A Generic Matrix Method to Model the Magnetics of Multi-Coil Air-Cored Inductive Power Transfer Systems

Transcription

1 Delft Univesity of Tenology A Genei Mtix Meto to Moel te Mgnetis of Multi-Coil Ai-Coe Inutive Powe Tnsfe Systems Psnt Venugopl; Bnyopyy Soumy; Bue Pvol; Feei Bm DOI 1339/en16774 Pulition te 17 Doument Vesion Pulise's PDF lso known s Vesion of eo Pulise in Enegies Cittion (APA) Psnt V Bnyopyy S Bue P & Feei J A (17) A Genei Mtix Meto to Moel te Mgnetis of Multi-Coil Ai-Coe Inutive Powe Tnsfe Systems Enegies 1(6) DOI: 1339/en16774 Impotnt note To ite tis pulition plese use te finl pulise vesion (if pplile) Plese ek te oument vesion ove Copyigt Ote tn fo stitly pesonl use it is not pemitte to ownlo fow o istiute te text o pt of it witout te onsent of te uto(s) n/o opyigt ole(s) unless te wok is une n open ontent liense su s Cetive Commons Tkeown poliy Plese ontt us n povie etils if you elieve tis oument ees opyigts We will emove ess to te wok immeitely n investigte you lim Tis wok is ownloe fom Delft Univesity of Tenology Fo tenil esons te nume of utos sown on tis ove pge is limite to mximum of 1

2 enegies Atile A Genei Mtix Meto to Moel te Mgnetis of Multi-Coil Ai-Coe Inutive Powe Tnsfe Systems Psnt Venugopl * Soumy Bnyopyy Pvol Bue n Jn Am Feei Deptment of Eletil Sustinle Enegy Delft Univesity of Tenology (TU Delft) Mekelweg 4 68 CD Delft Te Netelns; snyopyy-1@tuelftnl (SB); pue@tuelftnl (PB); jfeei@tuelftnl (JAF) * Coesponene: vpsnt@tuelftnl; Tel: +31-() Tis ppe is n extene vesion of ou onfeene ppes Psnt V; Bnyopyy S; Bue P; Feei JA Anlysis n ompison of multi-oil inutive powe tnsfe systems In Poeeings of te 16 IEEE Intentionl Powe Eletonis n Motion Contol Confeene (PEMC) Vn Bulgi 5 3 Septeme 16; pp n Psnt V; Bue P; Feei JA A setionl mtix meto fo IPT oil spe optimiztion In Poeeings of te Intentionl Confeene on Powe Eletonis n ECCE Asi (ICPE-ECCE Asi) Dejeon Koe 5 6 June 15; pp Aemi Eito: Selon S Willimson Reeive: 7 Apil 17; Aepte: 3 My 17; Pulise: 3 June 17 Astt: Tis ppe els wit genei metoology to evlute te mgneti pmetes of onttless powe tnsfe systems Neumnn s integl s een use to ete mtix meto tt n moel te mgnetis of single oils (ile sque etngle) Te piniple of supeposition s een utilize to exten te teoy to multi-oil geometies su s oule iul oule etngle n oule etngle qutue Numeil n expeimentl vlition s een pefome to vlite te nlytil moels evelope A igoous pplition of te nlysis s een ie out to stuy mislignment n ene te effiy of vious geometies to mislignment tolene Te ompison of single-oil n multi-oil inutive powe tnsfe systems (MCIPT) onsieing oupling vition wit mislignment powe tnsfee n mximum effiieny is ie out Keywos: i-oe; onttless; oupling; inutive powe tnsfe; mgnetis; mtix; moeling; multi-oil 1 Intoution Inutive powe tnsfe (IPT) elies on eletomgneti fiels to tnsfe enegy etween iuits tt e not pysilly onnete Loosely-ouple oils tt e use in IPT systems suffe fom ig lekge fiels tt emn etive powe onstiting lge powe tnsfe t ig effiieny To nullify tis effet pitive ompenstion is ie out su tt etive powe exnge tkes ples etween te pitos n inutos wit te soue ietly onnete to te lo impoving te powe fto powe tnsfe n effiieny Inutive powe tnsfe systems ue to tei non-ontt ntue llow effiient powe flow to ppen wit eue mintenne eing sfe len n elile Tus pplitions spnning fom low powe meil evies (mw) to mining (MW) ve een foun in te litetue 1 Ote pplitions inlue onsume eletonis EVs unewte powe elivey et 3 A nume of esonnt topologies s een popose n sevel oil spes n esigns ve een esee in tis fiel 1 Howeve n nlytil fmewok tt stuies te impt of oil spe n mislignment in IPT systems in igoous mnne is missing Enegies ; oi:1339/en16774 wwwmpiom/jounl/enegies

3 Enegies of 17 Te mgneti esign n its optimiztion e impotnt steps in te esign of IPT systems Typilly oil optimiztion n mgneti pmete estimtion (L 1 L M k) e pefome elying on eletomgneti (EM) fiel solves n/o oming wit evolutiony lgoitms 45 In ote wok numeil teniques (solving look-up tles (ook of Gove 6) solving Bessel funtions 7 solving elliptil integls 8) n ptil element equivlent iuit (PEEC) solves 91 e use to ieve te sme In Gove s ook tee e ville lose-fom expessions fo self-inutne of nume of polygonl spes Howeve ll of te equtions e evelope fo single tuns ignoing te effet of te i-gp etween tuns esulting in eution n in eue fill fto In tis ppe we ige tis gp y tking into ount te effet of tuns (inese of te peimete fo evey new tun) s well s ny inipient i-gp y using mtix mnipultion Tis extens to ot single n multi-oil geometies n tei mgneti evio is nlyze Neumnn s Integl Te mutul inutne etween two uent-ying iuits ssuming unifom oss-setionl uent ensity n negleting ition n e witten in tems of te iffeentil lengt veto of te two iuits l1 l septe y istne 1 in tems of vuum pemeility µ = 4π 1 7 H/m s: L 1 = λ = µ i 1 4π 1 l1 l 1 (1) In Eqution (1) ontous 1 n e long te mile ege of te iuits 1 n (pimy n seony) espetively Tis eqution is genei oe inepenent n n e pte to moel self-inutne y onsieing te ontous 1 n s long te mile ege of te onuto n te inne ege of te wie 1 Ciul Coils In te se of pi of iul oils te pplition of Neumnn s integl s in (1) te two ontous 1 n epesent te ontou of uent filments ssume to e in te mile of te pimy n seony Now onsie te se of misligne iul oil pi ompose of wies of te iul oss-setion of ius n wit n i-gp l g etween tuns Su oil pi is inite in Figue 1 (x y ) R k () R n Figue 1 A ouple iul oil system wit te pimy ving i = 1 n tuns n te seony ving j = 1 k tuns; te ii of te mi-uent ontou of te n-t pimy tun n k-t seony tun e R n n R k

4 Enegies of 17 Consie R p n R s s te ii of te mile ontou of te fist tun of te pimy n seony Te inne ii of te i-t tun of te pimy n te j-t tun of te seony e elte s R i = R p + (i 1)( + l g ) R j = R s + (j 1)( + l g ) espetively In su se te ptil mutul inutne is witten in tems of zimuts φ i n φ j of te espetive oils s: wee I R i R j e efine s: M ij = µ 4π π φ i = π φ j = Iφ i φ j () I = R i R j sin φ i sin φ j + R i R j os φ i os φ j (Ri os φ i (x + R j os φ j ) ) + ( Ri sin φ i (y + R j sin φ j ) ) (3) Te finl mutul inutne n e efine fo te pimy ving n tuns n te seony wit k tuns s: M = n k i=1 j=1 M ij (4) Te self-inutnes n e extte similly fom (4) y efining te ius of te mile ege n te inne ege of e tun Retngul Coils A single tun etngul oil is sown in Figue A etngul stutue n e split into fou setions (l 1 l l 4 ) e of wi efes to onutos in te top ottom left n igt espetively In su se (1) n e witten in tems of te vious setions of te oil s: L = µ 4π l1 l 1 l l 1 l3 l 1 l4 l l l l l 1 1 l l l l Tis n e witten s mtix in te fom wee te ows epesent te setion of te onuto tt ies te uent (setion of te ontou of te ente) n olumns epesent te setion on wi te inutne ontiution is onsiee E element of te mtix is ptil inutne (self-ptil inutne (i = j) n mutul ptil inutne (i = j)) L ij = µ 4π l 1 l 3 l 1 l l 1 1 l l l l 1 1 l 1 l l 1 l 4 l 3 l l 3 l 4 l l 1 1 l l 1 l l 1 l l l l 3 l l 3 l 4 l l 4 Self-inutne of tis etngul oil n e witten s: L = 4 4 i=1 j=1 l 1 l 3 l 1 l l l l l l l 4 l 4 l 3 l l 4 l l (5) (6) L ij (7)

5 Enegies of 17 Sine te otogonl tems in te veto ot pout eue to zeo fo exmple: ( l1 l = x 1 î yĵ = ) L 11 L 13 L L = L 4 L 31 L 33 L 4 L 44 Tus te totl extenl self-inutne n e witten in tems of L = L 11 = L 33 L = L = L 44 M = L 13 = L 31 M = L 4 = L 4 s: L = (L + L M M ) (9) wee te self-ptil inutnes (L L = L ( ) ) e given s n integtion of te iffeentil lengts of te inne ege x 1 n mile ege x of te top setion s: L = µ 4π x x 1 + (x x 1 ) + + L = ( ) ln + ( ) ( + ) + ln ( + ( ) ) ( + ( + ) ) (8) (1) n te mutul ptil inutnes (M M = M ( ) ): M = µ 4π + x 3 x (x x 3 ) + ( ) (11) P α l 1 ' P P α ' l P ' l 4 ' l ' P δ ' P γ ' P δ l 3 ' P γ Figue Definition of te ontou of te elementy inne ege of single tun etngul oil l n te vious setions of te ontou of te elementy line long te ente of te wie (l 1 l l 4 ) Fo fute evlution te ontou of l n e split t te top igt ottom n left setions s (l 1 l l 4 )

6 Enegies of 17 3 Multi-Tun Cge Ps A multi-tun oil is sown in Figue 3 Consie te pe-tun inutne witten s L ijlk wi epesents te ptil inutne ontiution ue to uent flowing toug te i-t tun j-t setion on te l-t tun k-t setion In su se it is impotnt to eive te expessions of te mutul ptil inutnes onsieing tt te imensions of te oil nge wit oesponing nge in te nume of tuns It is useful to list te veties of te extemes of te ontou long te ente of te wie s well s long te inne ege of te wie fo te N-t wining 13Ntuns N 1 l N 1 l g P Nα g Top setion (1) N 1 l N 1 l P Nβ g g P α P l g Left setion (4) () Rigt setion () P δ P γ N 1 l N 1 l g P Nδ g Bottom setion (3) N 1 l N 1 l g P Nγ g Figue 3 A multi-tun inuto wit imensions efine fom te ente of wie of iul setion wit ius n woun in mnne su tt te i gp is unifom (l g ) Te N-t tun α vetex s its mile ege n inne ege wit veties P Nα = (N 1)( + l g) + (N 1)( + l g) ( n P Nαi = + ) ( (N 1)( + l g ) ) + (N 1)( + l g ) Te ptil self-inutne of te N-t tun (ue to te fist setion) n e eive s: L N1N1 = µ 4π k β x x 1 k 1 α (x x 1 ) + (1) wee k 1 = ( ) ( ) + (N 1)( + l g ) k = + (N 1)( + l g ) α = (N 1)( + l g) β = + (N 1)( + l g) (13) Te esult of su n integtion is: µ I(C = β) I(C = α) (14) 4π

7 Enegies of 17 wee I(C) = + (C k ) + (C k 1 ) + ln ( + (C k 1 ) + (C k 1 ) ( + (C k ) + (C k ) ) (C k1 ) ) (C k ) (15) Te self-inutne mtix n e witten s: L ijlk = µ 4π N i=1 N l=1 N i=1 N l=1 L i1l1 L i3l1 L i1l3 L il L i4l L i3l3 L il4 L i4l4 (16) Te igonl tems in te ove mtix e te setionl ptil self-inutne n te off-igonl tems e te setionl ptil mutul inutne Note tt te signs of setionl self-inutne e positive n tose of te setionl ptil mutul inutne e negtive fo etngul stutues Te summtion tems n e evlute y lulting some genel mties like L N1k1 L N1k3 Te inutne ontiutions of L Nk L Nk4 n e otine y inveting in te pevious set of genel expessions Te net self-inutne n ten e witten s: Setionl Ptil Inutnes L = N i=1 4 j=1 N l=1 4 k=1 L ijlk (17) Te setionl ptil self-inutne is efine s te sum of te ptil self- n ptil mutul inutne ontiutions of uent in ptiul setion on te sme setion on ll possile tuns Te setionl ptil mutul self-inutne is efine s te sum of te ptil mutul inutne ontiutions of te uent in ptiul setion on iffeent setion fo ll omintions of possile tuns Following te pevious poeues te ptil self-inutne ue to uent in te N-t tun fist setion on te k-t tun fist setion is given y: L N1k1 = µ 4π k β x x 1 k 1 α (x x 1 ) + ( + (N k)( + l g ) ) Symols: k 1 = ( + ) (k 1)( + l g ) k = ( ) + (k 1)( + l g ) α = (N 1)( + l g) β = + (N 1)( + l g) (18)

8 Enegies of 17 Te esult of tis integtion is te sme s (14) wit I(C) efine s: I(C) = ( + (N k)( + l g )) + (C k ) ( + (N k)( + l g )) + (C k 1 ) ( ) (C k1 ( + (N k)( + l g )) + (C k 1 ) ) + (C k 1 ) + ln ( ) (C k ( + (N k)( + l g )) + (C k ) ) + (C k ) Similly te ptil mutul self-inutne n e witten s: k L N1k3 = µ 4π x 1 k 1 β α x (x x 1 ) + ( ( ) + ( + l g )(N + k ) ) Symols: k 1 = ( ) ( ) + (k 1)( + l g ) k = + (k 1)( + l g ) (19) () α = (N 1)( + l g) β = + (N 1)( + l g) Agin te esult of tis integtion is te sme s (14) wit I(C) efine s: I(C) = ((N + k )( + l g ) + ( )) + (C k ) ((N + k )( + l g ) + ( )) + (C k 1 ) ( ) (C k1 ((N + k )( + l g ) + ( )) + (C k 1 ) ) + (C k 1 ) + ln ( ) (C k ((N + k )( + l g ) + ( )) + (C k ) ) + (C k ) (1) 4 Mutul Inutne etween Retngul Coils A simple esiption of te mutul inutne senio of single tun pimy n single tun seony is epite in Figue 4 As n extension of te teoy peviously evelope te mutul inutne fo multi-tun etngul oil n e witten in tems of te ontiutions ue to uent flowing toug te i-t tun j-t setion of te pimy on te l-t tun k-t setion on te seony Te setionl mutul inutne mtix n e witten s: M ijlk = µ 4π N i=1 N l=1 M i1l1 M i3l1 M i1l3 M il M i4l M i3l3 M il4 M i4l4 ()

9 Enegies of 17 P α P P δ P γ P α P P δ P γ l 1 ' l ' l 3 ' l 4 ' P α P P δ P γ P α P P δ P γ l 1 l l 3 P α P P δ P γ l 1 l l 3 s P α P P δ P γ l 1 ' l ' l 3 ' l 4 ' P α P P δ P γ l 1 l l 3 s Figue 4 Mutul inutne etween genel pimy single tun n seony single tun Te lengt n et of te pimy e ( ) wile tose of te seony e ( ) Te vetil isplement etween te pimy n seony is 5 Extension to Multi-Coil Cge P (MCCP) Consie line mgneti system exite y pue sinusoil (non-moni) voltge onsisting of pimy n pikup ompose of sevel segmente oils s sown in Figue 5 Te oils n e iniviully onnete seilly o in pllel to ompose te multi-oil ge-p Let te pimy e ompose of n oils (1 n) n te pikup wit m n oils (n + 1 n + m (m > n)) Consequently te voltge mtix V fo ll of te oils n e witten in tems of uents i n time-eivtive of uents i t : V = L i t + R i (3) wee te mties e efine s: V = v 1 v v n v n+1 v n+ v m i t = i = i 1 i i n i n+1 i n+ i m i = i 1 i i n i n+1 i n+ i m R = R 1 R R 8 (4)

10 Enegies of 17 Finlly L is efine s: L 11 L 1 L 1n L 1(n+1) L 1(n+) L 1(m) L 1 L L n L (n+1) L (n+) L (m) L = L n1 L n L nn L n(n+1) L n(n+) L n(m) L (n+1)1 L (n+1) L (n+1)n L (n+)1 L (n+) L (n+)n L m1 L m L mn (5) Pikup iuit i s v s R L vn+1 vn+ Seies i n+1 i n+ i m vm Z igp Seies Pllel L 11 L L nn i 1 i i n v n v 1 v v n v p i p Pimy iuit Figue 5 Defining n inutive powe tnsfe (IPT) system wit te pimy n seony ompose of multiple oils wit self-inutnes s (L ij i = j) n mutul inutnes s (L ij i = j) Te seies n pllel omintion n now e eompose fom tis multi-oil omintion In te se of seies onnete set of oils i p = i 1 = i = i n n i s = i n+1 = i n+ = i m Futemoe in te se of te pllel set of oils i p = i 1 + i + i n n i s = i n+1 + i n+ + i m Afte su tnsfomtion it eomes esy to eue su system of pllel o seies oils into single oil-pi In su system fo ot te seies n pllel system of oils it n e esy to pove tt:

11 Enegies of 17 n i=1 v i m j=n+1 v j = n i=1 m j=n+1 n j=1 L ij n i=1 n i=1 L ij m L ij j=n+1 m m L ij j=n+1 i=n+1 i p i s + n i=1 R i m R j j=n+1 i p i s (6) Eqution (6) inites tt it is possile to onvet line mgneti system wit multi-oils into system of single oil pi y lulting te iniviul ontiutions Su n equivlent oil system is sown in Figue 6 Su tnsposition mkes it esy to nlytilly moel multi-oil line mgneti systems y using te piniples of single oils ley evelope peviously n i1 R i n m L i1 jn1 ij L 1 jn1 R 1 R m R j n i1 V i i p i s v p L 11 L R L v s jn1 n n L i1 j1 ij m m jn1in1 L ij m V j Figue 6 Equivlent single oil pi fo system of oils wit (1 n) oils in te pimy n (n + 1 n + m) oils in te pikup 6 Vlition of Anlytil Moel To vlite te nlytil moels tt e evelope in te pevious setions finite element meto (FEM) simultion n expeimenttion e ie out Ciul n etngul spes e ompe Te pysil popeties of te oils e tulte in Tle 1 To sow te effiy of nlytil expessions eue fill fto ws employe fo etngul oils y mintining n i-gp of 6 m etween te tuns Tle 1 Popeties of te ompe iul n etngul oils Type of Coil (m) (m) l g (m) N (tuns) Retngul (R1) Retngul (R) Ciul (C) inne imete = 55 m 14 Litz wie use 6 71 mm 1 mm i ovell Te onstute oils e sown in Figue 7 Te mesuements nlysis n simultions e ie out t vile z-gps etween te oils n lso t sevel misligne positions Te z-gps e simulte t n 9 m of oil isplements in te z-ietion tking vetil mislignment into onsietion In te se of ltel mislignment pefet lignment 75% 5% n 5% lignments e osen long te x-xis Te esults long te y-xis fo symmetil spes follows te sme ten s te x-xis n ene not onsiee Mesuements e me y using te Agilent 494A impene nlyze (Agilent Tenologies Snt Cl CA USA) wit te fequeny set to 85 khz Te mutul inutnes e extte fom self-inutnes y ying out onstutive n estutive flux mesuement y onneting te oils seilly fom one en to te ote n ten swpping one of te ens (L onst L es ) Te expessions use fo extting te mutul inutne n oupling e:

12 Coupling oeffiient 5 Enegies of 17 M = L onst L es 4 k = M (7) L1 L Figue 7 Expeimentl ompison of etngul n iul oils wit pmetes s tulte in Tle 1 Te nlytil expessions fo iul oils e lulte fom Equtions (1) (4) Futemoe fo etngul oils Equtions (1) () e ompute MATLAB sipts e witten septely fo e of te omputtions n softwe tool fo self- mutul n oupling omputtions is evelope fo i-oe oils A ompison of oupling otine nlytilly n y mking mesuements fo iul oils is pesente in Figue 8 Te esults sow lge egee of geement etween te nlytil expessions n te mesue esults Mismtes in te esults e ue to te use of te litz wie in te expeiments (unlike soli onuto use in te nlysis) n ey uents (poximity effets) in te oils tt e not onsiee in te nlytil expessions Some instumentl uy limittions lso to tis eo Howeve most osevtions e witin 1% uy exept fo n o set in te neigooo of 6% Tese uy mesues e eptle fo mgneti nlysis Z-gp = 3 m Anlytil Pefet lignment Anlytil 75% ligne Anlytil 5% ligne Anlytil 5% ligne Mesue Pefet lignment Mesue 75% ligne Mesue 5% ligne Mesue 5% ligne 15 Z-gp = 5 m 1 Z-gp = 7 m 5 Z-gp = 9 m Z-gp etween te two oils Figue 8 Te nlytil n expeimentl ompison of te oupling oeffiient of iul oils wit z-gps of n 9 m wit oils of pmetes s tulte in Tle 1

13 Self-Inutnes of oils (H) Coeffiient of oupling Enegies of 17 FEM moels wee ete n simulte so s to pefom te numeil evlution of te oils onsiee Te FEM moels evelope using COMSOL Multipysis 51 e pesente in Figue 9 Figue 9 FEM simultion moels of te etngul oil (top-left) iul oil (top-igt) n te etngul oil (ottom) ouple Te etngul oils e moele in te 3D omin wile te iul oils ue to tei ottionl symmety e moele in te D omin Te oupling n self-inutnes of iul n etngul oils e ompe nlytilly using FEM simultions n expeimenttion Te esults e pesente in Figue 1 te oupling eing eoe t pefet lignment n vile z-gps wile self-inutnes mesue fo ll vile spes All mesuements sow te sme ten n tee is lose mt etween nlytil osevtions FEM simultions n mesuements 35% 3% 5% % 15% 1% 5% % 36% 93% 988% 168% 155% 1546% 96% 83% 87% 58% 54% 448% 3mm 5mm 7mm 9mm Simulte Mesue Anlytil 4E-5 35E-5 3E-5 5E-5 E-5 15E-5 1E-5 5E-6 E+ 381E E E-5 18E-5 17E-5 1E-5 674E-6 79E E-6 R1 R C Simulte Mesue Anlytil Figue 1 Coupling oeffiient n self-inutnes of i-oe ge ps of vious spes Te oupling is mesue t vious z-gps t te est ligne point Te pmetes of te oils e s pesente in Tle 1

14 Enegies of 17 7 Spe n Pefomne of Ai Couples Te effet of spes in IPT systems n e nlyze fo i-oe ouples se on te mtemtil nlysis tt s een eive peviously To mke su ompison few pefomne pmetes e onsiee Tey e te open iuit voltge v o sot iuit uent i s unompenste powe s unomp n mximum effiieny η mx Open iuit voltge is te mximum voltge tt te IPT system n soue n sot iuit uent is te mximum uent tt te sme n elive Fo ouple ge-p if L 1 n L e te self-inutnes of te two ouples wit M s te mutul inutne n opete t ngul fequeny ω eting uent i 1 toug te pimy te open-iuit voltge is efine s v o = jωmi 1 n uing te sot-iuit if i s is te uent flowing in te pikup i s = v o = Mi 1 Now lo inepenent unompenste etive powe VA jωl L is efine s: s unomp = v o i s = (i 1 M ω) L (8) Fo te ske of ompleteness te output el powe fo pimy n seony ompenste system is efine in tems of loe qulity fto of te pikup Q L = (ω L )/(R L + R ) wee R L is te lo esistne n R is te AC esistne of te pikup ge-p s: P out = v o i s Q (L) = (i 1 M Q (L) ω) L (9) Te lo inepenent unompenste VA of te pikup is use fute in tis ppe (8) Futemoe te mximum effiieny of IPT systems s een eive inepenent of ompenstion pplie n lo pesent in tems of ntive qulity ftos of te pimy (Q 1 ) n pikup (Q ) s 11: η mx = k Q 1 Q + k Q 1 Q (3) Tese pmetes ve een use to ompe nume of iffeently-spe i-oe ge-ps All spes onsiee ve een nlyze keeping e onseve Tis wy geneliztions of te evio of fiels n ene oupling powe tnsfee n ote pmetes e possile Sevel nlyses wee lso ie out keeping te peimete onseve n multi-tuns wit simil esults In ition tese esults lso oespon n n e genelize to ge-ps wit flux-enning mteils su s feite Tis enne oupling is otine y pling feites long te ntul ietion of flux lines Hene te si teneny of te spe in tems of oupling n its gient is simil in ll IPT pplitions Te ompe spes e liste in Tle All onsiee spes ve een simulte wit one tun oil n z-gp of 1 m Tis so tt te effets of spes e moe enne Tle Pysil pmetes of vious oil spes use in te i-oe ouple Consiee Spe Pmetes Self-Inutnes H Retngle imension 65 & 4 mm Sque imension 599 & 599 mm Cile ius 876 mm Doule ile (DC) imension 34 mm Doule etngle (DR) symmeti imension 4596 & 88 mm Doule etngle + qutue symmeti imension (DR + Q) 3753 & 39 mm (DR) & (Q) Ae 6 (m )

15 oeffiient of ouping 5 Enegies of 17 Te multi-oil spes e ompose of multiple symmeti oils tt e ple lose to e ote wit te oils ying uents in te opposite ietion Te mutul inutne n oupling of tese ge-ps e otine y nlyzing (6) n using te mtemtil nlysis of single oils A stuy of oupling y misligning te oils long x-ietion (ltel isplement) is pesente in Figue k i k et k sq k DC k DR k DRp -DR s k DRp -Q s % oupling long X-ietion epesente s peent of etngle ege = 65mm Figue 11 Coupling oeffiients of single n multi-oil spes wit x-ietionl mislignment of oils in Tle It n e infee tt ile n fou-sie spes iffe in te tolene to oupling vitions wen sujete to ltel mislignment Te oupling of etngul n sque oils tens to ey gully wile te iul spe sees spe op wit mislignment Te iul spe ue to te ft tt it s te igest e fo given peimete mong lose spes s te igest oupling t te est ligne point Te oule oils lso se te sme fetue ut wit lge extension of te powe pofile It is impotnt to note tt in tis nlysis sine te e is kept onseve te peimete vies etween te spes n ene it is impotnt to keep tens in min te tn solute vlues Null-oupling points in oule etngle (DR) n oule ile (DC) oils ou t positions wee pik-up oil is onfonte wit opposing flux of equl mgnitue fom te pimy ge-p Among te oule oils te DC geomety s gete est-ligne oupling tn tt of DR geomety Howeve te mislignment pofile fo DR oils is oe tn tt of DC oils n ene it is well suite to pplitions wee lge mislignment evio is expete fo exmple EVs Wen su n nlysis ws oene to inlue te evio of DR pimy n DRQ (DR+Q) pik-up te Q piking up flux emnting fom DR pimy eves est t te misligne points wile te wost t te est-ligne point On te onty te DR pik-up eves omplementy to te Q pik-up wit DR pimy Powe tnsfee to te pik-up is evlute fom Eqution (8) Te unompenste powe lulte wen sujete to ltel mislignment is sown in Figue 1 Among single oils te iul oil s sp mislignment n wile te fou-sie spes ve gete tolene Te oule spes follow te fetues of tei single equivlents wit te iffeene tt tee is mislignment point wen single oil mong ot te pimy n pik-up eeives powe Tis etes two moe zones of powe tnsfe pt fom te est ligne point In tese points te powe is eue to <5% s te pik-up voltge is eue to lf wi in tun lves te pik-up uent Howeve tese oule spes suffe fom no-powe zone ete t te null oupling points Tese null powe points n e eliminte y using qutue oil te oupling of wi is omplementy to te min oils n ene n ition of powe fom te qutue oils

16 Unompenste powe s mx in pu Enegies of 17 emoves tese null zones It is impotnt to note tt in n tul implementtion te mgnitues of tese uves will epen on te nume of tuns of e oil te mteils pesent te soue teisti-voltge/uent esonnt evio et Ciul Retngul Sque DC DR DR p -(DR+Q) s % Mislignment long X-ietion wit ege of te etngle = 65mm Figue 1 Unompenste powe nlyze on te sis of unit uent flowing toug vious spes of single tun n equl e s inite in Tle Te mislignment is onsiee long te x-ietion Te mximum effiieny s pesente in Eqution (3) s epenene on te qulity fto wi in tun epens on te AC esistnes of te oils Te AC esistnes fo te litz wie use e extte fom tultion tenique s pesente in 1 Te lulte AC esistne fto inluing ot skin n poximity effets fo te litz wie inite in Tle 1 is R R = 19 Te esult of mximum effiieny omputtion wen sujete to vile oupling uing mislignment is sown in Figue 13 Tis plot epesents te teoetil mximum effiieny tt n e expete t vious misligne points fo vious spes Te effiieny vlues floo t te powe null points s expete Mximum effiieny pofile fo tking mx Ciul 3 Retngul Sque DC DR 1 DR p -DR s DR -Qs p % Mislignment long X-ietion wit ege of te etngle = 65mm Figue 13 Mximum effiieny pofile tking wit x-ietionl mislignment of oils in Tle

17 Enegies of 17 8 Disussion In tis ppe genei nlytil tool tt is useful to moel te mgnetis of single n multi oil geometies is evelope Te nlytil equtions evelope n e extene to polygonl spes n n e use to moel n-multi-oil geometies s well Te nlytil expessions ve te stengt tt tey e omputtionlly effiient eg te omputtion of inutnes n oupling of single tun etngul ge-p tke 653 s (-GHz Intel i3-poesso n 4 GB RAM) In te se of FEM nlysis e iniviul lultion tkes sevel seons Tis iffeene gets exggete fo multi-oil IPT systems n te nlytil fomultion yiels ute n fst esults Su n nlytil ppo n yiel te vition in mgneti pmetes ue to ouple geomety Now iffeent pplitions of IPT systems n ve iffeent ojetives: minimiztion of gient of oupling in igly mislignment-tolent EV IPT systems min( x k y k ); elimintion of powe null points in powe-sensitive pplitions (P xy = ) Tus iffeent sttegies n e evolve se on te sptil vition of oupling effiieny n/o powe tnsfe Tis ppe n empowe tis eision mking efoe going in fo etile multi-ojetive optimiztion fte fixing geomety suite to te pplition Howeve limittion tt tis ppo s is tt te piniple of supeposition ols fo line mgneti systems Tus non-lineities in te system su s stution e neglete in te stuy Tis is vli ssumption fo i-oe geometies n ene te stuy yiels goo esults Howeve intefes of iffeent mteils in ig powe IPT systems su s feites n sieling mteils (luminum) nee to espet ouny onitions to ompute mgneti pmetes Tus te equtions nee to e pte fo ounies n tis extension is eyon te sope of tis ppe In elte wok n nlytil LCL filte esign wee intefes e moele y using te meto of imges is pesente in 13 Te imge meto n e pplie to te nlysis in tis ppe to moel te pmetes of ouples wit sevel mteil intefes Aitionlly te effet of fequeny on inutnes (ue to ey uents) is not onsiee in tis ppe A etile numeil optimiztion se on te inputs fom tis stuy so s to optimize feite luminum n ote mteils tt my e pesent in ge-ps is te next step Su n FEM optimiztion fo 1-kW DR system is pesente in 14 Some useful esults otine fom te nlysis e: 1 Te nlysis ompe wit FEM n expeiments s goo mt Almost ll osevtions ve n eo less tn 1% Tis is eptle fo mgneti nlysis Te oupling of single oils is su tt iul oils ve te est oupling t te well-ligne point n te fou spes of oils ve lge mislignment-tolent n Tus etngul oils n e use fo moe mislignment-tolent esigns n iul fo well-ligne pplitions 3 Te oupling evio of multi-oil geometies follows te ten of single-oil spes ut ving null-oupling points By esigning Q oil lote etween te mi-points of te single oils flux n e ptue t te null-oupling points 4 Te Q n DR pikup ve omplementy oupling-mislignment evio At te est ligne point te Q piks up no flux n t te mislignment point of null-oupling of te DR pikup te Q piks up te mximum flux 5 Te DR n DC spes n effetively exten te nge of powe tnsfe to lge misligne positions Te ition of Q to te pikup n emove null-oupling points fom te powe pofile 6 Retngul oils lso pefom well wit te sme enlose e s multi-oil geometies wit lesse zone of powe tnsfe 7 Te totl enlose e of te spes s een kept onstnt to mke fi ompison Howeve it is possile to influene te tuns in te Q oils in DRQ n tis impts te peks otine in te mislignment points Fo esigning IPT systems tt e pte to mislignment s in EVs uing motion ynmi powe tnsfe DR ge p on te owy woul e goo

18 Enegies of 17 solution onsieing te exess mteil osts involve in uiling DRQ ps In ition EVs tveling long te egions of powe null fo long time is limite Howeve fo sttiony ging mislignment tolent DRQ ge p fo ot te pimy n seony is goo oie fo goo powe tnsfe Futemoe inteopeility is possile etween tese ps tus mking it possile to ve te sme veile ps fo ot moes of opetion Auto Contiutions: Psnt Venugopl is te pimy investigto Soumy Bnyopyy me sevel numeil moels to evlute te teoy evelope Pvol Bue n Jn Am Feei e te supevisos wo iete te stuy n gve vlule suggestions n se tei expeienes in tis fiel Conflits of Inteest: Te utos ele no onflit of inteest Refeenes 1 Covi GA; Boys JT Moen Tens in Inutive Powe Tnsfe fo Tnspottion Applitions IEEE Tns Emeg Sel Topis Powe Eleton Psnt V; Bue P Distiute IPT Systems fo Dynmi Poweing: Mislignment Anlysis IEEE Tns In Eleton Sek A; Psnt V; Bue P; Bole M Eonomi Viility Stuy of n On-Ro Wieless Cging System wit Genei Diving Rnge Estimtion Meto Enegies Bui M; Covi GA; Boys JT Design n optimiztion of iul mgneti stutues fo lumpe inutive powe tnsfe systems IEEE Tns Powe Eleton Sin J; Sin S; Kim Y; An S; Lee S; Jung G; Jeon S-J; Co D-H Design n Implementtion of Spe Mgneti-Resonne-Bse Wieless Powe Tnsfe System fo Rowy-Powee Moving Eleti Veiles IEEE Tns In Eleton Gove FW Inutne Clultions: Woking Fomuls n Tles In Dove Pulitions; Couie Copotion: Not Celmsfo MA USA Convwy JT Inutne lultions fo nonoxil oils using essel funtions IEEE Tns Mgn Mxwell JC A Tetise on Eletiity n Mgnetism; Cmige Univesity Pess: Cmige UK 1 9 Rueli A; Pul C; Gett J Inutne lultions using ptil inutnes n momoels In Poeeings of te Intentionl Symposium on Eletomgneti Comptiility Atlnt GA USA 1995; pp Musing A; Ekmn J; Kol JW Effiient lultion of non-otogonl ptil elements fo te pee meto IEEE Tns Mgn Tknsi H; Sto Y; Kneko Y; Ae S; Ysu T A lge igp 3 kw wieless powe tnsfe system fo eleti veiles In Poeeings of te Enegy Convesion Congess n Exposition (ECCE) Rleig NC USA 15 Septeme 1; pp Temn FE Rio Enginee s Hnook; MGw-Hill: New Yok NY USA Mületle J; Kol JW; Eklee A Loss moeling of inutive omponents employe in powe eletoni systems In Poeeings of te 8t Intentionl Confeene on Powe Eletonis ECCE Asi Jeju Koe 3 My 3 June 11; pp Bnyopyy S; Psnt V; Bue P; Feei JA Multi-Ojetive Optimistion of Distiute IPT Systmes fo ging of Eleti Veiles In Poeeings of te 16 IEEE Intentionl Tnspottion Eletifition Confeene n Expo (ITEC) Detoit MI USA 7 9 June y te utos Liensee MDPI Bsel Switzeln Tis tile is n open ess tile istiute une te tems n onitions of te Cetive Commons Attiution (CC BY) liense (ttp://etiveommonsog/lienses/y/4/)