A Witricity-Based High-Power Device for Wireless Charging of Electric Vehicles

Transcription

1 eergies Article A Witricity-Based High-Power Device for Wireless hargig of Electric Vehicles hogyu Dai, Juhua Wag *, egjiao og ad Hog Huag School of Electrical Egieerig, Wuha Uiversity, Wuha 437, hia; zhogyudai_gt@63.com (.D.); logmj96@gmail.com (..); hoghuag94@foxmail.com (H.H.) * orrespodece: juhuawag@whu.edu.c; Tel.: Academic Edir: Sheldo S. Williamso eceived: 4 Jauary 7; Accepted: arch 7; Published: 7 arch 7 Abstract: I this paper, a Witricity-based high-power device is proposed for wireless chargig of electric vehicles. Accordig specific ruiremets of three-stage chargig for electric vehicles, four compesatio modes of Witricity system are aalyzed by oosely oupled Theory amog trasformer coils ad Substitutio Theorem i circuit ory. I additio, whe combiig voltage withstad levels, curret withstad capability, switchig fruecy of electroic switchig tubes, ad features of resoat circuit, series-parallel (SP) compesatio mode is selected as best compesatio mode for matchig capacir of system. The performaces of coils with differet core arragemets are compared by simulatios ad models. The feasibility of system is verified oretically ad system fuctios are evaluated by joit simulatio of Simplorer ad axwell. Fially, a Witricity-based high-power device is proposed as desiged, ad correctess of oretical aalyses ad simulatio results are verified. Keywords: electric vehicles; Witricity; joit simulatio; compesatio modes; high-power device. Itroductio Witricity techology has received much attetio ad realized rapid developmet sice cocept was recalled i 7 []. This techology based o magetic resoace couplig ca trasfer electric eergy or power over a distace without use of wires. It has bee playig a importat role i various fields from daily products medical uipmet ad aerospace fields [ 8]. Especially i recet years, umber of electric vehicles has icreased rapidly. However, more ad more people have realized that re are essetial limitatios o charger for wide-spread applicatios of evirometally friedly electric vehicles. Therefore, researchers are payig more attetio research i wireless chargig techology for electric vehicles [9 9]. There are two typical chargig modes for electric vehicles, amely costat curret ad costat voltage mode. Uder cosideratio of battery characteristics ad chargig speed performaces, three-stage chargig method is most commoly used method i practice, wherei chargig process starts with a costat curret ad a rapidly icreased voltage. Whe voltage reaches a specified level, charger goes i costat voltage mode util chargig curret decreases early zero. Therefore, chargig system ca ot oly be uivalet a costat curret source but also a costat voltage source whe Witricity techology is used charge electric vehicles. I this paper, four compesatio modes were aalyzed based o ory of loosely coupled trasformer ad uivalet circuit model, amely odel A ad odel B. Oly series-parallel (SP) compesatio mode ad parallel-series (PS) compesatio mode ca meet ruiremets for system ca be uivalet a costat curret or a costat voltage source. osiderig characters of electroic compoets ad performace of power source, such as withstad voltage, withstad curret, switchig fruecy, ad ripple voltage, SP Eergies 7,, 33; doi:.339/e333

2 Eergies 7,, 33 of 4 ruiremets for system ca be uivalet a costat curret or a costat voltage source. osiderig characters of electroic compoets ad performace of power source, Eergies 7,, 33 of 4 such as withstad voltage, withstad curret, switchig fruecy, ad ripple voltage, SP compesatio mode is suitable for system. The simulatios based o joit compesatio simulatio of Simplorer mode is suitable ad axwell for also system. have bee The coducted simulatios for based coils o with differet joit simulatio cores of Simplorer select ad axwell best match. also have Fially, beea coducted Witricity-based for coils with high-power differetdevice cores was proposed. select best The match. experimets Fially, also a Witricity-based have bee carried high-power out device test was proposed. ory ad The experimets simulatio also results, have bee ad carried explaatios out for test ory discrepacy ad betwee simulatio results, experimetal ad explaatios results ad for oretical discrepacy results betwee are demostrated. experimetal results ad oretical results are demostrated.. Fudametal Aalysis Series resoat ad ad parallel resoat resoat are are two two basic basic resoat resoat modes. modes. I I Witricity Witricity circuit, circuit, primary primary ad ad secodary secodary sides sides both both eed eed be compesated be compesated with awith resoat a resoat capacir. capacir. shows shows four compesatio four compesatio modes; series-series modes; series-series (SS) compesatio, (SS) compesatio, series-parallel series-parallel (SP) compesatio, (SP) parallel-series compesatio, (PS) parallel-series compesatio, (PS) ad compesatio, parallel-parallel ad parallel-parallel (PP) compesatio. (PP) compesatio. I I I I U U I I I I U U (c) (d). Four compesatio modes. series-series (SS) compesatio; series-parallel (SP). Four compesatio modes. series-series (SS) compesatio; series-parallel (SP) compesatio; (c) parallel-series (PS) compesatio; (d) parallel-parallel (PP) compesatio. compesatio; (c) parallel-series (PS) compesatio; (d) parallel-parallel (PP) compesatio. I Witricity system, iductace of coil ad compesatio capacitace should be matched I Witricity costitute system, a resoace iductace circuit with of a fixed coil ad operatio compesatio fruecy. The capacitace values of should ad be matched are chose such costitute that: a resoace circuit with a fixed operatio fruecy. The values of ad are chose such that: fr f r = π π f r = π () () fr = For simplicity, circuit should be uivaletly π trasformed aalyze characteristics. shows uivalet trasformatio process of circuit, where ad are primary ad secodary For simplicity, tal impedaces, circuit should respectively. be uivaletly The uivalet trasformed circuit A, based aalyze o loosely characteristics. coupled shows uivalet trasformatio process of circuit, where ad trasformer, is show i a. I b, circuit based o ature of ideal trasformer are is decoupled, primary ad amely secodary uivalet tal impedaces, circuit B. respectively. The uivalet circuit A, based o loosely coupled trasformer, is show i a. I b, circuit based o ature of ideal trasformer is decoupled, amely uivalet circuit B. = (ω) or = (ω) u = ( jωu () ω) ( ω) = or = I followig, uivalet circuits A ad B are used aalyze uivalet trasformatio () jωu of four compesatio modes i u = Witricity circuit.

3 Eergies 7,, 33 3 of 4 σ σ i i Eergies 7,, 33 3 of 4 Eergies 7,, 33 3 of 4 u i σ σ i i σ σ i i i σ σ i u u : i σ σ i u σ i i σ i i σ i σ u or : u i σ σ i u u σ i i σ or u σ i σ i u u. The uivalet circuit. The uivalet circuit A; The uivalet circuit B. u I followig, uivalet circuits A ad B are used aalyze uivalet trasformatio of four compesatio modes i Witricity circuit.. The uivalet circuit. The uivalet circuit A; The uivalet circuit B.. The uivalet circuit. The uivalet circuit A; The uivalet circuit B... The SS ompesatio ircuit I followig, uivalet circuits A ad B are used aalyze uivalet.. The trasformatio SS ompesatio 3 shows of ircuit four uivalet compesatio trasformatio modes i process Witricity of circuit. SS compesatio Witricity circuit 3 shows uivalet trasformatioprocess of SS compesatio Witricity circuit based o uivalet circuit A, where ad based.. The oss ompesatio uivaletircuit circuit A, where ad are chose resoate with ad are chose resoate with ad i i Equatio (). Thus, Witricity circuit ca be ual a load-idepedet voltage source. 3 shows uivalet trasformatio process of SS compesatio Witricity circuit based o uivalet circuit A, where I ad are chose resoate with ad I i Equatio (). Thus, Witricity circuit ca be ual a load-idepedet voltage source. U U U U U I I I I I I U U 3. The SS compesatio Witricity circuit usig uivalet circuit A. 3. The SS compesatio Witricity circuit usig uivalet circuit A. U Whe usig uivalet circuit B uivaletly trasform SS compesatio Witricity circuit, Whe secodary usig uivalet uivalet circuit impedace B uivaletly is calculated trasform as: SS compesatio Witricity circuit, secodary 3. uivalet The SS compesatio impedacewitricity is calculated circuit usig as: uivalet circuit A. ( ) ( ) ω ω Whe usig uivalet circuit = B (ω) uivaletly = trasform SS compesatio Witricity circuit, secodary uivalet impedace j is calculated + (3) = ω + jω + = (ω) (3) jω as: jω + ( ω ) ( ω ) The uivalet chage process is show = i 4. = jω + + jω (3)

4 Eergies 7,, 33 4 of 4 Eergies 7,, 33 4 of 4 The uivalet chage process is show i 4. I I U U U ( ω ) ( ω ) 4. The SS compesatio Witricity circuit usig uivalet circuit B. The The SS SS compesatio Witricity circuit circuit ca ca oly oly be be uivalet a a ideal ideal voltage source from from above above aalysis... The SP ompesatio ircuit 5 shows SP compesatio Witricity circuit uivalet chage process usig uivalet circuit A. Obviously, Witricity circuit ca ca be be ual a a ideal curret source. I I U I I I U U U j ω U j ω 5. The SP compesatio Witricity circuit usig uivalet circuit A. 5. The SP compesatio Witricity circuit usig uivalet circuit A. If SP compesatio Witricity circuit uivaletly trasforms accordig uivalet If SP compesatio Witricity circuit uivaletly trasforms accordig uivalet circuit circuit A, secodary uivalet impedace would be give by: A, secodary uivalet impedace would be give by: ω jω jω + ( ω ) (ω) = (ω) = j + = (4) (4) jω jjω ω + + +jω

5 Eergies 7,, 33 5 of 4 Eergies 7,, 33 5 of 4 From (), it is kow that ω = ω From (), it is kow that ω = ω. Therefore, (4) ca be simplified i:. Therefore, (4) ca be simplified i: = jω = jω (5) (5) If a series iductace S = is added primary circuit, Witricity circuit ca be If a series iductace S = is added primary circuit, Witricity circuit ca be uivalet a load-idepedet voltage source, show i i I I U U jω U U 6. The SS compesatio Witricity circuit usig uivalet circuit B. B. From above aalysis of of SP SP compesatio Witricity circuit circuit by by usig usig uivalet circuit circuit A ad A ad B, B, Witricity Witricity circuit circuit ca be ca uivalet be uivalet ot oly ot a oly ideal a curret ideal curret source but source a but ideal a voltage ideal source voltage assource well. as well..3. The PS ad PP ompesatio ircuit Similar aalysis preseted i Sectios. ad., PS ad PP compesatio circuit uivalet trasformatio process o basis of uivalet circuit A is is show i i If aa compesatio capacitace S is added S is added desiged desiged circuit circuit resoate with resoate iductace with iductace +, Witricity circuit is a load-idepedet voltage source. Similar PS compesatio, Witricity circuit is a load-idepedet voltage source. Similar PS circuit, whea compesatio + capacitace S is added meet capacitace S + ad resoates with compesatio iductace circuit, + whe + a compesatio, Witricitycapacitace circuit ca be S ual is added a load-idepedet meet capacitace curret source, ad curret ca be calculated by: S + ad resoates with iductace + +, Witricity circuit ca be ual a U I load-idepedet curret source, = ad jω(curret + ca be + calculated (6) ) by: 8 shows uivalet chage U I = process of PS ad PP compesatio Witricity circuit (6) usig uivalet circuit B. jω ( + + ) 8 shows uivalet chage process of PS ad PP compesatio Witricity circuit usig uivalet circuit B.

6 Eergies 7,, 33 6 of 4 Eergies 7,, 33 6 of 4 Eergies 7,, 33 6 of 4 I I I I I I I U I U U U U U I I I I U U I I I I U U U ju ω jω U ju ω jω U U S S U + U + I I S S U I + U I + 7. The SP ad PP compesatio Witricity circuit usig uivalet circuit A. The SP 7. The SP ad PP compesatio Witricity circuit usig uivalet circuit A. The SP compesatio 7. The Witricity SP ad PP circuit; compesatio The PP Witricity compesatio circuit Witricity usig circuit. uivalet circuit A. The SP compesatio Witricity circuit; The PP compesatio Witricity circuit. compesatio Witricity circuit; The PP compesatio Witricity circuit. I I I I I I I U I U U U U U ω ω ( ) ( ) U U ω ω ( ) ( ) jωu jωu jωu jωu ( ω ) ( ω ) ( ω ) ( ω ) ( ω ) ( ω ) jωu jωu ( ω ) ( ω ) jωu jωu 8. The SP ad PP compesatio Witricity circuit usig uivalet circuit B. The SP compesatio 8. The Witricity SP ad PP circuit; compesatio The PP Witricity compesatio circuit Witricity usig circuit. uivalet circuit B. The SP 8. The SP ad PP compesatio Witricity circuit usig uivalet circuit B. The SP compesatio Witricity circuit; The PP compesatio Witricity circuit. compesatio Witricity circuit; The PP compesatio Witricity circuit. I 8, PS compesatio Witricity circuit is a load-idepedet curret source after uivalet chage, while PP compesatio Witricity circuit is a load-idepedet voltage source.

7 Eergies 7,, 33 7 of 4 Eergies 7,, 33 7 of 4 I 8, PS compesatio Witricity circuit is a load-idepedet curret source after uivalet chage, while PP compesatio Witricity circuit is a load-idepedet voltage source. From above uivalet simplificatio of offour kids of ofcompesatio circuits, it itis isobvious that SS SSad PP PPcompesatio Witricity circuit ca oly be beual a aload-idepedet curret or or voltage source, while SP SPad PS PScompesatio Witricity circuit is isot oly a aload-idepedet curret source but also also a a load-idepedet voltage voltage source source whe awhe matched a matched capacitace capacitace or iductace or iductace is added is added circuit. If Witricity circuit. techology If Witricity istechology used charge is used electric charge vehicle, electric it should vehicle, meet it should ruiremet meet of ruiremet most commoly of most usedcommoly chargig scheme, used chargig also called scheme, three-stage also called chargig, three-stage which chargig, cotais two which domiat cotais chargig two domiat stages ofchargig costat curret stages ad of costat curret voltagead modes. costat I or voltage words, modes. circuit I or is ruired words, becircuit uivalet is ruired a load-idepedet be uivalet curret a load-idepedet source ad a load-idepedet curret source ad voltage a load-idepedet source at same voltage time. source Therefore, at we same catime. drawtherefore, a coclusio we from ca draw abovea aalyses coclusio that from oly above SPaalyses ad PS compesatio that oly SP Witricity ad PS circuit compesatio ca meet Witricity ruiremets. circuit ca meet ruiremets. I I resoat circuit, quality facr Q ca be becalculated by: Q ω Q = = (7) (7) I I iductace-capacitace () series series resoace resoace circuit, circuit, it isit well is well kow kow that that voltage voltage values values o ad o ad are idetical, are idetical, while while phases are phases opposite. are opposite. Thus Thus sum of sum two of voltage two vecrs voltage is vecrs zero, ad is zero, withstad withstad voltage ofvoltage iput of power iput source power casource be reduced. ca be However, reduced. However, voltages of voltages ad of are Qad times are iput Q times voltage iput voltage parallel i resoace parallel circuit. resoace As a cosuece, circuit. As a cosuece, withstad voltage withstad of iput voltage power of source iput maypower be Q times source its may supply. be Q Itimes meatime, its supply. much I of meatime, reactive much curret of is reactive delivered curret betwee is delivered iductace betwee ad iductace capacitace ad i capacitace parallel i resoace parallel circuit. resoace Hece, circuit. load ca Hece, receive more load ca active receive power. more Foractive device power. based For o Witricity device based techology, o Witricity electroic techology, switchig electroic tube is switchig most importat tube is device, most decidig importat performace device, decidig of whole performace device. The of electroic whole switchig device. The tubeelectroic usually ca switchig withstadtube highusually curretca butwithstad ot high voltage. high curret Therefore, but ot high series voltage. compesatio Therefore, mode is chose series compesatio i primary mode circuit. is For chose secodary i primary circuit, circuit. output For more secodary active power, circuit, output parallel more compesatio active power, mode is better. parallel For compesatio or parts of mode circuit is better. structure, For aor threeparts phaseof full-bridge circuit cotrolled structure, rectifier, a three aphase full bridge full-bridge iverter, cotrolled ad a full-wave rectifier, rectifier a full bridge are chose. iverter, Above ad all, a full-wave SP compesatio rectifier are chose. WitricityAbove circuitall, selected SP for compesatio high-power wireless Witricity chargig circuit selected of electric for vehicles high-power is show wireless i chargig 9. of electric vehicles is show i 9. U a U b U c D D D 3 OS OS OS 3 OS 4 S S S T P D7 D8 D4 D5 D 6 D9 D High-power wireless chargig circuit of of electric vehicles withsp SP compesatio Simulatio The square coil ad circular coil coil are are typical typical structures structures used i used Witricity i Witricity circuit. circuit. shows ir shows magetic ir magetic field distributios field distributios based simulatio. based simulatio. Obviously, for Obviously, square for coil, re square are coil, magetic re are abormalities magetic abormalities because of itsbecause rectagular of its structure, rectagular which structure, may decrease which may decrease sufficiecy of sufficiecy power tractio of power ad utilizatio tractio ad icrease utilizatio ad temperature. icrease Especially temperature. whe Especially trasmissio whe power trasmissio large, disadvatages power large, are much disadvatages more obvious. are much Therefore, more obvious. circular Therefore, coil is a better circular selectio coil is for a better Witricity selectio circuit. for Witricity circuit.

8 Eergies 7,, 33 8 of 4 Eergies7, 7,,,33 33 Eergies 4 88ofof4..The Themagetic magetic fluxdistributios. distributios. The The squarecoil; coil; The Thecircular circularcoil. coil.. The magetic flux flux distributios. Thesquare square coil; The circular coil. Toimprove improve couplig coupligefficiecy efficiecybetwee betwee coils coilsad adreduce reduce leakage leakageof of magetic magetic To To improve are couplig betwee ad reduce leakage of magetic field, field, cores cores areadded addedefficiecy coils. coils. coils shows some simulatio ofcoils coils with differet field, shows some simulatio of with differet cores arewhich addedhave bee coils.coducted shows some simulatio of coilsii with differet cores, cores, which have bee coducted compare compare performaces performaces order icrease icrease cores, order which have bee coducted compare performaces i order icrease couplig coefficiet. couplig coefficiet. The couplig coefficiet represetig couplig degree betwee coils ca couplig coefficiet. The couplig coefficiet represetig couplig degree betwee coils ca calculated by: The couplig coefficiet represetig couplig degree betwee coils ca calculated by: calculated by: κ== κ κ= AA BB. ot. (8)(8) (8)

9 Eergies 7,, 33 9 of 4 Eergies 7,, 33 9 of 4 (c) D (d) E (e). The coils with differet cores, magetic flux distributios, ad magetic lie. The coils with differet cores, magetic flux distributios, ad magetic lie distributios. A-without cores; B-with a flat plate core; (c) -with a E distributios. A-without cores; B-with a flat core; E (c) -with a E core; (d) D-with a hollow E core; ad (e) E-with aplate improved hollow core. core; (d) D-with a hollow E core; ad (e) E-with a improved hollow E core. It is well kow that trasmissio efficiecy is closely correlated with directio of magetic Thethat magetic flux distributios ad lie distributios of five coils It is well lies. kow trasmissio efficiecy is magetic closely correlated with directio of with differet cores have bee show i. Obviously, for coil A without a core, magetic lies. The magetic flux distributios ad magetic lie distributios of five coils most of magetic lies through coil are used trasmit power, but re are some magetic with differet cores have bee show i. Obviously, for coil A without a core, lies leakig through air. ompared with coil A, directio of magetic lies is most costraied of magetic lies through coil are used trasmit power, but re are some magetic so that more of m pass through coils icrease trasmissio efficiecy i coil lies leakig through air.core. ompared with, coil directio of magetic lies B with a flat plate From A, trasmissio efficiecy of coil with ais E costraied so that more of highest. m pass coils E icrease efficiecy i coilefficiecy B with a flat core is oilthrough D with a hollow core hastrasmissio almost same trasmissio plate as From, trasmissio efficiecy of. coil with E hollow core is coil,core. but weight of core is about half that of coil oil E has a a improved E up of E small core which are iexpesive adefficiecy easy obtai, but highest. oil Dcore, withmade a hollow core haspieces, almost same trasmissio as coil, but bidig effect of magetic lies drops rapidly. weight of core is about half that of coil. oil E has a improved hollow E core, Table ad reveal that are iexpesive self-iductace, mutual-iductace, ad bidig coupligeffect made up of small core pieces, which ad easy obtai, but coefficiet of coil are highest of all, ad couplig coefficiet of coil D is slightly lower. of magetic lies drops rapidly. However, amout of core i coil D is just about half of that i coil, which cuts costs Table ad reveal that self-iductace, mutual-iductace, ad couplig coefficiet ad reduces weight. Thus coil D is a better choice for Witricity circuit for wireless chargig of of coilelectric arevehicles. highest of all, ad couplig coefficiet of coil D is slightly lower. However, amout of core i coil D is just about half of that i coil, which cuts costs ad reduces weight. Thus Table coil D. is a better choice for Witricity wireless chargig ofcoils. electric vehicles. Self-iductace, mutual-iductace, ad circuit coupligfor coefficiet of five differet μh Table. Self-iductace, mutual-iductace, ad coupligμh coefficiet of five differet coils. Name A B Name A D B E D E Self-Iductace ( ) utual-iductace ( ) ouplig oefficiet Self-Iductace (µh) utual-iductace (µh) ouplig oefficiet

10 TX ix_wwtx_woutx_w ioueergies 7,, 33 of 4 Eergies 7,, 33 of 4 Iductace Self-iductace(uH) utual-iductace(uh) ouplig coefficiet A B D E ouplig coefficiet. Self-iductace, mutual-iductace, ad couplig coefficiet of five differet coils. Through Through discussio discussio above, above, simulatio simulatio of of Witricity Witricity system system based o based joit o simulatio joit simulatio method of Simplorer method of ad Simplorer axwell is ad carried axwell out, as is show carried i out, as 3. show The SP i compesatio 3. Witricity The SP compesatio circuit model is Witricity built accordig circuit model Simplorer is built ad accordig coil idetified Simplorer i axwell. ad coil I order idetified make i axwell. coils work I order uder make fixed operatig coils work fruecy, uder f = fixed operatig khz, coils fruecy, f = khz must be revised with, coils compesatio must be revised capacitace with S = compesatio P = 6358 pf. capacitace S = P = 6358 pf. 5 PW PW PW PW E E E3 3 D D D3 3 OSFET_BIDGE + W W 3 4 OSFET_BIDGE S + W W 6 S S P D + W W3 D9 + W W4 D4 D5 D6 tud8 D7 3. The joit simulatio methodof of Simplorer ad axwell. The joit simulatio results are show i 4. To simplify aalysis ad recogize The joit simulatio results are show i 4. To simplify aalysis ad recogize results more clearly, 4a,b show results from ms, while 4c f is from 4 results more clearly, 4a,b show results from ms, while 4c f is from 4 4. ms. The three-phase iput voltage is show i 4a. The amplitudes are 3 V, while 4. ms. The three-phase iput voltage is show i 4a. The amplitudes are 3 V, while phase differece betwee m is. The D voltage is obtaied after three-phase ucotrolled phase differece betwee m is. The D voltage is obtaied after a three-phase ucotrolled rectifier, o a scale of 48 V 536 V, as show i 4b. It is easy fid that, withi rectifier, o a scale of 48 V 536 V, as show i 4b. It is easy fid that, withi fluctuatio fluctuatio fruecy, f t = 3 Hz, value of D voltage is early uchaged withi. fruecy, f t = 3 Hz, value of D voltage is early uchaged withi. millisecod. I millisecod. 4c, W.V I is 4c, D W.V voltage is of about D voltage 536 V, W.V of about represets 536 V, W.V square represets voltage obtaied square voltage after full obtaied bridge iverter after full withi bridge iverter fruecy, withi f fruecy, f = khz, ad W3.V is = khz, ad W3.V is secodary voltage, secodary waveform voltage, of which iswaveform similar of sie which wave is withi similar fruecy sie f S = wave f = withi khz. fruecy 4d shows f khz S = f = curret.. W.I is 4d shows rectified curret. W.I ad is W3.I rectified represet curret. primary W.I ad curret W3.I ad represet secodary curret, primary respectively, curret ad which secodary are similar curret, sie respectively, wave withi which fruecy are similar f = khz, sie wave ad ir withi amplitudes fruecy are about f khz = 7.5 A ad, ad 8.ir A. Iamplitudes 4e, are W.P about is 7.5 A output ad 8. power A. I of 4e, full-wave W.P bridge is rectifier, output which power has of almost full-wave samebridge waveform rectifier, as W.P, which has primary almost power, same waveform shape of which as W.P, ca be approximated primary power, as a sie shape fuctio of which p = ca p be = 3.7 approximated si( as 5 a πt) sie. Similarly, fuctio 5 5 p = sie p = fuctio 3.7 si( p 3 = π.5 t). Similarly, +.5 si(4 sie fuctio 5 πt + π/) p3 = is.5 fit+ for.5 W3.P, si(4 secodary πt+ π ) is power. fit for For 4f, W3.I, W3.V, ad W3.P are iput curret, voltage, ad power of W3.P, secodary power. For 4f, W3.I, W3.V, ad W3.P are iput curret, secodary side, respectively, of full-wave bridge rectifier, while W4.I, W4.V, ad W4.P are voltage, ad power of secodary side, respectively, of full-wave bridge rectifier, while output of full-wave bridge rectifier. It ca be cocluded from 4f that re is hardly W4.I, W4.V, ad W4.P are output of full-wave bridge rectifier. It ca be cocluded from 4f that re is hardly ay power loss for full-wave bridge rectifier. It is well kow

11 Eergies 7,, 33 of 4 Eergies 7,, 33 of 4 ay power loss for full-wave bridge rectifier. It is well kow that average efficiecy is similar that efficiecy average efficiecy of eergy is trasfer similar i a time efficiecy period. Wof eergy ad Wtrasfer 4 are iput a time eergy period. adw ad output W 4 are eergy iput a time eergy period, ad respectively, output eergy ad ca i be a time derived period, by: respectively, ad ca be derived by: W = T p 3T W 3 p dt W 4 = = pdt T p 4 dt pdt T 3 T T3 p 3 dt W = p dt p dt Therefore, overall efficiecy of Witricity circuit ca be calculated by: Therefore, overall efficiecy of Witricity circuit ca be calculated by: T T (9) (9) η = W4 4 η = 87% () W 87% () W (c) (d) (e) (f) 4. The joit simulatio results. The three-phase iput voltage; The three-phase 4. The joit simulatio results. The three-phase iput voltage; The three-phase ucotrolled rectifier; (c) The voltage of rectifier termial, primary side, ad secodary side; (d) ucotrolled rectifier; (c) The voltage of rectifier termial, primary side, ad secodary side; The curret of rectifier termial, primary side, ad secodary side; (e) The power of rectifier (d) The curret of rectifier termial, primary side, ad secodary side; (e) The power of rectifier termial, primary side, ad secodary side; (f) The full-wave bridge rectifier of secodary side. termial, primary side, ad secodary side; (f) The full-wave bridge rectifier of secodary side. 4. Experimetal Evaluatio 4. Experimetal Evaluatio To verify above aalysis, a high-power device based o Witricity techology for To verify above aalysis, a high-power device based o Witricity techology for wireless wireless chargig of electric vehicles has bee built with SP compesatio mode, as show i chargig of electric vehicles has bee built with SP compesatio mode, as show i I experimet, distace betwee trasmittig ad receivig coil is 3 cm, iput voltage has commercial power of 38 V, ad compesatio capacitace is 7 F. Through adjustig iput power, trasformer parameters ca be measured ad are listed i Table.

12 Eergies 7,, 33 of 4 Eergies 7,, 33 of 4 etric data system The primary power supply eceive coil Eergies 7,, 33 of 4 etric data system The primary power supply eceive coil D Power supply The load Trasmit coil Witricity-based high-power forfor wireless chargig of electric vehicles. 5.5.AAWitricity-based high-powerdevice device wireless chargig of electric vehicles. Table. The measured D parameters of iput side ad output side.coil Power supply The load Trasmit I experimet, distace betwee trasmittig ad receivig coil is 3 cm, Iput Iput Iput Power Output Output Output 5. Acommercial Witricity-based high-power for wireless chargig of electric Trasmissio vehicles. iput voltage has power of 38device V, ad compesatio capacitace is 7 F. Through Voltage (V) urret (A) (kw) Voltage (V) urret (A) Power (kw) Efficiecy adjustig power, trasformer parameters ca be measured i Table. 54 iput ad are listed 8.9% Table. The measured parameters of iput side ad output side % Table. The Iput measured parameters side ad Iput Iput Output Output Output Trasmissio Power 53 of iput output side. 8.69% Voltage (kw) Voltage urret Power Efficiecy 35 (V) urret 38.5 (A) (V) 7.77 (A).3(kW) 8.3% Power Output Output 8.88% 8.9% Iput Voltage Iput urret Iput Output Trasmissio (V) (A) (kw) Voltage (V) 9.8 urret (A).44 Efficiecy Power (kw)8.4% 8.55% % % % % 8.55% % % 8.69% % % 8.4% 8.3% % 8.88% % % 6 ad 7, voltage, 74 curret, ad.59 power 357From s of device s 3.59 output side 8.% % icrease with chage of iput rate of iput voltage4.7 is slower tha 8.55% side. The chagig % 8.9% secodary side, while chagig rate of curret is opposite of voltage s chagig % tedecy. This is because secodary voltage has bee desiged o stadard iterfaces ad From s 6 ad 7, voltage, curret, ad power of device s output side procols of D charge spots, output voltage of which rages from 5 V 75 V. However, icrease with chage of iput side. The chagig rate of iput voltage is slower tha iputs voltage ca oly 7, chage 38 From 6 ad from voltage, V.curret, ad power of device s output side secodary side, while chagig rate of curret is opposite of voltage s chagig The treds of iput voltage, iput curret, output voltage, output curret are show i icrease with This chage of secodary iput side. The has chagig rate ad of o iput voltage is slower tedecy. is because voltage bee desiged stadard iterfaces ad tha 6, while power ad trasmissio efficiecy are show i 7. secodary while spots, chagig rate of curret opposite voltage s chagig procols ofside, D charge output voltage of whichisrages from 5of V 75 V. However, tedecy. This is because chage secodary iput voltage ca oly from voltage 38 V.has bee desiged o stadard iterfaces ad 8 6 Voltage procolsthe of Dofcharge spots, Iput output voltage of which rages from 5 V are 75show V. However, treds iput voltage, iput curret, output voltage, ad output curret i Output Voltage 7 ad trasmissio efficiecy are show i 7. voltage 6, while oly power iput ca chage from 38 V. Iput urret 5 Output urret urret(a) Iput Voltage Output Voltage Iput urret Output urret 35 4 Voltage(V) urret(a) Voltage(V) 8 5 Times output curret. 6. The iput voltage, output voltage, iput curret, ad Times TheThe iput voltage, voltage, iput iput curret, output curret. iput voltage, output output voltage, curret, adad output curret.

13 Eergies 7,, 33 3 of 4 The treds of iput voltage, iput curret, output voltage, ad output curret are show i Eergies 7,, 33 3 of 4 6, while power ad trasmissio efficiecy are show i shows measured trasmissio efficiecy fluctuatig aroud.8 with chage of of trasmissio power, power, which which is lower is lower tha tha oretical oretical result. Through result. Through aalyses aalyses ad summary, ad summary, some reasos some ca reasos be cocluded ca be cocluded as follows. as follows. The The simulatio model, model, built built i i a a ideal ideal circumstace, has has less less power power loss loss tha tha actual actual circuit. The The electromagetic shieldig shieldig effectiveess of of core, core, which whichis is made madeof of small small blocks, blocks, is is worse worse tha tha whole whole core core built built i iaxwell. (c) (c) There There are are measuremet measuremet error error ad ador or extraeous extraeous facrs facrs affectig affectig trasmissio trasmissioefficiecy. Power(kW) Iput power Output power Trasmissio efficiecy Trasmissio efficiecy Times.7 7. The power ad trasmissio efficiecy. 7. The power ad trasmissio efficiecy oclusios oclusios Based Basedo o Witricity cocept ad compesatio mode mode research, research, oe oe applicatio applicatio method method for for wireless wireless chargig chargig of electric of electric vehicles vehicles is proposed is proposed ad studied ad through studied simulatios through simulatios ad experimets. ad experimets. I additio, I four additio, compesatio four compesatio modes havemodes bee aalyzed have bee aalyzed fid oe fid best suited oe best suited circuit. The joit circuit. simulatio The joit ofsimulatio Witricity of system Witricity basedsystem o Simplorer based o adsimplorer axwellad wasaxwell carried out was as carried well. The out experimetal as well. The results experimetal are preseted results are evaluate preseted performace evaluate of performace derived protype, of derived ad reasos protype, for ad differeces reasos betwee for differeces measured betwee parameters measured ad oretical parameters result ad have oretical bee cocluded. result have bee cocluded. Ackowledgmets: This work was supported i part by Natioal Natural Sciece Foudatio of Ackowledgmets: hia (Grat Number This work 5574) was supported ad i part i part by by Natural Natioal Sciece Natural Foudatio Sciece Foudatio of Hubei of Provice hia (Grat (Grat Number5574) 4FB7). ad i part by Natural Sciece Foudatio of Hubei Provice (Grat Number 4FB7). Author otributios: hogyu Dai proposed compesatio mode ad coil structure, coducted Author modelig otributios: aalysis, hogyu ad performed Dai proposed experimets. compesatio The mauscript mode ad was coil structure, improved coducted ad revised by modelig Juhua Wag, aalysis, egjiao ad performed og, ad Hog experimets. Huag. All The of mauscript authors cotributed was improved ad paper revised writig. by Juhua Wag, oflicts egjiao of Iterest: og, The ad authors Hog Huag. declareall oof coflict authors of iterest. cotributed paper writig. oflicts of Iterest: The authors declare o coflict of iterest. efereces efereces. Karalis, A.; Joaopoulos, J.D.; Soljačić,. Efficiet wireless o-radiative mid-rage, eergy trasfer. A. Phys. 8, 33, [rossef]. Karalis, A.; Joaopoulos, J.D.; Soljačić,. Efficiet wireless o-radiative mid-rage, eergy trasfer.. Jiag, H.; hag, J.; a, D.; hao, K.K.; iou, S.; Shahasser, H.; Fechter,.; Hirose, S.; Harriso,.; oy, S. A. Phys. 8, 33, A low-fruecy versatile wireless power trasfer techology for biomedical implats. IEEE Tras. Biomed.. Jiag, H.; hag, J.; a, D.; hao, K.K.; iou, S.; Shahasser, H.; Fechter,.; Hirose, S.; Harriso,.; oy, ircuits Syst. 3, 7, [rossef] [Pubed] S. A low-fruecy versatile wireless power trasfer techology for biomedical implats. IEEE Tras. Biomed. ircuits Syst. 3, 7, Nair, V.V.; hoi, J.. A Itegrated hip High-Voltage Power eceiver for Wireless Biomedical Implats. Eergies 5, 8,

14 Eergies 7,, 33 4 of 4 3. Nair, V.V.; hoi, J.. A Itegrated hip High-Voltage Power eceiver for Wireless Biomedical Implats. Eergies 5, 8, [rossef] 4. izuo, K.; iyakoshi, J.; Shiohara, N. Wireless power trasfer usig resoat couplig ad i vitro study. I Proceedigs of 4 IEEE Geeral Assembly ad Scietific Symposium, Beijig, hia, 6 3 August 4; pp ruciai, S.; ampi, T.; aradei, F.; Feliziai,. Numerical simulatio of Wireless Power Trasfer system recharge battery of a implated cardiac pacemaker. I Proceedigs of Iteratioal Symposium o Electromagetic ompatibility, aleigh, N, USA, 4 September 4; pp izuo, K.; Shiohara, N.; iyakoshi, J. Expressio of Heat Shock Proteis i Huma Fibroblast ells uder agetic esoat ouplig Wireless Power Trasfer. Eergies 5, 8, 8. [rossef] 7. Torra, G.; ulaa, F.; iuti, G.; Dario, P.; eciassi, A. Iductive-Based Wireless Power echargig System for a Iovative Edoscopic apsule. Eergies 5, 8, [rossef] 8. ao, S.; hiao, J.. Body Electric: Wireless Power Trasfer for Implat Applicatios. IEEE icrow. ag. 5, 6, [rossef] 9. he, W.; iu,.; ee,.; Sha,. ost-effectiveess ompariso of oupler Desigs of Wireless Power Trasfer for Electric Vehicle Dyamic hargig. Eergies 6, 9, 96. [rossef]. Sog, X.; iu, G.; hao,.; Xia, H.; hag,.u.; Xu, X.Y. esoace Wireless hargig Techology i Separate Groups for Power Battery Packs of Electric Buses. Diagog Jishu Xuebao 3, 8, Hou,..; hag, K.Y. Iductive Power Trasfer Systems for Bus-Sp-Powered Electric Vehicles. Eergies 6, 9, 5. [rossef]. Jag, Y.J.; Jeog, S.; i, S.. Iitial Eergy ogistics ost Aalysis for Statioary, Quasi-Dyamic, ad Dyamic Wireless hargig Public Trasportatio Systems. Eergies 6, 9, 483. [rossef] 3. Naberezhykh, D.; Theodoropoulos, T.; eed, N.; Ogissa, F.; Bludszuweit, H. Operatioal ruiremets for dyamic wireless power trasfer systems for electric vehicles. I Proceedigs of IEEE Electric Vehicle oferece, Florece, Italy, 7 9 December 4; pp Batra, T.; Schaltz, E.; Ah, S. eductio of magetic emissio by icreasig secodary side capacir for geometry based series-series pology for wireless power trasfer vehicles. I Proceedigs of Europea oferece o Power Electroics ad Applicatios, appeerata, Filad, 6 8 August 4; pp.. 5. i, S.; i,.. Wireless Power Trasfer for Electric Vehicle Applicatios. IEEE J. Emerg. Sel. Top. Power Electro. 5, 3, Shekhar, A.; Prasath, V.; Bauer, P.; Bolech,. Ecoomic Viability Study of a O-oad Wireless hargig System with a Geeric Drivig age Estimatio ethod. Eergies 6, 9, 76. [rossef] 7. Wag,.; Wei, X.; Dai, H. Desig ad otrol of a 3 kw Wireless Power Trasfer System for Electric Vehicles. Eergies 5, 9,. [rossef] 8. Gao, Y.; Farley, K.B.; Tse,.T.H. A Uiform Voltage Gai otrol for Aligmet obustess i Wireless EV hargig. Eergies 5, 8, [rossef] 9. Budhia,.; Boys, J.T.; ovic, G.; Huag,.-Y. Developmet of a Sigle-Sided Flux agetic oupler for Electric Vehicle IPT hargig Systems. IEEE Tras. Id. Electro. 3, 6, [rossef] 7 by authors. icesee DPI, Basel, Switzerlad. This article is a ope access article distributed uder terms ad coditios of reative ommos Attributio ( BY) licese (