research article modelling and practical implementation of 2 ...-coil power transfer system is...

Research ArticleModelling and Practical Implementation of 2-Coil WirelessPower Transfer Systems

Hong Zhou Bin Zhu Wenshan Hu Zhiwei Liu and Xingran Gao

Department of Automation School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China

Correspondence should be addressed to Wenshan Hu wenshanhuwhueducn

Received 4 April 2014 Revised 8 August 2014 Accepted 21 August 2014 Published 3 September 2014

Academic Editor Adam Panagos

Copyright copy 2014 Hong Zhou et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Wireless power transfer (WPT) based on inductive coupling could be potentially applied in many practical applications It hasattracted a lot of research interests in the last few years In this paper the modelling design and implementation of a 2-coil WPTsystem are represented The prototype system can be implemented using conventional power electronic devices such as MOSFETswith very low costs as it works in relative low frequency range (less than 1MHz) In order to find out about the optimal working areafor the WPT system the circuit model based on the practical parameters from the prototype is built The relationships betweenthe exciting frequency coupling and output power are analyzed based on the circuit and magnetic principles Apart from thetheoretic study the detailed implementation of the WPT prototype including the coil design digital frequency generation andhigh frequency power electronics is also introduced in this paper Experiments are conducted to verify the effectiveness of thecircuit analysis By carefully tuning the circuit parameters the prototype is able to deliver 20W power through 22 meter distancewith 20ndash30 efficiency

1 Introduction

Wireless power transfer (WPT) technology can be potentiallyused inmany industrial applications in case that the intercon-necting wires are inconvenient dangerous or even impossi-ble It has attracted much of research attention in the last fewyears There are several WPT techniques being researchedpresently Far-field techniques use propagating electromag-netic waves that transfer energy the same way radiostransmit signals but with much bigger transmission power[1] Inductive coupling (or near-field) techniques operate atdistances less than a wavelength of the signal being trans-mitted which operates at a relative low frequency comparingwith the far-field methods [2]

The early research and analysis of inductive coupling[3 4] are mainly based on the pure physical theories whichcould be difficult for the researchers from electrical engi-neering background to fully understand Recent researches[5ndash7] start to use circuit and magnetic theory to study thefundamental principle of the magnetic resonance couplingwhich makes the technology more tangible for a wider range

of researchers especially for electrical and electronics engi-neers

Potentially inductive coupling WPT systems can be usedin many industrial applications such as power supplies formoving sensors and transducers [8] medical implants [9 10]and wireless electric car charging stations [11]

In power industry due to the importance of high voltage(HV) cables in the transmission network on-site conditionmonitoring is a very important issue [12 13] However thepower supply is always a major problem for the reliabil-ity of the monitoring devices which operate in the harshoutdoor environment with no reliable power sources Someapplications try to use the solar and wind power to solvethe problem but these power sources are not guaranteed incase of continuous bad weather condition which could occurfrequently in some places like the mountain areas in SouthWest China

However using the WPT technology a tiny amount ofthe power can be harvested from the magnetic field aroundthe HV power cables using induction coils and then trans-ferred through the insulator (a fewmeters distance) to power

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2014 Article ID 906537 8 pageshttpdxdoiorg1011552014906537

2 Journal of Electrical and Computer Engineering

the monitoring devices installed on the towers which couldbe the potential solution for the problem For this kindof applications the key requirement is to deliver sufficientpower to the load with relative high power transfer efficiency(PTE) and considerable distance Robustness and reliabilitiesare also important issues especially for case of the HV cablesmonitoring

There are many configurations ofWPT system developedrecently including the 2-coil [14 15] 3-coil [16] and 4-coil[17 18] links The multicoil structures are able to increase thePTE in some cases but the price is the increasing complexityof the system structure Each coil has its own parameters suchas resistance inductance and capacitance Some parametersmay be sensitive to the external environment like temperatureand humidity More coil loops mean that more tuningwork is required to get all the parameters aligned It couldbe difficult to maintain the optimal performance in someharsh environment for the practical applications Balancingthe performance complexity and reliability the simple 2-coil structure may be the best option for some industrialapplications

In [14] the optimum design of an inductively coupled2-coil power transfer system is studied using the conjugateimage impendence theory [15] Theoretically the optimumparameters of WPT systems can be calculated to maximumpower transfer However in some applications it could bedifficult or costly to change the intrinsic circuit parameterswhich is required by the theory

In this paper a WPT solution could be potentially usedfor HV power cable monitoring is introduced In order tooptimize the working conditions the circuit models with thepractical parameters are analyzed and simulated Based onthe theoretical study aWPT prototype designed for practicalHV power cable monitoring is set up It is able to deliver20W power for a distance of 22m As it is designed for thepractical applications the resonant frequency is reduced toseveral hundred kilohertz which are within the ranges ofconventional power electronics components such MOSFETsIt can be easily commercialized as all the power electriccomponents can be purchased with low costs

2 Circuit and Magnetic Principle of2-Coil WPT Systems

21 Optimal Circuit Model Figure 1 shows the equivalentcircuit model of the 2-coil WPT system using magneticallycoupled resonator where the coil systemwith self-inductance1198711and 119871

2 mutual inductance 119872 and copper loss 119903

1and

1199032 As both coils are air core inductors the iron loss is

not considered Both Tx and Rx coils are connected to theresonant capacitors 119862

1and 119862

2 1198771198881and 119877

1198882are the parasitic

resistance of1198621and119862

2 119903119901is the impendence of theACpower

source 119877119871is the load resistance of the output

For the system shown in Figure 1 the optimal parameterswhich maximize the wireless power transfer are analyzed in

Rc1 C1

rp

AC

r1

L1 minus M L1 minus M

M

r2 C2

Rc2

RL

Figure 1 Equivalent circuit model of two-coil WPT system

Table 1 Circuit parameters

Parameter Value1198711 1198712

298 uH1198621 1198622

200 pF1199031 1199032

2Ω119903119901

2Ω1198771198881 1198771198882

3Ω119877119871

7Ω119896 00001 to 01AC voltage 30VAC frequency 620 kHz to 680 kHz

[14] For a given coil system the optimal loading capacitanceand port impendence are calculated as

1198771199041= 1199031radic1 +

(120596119872)2

11990311199032

(1)

1198771199042= 1199032radic1 +

(120596119872)2

11990311199032

(2)

1198621=

1

12059621198711

(3)

1198622=

1

12059621198712

(4)

where 1198771199041is the sum of 119903

119901and 119877

1198881 1198771199042is the sum of 119877

1198882and

119877119871 Equations (1) and (2) represent the resistance matching

condition and (3) and (4) depict the resonance conditionFrom (3) and (4) it can be seen that in order to maximize thepower transmission the two coils on both sides are requiredto work at the resonant frequency as

1205960= radic119871

11198621= radic119871

21198622 (5)

Theoretically (1)ndash(4) are able to find out the optimumparameters elegantly However in practical applications as1198771198881 1198771198882 and 119903

119901are parasitic values there is little flexibility

for engineers to actually choose circuit parameters for theresistance matching For a given WPT system 119877119888

1 1198771198882 119877119901

and 119877119871are fixed values where it is not possible or convenient

to change them

22 Practical Circuit Model An experimental test rig whosemeasured circuit parameters are listed in Table 1 is set up

Journal of Electrical and Computer Engineering 3

in the laboratory Both Tx and Rx sides have the sameinductance and capacitance so they share the same resonantfrequency as required in (5) However for the resistance partthere is little flexibility for the parameter changes All theresistance values such as 119903

1 1199032 1198771198881 and 119877

1198882are the practical

measurement from the test rigNormally the distance between the two coils can be

several times of the coil radius which makes the couplingcoefficient 119896 a very small value around 0001 to 001 Only asmall amount of the flux generated by Tx coil is able to gothrough the Rx coil However a large amount of magneticenergy can still be transferred through the limited amountof flux with relatively high efficiency (around 20 to 30)when the Rx and Tx coils are in the resonant state Thisphenomenon can be explained by the circuit and magnetictheory

The two-coil model depicted in Figure 1 can be analyzedusing Kirchhoff rsquos voltage law (KVL) as follows

1198681(1198771+ 119895120596119871

1+

1

1198951205961198621

) + 1198951205961198682119872 = 119881

119904 (6)

1198682(1198772+ 119895120596119871

2+

1

1198951205961198622

) + 1198951205961198681119872 = 0 (7)

where

1198771= 1198771198881+ 1199031+ 119877119901

1198772= 1198771198882+ 1199032+ 119877119871

(8)

and the 119872 is the mutual inductance between Tx and Rxcoils The relationship between the mutual inductance andcoupling coefficient is defined as

119872 = 119896radic11987111198712 (9)

In order to simplify the the two circuit equations (6) and(7) 1198851and 119885

2are defined as the impendence of both circuit

loops as follows

1198851= 1198771+ 119895120596119871

1+

1

1198951205961198621

1198852= 1198772+ 119895120596119871

2+

1

1198951205961198622

(10)

The two KVL equations (6) and (7) can be solved as

1198681=

1198852119881119904

11988511198852+ 12059621198722

1198682= minus

11989512059611987212119881119904

11988511198852+ 12059621198722

(11)

Therefore the input power119875119868which energizes the Tx coil and

output power 119875119874which are consumed on the load 119877

119871can be

calculated as

119875119868=10038161003816100381610038161198811199041198681

1003816100381610038161003816 cos (ang119881119904 minus ang1198681) 119875119874=100381610038161003816100381610038161198771198711198682

2

10038161003816100381610038161003816 (12)

25

20

15

10

5

0006

004

002

0

Pow

er (W

)

Over coupledUndercoupled

kc62

64

6668

times105

Frequency (Hz)

Coupling coefficient k

f0004

002

Over coupledpledOv r dUnncoucou

kkkc 64

666

timesy (Hz)coeffici

f0ff

Figure 2 Output power 119875119874as a function of frequency and coupling

coefficient 119896 using the parameter given in Table 1

The overall WPT efficiency is

119864 =119875119874

119875119868

=1198771198711198682

2

100381610038161003816100381611988111990411986811003816100381610038161003816 cos (ang119881119904 minus ang1198681)

(13)

Using data in Table 1 the output power against theexciting frequency and coupling coefficient can be plotted inFigure 2 When the coil distance is small and coupling coeffi-cient between the two coils is big theWPT works in the overcoupled regime as marked in Figure 2 Frequency splittingcan be clearly observed as there are two peak output powersWhen the coupling between the two coils decreases with theincrement of the distance the systemgoes into the under cou-pled regime The frequency separation between the two peakvalues decreases until they converge at a single frequency119891119904= 1198910(1 minus 119896

2)14 where 119891

0is the resonant frequency of

both coils [14]

23 Analysis of Practical Parameters Due to the relative longdistance between the two coils the coupling efficient 119896 is verysmall (0001 to 001)Therefore119891

0can be considered as a close

approximation of 119891119904

In practical applications without loss of too much accu-racy technically it can be considered the two-split frequencymerged at the resonant frequency 119891

0when the coupling is 119896

119888

as marked in Figure 2 For a practical WPT system with high119876 coils 119896

119888can be considered as the critical point between the

over coupled and under coupled regimesFor practical system the circuit parameters for Tx and Rx

coils need to be aligned in order to get the maximum WPTpower and efficiency which means that

1198711= 1198712 119862

1= 1198622 120596

1198881= 1205961198882 (14)

where 1205961198881and 120596

1198882are the angular resonant frequency for the

Tx and Rx coils respectively The resistance on the Rx side isnormally bigger than that on the Tx side as the load resistanceis connected in serial with the coil circuits


0

20

40

00010020030040050

50

100

Out

put p

ower

(W)

Effici

ency

()

Pmax

Coupling k kc

Output powerEfficiency

Figure 3 Output power and efficiency when 119891 = 1198910

From the engineering point of view 1198910can be used as a

very close approximation to 119891119904without inducing big calcula-

tion errorsTherefore theWPT system at resonant frequencycan be analyzed to find out the optimal operating area When119891 = 119891

0 both the power 119875

119874and efficiency 119864 against coupling

119896 are plotted in Figure 3 It can be seen that the overallefficiency drops when the coupling 119896 is decreased Howeverthe output power increases with the decreasing coupling119896 at the beginning until it reaches the peak value 119875maxThen it drops dramatically with the decrease of the coupling

To simplify the analysis it is assumed that both the Txand Rx loops have the same inductance and capacitance as119871 = 119871

1= 1198712and 119862 = 119862

1= 1198622 The resonant frequency for

both of the two coils is

1205960=

1

radic119871119862

(15)

When 120596 = 1205960 combining (11) (12) and (15) the output

power can be obtained as

119875119874

1003816100381610038161003816120596=1205960= 119877119871

(1119862) 11989621198711198812

119904

(11987711198772+ (1119862) 119896

2119871)2 (16)

In order to get corresponding value of coupling 119896119888at the

maximum power the derivative of (16) is taken with respectto 119896 By setting the result to zero and solving the equation 119896

119888

is obtained as

119896119888= radic

11987711198772119862

119871 (17)

For the two coils their series quality factor is defined as

1198761=

1

1198771

radic119871

119862 119876

2=

1

1198772

radic119871

119862 (18)

Combining (17) and (18) the relationship between 119896119888and the

quality factors is

119896119888=

1

radic11987611198762

(19)

The coupling 119896 is roughly reversely proportional to thethird power of the coil distance In order to get the maximumpower at long distance 119896

119888should be as small as possible

which means that 119876 factors of both coils are very importantparameters for the performance of the WPT However high119876 coils are very difficult to make due to the limitation of coilsize material and so forth For the case that the distance isseveral times of the coil diameter normally the operating areais around the critical point as shown in the shadowed area inFigure 3

3 Practical Implementation of WPT Systems

There are many existing WPT systems which successfullydemonstrated the potential of the new technology in recentyears However most of them are working with very highfrequency around 10MHz which is far beyond the capacityof the normal switching power electronics such as IGBTsand MOSFETs Therefore for a WPT system which can beeasily manufactured using the normal power electronic com-ponents the switching frequency must be lower than 1MHz(for MOSFETs)

31 General Structure Figure 4 is the diagramof the practicalapplication of the proposed WPT system A DDS (directdigital synthesizer) module AD9850 controlled by a MCU(microcontroller unit) controller is adopted to generate theaccurate square wave exciting signal The frequency signal isamplified by a gate driver module and then drives aMOSFETH-bridge to generate a high frequencyACTheTx coil is ener-gized by theAC and transmits the power to theRx coil thoughthe inductive coupling The high frequency AC is rectifiedto DC using bridge rectifier on the Rx sideThe DC is filteredby capacitors before it drives the load

32 Coil Design In order to get a less than 1MHz resonantfrequency for the Tx and Rx coils both the inductance andcapacitance need to be significantly bigger than the highfrequency onesThe radius of the two coils is 20 cmThey arewinded by 19 turns using Litz cable with 500 strands whichforms inductance of 298 uH

Low resonant frequency requires bigger capacitance aswell as big inductance whichmeans the parasitic capacitanceof the coil winding itself is not big enough and add-oncapacitors connected in serial with the winding are necessaryFrom (12) it is clear that lower capacitance can increase the119876 factor of the circuit and improve the performance of thesystem However capacitors with small capacitance normallyinduce bigger parasitic resistance which affects the 119876 factoron an opposite way In some cases capacitors need to beconnected in parallel to get smaller paralytic resistance at theexpense of bigger capacitance

Figure 5 is the circuit model for a practical coil designin which more than one high voltage ceramic capacitor isconnected in parallel to decrease the overall parasitic resis-tance The overall parasitic resistance is

119877coil =1

119899119877119888+ 119877119871 (20)


Rc1

Rp1 Rp2

C1

rp

r1L1 minus M L1 minus M

M

r2 C2

Rc2

RL

S1

S2

Vd

+

minus

D1

D2

D3

D4

S3

S4

Controller DDSfrequencygeneration

To S2 and S3

To S1 and S4

Figure 4 Diagram of the practical implementation

Rc1

Rc2

C1

C2

RcnCn

L

RL

AC

Figure 5 Circuit model for parallel connected capacitors

where 119877119888is the parasitic resistance for each individual

capacitor and the overall capacitance is

119862coil = 119899119862 (21)

Therefore the 119876 factor of the coil can be calculated as

119876coil =1

119877coilradic119871coil119862coil

=119899

119877119888

radic119871coil

119899119862 + 119877119871

(22)

For a given type of capacitor the number of the capacitors119899 needs to be calculated and balanced in order to getthe optimal 119876 factor In this case two 100 pFHV ceramiccapacitors are connected in serial to get the best performanceTogether with the 298 uHwinding inductance the resonancefrequency for both of the two coils is around 642 kHz

33 Frequency Generation Because of the high 119876 factors ofthe coils the WPT is very sensitive to the frequency driftingand jigging A small variation of inciting frequency couldresult in significant performance drop which can be seen inFigure 2 Conventional analog signal generation cannot meetthe precision requirement of the WPT system Thereforea digital method based on direct digital synthesizer (DDS)technology is selected as the solution

Figure 6 DDS frequency generation with MCU

Figure 7 High frequency inverter

A direct digital synthesizer (DDS) module AD9850 con-trolled by aMCU (microcontroller unit) as shown in Figure 6is adopted to generate the accurate square wave excitingsignal Using the keyboard on theMCU controller the outputfrequency can be tuned from 01ndash1MHz with the step sizeof 10Hz The output square wave is highly stable comparedwith the analog circuit due to the explicit advantages of digitalfrequency generation

34 High Frequency Inverter and Rectifier The coil designmakes the whole WPT system switch at 642 kHz which iswithin the range ofUltra-fastMOSFETAMOSFETH-bridgeis built to amplify the high frequency signal generated by theDDSmodule and energizes the Tx coil to transmit the electricpower


(a) (b)

(c)

Figure 8 Picture of the WPT system (a) Coil structure (b) Power electronics (c) Test rig

Assuming the DC input of the inverter is 119881119904and using

Fourier expansion the square wave AC output put can berepresented in infinite serials of the form

119881square

=4119881119904

120587(sin (2120587119891119905) + 1

3sin (6120587119891119905) + 1

5sin (10120587119891119905) sdot sdot sdot )

(23)

where the square wave is transformed into a serial of sinu-soidal waves with different aptitudes and frequency

From Figure 2 it can be seen that only the signals a verynarrow band of the frequency are able to pass through theWPT systemand the gain for other frequencies is significantlylow The WPT system actually operates like a very sensitiveband pass filter Even though the H-bridge inverter can onlygenerate square waves only the fundamental frequency isable to go through and other parasitic frequencies are cut offTherefore the theoretical analysis based on the AC source isstill applicable for the case of H-bridge inverters

Figure 7 is the picture of the inverter in which four Ultra-fast MOSFET IRF740s forms the H-bridge The H-bridge isdriven by two half-bridge gate driver IR2110 IR2110 has abuild-in dead-band of 10 ns It is expanded to 50 ns to preventthe possible shoot-though because of the high speed switch-ing On the Rx side due to the high working frequency con-ventional diodes are not fast enough to rectify high frequencyACwithout inducing significant lossesTherefore the electricenergy received by the coil is rectified to DC by a high speedbridge rectifier made of Shockley diodes Shockley diodeshave very small reverse recovery time (less than 50 ns) whichreduces the loss greatly at the high working frequency

4 Experimental Results

The radius of the both coils is 20 cm and the distance betweenthe two coils is 22m On the Rx side a bulb which is selectedas the load is illuminated using the energy received from themagnetic resonance as shown in Figure 8



Frequency Load voltage Load current Power Efficiency638 kHz 6V 083A 50W 112639 kHz 10V 139A 139W 238640 kHz 119 V 165A 196W 269641 kHz 121 V 168A 203W 280642 kHz 12V 166A 199W 278643 kHz 121 V 168A 203W 275644 kHz 115 V 160A 184W 265645 kHz 9V 125A 113W 224646 kHz 55 V 076A 42W 96

0

5

10

15

20

25

Pow

er (W

)

638 639 640 641 642 643 644 645 6460

20

40

60

80

100

Effici

ency

()

PowerEfficiency

Figure 9 Experimental results

The power supply for WPT prototype is a 40V 5A DCpower source The resonant frequencies of the Tx and Rxcoils are well matched by adjusting both circuits carefullyThe input power load voltage and load current aremeasuredTherefore both the output power and overall efficiency (withthe loss on the power electronics) can be calculated Theexperimental results are shown in Table 2 Both the outputpower and efficiency against the frequency are plotted inFigure 9 It can be seen that high transfer efficiency (morethan 20) can be maintained for a quite wide range from639 kHz to 645 kHz

Because the coupling is bigger than the critical value119896119888 the output power does not reach the maximum at the

resonant frequency when the resonant frequencies are wellaligned The frequency splitting can be observed clearly asthere are two peaks for the output power which are placed onboth sides of 119891

0 which is indicated from the circuit analysis

in Section 2

5 Conclusion and Future Work

In this paper the circuit modelling and implementation ofa practical 2-coil WPT system have been introduced Using

the circuit theory the relationship between the circuit param-eters coupling coefficient power transfer and efficiency areanalyzed The optimal working area balancing the efficiencyand distance is recommended based on the analysis In orderto verify theWPT proposed circuit theories a practical WPTprototype is designed and implemented in this paper Thedetailed structure of the prototype including the Tx andRx coils frequency generation and high frequency powerelectronics has also been explained in this paper

Using the prototype theWPTexperiments at the distanceof 22m are conductedThe experiments results show that theWPT prototype can achieve 20W power transfer at relativehigh overall efficiency (more than 20)The voltage splittingphenomenon can be clearly observed as it is predicted fromthe theoretical analysis

Since all the components utilized to build the prototypeare made of normal electric and electronics componentswhich can be purchased easily from the market with verylow costs there is great potential for the prototype to becommercialized in the future

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research was supported by the National Science Founda-tion of China under Grant 61374064 and 61304152

References

[1] A P Sample D J Yeager P S Powledge A V Mamishev and JR Smith ldquoDesign of anRFID-based battery-free programmablesensing platformrdquo IEEE Transactions on Instrumentation andMeasurement vol 57 no 11 pp 2608ndash2615 2008

[2] A Kurs A Karalis R Moffatt J D Joannopoulos P Fisherand M Soljacic ldquoWireless power transfer via strongly coupledmagnetic resonancesrdquo Science vol 317 no 5834 pp 83ndash862007

[3] A Karalis J D Joannopoulos and M Soljacic ldquoEfficientwireless non-radiative mid-range energy transferrdquo Annals ofPhysics vol 323 no 1 pp 34ndash48 2008


[4] R E Hamam A Karalis J D Joannopoulos and M SoljacicldquoEfficient weakly-radiative wireless energy transfer an EIT-likeapproachrdquoAnnals of Physics vol 324 no 8 pp 1783ndash1795 2009

[5] Z N Low R A Chinga R Tseng and J Lin ldquoDesign and testof a high-power high-efficiency loosely coupled planar wire-less power transfer systemrdquo IEEE Transactions on IndustrialElectronics vol 56 no 5 pp 1801ndash1812 2009

[6] L Chen S Liu Y C Zhou and T J Cui ldquoAn optimizable circuitstructure for high-efficiency wireless power transferrdquo IEEETransactions on Industrial Electronics vol 60 no 1 pp 339ndash3492013

[7] M Kiani and M Ghovanloo ldquoThe circuit theory behindcoupled-modemagnetic resonance-basedwireless power trans-missionrdquo IEEE Transactions on Circuits and Systems I RegularPapers vol 59 no 9 pp 2065ndash2074 2012

[8] J de Boeij E Lomonova J L Duarte and A J A VandenputldquoContactless power supply for moving sensors and actuatorsin high-precision mechatronic systems with long-stroke powertransfer capability in x-y planerdquo Sensors and Actuators APhysical vol 148 no 1 pp 319ndash328 2008

[9] P Li and R Bashirullah ldquoA wireless power interface forrechargeable battery operated medical implantsrdquo IEEE Trans-actions on Circuits and Systems II Express Briefs vol 54 no 10pp 912ndash916 2007

[10] P Si A P Hu S Malpas and D Budgett ldquoA frequency controlmethod for regulating wireless power to implantable devicesrdquoIEEETransactions on Biomedical Circuits and Systems vol 2 no1 pp 22ndash29 2008

[11] J L Villa J Sallan A Llombart and J F Sanz ldquoDesign of ahigh frequency inductively coupled power transfer system forelectric vehicle battery chargerdquo Applied Energy vol 86 no 3pp 355ndash363 2009

[12] S Jones G Bucea A McAlpine et al ldquoCondition monitoringsystem for TransGrid 330kV power cablerdquo in Proceedings of theInternational Conference on Power System Technology (POWER-CON rsquo04) pp 1282ndash1287 Singapore November 2004

[13] E Gulski P Cichecki J J Smit P P Seitz B Quak and Fde Vries ldquoOn-site condition monitoring of HV power cablesup to 150kVrdquo in Proceedings of the International Conference onCondition Monitoring and Diagnosis (CMD rsquo08) pp 1199ndash1202April 2008

[14] N Inagaki ldquoTheory of image impendence matching for induc-tively coupled power transfer systemsrdquo IEEE Transactions onMicrowave Theory and Techniques vol 62 pp 901ndash908 2014

[15] R Roberts ldquoConjugate-image impendencesrdquo Proceeding of theIRE vol 34 no 4 pp 198ndash204 1946

[16] M Kiani U-M Jow and M Ghovanloo ldquoDesign and opti-mization of a 3-coil inductive link for efficient wireless powertransmissionrdquo IEEE Transactions on Biomedical Circuits andSystems vol 5 no 6 pp 579ndash591 2011

[17] A P Sample D A Meyer and J R Smith ldquoAnalysis experi-mental results and range adaptation of magnetically coupledresonators for wireless power transferrdquo IEEE Transactions onIndustrial Electronics vol 58 no 2 pp 544ndash554 2011

[18] T C Beh M Kato T Imura S Oh and Y Hori ldquoAutomatedimpedance matching system for robust wireless power transfervia magnetic resonance couplingrdquo IEEE Transactions on Indus-trial Electronics vol 60 no 9 pp 3689ndash3698 2013

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the monitoring devices installed on the towers which couldbe the potential solution for the problem For this kindof applications the key requirement is to deliver sufficientpower to the load with relative high power transfer efficiency(PTE) and considerable distance Robustness and reliabilitiesare also important issues especially for case of the HV cablesmonitoring

There are many configurations ofWPT system developedrecently including the 2-coil [14 15] 3-coil [16] and 4-coil[17 18] links The multicoil structures are able to increase thePTE in some cases but the price is the increasing complexityof the system structure Each coil has its own parameters suchas resistance inductance and capacitance Some parametersmay be sensitive to the external environment like temperatureand humidity More coil loops mean that more tuningwork is required to get all the parameters aligned It couldbe difficult to maintain the optimal performance in someharsh environment for the practical applications Balancingthe performance complexity and reliability the simple 2-coil structure may be the best option for some industrialapplications

In [14] the optimum design of an inductively coupled2-coil power transfer system is studied using the conjugateimage impendence theory [15] Theoretically the optimumparameters of WPT systems can be calculated to maximumpower transfer However in some applications it could bedifficult or costly to change the intrinsic circuit parameterswhich is required by the theory

In this paper a WPT solution could be potentially usedfor HV power cable monitoring is introduced In order tooptimize the working conditions the circuit models with thepractical parameters are analyzed and simulated Based onthe theoretical study aWPT prototype designed for practicalHV power cable monitoring is set up It is able to deliver20W power for a distance of 22m As it is designed for thepractical applications the resonant frequency is reduced toseveral hundred kilohertz which are within the ranges ofconventional power electronics components such MOSFETsIt can be easily commercialized as all the power electriccomponents can be purchased with low costs

2 Circuit and Magnetic Principle of2-Coil WPT Systems

21 Optimal Circuit Model Figure 1 shows the equivalentcircuit model of the 2-coil WPT system using magneticallycoupled resonator where the coil systemwith self-inductance1198711and 119871

2 mutual inductance 119872 and copper loss 119903

1and

1199032 As both coils are air core inductors the iron loss is

not considered Both Tx and Rx coils are connected to theresonant capacitors 119862

1and 119862

2 1198771198881and 119877

1198882are the parasitic

resistance of1198621and119862

2 119903119901is the impendence of theACpower

source 119877119871is the load resistance of the output

For the system shown in Figure 1 the optimal parameterswhich maximize the wireless power transfer are analyzed in

Rc1 C1

rp

AC

r1

L1 minus M L1 minus M

M

r2 C2

Rc2

RL

Figure 1 Equivalent circuit model of two-coil WPT system


Parameter Value1198711 1198712

298 uH1198621 1198622

200 pF1199031 1199032

2Ω119903119901

2Ω1198771198881 1198771198882

3Ω119877119871

7Ω119896 00001 to 01AC voltage 30VAC frequency 620 kHz to 680 kHz

[14] For a given coil system the optimal loading capacitanceand port impendence are calculated as

1198771199041= 1199031radic1 +

(120596119872)2

11990311199032

(1)

1198771199042= 1199032radic1 +

(120596119872)2

11990311199032

(2)

1198621=

1

12059621198711

(3)

1198622=

1

12059621198712

(4)

where 1198771199041is the sum of 119903

119901and 119877

1198881 1198771199042is the sum of 119877

1198882and

119877119871 Equations (1) and (2) represent the resistance matching

condition and (3) and (4) depict the resonance conditionFrom (3) and (4) it can be seen that in order to maximize thepower transmission the two coils on both sides are requiredto work at the resonant frequency as

1205960= radic119871

11198621= radic119871

21198622 (5)

Theoretically (1)ndash(4) are able to find out the optimumparameters elegantly However in practical applications as1198771198881 1198771198882 and 119903

119901are parasitic values there is little flexibility

for engineers to actually choose circuit parameters for theresistance matching For a given WPT system 119877119888

1 1198771198882 119877119901

and 119877119871are fixed values where it is not possible or convenient

to change them

22 Practical Circuit Model An experimental test rig whosemeasured circuit parameters are listed in Table 1 is set up



1 1199032 1198771198881 and 119877





1198681(1198771+ 119895120596119871

1+

1

1198951205961198621

) + 1198951205961198682119872 = 119881

119904 (6)

1198682(1198772+ 119895120596119871

2+

1

1198951205961198622

) + 1198951205961198681119872 = 0 (7)

where

1198771= 1198771198881+ 1199031+ 119877119901

1198772= 1198771198882+ 1199032+ 119877119871

(8)


119872 = 119896radic11987111198712 (9)



loops as follows

1198851= 1198771+ 119895120596119871

1+

1

1198951205961198621

1198852= 1198772+ 119895120596119871

2+

1

1198951205961198622

(10)


1198681=

1198852119881119904

11988511198852+ 12059621198722

1198682= minus

11989512059611987212119881119904

11988511198852+ 12059621198722

(11)



119871can be

calculated as

119875119868=10038161003816100381610038161198811199041198681

1003816100381610038161003816 cos (ang119881119904 minus ang1198681) 119875119874=100381610038161003816100381610038161198771198711198682

2

10038161003816100381610038161003816 (12)

25

20

15

10

5

0006

004

002

0

Pow

er (W

)


kc62

64

6668

times105

Frequency (Hz)


f0004

002


kkkc 64

666

timesy (Hz)coeffici

f0ff




119864 =119875119874

119875119868

=1198771198711198682

2

100381610038161003816100381611988111990411986811003816100381610038161003816 cos (ang119881119904 minus ang1198681)

(13)


2)14 where 119891


both coils [14]






119888





1198711= 1198712 119862

1= 1198622 120596

1198881= 1205961198882 (14)

where 1205961198881and 120596




0

20

40

00010020030040050

50

100

Out

put p

ower

(W)

Effici

ency

()

Pmax

Coupling k kc










1= 1198712and 119862 = 119862



1205960=

1

radic119871119862

(15)



119875119874

1003816100381610038161003816120596=1205960= 119877119871

(1119862) 11989621198711198812

119904

(11987711198772+ (1119862) 119896

2119871)2 (16)



119888

is obtained as

119896119888= radic

11987711198772119862

119871 (17)


1198761=

1

1198771

radic119871

119862 119876

2=

1

1198772

radic119871

119862 (18)


quality factors is

119896119888=

1

radic11987611198762

(19)










119877coil =1

119899119877119888+ 119877119871 (20)


Rc1

Rp1 Rp2

C1

rp


M

r2 C2

Rc2

RL

S1

S2

Vd

+

minus

D1

D2

D3

D4

S3

S4


To S2 and S3

To S1 and S4


Rc1

Rc2

C1

C2

RcnCn

L

RL

AC




119862coil = 119899119862 (21)


119876coil =1


=119899

119877119888

radic119871coil

119899119862 + 119877119871

(22)








(a) (b)

(c)




119881square

=4119881119904

120587(sin (2120587119891119905) + 1

3sin (6120587119891119905) + 1


(23)









0

5

10

15

20

25

Pow

er (W

)

638 639 640 641 642 643 644 645 6460

20

40

60

80

100

Effici

ency

()

PowerEfficiency






in Section 2








Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1 1199032 1198771198881 and 119877





1198681(1198771+ 119895120596119871

1+

1

1198951205961198621

) + 1198951205961198682119872 = 119881

119904 (6)

1198682(1198772+ 119895120596119871

2+

1

1198951205961198622

) + 1198951205961198681119872 = 0 (7)

where

1198771= 1198771198881+ 1199031+ 119877119901

1198772= 1198771198882+ 1199032+ 119877119871

(8)


119872 = 119896radic11987111198712 (9)



loops as follows

1198851= 1198771+ 119895120596119871

1+

1

1198951205961198621

1198852= 1198772+ 119895120596119871

2+

1

1198951205961198622

(10)


1198681=

1198852119881119904

11988511198852+ 12059621198722

1198682= minus

11989512059611987212119881119904

11988511198852+ 12059621198722

(11)



119871can be

calculated as

119875119868=10038161003816100381610038161198811199041198681

1003816100381610038161003816 cos (ang119881119904 minus ang1198681) 119875119874=100381610038161003816100381610038161198771198711198682

2

10038161003816100381610038161003816 (12)

25

20

15

10

5

0006

004

002

0

Pow

er (W

)


kc62

64

6668

times105

Frequency (Hz)


f0004

002


kkkc 64

666

timesy (Hz)coeffici

f0ff




119864 =119875119874

119875119868

=1198771198711198682

2

100381610038161003816100381611988111990411986811003816100381610038161003816 cos (ang119881119904 minus ang1198681)

(13)


2)14 where 119891


both coils [14]






119888





1198711= 1198712 119862

1= 1198622 120596

1198881= 1205961198882 (14)

where 1205961198881and 120596




0

20

40

00010020030040050

50

100

Out

put p

ower

(W)

Effici

ency

()

Pmax

Coupling k kc










1= 1198712and 119862 = 119862



1205960=

1

radic119871119862

(15)



119875119874

1003816100381610038161003816120596=1205960= 119877119871

(1119862) 11989621198711198812

119904

(11987711198772+ (1119862) 119896

2119871)2 (16)



119888

is obtained as

119896119888= radic

11987711198772119862

119871 (17)


1198761=

1

1198771

radic119871

119862 119876

2=

1

1198772

radic119871

119862 (18)


quality factors is

119896119888=

1

radic11987611198762

(19)










119877coil =1

119899119877119888+ 119877119871 (20)


Rc1

Rp1 Rp2

C1

rp


M

r2 C2

Rc2

RL

S1

S2

Vd

+

minus

D1

D2

D3

D4

S3

S4


To S2 and S3

To S1 and S4


Rc1

Rc2

C1

C2

RcnCn

L

RL

AC




119862coil = 119899119862 (21)


119876coil =1


=119899

119877119888

radic119871coil

119899119862 + 119877119871

(22)








(a) (b)

(c)




119881square

=4119881119904

120587(sin (2120587119891119905) + 1

3sin (6120587119891119905) + 1


(23)









0

5

10

15

20

25

Pow

er (W

)

638 639 640 641 642 643 644 645 6460

20

40

60

80

100

Effici

ency

()

PowerEfficiency






in Section 2








Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

20

40

00010020030040050

50

100

Out

put p

ower

(W)

Effici

ency

()

Pmax

Coupling k kc










1= 1198712and 119862 = 119862



1205960=

1

radic119871119862

(15)



119875119874

1003816100381610038161003816120596=1205960= 119877119871

(1119862) 11989621198711198812

119904

(11987711198772+ (1119862) 119896

2119871)2 (16)



119888

is obtained as

119896119888= radic

11987711198772119862

119871 (17)


1198761=

1

1198771

radic119871

119862 119876

2=

1

1198772

radic119871

119862 (18)


quality factors is

119896119888=

1

radic11987611198762

(19)










119877coil =1

119899119877119888+ 119877119871 (20)


Rc1

Rp1 Rp2

C1

rp


M

r2 C2

Rc2

RL

S1

S2

Vd

+

minus

D1

D2

D3

D4

S3

S4


To S2 and S3

To S1 and S4


Rc1

Rc2

C1

C2

RcnCn

L

RL

AC




119862coil = 119899119862 (21)


119876coil =1


=119899

119877119888

radic119871coil

119899119862 + 119877119871

(22)








(a) (b)

(c)




119881square

=4119881119904

120587(sin (2120587119891119905) + 1

3sin (6120587119891119905) + 1


(23)









0

5

10

15

20

25

Pow

er (W

)

638 639 640 641 642 643 644 645 6460

20

40

60

80

100

Effici

ency

()

PowerEfficiency






in Section 2








Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Rc1

Rp1 Rp2

C1

rp


M

r2 C2

Rc2

RL

S1

S2

Vd

+

minus

D1

D2

D3

D4

S3

S4


To S2 and S3

To S1 and S4


Rc1

Rc2

C1

C2

RcnCn

L

RL

AC




119862coil = 119899119862 (21)


119876coil =1


=119899

119877119888

radic119871coil

119899119862 + 119877119871

(22)








(a) (b)

(c)




119881square

=4119881119904

120587(sin (2120587119891119905) + 1

3sin (6120587119891119905) + 1


(23)









0

5

10

15

20

25

Pow

er (W

)

638 639 640 641 642 643 644 645 6460

20

40

60

80

100

Effici

ency

()

PowerEfficiency






in Section 2








Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c)




119881square

=4119881119904

120587(sin (2120587119891119905) + 1

3sin (6120587119891119905) + 1


(23)









0

5

10

15

20

25

Pow

er (W

)

638 639 640 641 642 643 644 645 6460

20

40

60

80

100

Effici

ency

()

PowerEfficiency






in Section 2








Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0

5

10

15

20

25

Pow

er (W

)

638 639 640 641 642 643 644 645 6460

20

40

60

80

100

Effici

ency

()

PowerEfficiency






in Section 2








Acknowledgment


References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article modelling and practical implementation of 2 ...-coil power transfer system is...

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