AMSE JOURNALS 2014-Series: Modelling A; Vol. 87; N 3; pp Submitted Aug. 2014; Revised Nov. 16, 2014; Accepted Nov. 30, 2014

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1 ASE JOUNALS 04-Serie: oelling A; ol. 87; N 3; pp 0-9 Submitte Aug. 04; evie Nov. 6, 04; Accepte Nov. 30, 04 Pre-Determination an Experimental erification of oltage egulation from the Output Equivalent ircuit in a Force eonant nuctive ouple Wirele Power ranfer Sytem *Hema amachanran, **Binu G. Abtract *Department of Electrical Engineering, ollege of Engineering, Univerity of Kerala hiruvananthapuram, Kerala, nia hemaachuth@gmail.com **Department of Electrical Engineering, Univerity of Kerala, hiruvananthapuram, Kerala, nia bgr00@gmail.com An analytical two port lumpe element network moel of a reonant inuctive couple wirele power tranfer ytem with helical olenoi geometry i evelope to formulate it input an output equivalent circuit. he lumpe element network i evelope a a conoliation of variou itribute element patially itribute throughout the length of the helical olenoi geometry. he generate lumpe element network ue the near fiel criterion that the phyical length of the wire forming the entire network i le than the wavelength of operation of the circuit. he two port network i analye uing parameter without ource an loa to etermine the riving an tranfer impeance. With ource an loa connecte, the input an output equivalent circuit are evelope. he output equivalent circuit i ue to preetermine the voltage regulation of the near fiel ytem. Experimental verification of voltage regulation of the wirele power tranfer ytem i performe at a force reonant frequency of.hz. he analytical moel i in cloe agreement with the experimental reult. Key wor: Wirele power tranfer ytem moel, near-fiel coupling, high frequency power ytem, air-core tranformer moel, voltage regulation. ntrouction any of the recent reearch into reonant inuctive coupling in wirele power tranfer ytem focu on improving the performance uing varying coil geometrie Alanon P. Sample et al, 99. Development of a ynamic ytem moel i eential for analyzing the performance of the ytem at reonant frequency of the tranmitter an receiver coil in thee ytem. 0

2 oreover, an in-epth tuy of coil geometry i require a the parameter of the ytem are ignificantly influence by coil geometry izuno et al, 0. Solenoi geometrie are the mot commonly ue coil operating in a wie range from a few KHz to 0Hz J.G. hu et al, 996. he coil ue are cylinrical air-core an have iameter of the coil larger than the length. ariou network topologie are alo in ue for realizing thee ytem.s. Wang et al, 004. Since thee ytem operate in the near fiel region of wavelength λ ranging from m, the ue of an appropriate element moel i alo neceary. After careful conieration of the pat invetigation, it ha been foun that an analytical moel for the reonant inuctive couple power tranfer ytem bae on helical olenoi geometry which account for the itribute effect ha not been formulate. From the evelope analytical moel the voltage regulation of the ytem i pre-etermine from it output equivalent circuit. hi paper i organize a follow: he evelopment of a high frequency reflecte impeance terminal moel uing Parallel-Parallel PP network topology with top coupling incorporating itribute effect of all the parameter of the tranmitter an receiver coil conoliate to a lumpe element moel i preente in Section. Formulation of a two port network from the evelope analytical moel i preente in ection 3. he evelopment of input an output equivalent circuit for the pre-etermination of voltage regulation i preente in Section 4. Section 5 icue the experimental verification of voltage regulation at.hz force reonant frequency.. Development of High Frequency eflecte mpeance erminal ranformer oel employing Parallel-Parallel opology with op oupling he tranmitter an receiver coil in the wirele power tranfer ytem are air core coil with helical geometry an power tranmiion i enable through air. he coupling between the coil i very mall an mot of the inuctance i leakage. he flux an current relationhip i linear, ue to large magnetizing current require for tranmiion. eonant inuctive couple linear high frequency tranformer moel i etablihe by creating force reonant L circuit in the primary an econary looely couple circuit an tranferring power uing electromagnetic coupling. A magneto quai tatic interaction between the tranmitter an receiver coil have been aume with receiver coil iplace at a itance from the near fiel of the tranmitter coil obeying the inequality < λ/π. he author have evelope the lumpe element moel of the helical ingle layer olenoi by merging the itribute element moel between the turn a in Fig. a of a ingle layer olenoi. he itribute element moel conier the inuctance between the turn L turn by

3 ubtracting inuctance for inulation pace. Along with thi, the internal inuctance contribution ue to kin effect L i an lea wire inuctance L l effect ha been taken into account. he itribute element moel ha been conoliate for the olenoi an ha been rolle up into a ingle lumpe element inuctance L. Similarly the overall effect of itribute capacitance between the turn an turn to groun capacitance forming turn, along with lea wire capacitance l ha been coniere a a ingle lumpe capacitance in parallel with the coil. he itribute effect of reitance between the turn in erie D with itribute reitance ue to kin an proximity effect A an raiative reitance ra ha been combine into a ingle reitance for the whole coil. hi lumpe moel a in Fig.b i appropriate ince the circuit length i le than the wavelength. a b Fig.a he itribute moel incorporating itribute effect of inuctance, reitance an capacitance.

4 b. onoliate lumpe element moel generate from the itribute element moel, where the element are n turn i l turn l n L L + L + L, +, D + A + he elf-inuctance L an L with it paraitic coil reitance an an the itribute paraitic capacitance an of the tranmitter an receiver coil are conoliate bae on the formulation in Fig. b, to form a lumpe terminal network. With phyical arrangement of the capacitance eciing the topology of the network, a Parallel-Parallel topology PP O.H. Stielau et al, 000 ha been ientifie for the linear high frequency tranformer moel. When the tranmitter coil i energize from a high frequency alternating voltage ource having internal reitance, mutual inuctance i etablihe between the tranmitter an receiver coil, which i a function of coil poition, ize an geometry. Accumulation of electrotatic charge aroun the coil prouce a mutual capacitance or op coupling which vary with itance between the coil. he evelope moel for reonant inuctive wirele power tranfer ytem can be ientifie a PP network topology with top coupling. t ha all the functional capabilitie of high frequency reflecte impeance linear terminal tranformer moel an i preente in Fig.. n ra Fig..Analytical reflecte impeance terminal tranformer moel of the wirele power tranfer ytem uing PP network topology with top coupling. he elf-inuctance of the tranmitter an receiver coil evelope by the author for the helical olenoi L an L, where the firt factor i the Nagaoka elf-inuctance which take into account the effect of the en for long olenoi, econ i euction of correction for inulation pace for helice of roun wire, thir an fourth factor are internal inuctance contribution an lea wire contribution an i given by 3

5 L elf kµ 0 AN l + µ l 0 w δ π 5 µ 0rN ln 4 w tanϕ 4l ln w w 3 ln N 6N N he elf-capacitance of the tranmitter an receiver coil an are foun where the firt factor i the conoliate elf-capacitance between the turn of a coil which alo inclue the capacitance between the turn an groun an the econ factor i the capacitance ue to lea wire an i given by elf 4r N D ε 0µ l L co elf ϕ + D.3950 l ε 0 lw + h ln w 0 0 he mutual inuctance J.E. lem, 97 between the receiver coil of raiu a, length m, turn per unit length n an the tranmitter coil of raiu A, length m an turn per unit length n eparate by a mall itance i foun from the tranformer moel, where A r n A + x n an B n are function which epen on r n a an, an i given by A 0.00π a nn [ r B r B r B r B ] 3 he capacitance in between the parallel roun conuctor ituate in air, neglecting their inulation coating arian K. Kazimierczuk, 009, where c i the itance between the centre of the two conuctor i given by π ε D coh 0 c w 4 he A reitance ue to kin an proximity effect an the econ i the raiation reitance of an ieal Hertzian ipole an i given by p φ A φ D + ra rw δ p w l D w ρ lw π l + η 0 π r 3 λ w 5 3. Development of wo Port Network 4

6 he reflecte impeance terminal moel i further reuce uing circuit tranformation an reuction technique to a π equivalent network. he π equivalent network Kang Lin et al, 009 i repreente in the form of a two port network. he circuit tranformation an reuction technique are ummarize below. 3. oltage Source to urrent Source ranformation he firt reuction of the reflecte impeance moel involve converting the contant voltage ource to contant current ource uing voltage ource to current ource tranformation. he current ource i hown in Fig.3 a, the value of which i given by 6 a b Fig.3 a urrent ource in parallel with internal reitance. b Parallel reitance converte to erie reitance L 5

7 3. onverion of Parallel eitance to Serie eitance From circuit theory, any erie circuit coniting of inuctance L an reitance erie circuit can be converte to it equivalent parallel circuit of inuctance L p an reitance p by equating their amittance an i given by p + L L + 7 he Quality factor alo calle the unloae Q of the coil, which i a meaure of purity of the inuctance i efine a the ratio of coil reactance to reitance an i given by. Q L Since the coil quality factor Q i very large L >> in the frequency range of operation, the moifie form i given by p L he parallel reitance of the reonant wirele power tranfer moel in Fig.3 a i converte to erie reitance erie an the converion i hown in Fig.3 b. 8 9 erie L urrent Source to oltage Source ranformation he Norton current ource i then converte to hevenin voltage ource multiplying with the parallel impeance. he converion i repreente in Fig.4 a. hi voltage ource i in erie with given by, by 6

8 a b Fig4 a. urrent ource converte to voltage ource which i in erie with. b epreentation of coupling part in otte box of the reonant wirele power tranfer ytem in term of impeance. 3.4 Equivalent mpeance of the agnetically ouple part of the Wirele Power ranfer Sytem he magnetic coupling part of the reonant couple wirele power tranfer ytem hown in otte box with impeance a hown in Fig.4 b. he impeance of the tranmitter coil, the impeance on the receiver coil with the mutual impeance,varying with itance can be repreente a follow. + L + + L + + L 3 7

9 agnetically ouple part of the Wirele Power ranfer Sytem converte to a π Equivalent Network. he reonant inuctive couple wirele power tranfer moel of Fig.4 b i then converte to a π equivalent network to remove the magnetic coupling between the tranmitter an receiver coil. Wwith a common groun impoe on the couple circuit, the voltage current relationhip give the matrix equation given by 5 Equation 5 on matrix inverion i given by 6 he π equivalent network replacing the couple part of the wirele power tranfer ytem moel i repreente in Fig.5 a. he voltage acro the noe an are repreente a an an the correponing current flowing into the noe are an. Noal analyi at an the terminal equation can be repreente a B A

10 9 Fig.5 a.he π equivalent network on the couple part of the wirele power tranfer ytem. b wo port network moel of the power tranfer ytem without ource an loa Equation 6 an 7 are repreentation of amittance matrice of the coupling part of Fig.4 b an Fig.5 a. hee amittance matrice are equate to get the impeance of the π equivalent network repreente by A, B an. 8 A 9 B he wo Port Network oel a b

11 he π equivalent network Kang Lin, 009 i finally repreente by a two port network. he two-port network moel of the wirele power tranfer ytem wa analye without ource an loa an i hown in Fig. 5b. he parameter of the two port without ource an loa are foun by open circuit tet on both the port an are repreente in able. able. Parameter of the wo Port eonant ouple Sytem port conition Equivalent terminal impeance at port A B + 0 A + B + A B 0 A + B + A B 0 A + B + B A Development of nput Equivalent ircuit an Pre-Determination of oltage egulation from Output Equivalent ircuit 4.. wo port connecte to ource an loa When the two port network i connecte to ource an loa L, the two port network with input impeance in an output impeance ou are repreente a in Fig.6. n the characteriation of the two port, the output port current - i meaure a leaving port. A B Fig.6. he two port network connecte to ource an loa L he impeance matrix equation a viewe from the input ie port of the two port with loa connecte to port i repreente a follow. 0

12 L he value of i given by 3 Subtituting + the value of in equation, to get the repreentation of input impeance in a follow: L in + L 4 5 in + L Equation 5 give an account of the input impeance of the tranmitter coil viewe from the input ie of the two port. he impeance conit of the inherent impeance of the tranmitter coil along with the reflecte impeance from the receiver coil. he output impeance ou i etermine by revering the role of upply an loa with voltage ource horte. he impeance matrix equation repreente by L 0 Equation 6 i re-arrange to get 6 7 L + 8 Subtituting the value of in 7 to get 9. L L he output impeance i given by

13 ou L + 30 Equation 30 give an account of the output impeance of the receiver coil viewe from the output ie of the two port. he impeance conit of the inherent impeance of the receiver coil an the reflecte impeance from the tranmitter coil. 4.. Development of nput an Output Equivalent ircuit he input an output impeance pre-etermine in ection 4. enable to replace the two port of Fig.6 by input an output equivalent circuit. he two port an the loa i replace by the input impeance in connecte at port. he value of in i given by equation 5. he ource voltage, the tranforme ource reitance along with the input impeance in an the port current, ha been reuce to a ingle circuit to form the input equivalent circuit. he input equivalent circuit a een from the tranmitter coil en i hown in Fig.7. Fig.7. he input equivalent circuit of the reonant inuctive wirele power tranfer ytem. he ource an the two port can be replace by hevenin equivalent circuit connecte at port. he hevenin open circuit voltage i obtaine with loa open circuit 0 from the meh equation at port. L th 3 3

14 th 33 he hevenin impeance L + th i the output impeance ou obtaine from equation 30, with input voltage horte. th ou L + he loa voltage can be etermine from the loa reitance L an hevenin impeance th. he hort circuit current at port in term of loa voltage an loa impeance L i given a follow: 34 th 35 th + L 36 he hevenin equivalent circuit alo calle a the output equivalent circuit i repreente in Fig.8. L Fig.8. he output equivalent circuit of the wirele power tranfer ytem Pre-etermination of oltage egulation from the Output Equivalent ircuit oltage regulation of the wirele power tranfer ytem i pre-etermine by the author from the output equivalent circuit. t i the percentage change in the output voltage from no-loaing of the receiver coil to full-loaing of the receiver coil. he voltage regulation of the ytem i analogou to a tranformer an i ynamic an loa-epenent. he open circuit voltage acro the receiver i th an i given by equation 33. With a reitive loa L ue at the output of the receiver coil, there i a voltage rop acro the reitance an i given by in equation 35. he 3

15 output voltage acro the loa i le than the open circuit receiver coil voltage th an account for poitive voltage regulation. he percentage voltage regulation i given by equation37. he change in output voltage acro the receiver coil from no loa to full loa, repreente on a phaor iagram an i hown in Fig.9. th 00% e ou + m ou 00% 37 Fig. 9.Phaor iagram for voltage regulation. 5. Experimental Sytem a 4

16 b Fig.0.a he chematic of experimental etup with F power upply of a reonant inuctive wirele power tranfer ytem. b. eonant inuctive wirele power tranfer ytem powering a light loa of 00W. he analytical moel of the wirele power tranfer ytem ecribe in Section 4 wa tete with the experimental etup hown in Fig.0 a an b Hema amachanran et al 03. he ytem conit of an F power upply unit, tranmitter coil, capacitor for tuning the tranmitter coil, receiver coil with tuning capacitor an a light loa of 30,00W.he F power upply ytem ue an A-D converter, D-D converter for witching at.hz, D-A converter for inverion Sahu, S et al, 006 an a 6: loa matching tranformer Jha et al, 03. he output of the loa matching tranformer i fe through erie capacitor to the tranmitter coil. he tranmitter coil employe a helical olenoi geometric contruction ue 8 parallel Litz conuctor forming a ingle turn each of cro ectional area.5 q.mm an wa woun on a wooen bobbin of iameter 35cm an length 0.8cm. he tranmitter coil wa forcefully reonate at. Hz by connecting it to 0.06µF capacitor in erie. he receiver coil alo employe Litz conuctor of iameter 8cm an length 0.3cm wa woun with 5 turn of wire in erie having the ame cro ectional area a that of the tranmitter coil. he receiver coil wa force reonate at.hz by connecting acro it.4nf capacitance forme uing four number of 0.0 µf capacitor in erie. he maximum current flow in the receiver coil wa 5

17 limite to about 0.8A. he receiver coil wa attache to a 00W, 30 bulb a the reitive loa with a reitance of 530Ω. he receiver coil wa et to varying coil poition in coaxial orientation from the tranmitter coil at itance 0, 0, 0 an 30cm thereby varying the power tranferre to the loa an efficiency of power tranfer. 5.. eult an icuion he extracte coil parameter of the tranmitter an receiver coil at.hz are preente in able. able. Extracte oil Parameter Parameter ranmitter coil eceiver coil Self- nuctance L, L.0 µh.05µh Self-apacitance, µf.463 nf eitance, 0.Ω 0.3Ω Unloae Quality factor Q, Q he power input from the F power upply wa aute to evelop a voltage input of 546 acro the tranmitter coil. he open circuit voltage acro the receiver coil wa meaure with a potential tranformer having a turn ratio of 0 before an after loaing. he current flowing through the loa wa meaure uing a current tranformer with a turn ratio of 5. he experimental plot are preente in Fig.a, b an c. a 6

18 b c Fig. a.ariation of percentage regulation with loa current. b Phaor iagram of voltage regulation with maximum loa current of 0.58A. c Plot of efficiency an output power with itance of the receiver coil. he hevenin open circuit voltage acro the receiver coil at no loa with coaxial itance i 8.5, while with loa it rop to correponing to a poitive maximum percentage regulation of 0.4 %. he maximum efficiency a obtaine from the experiment alo coincie with coaxial itance an wa 0.6% when power tranferre to the loa i 73.89W, he reitive light loa glow bright. A itance increae, the current through the loa rop to about 0.8A at 30cm itance a the evanecent near fiel ie own ratically. At a itance of 0 cm, the open circuit voltage rop to while the voltage acro the loa become he efficiency at 0cm itance wa 9.9%. he percentage voltage regulation wa alo very negligible Hema amachanran et al 0 correponing to a loa current of 0.8A. he efficiency roppe to 3% at a itance of 30 cm at which the power tranferre to the loa wa only 9.3W, where the lamp howe a minimal flicker. he voltage regulation in reonant wirele power tranfer wa imilar to a conventional terminal tranformer with reitive loaing. 7

19 he rop acro the loa an the reitive part of the output impeance wa preominant over the reactive rop acro the output impeance. he pre-etermine theoretical value were within % of the experimental reult. 6. oncluion oltage regulation tuy ha been conucte on the experimental force reonant inuctive wirele power tranfer ytem uing a high frequency reflecte impeance terminal analytical moel. A reitive loa attache to the ytem moel how a voltage regulation which increae with loa current. he moel can be experimente on capacitive an inuctive loa a well. With inuctive an capacitive loa the real part of the output impeance may lea or lag the output voltage which can lea to a rift in reonant frequency an lowering of power tranfer efficiency. Hence it might be neceary to retune the external capacitance that terminate the receiver coil for realizing reonant power tranfer. hi require avance control circuitry an i a cope for further work in thi area. Acknowlegement he firt author acknowlege the Spee- fellowhip of the Government of Kerala, nia. he author alo thank the funing grant from the Kerala State ouncil for Science, echnology an Environment. eference. Alanon P. Sample, Davi A. eyer an Johua.Smith 00 Analyi, experimental reult an range aaptation of magnetically couple reonator for wirele power tranmiion, EEE ran. n. Electron., pp.-.. izuno, Yachi S, Kamiya A, Yamamoto D 0 mprovement in Efficiency of wirele power tranmiion of agnetic eonant oupling uing agneto plate wire, EEE ran. agnetic; vol.47, iue 0, pp J.G.hu et al 996 A generalize ynamic circuit moel of magnetic core for low an high frequency application, EEE ran. Power Electronic, vol., no., pp S. Wang et al 004 Power tranfer capability an bifurcation phenomena of looely couple inuctive power tranfer ytem, EEE ran. n. Electron. vol. 5, no., pp O.H. Stielau et al 000 Deign of looely couple inuctive power tranfer ytem, in Proc. nt. onf. Power Syt. 4-7 December, Perth, pp

20 6. J. E. lem97 echanical force in ranformer. ran. EE, arian K. Kazimierczuk, High frequency magnetic component, John Wiley & Son, New York, Kang Lin, Keith E. Holbert 009 Applying the equivalent pi circuit to the moeling of hyraulic preurize line", ran. AS, Elevier; vol.79, iue 7, pp Hema amachanran, Binu G. 03 " Wirele powering of Utility Equipment in a Smart Home Uing agnetic eonance, Proceeing of the EEE nternational onference on ecent Avance in ntelligent omputational Sytem AS, December, rivanrum, 9-, Kerala, nia 0. Jha., Qurehi,.F, Srivatav. P 03 " Deign of aaptive grey fuzzy PD controller with variable preiction tep-ize for power ytem ynamic tability control an it on-line rule training", A..S.E Journal, Avance, vol.68, iue, pp. -.. Sahu, S, hanra S, hkrabarthy B, Pal. 006 " A high frequency low voltage current voltage controlle ocillator uing moifie emitter couple logic EL inverter", A..S.E ournal, Avance, vol.6, iue 3, pp Hema amachanran, Binu G. 0 Wirele harging of Lighting Gaget uing Low Q eonant oupling, Proceeing of the nternational onference on Avance in omputing, ommunication an nformatic, pp.75-78, 3-5, Augut, hennai, nia. 9