
(20)
GP GS h
(21)
Where GP and GS are the perimeters of the transmitting coil, LS and the receiving coil LS , and the h is the distance between the transmitting coil and the receiving coil, and the μ0 is the vacuum permeability. For the Planar Spiral Coil Wound by High Frequency Liz wire with its outer diameter as R1 , R2 , turns as N1 , N2 and the same wire diameter of D, its mutual inductance is:
M=
μoπ N1 N2 [2R1 − (N1 − 1 )d][2R2 − (N2 − 1 )d] 16h
(22)
Coil inductance can be calculated by empirical formula [20]: 5
L = 2.15 ∗ 10−6 aN 3 ln
8a b
(23)
Where a is the average radius of the plane spiral coil, b is the width of the coil, and N is the number of turns of the coil. The inductance of the planar spiral coil:
L p = 2.15 ∗ 10
−6
R1 −
(N1 − 1 ) 2
5 3
d N1 ln
8 R1 − (N12−1) d N1 d
(24)
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Fig. 11. The curve of coupling coefficient K to α .
Defining the mutual inductance coefficient is:
K=
M
(25)
LP LS
The mutual inductance coefficient of the coil is:
K=
M
LP LS
1
=
π μ0 (N1 N2 ) 6 [2R1 − (N1 − 1 )d][2R2 − (N2 − 1 )d] 3.44∗10−5 h a1 (N1 ) ln 8ca(1N(N)1 ) a2 (N2 ) ln 8ca(2N(N)2 ) 1 2
where, a1 (N1 ) = R1 −
(N1 −1 )d 2
(26)
represents the average radius of the transmitting coil. c(N1 ) = N1 d represents the width of the
transmitting coil. Similarly, a2 (N2 ) = R2 − the width of the transmitting coil.
(N2 −1 )d 2
, represents the average radius of the receiving coil. c(N2 ) = N2 d represents
3.2. The formulation and analysis of evaluation function Since the value of mutual inductance coefficient K is related to many variables, the analysis is very complex and it is difficult to guide the actual design of the coupling coil. For the analysis of multivariable complex systems, constructing the evaluation function is taken as a common method. According to the principle of the evaluation function and the characteristic parameters of the coupled coil model, the parameters in the model studied in this paper are defined as follows: α = R2 / R1 , β = N2 / N1 , γ = h / R2 , the curves of mutual inductance corresponding to α , β and γ are plotted using Mathcad as shown in Figs. 11–13. Defining evaluation index as Qk = αβ /γ , the curve of coil coupling coefficient to Qk can be plotted Using Mathcad as is shown in Fig. 14. In engineering practice, there are usually two principles: 1) γ >0.5. On the one hand, this is to make the transmission distance to meet the requirements of the vehicle chassis height; on the other hand, it is minimizing to the receiving coil area so that the receiving coil can be easily loaded into the space of the car. 2) α and β should be less than 1 in actual design. On the one hand, taking into account the limited space for cars, receiving coil cannot be too large; on the other hand, from the perspective of the electromagnetic coupling mechanism, transmitting coil area should be larger than that of the receiving coil area so as to effectively prevent energy lost due to the shift of the coil. Combined with the above principles and the curves, it can be concluded that when the evaluation index Qk lies in the interval [1.3,2.2], coils have a larger coupling coefficient, and thus better performance of the system. 4. Experimental verification of WPT system based on optimization design of coupling coils According to the above theory, we have set up a set of 3.3KW wireless charging experimental prototype. The electronic device parameters are shown in Table 1, and the experimental prototype hardware structure is shown in Fig. 15.
J. Xu, Y. Xu and Q. Zhang / Computers and Electrical Engineering 80 (2019) 106470
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Fig. 12. The curve of coupling coefficient K to β .
Fig. 13. The curve of coupling coefficient K to γ .
When the output frequency of the inverter is the resonant frequency and the waveform of the output voltage and current of the inverter are shown in Fig. 16. It can be seen from the figure, the inverter output voltage phase is slightly ahead of the inverter output current phase, and the inverter switch tube is working in (Zero Voltage Switch) ZVS. At the same time, the phase lag is very small, which can be regarded as the same phase of voltage and current. This shows that the inverter only needs to provide active power, when the load is purely resistive. While the input impedance of the transmitter is ZP, which is consistent with the theoretical analysis of the first part. Using the control variable method, taking the input voltage and load impedance as variables respectively in the experiment, the measured data are shown in Table 2. According to the data in the table to make the curve of load current and input voltage as well as the load impedance, which is shown in Figs. 17 and 18. According to the fitting curve, the load current is proportional to the input voltage, which is independent of the load resistance. The WPT system is working as a voltage controlled constant current source, which is consistent with the analysis above. In order to verify the feasibility of the evaluation index, we designed two sets of charging experiments based on different evaluation indexes, and the experimental data are shown in Table 3.
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Fig. 14. The curve of coupling coefficient K to Qk.
Table 1 Experimental parameters of WPT prototype. Parameters
Values
f/kHz L1 /uH C1 /nf LP /uH CP /nf LS /uH CS /nf L2 /uH C2 /nf R1 /cm N1 /turn h/cm
85 140 25 405 13 320 12 32 110 35 18 15 0.857 1 0.5
α β γ
Table 2 Experimental data of output current of WPT prototype. Input voltage UIN (V)
Load impedance ZL ( )
Load current IL (A)
90 100 110 120 130 140 150 150 150 150
1 1 1 1 1 1 1 2 3 4
3.9 4.4 4.9 5.3 5.7 6.1 6.6 6.5 6.5 6.6
According to the data in the table, curves of output power and efficiency under different load impedance of coupling coil group are plotted in Figs. 19 and 20, respectively. By comparing Figs. 17 with 18, we can see that the output power and efficiency of the coupling coil group A is lower than that of the coupling coil group under different load B. That is because the coupling coil group A’s Qk = 1.714 in the above mentioned optimization interval [1.3.2.2], and the coupling coil group B’s Qk = 1.07. It shows that the performance of
J. Xu, Y. Xu and Q. Zhang / Computers and Electrical Engineering 80 (2019) 106470
Fig. 15. WPT experimental device.
Fig. 16. The waveform of operating characteristics of the experimental device.
Fig. 17. Relationship between load current and input voltage.
11
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J. Xu, Y. Xu and Q. Zhang / Computers and Electrical Engineering 80 (2019) 106470
Fig. 18. Relationship between load current and input voltage.
Fig. 19. Output power curve of coupling coil group under different loads.
Table 3 Experimental data of output performance of WPT system with different coupling coils. Coupling coil group A (QK = 1.714) Load impedance ZLA ( )
Output power PA (W)
Efficiency ηA (%)
4 8 12 16
866.4 1584.0 2324.9 3105.3
84.0 85.5 88.5 90.9
Coupling coil group B (QK = 1.07) Load impedance ZLB ( )
Output power PB (W)
Efficiency η B (%)
4 8 12 16
755.4 1329.6 2052.6 2641.7
74.0 77.1 78.6 80.1
the coupling coil group A performance index is better than the performance of the coupling coil group B. It is proved that the evaluation index mentioned above can realize the optimization design of the coupling coil.
J. Xu, Y. Xu and Q. Zhang / Computers and Electrical Engineering 80 (2019) 106470
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Fig. 20. Efficiency curve of coupling coils under different loads.
5. Conclusion Mutual inductance and coupling coefficient have great influence on the power and efficiency of magnetic coupled resonant wireless power transmission system. The design of the coupled coil directly determines the performance of the wireless power transmission system. In light of the technological challenges in current research trend of WPT system, this paper puts forward the innovative viewpoints and methods for optimizing the coupling coil combining the state of the art the existing research results in the literature. The contributions of the work can be summarized as and follows: (1) The performance of WPT system with dual LCCL resonant network is analyzed and deduced. (2) According to engineering practice, the ideal double LCCL resonant network is adjusted, and the formula of output power POUT and system efficiency η of the modified WPT system is deduced. (3) The formula of mutual inductance M and coupling coefficient K is deduced for the closely wound spiral coil, and the optimal design of the coil is proposed by using the evaluation index Qk. (4) Using the theory of this paper, a set of 3.3KW car wireless power transfer experimental prototype is designed. The experimental results prove that the optimal design of the coupling coil can be achieved by using the evaluation index Qk, and the performance index of WPT system is improved. In this paper, the method to optimize the design of the coupling coil by using of evaluation indexes to improve the performance system is proposed and verified by the experiment, which has significant value to the development of EV wireless power transfer technology. Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. References [1] Ahson SA, Ilyas M. RFID handbook: applications, technology, security and privacy. Boca Raton, FL: CRC; 2008. [2] Covic GA, Boys JT, Kissin MLG, Lu HG. A three-phase inductive power transfer system for roadway-powered vehicles. IEEE Trans Ind Electron Dec. 2007;54(6):3370–8. [3] Keeling NA, Boys JT, Covic GA. Unity power factor inductive power transfer pick-up for high power applications//2008. In: 34th annual conference of IEEE Industrial Electronics. IEEE; 2008. p. 1039–44. [4] Budhia M, Covic G, Boys J. A new IPT magnetic coupler for electric vehicle charging systems. In: Proc. 36t IEEE IECON; 2010. p. 2487–92. [5] Budhia M, Covic GA, Boys JT. Design and optimisation of magnetic structures for lumped inductive power transfer systems. In: Proc. IEEE ECCE; 2009. p. 2081–8. [6] Zhen NL, Chinga RA, Tseng R. Design and test of a high-power high-efficiency loosely coupled planar wireless power transfer system. IEEE Trans Ind Electron 2009;56(5):1801–12. [7] Zhen NL, Casanova JJ, Maier PH. Method of load/fault detection for loosely coupled planar wireless power transfer system with power delivery tracking. Ind Electron IEEE Trans 2010;57(4):1478–86. [8] Moradewicz AJ, Kazmierkowski MP. Contactless energy transfer system with FPGA-Controlled resonant converter. Ind Electron IEEE Trans 2010;57(9):3181–90.
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[9] Jiang WX, Chin JY, Li Z. Analytical design of conformally invisible cloaks for arbitrarily shaped objects. Phys Rev E Stat Nonlinear Soft Matter Phys 2008;77(6 Pt 2):066607. [10] Yang Y, Xie X, Li G. A combined transmitting coil design for high efficiency WPT of endoscopic capsule. IEEE International Symposium on circuits and systems. IEEE; 2015. [11] Prengel S, Helwig M, Modler N. Lightweight coil for efficient wireless power transfer: optimization of weight and efficiency for WPT coils//. In: Wireless power transfer conference. IEEE; 2014. p. 96–9. [12] Zhongni Z, Jie L, Qingguo S. Research on the development and application of the magnetic resonance radio transmission technology (J). J. Airf Early Warn Coll 2014;28(1):37. [13] Chen L, Liu S, Zhou YC. An optimizable circuit structure for high-efficiency wireless power transfer. Ind Electron IEEE Trans 2013;60(1):339–49. [14] Huangpu G. Two circular coil mutual inductance and coupling coefficient on. J Weinan Teachers Univ 2015(14):24–9 edition. [15] Liu C, Guo Y, Ge S. Characteristics analysis and experimental verification of the double LCL resonant compensation network for electrical vehicles wireless power transfer. Dissertations & Theses - Gradworks; 2015. [16] Jiong Z, Peihuang L, Xiaoming Q. Based on double LCL compensation of contactless power supply system. Trans China Electrotechn Soc 2013;28(10):19–24. [17] Ye X, Hao M. Series voltage compensation type non-contact electric energy transmission converter. Power Electron Technol 2008;42(3):4–6. [18] Wangsness RK. Electromagnetic field. New York: John Wiley & Sons; 1986. p. 278–9. [19] Dill HG. Designing inductors for thin-film applications. Electron Des 1964;17(1):52–60. [20] Hoki K, Kaneko T. Large-scale optimization for evaluation functions with minimax search. J Artif Intell Res 2014;49(49):527–68. Jin Xu received the Ph.D. degrees in electrical engineering from the South East University, Nanjing, China, in 2007. He is currently a Professor in Nanjing Agricultural University. His current research interests include Wireless Power Transformer(WPT), High-frequency switching mode power supply, Control of Buck-Bost DC-DC Converter, soft-switching inverter, high-efficiency power electronics conversions for high power and energy applications. Yuhui Xu is currently working toward the B.S. degree in electrical engineering from the Virginia Polytechnic Institute and State University, Blacksburg, VA, USA. He is a junior student in this school. Since 2017, his research interests include Wireless Power Transformer(WPT), High-frequency switching mode power supply and Control of Buck-Bost DC-DC Converter. Qian Zhang received the B.S. degree from Nanjing Agriculture University, Nanjing, China. He is currently working toward M.S. degree in electrical engineering in Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China. Since 2015, his research interests include soft-switching inverter for renewable energy application, high-efficiency dc/dc converter, and contactless power transfer.