This journal issue contains selected papers from the 2014 IEEE International Magnetics (INTERMAG) ConferenceAP - Power and Control Magnetics Ipublished_or_final_versio

Chau, KT

Ching, TW

Li, F

Liu, C

Zhang, Z

IEEE Transactions on Magnetics

HKU Scholars Hub

Title Quantitative analysis of mutual inductances for optimal wirelesspower transfer via magnetic resonant couplingAuthor(s) Zhang, Z; Chau, KT; Liu, C; Li, F; Ching, TWCitationThe 2014 IEEE International Magnetics (INTERMAG) Conference,Dresden, Germany, 4-8 May 2014. In IEEE Transactions onMagnetics, 2014, v. 50 n. 11, article no. 8600504Issued Date 2014URL http://hdl.handle.net/10722/216933Rights IEEE Transactions on Magnetics. Copyright © Institute ofElectrical and Electronics Engineers.IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014 8600504Quantitative Analysis of Mutual Inductance for Optimal WirelessPower Transfer via Magnetic Resonant CouplingZhen Zhang1, K. T. Chau1, Fellow, IEEE, Chunhua Liu1, Fuhua Li1, and T. W. Ching21Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong2Department of Electromechanical Engineering, University of Macau, Macau, ChinaThis paper presents the quantitative analysis for the optimal design of wireless power transmission (WPT) systems based onmagnetic resonant coupling (MRC) mechanism. In this paper, the exemplified MRC-based WPT system adopts the series–seriestopology and one resonant coil, which shows that the energy efficiency and transferred power are both significantly affected by themutual inductance of the primary-resonant coils and the resonant-secondary coils. In addition, the simulated and experimental resultsare both provided to illustrate the influence of the mutual inductance on the performance of MRC-based WPT systems regulatingthe relative displacement among coils. Thus, this quantitative analysis can offer the significant theoretical and experimental basisfor the optimal design of MRC-based WPT systems in various application fields.Index Terms— Magnetic field analysis, magnetic resonant coupling (MRC), optimization, wireless power transmission (WPT).I. INTRODUCTIONRECENTLY, the wireless power transmission (WPT) tech-nology has made fruitful achievements [1]–[3], whichcan be utilized to various application fields, such as chargingportable electronic devices, implanted medical instruments,integrated circuits, and electric vehicles. This epoch-makingtechnique significantly influences our usage pattern of thetraditional and sustainable energies.In particular, the magnetic resonant coupling (MRC)mechanism has obtained increasing attentions to improvethe transmission performance of WPT systems. In [4], theMRC-based WPT system was experimentally demonstrated,which significantly extends the transmission distance by com-paring with the traditional inductive power transmission. Also,the MRC-based WPT system can fulfill transferring the energyto multiple receptors [5]. In addition, the transfer efficiencyand air-gap length can be maximized using the equivalentcircuit and Neumann formula [6]. In [7], the systematicdesign procedure was proposed to maximize the power trans-fer efficiency for bio-implantable devices. Besides, the char-acteristic of the frequency sensitivity was also utilized toencrypt the energy for improving the security performance ofWPT systems [8]. However, previous studies seldom focuson the matching issue of mutual inductances among coils foroptimal MRC-based WPT systems.This paper deals with the quantitative analysis for theoptimal design of MRC-based WPT systems. By adopting theseries–series topology, the exemplified experimental prototypeis utilized to reveal the influence of the mutual inductanceon the wireless transmission performance, which determinesthe optimal configuration of the relative displacement amongcoils. The presented quantitative analysis offers the theoreticalManuscript received March 6, 2014; revised May 21, 2014 and May 26,2014; accepted June 3, 2014. Date of current version November 18, 2014.Corresponding author: K. T. Chau (e-mail: ktchau@eee.hku.hk).Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMAG.2014.2329298and experimental basis for optimal MRC-based WPT systemsin various application fields.II. MRC-BASED WPT SYSTEMFig. 1 shows the MRC-based WPT system adoptingseries–series topology, which comprises of three basic com-ponents: 1) the primary unit; 2) the resonant unit; and 3) thesecondary unit, where rp , rr , and rs are the internal resistancesof the primary, resonant, and secondary coils, respectively,RL is the load resistance, Cp , Cr , and Cs are the capacitancesof the primary, resonant, and secondary units, respectively, andL p , Lr , and Ls are the inductances of the primary, resonant,and secondary units, respectively.A. Primary UnitThe impedance Z p can be calculated asZ p = jωL p + 1jωCp + rp (1)where ω is the switching frequency of the power supply.Meanwhile, the voltage of the power source Vsource can beexpressed asVsource = Vp + I prp + 1jωCp Ip (2)where Ip as the current of the primary unit, which is normallymaintained at a constant value. The primary coil voltage Vpcan be written asVp = jωL p Ip − jωL pr Ir (3)where L pr is the mutual impedance between the primary andresonant coils and Ir is the current of the resonant unit.B. Resonant UnitThe impedance Zr is given byZr = jωLr + 1jωCr + rr . (4)0018-9464 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.8600504 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014Fig. 1. Schematic view of exemplified MRC-based WPT system.Thus, the current Ir can be calculated based on the inducedpotential by the primary coil, which is given byIr = jωL pr IpZr . (5)C. Secondary UnitThe impedance Zs can be calculated asZs = jωLs + 1jωCs + rs . (6)Similarly, the current Is of the secondary unit can be obtainedfrom the induced potential by the resonant unit, which isgiven byIs = jωLrs IrZs (7)where Lrs denotes the mutual impedance between the resonantand secondary coils. Then, the secondary coil voltage Vs canbe expressed asVs = jωLrs Ir − jωLs Is . (8)Hence, the pickup voltage of the energy receptor Vpickup isgiven byVpickup = Vs − Isrs − 1jωCs Is . (9)In addition, the transferred power relies on the reflectedimpedances to the primary unit, which is given byP = Re (Zrp)I 2p (10)where Zrp is the reflected impedance from the resonant unitto the primary unit. It can be calculated byZrp =ω2 L2prZr + Zsr (11)where Zsr is the reflected impedance from the secondary unitto the resonant unit. It can be expressed asZsr = ω2 L2rsZs + RL . (12)TABLE IPARAMETERS OF THREE COILSThen, the energy efficiency η can be calculated asη = Re(Z p Zr (Zs +RL)+ω2L2rs Z pω2 L2pr (Zs + RL)+Z p Zr (Zs +RL)+ω2L2rs Z p).(13)Since the MRC-based WPT system works at the fixed switch-ing frequency, the transferred power and energy efficiencymainly depend on the mutual inductances among the primary,resonant, and secondary coils.III. SIMULATION RESULTSTo analyze the influence of mutual inductances on theperformance of MRC-based WPT systems, the simulationmodel is set up using MATLAB/SIMULINK. In addition,the electromagnetic field analysis is carried out using JMAG.In the exemplified prototype, the working frequency is chosenas 100 kHz. The corresponding key parameters are listedin Table I, where the coil inductance is directly measuredutilizing the LCR meter (ISO-TECH LCR821).Fig. 2(a) and (b) shows the dimensions of the primaryand resonant coils, where both have a hollow circular shapewith the inside diameter of 125 mm and the outside diameterof 215 mm. The secondary coil has a similar geometry asshown in Fig. 2(c), where the inside and outside diametersequal 50 and 94 mm. As shown in Fig. 2(d), the primary andresonant coils directly face each other. In addition, this papermainly discusses about the impact of the vertical displacementof coils on the optimal MRC-based WPT system based on theconstant horizontal configuration. Consequently, the horizontalZHANG et al.: QUANTITATIVE ANALYSIS OF MUTUAL INDUCTANCE FOR OPTIMAL WPT VIA MRC 8600504Fig. 2. Geometry of MRC-based WPT system. (a) Primary coil dimension.(b) Resonant coil dimension. (c) Secondary coil dimension. (d) Displacementsamong coils.Fig. 3. Simulated magnetic flux density.offset is constantly chosen as 40 mm between centers of theresonant and secondary coils. In the exemplified MRC-basedWPT system, the distance between the primary and resonantcoils is fixed at 160 mm and L pr constantly equals 5.3052 μH.In addition, the Lrs can be varied by regulating the distancelrs between the resonant and secondary coils.When the exemplified MRC-based WPT system worksin the magnetic resonant state, as shown in Fig. 3, theresonant and secondary coils can be effectively excitedand the corresponding flux density reach around 0.25 mT.By regulating lrs to vary Lrs , the numerical simulation verifiesthe influence of the mutual inductance on the transmissionperformance. Specifically speaking, Fig. 4 shows the simulatedload voltage and current, respectively. It illustrates that themaximum values can be obtained when Lrs equals around13.5152 μH. In addition, as shown in Fig. 5, the exemplifiedMRC-based WPT system can reach to the maximum energyefficiency (84.8%) when Lrs equals around 6.6327 μH and themaximum transferred power (31.6 W) when Lrs equals around13.5152 μH. Therefore, the MRC-based WPT system canobtain maximum transferred power and transmission efficiencyFig. 4. Simulated load voltage and current.Fig. 5. Simulated transmission performance.Fig. 6. Prototype of exemplified MRC-based WPT system.by regulating the configuration of mutual inductances accord-ing to various functional requirements.IV. EXPERIMENTAL RESULTAs shown in Fig. 6, the experimental prototype is alsoestablished according to the simulation parameters as listed8600504 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014Fig. 7. Measured load voltage and current.Fig. 8. Experimental transmission performance.in Table I. The power source is provided by the programmableac power supply (Amplifier Research 75A250A). The currentis sensed using a wideband current transducer (TektronixTM502A). In addition, the voltage and power are measuredusing a power analyzer (LeCroy WR6100A).By regulating the distance between the resonant andsecondary coils, the corresponding mutual inductance canbe changed within the range utilized in the aforementionednumerical simulation. Fig. 7 shows the measured load voltageand current, respectively. It shows that the load can obtainthe maximum voltage of 8.7 V and the maximum currentof 1.8 A when Lrs equals around 13.5 μH. In addition,Fig. 8 shows the wireless transmission performance of theexemplified MRC-based WPT system. The maximum energyefficiency can reach around 80.2% when Lrs equals around6.3 μH. In addition, the exemplified WPT system can offerthe maximum transferred power of around 15.3 W whenLrs equals around 13.5 μH. With respect to the varying Lrs ,the measured transferred power and the energy efficiency showthe similar changing trends as the simulated results. It illus-trates that the maximum transferred power and the maximumenergy efficiency can be obtained based on different mutualinductances, which means that the configuration of the coildisplacement is important for the optimal MRC-based WPTsystem in various applications. Therefore, the experimentalresults well agree with the aforementioned theoretical analysisand the simulated results, which quantitatively illustrates thatthe optimal design of MRC-based WPT systems needs toproperly regulating the configuration of mutual inductances.V. CONCLUSIONIn this paper, the quantitative analysis is carried out toillustrate the impact of mutual inductances among the primary,resonant, and secondary coils on the transmission performanceof MRC-based WPT systems. By properly regulating thedisplacement of coils to change the corresponding mutualinductances, the exemplified WPT system can effectivelyachieve the maximum transferred power or energy efficiencyto fulfill various functional requirements. For example, animplanted medical device needs the charging duration as shortas possible. Accordingly, the optimal wireless charging systemcan obtain the maximum transferred power by properly regu-lating the distance between the resonant and secondary coils.Besides, a large-scale charging system desires high-energyefficiency, especially for roadway-powered electric vehicles.Thus, the optimal design is also required to consider themutual inductance between the resonant and secondary coils.Finally, the simulated and experimental results well agree withthe theoretical analysis. Therefore, this paper provides thetheoretical and experimental basis to implement the optimaldesign of MRC-based WPT systems, which can be utilizedto meet different technical requirements for various industrialapplications.ACKNOWLEDGMENTThis work was supported by the Committee on Researchand Conference Grants, University of Hong Kong, Hong Kong,under Project SPF-201109176034.REFERENCES[1] C. Qiu, K. T. Chau, C. Liu, W. Li, and F. Lin, “Quantitative comparisonof dynamic flux distribution of magnetic couplers for roadway electricvehicle wireless charging system,” J. Appl. Phys., vol. 115, no. 17,pp. 17A334-1–17A334-3, May 2014.[2] C. Liu, K. T. Chau, C. Qiu, and F. Lin, “Investigation of energyharvesting for magnetic sensor arrays on Mars by wireless powertransmission,” J. Appl. Phys., vol. 115, no. 17, pp. 17E702-1–17E702-3,May 2014.[3] J. Shin et al., “Design and implementation of shaped magnetic-resonance-based wireless power transfer system for roadway-poweredmoving electric vehicles,” IEEE Trans. Ind. Electron., vol. 61, no. 3,pp. 1179–1192, Mar. 2014.[4] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, andM. Soljacˇic´, “Wireless power transfer via strongly coupled magneticresonances,” Science, vol. 317, no. 5834, pp. 84–86, 2007.[5] B. L. Cannon, J. F. Hoburg, D. D. Stancil, and S. C. Goldstein,“Magnetic resonant coupling as a potential means for wireless powertransfer to multiple small receivers,” IEEE Trans. Power Electron.,vol. 24, no. 7, pp. 1819–1825, Jul. 2009.[6] T. Imura and Y. Hori, “Maximizing air gap and efficiency of magneticresonant coupling for wireless power transfer using equivalent circuitand Neumann formula,” IEEE Trans. Ind. Electron., vol. 58, no. 10,pp. 4746–4752, Oct. 2011.[7] X. Luo, S. Niu, S. L. Ho, and W. N. Fu, “A design method of magnet-ically resonanting wireless power delivery systems for bio-implantabledevices,” IEEE Trans. Magn., vol. 47, no. 10, pp. 3833–3836, Oct. 2011.[8] Z. Zhang, K. T. Chau, C. Qiu, and F. Lin, “An efficient wirelesspower transfer system with security considerations for electric vehicleapplications,” J. Appl. Phys., vol. 115, no. 17, pp. 17A328-1–17A328-3,May 2014.

Quantitative analysis of mutual inductance for optimal wireless power transfer via magnetic resonant coupling

Zhen Zhang

K. T. Chau

Chunhua Liu

Fuhua Li

T. W. Ching

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Quantitative Analysis of Mutual Inductance for Optimal Wireless Power Transfer via Magnetic Resonant Coupling

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Quantitative analysis of mutual inductances for optimal wireless power transfer via magnetic resonant coupling

Quantitative analysis of mutual inductances for optimal wireless power transfer via magnetic resonant coupling

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