A Three-Phase Dynamic Wireless Charging System with Constant Output Voltage

Article A Three-Phase Dynamic Wireless Charging System with Constant Output Voltage

Ruikun Mai ID , Hongchao Li, Yeran Liu, Kunzhuo Zhou, Ling Fu * and Zhengyou He *

School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China; [email protected] (R.M.); [email protected] (H.L.); [email protected] (Y.L.); [email protected] (K.Z.) * Correspondence: [email protected] (L.F.); [email protected] (Z.H.); Tel.: +86-28-8760-2445 (L.F. & Z.H.)

Received: 7 November 2017; Accepted: 21 December 2017; Published: 1 January 2018

Abstract: A dynamic wireless power transfer (WPT) system is an effective method, which can reduce charging time and extend the driving range of the electric vehicles. In the dynamic WPT systems, the output voltage may fluctuate when the receiver moves along the transmitter coils. This paper proposes a three-phase dynamic WPT charging system with overlapped three-phase transmitter coils. The overlap length is optimized to depress the fluctuation of the output voltage. These coils are powered by a three-phase inverter to generate an even magnetic field, and a unipolar coil is employed as a receiver to simplify the coil structure of the secondary side. Based on the proposed three-phase coil structure, the output voltage characteristics of the system are analyzed in detail. A 500 W dynamic charging prototype is established to validate the proposed dynamic charging system. Experimental results show that the output voltage fluctuation is within ±3.05%. The maximum system efficiency reaches 89.94%.

Keywords: wireless power transfer; three-phase inverter; dynamic charging

1. Introduction Internal combustion engine vehicles, the most prevailing transportation in past decades, contribute to the undesired emission of global greenhouse gas, spurring research into electric vehicles (EVs) and the smart grid [1]. The wireless power transfer (WPT) has many advantages compared with wired charger technology (e.g., opportunity charging, safety, immunity to ice, water, spark and other chemicals), [2,3] which makes WPT an ideal charging implementation in mobile phones, pacemakers and underwater robots [4,5]. WPT systems mainly focus on stationary charging applications such as medical implants [6], household appliances and stationary EVs [7]. In a stationary EVs charging situation, the vehicle is required to park in the designated position, and the receiver coil should be well-aligned with the transmitter coil, which is worrisome [8]. Also, the battery limits the cruising range of the vehicles and needs to be frequently recharged. Although a huge battery increases the cruising range, the system suffers from increased weight, longer charging time and higher cost. Besides, frequent fast charging and deep discharging of batteries degrade the lifespan of the expensive onboard batteries [9,10]. The dynamic WPT system can solve these issues mentioned above. When the vehicle is moving on the track, it can be recharged continuously. Thus, the cruising range of the EV can be extended, and the weight and cost of the vehicles can be reduced with a small battery. The total length of the transmitter is 90 m in a 3460 m route in Korea [11,12], and the maximum charging power reaches 100 kW [13]. This system has few circuit components and a simple structure, but the maximum efﬁciency of the system is only about 74% at 27 kW output [14]. In [15,16], multiple short transmitters are arranged on the lane of the vehicle, and the system is ﬂexible for design and installation. However, it requires a great quantity of compensation components, and the output power reduces to almost zero between two transmitters

Energies 2018, 11, 45; doi:10.3390/en11010045 www.mdpi.com/journal/energies Energies 2017, 10, 45 2 of 12 Energies 2018, 11, 45 2 of 12 requires a great quantity of compensation components, and the output power reduces to almost zero betweendue to the two existence transmitters of a dead due pointto the [ 17exis]. Atence novel of T-typea dead compensation point [17]. A networknovel T-type is proposed compensation in [18], networkwhich keeps is proposed a stable transmissionin [18], which power. keeps aApart stable from transmissio the methodsn power. mentioned Apart from above, the the methods design mentionedof coil structures above, is the another design useful of coil method structures to reduceis another the useful output method power fluctuationto reduce the for output the dynamic power fluctuationWPT system. for Circularthe dynamic coils WPT are adopted system. Circular to charge coils electrical are adopted vehicle to when charge the electrical vehicles vehicle move when along the vehicles track [19 move]. However, along the the track output [19] power. However, diminishes the output at the power border diminishes of two adjacent at the coils.border To of solve two adjacentthis issue, coils. a three-phase To solve this bipolar issue WPT, a three system-phase is adoptedbipolar WPT in [20 system], which is canadopted create in a [20] broader, which power can createdelivery a broader zone than power a single-phase delivery zone track. than The a switchablesingle-phase transmitter track. The coils switchable are adopted transmitter in [21]. coils To keep are adoptedthe coupling in [21] of. theTo keep transmitters the coupling and receiver, of the transmitters the geometry and of receiver, the receiver the geometry is optimized. of the A receiver prototype is optimized.is set up for A medium prototype power is set transferup for medium (tens of power Watts). transfer A novel (tens array-type of Watts). coils A designnovel array is presented-type coils to designovercoming is presented the coil misalignmentto overcoming in [the22] forcoil the misalignment static charging. in [22] In [23 for], athe homogeneous static charging. wireless In [23] power, a homogeneoustransfer system wireless is proposed. power The transfer alternate system transmitter is proposed. coils The are utilizedalternate to transmitter enhance the coils magnetic are utilized field todensity. enhance The the paper magnetic mainly fieldfocuses density. on the The coupling paper between mainly the focuses transmitter on the coils. coupling In order between to balance the transmitterthe three-phase coils. currents, In order the to system balance had the to three add- additionalphase currents, compensation. the system The had fluctuation to add additional of output compensation.power is almost The± 20%.fluctuation In [24 ],of both output the power transmitters is almost and ±20 the%. receiverIn [24], both are usingthe transmitters the LCC network. and the receiverThe inter-coupling are using th betweene LCC network. adjacent The coils in areter investigated-coupling between in detail. adjacent The maximal coils are valueinvestigated of output in detail.power isThe about maximal three timesvalue largerof output than thepower minimal is about value three of output times power.larger than To reduce the minimal the fluctuation value of of outputmagnetic power. fields To along reduce the track,the fluctuation the coils are of arrangedmagnetic closely fields inalong [25]. the The track, mutual the inductance coils are arranged between closelytransmitter in [25] coils. The is compensatedmutual inductance by extra between capacitors. transmitter coils is compensated by extra capacitors. This paper isis mainlymainly focusedfocused on on the the suppression suppression of of the the fluctuation fluctuation by by optimizing optimizing the the overlap overlap of the of thetransmitter transmitter coils, coils, which which is not is takennot taken into into account account by the by aforementionedthe aforementioned research. research. Six transmitter Six transmitter coils coilsare adopted are adopted to form to a track, form and a track, all the and coils all are the powered coils are by powered a three-phase by a inverter. three-phase Each transmitter inverter. Each coil transmitterhas its own compensationcoil has its own circuits, compensation and different circuits, transmitter and different coils are transmitter connected incoils parallel. are connected The overlap in parallel.of the adjacent The overlap transmitter of the coils adjacent and the transmitter circuit parameters coils and are thedesigned circuit to parameters minimize the are output designed voltage to minimizefluctuations. the Theoreticaloutput voltage analysis fluctuations. has been Theoretica experimentallyl analysis verified, has andbeen the experimentally output voltage verified, fluctuation and theis within output± voltage3.05% of fluctuation the average is voltage.within ±3.05% of the average voltage. TThishis paper paper isis organized organized as as follows: follows: Section Section2 describes 2 describes the optimization the optimization of transmitter of transmitter coils arrays. coils arrays.Section Section3 analyzes 3 analyzes the output the output voltage vol basedtage onbased the fundamentalon the fundamental harmonic harmonic model model of dynamic of dynamic WPT WPTsystem. system. The proposedThe proposed design design is validated is validated by experiments by experiments in Section in Section4. The 4. The conclusion conclusion is drawn is drawn in inSection Section5, finally. 5, finally.

2. Design Design and and Optimization Optimization of Coil Structure For the dynamic charging charging systems, systems, the the transmitter transmitter coils coils are are usually usually arranged arranged in in an an array array [11,12] [11,12].. The mutual inductance between the transmitter coil and the receiver coil varies with the position of the receiver coil. Accordingly, Accordingly, the induced voltage of of the receiver coil var variesies with the fluctuation ﬂuctuation of mutual inductance. The coil structure of the dynamic charging system is depicted in Figure 11.. SixSix squaresquare unipolarunipolar coils are arranged closely on the ferrite plates. The size of a single squaresquare coil is l.l .

Phase A Moving direction Phase B Phase C x Receiver Ferrite

0 l 2l 3l 4l 5l 6l

Figure 1. Structure of the transmitters and receiver. Figure 1. Structure of the transmitters and receiver.

EnergiesEnergies 20182017,, 1110,, 4545 33 ofof 1212

The equivalent circuit for the three-phase system is shown in Figure 2. The phasors of the The equivalent circuit for the three-phase system is shown in Figure2. The phasors of the induced induced voltages. . VAS , .VBS and VCS in the receiver can be expressed as: voltages V AS, VBS and VCS in the receiver can be expressed as: VjMI   . ASASTA . V ASVjMI= jωMAS ITA  . BSBSTB . (1)  VBS = jωMBS ITB (1) .VjMICSCSTC .  VCS = jωMCS ITC where  is the angular frequency of the system, and I , I and I are the phasors of the . . TA TB . TC wherecurrentω inis transmit the angularter A, frequency B and C, respec of thetively. system, Therefore, and ITA, ItheTB sumand IofTC inducedare the phasorsvoltage on of the receiver current inside transmitter is as follows: A, B and C, respectively. Therefore, the sum of induced voltage on the receiver side is as follows: . . . . VjMIjMIjMI (2) VS = SASTABSTBCSTCjωMAS ITA + jωMBS ITB + jωMCS ITC (2)

jL TA ITA

jMI ASS

VA jMI ABTB

IS jMI CATC jL jL TB S ITB

jMI BSS VAS

VS VB j MIAB TA VBS

jMI BCTC

VCS jL TC ITC

jMI CSS

VC j MICA TA

j MIBC TB

FigureFigure 2.2. Circuit topologytopology ofof thethe proposedproposed coilcoil structure.structure.

The mutual inductance between the transmitter and receiver coils is calculated using a 3-D FEA The mutual inductance between the transmitter and receiver coils is calculated using a 3-D tool, ANSYS Maxwell (Ozen Engineering, Inc., Silicon Valley, CA, USA). The specifications in FEA tool, ANSYS Maxwell (Ozen Engineering, Inc., Silicon Valley, CA, USA). The speciﬁcations in simulation and experiment are listed in Table 1. x is defined as the relative position between the simulation and experiment are listed in Table1. x is deﬁned as the relative position between the transmitter and receiver. The simulated mutual inductance between the transmitter and receiver coils transmitter and receiver. The simulated mutual inductance between the transmitter and receiver coils is shown in Figure 3. is shown in Figure3. Table 1. Parameters of the transmitter and the receiver. Table 1. Parameters of the transmitter and the receiver. Parameters Value LengthParameters of a Q coil [26] l /mm 200 Value

LengthAir of agap Q coildistance [26] l /mmlG /mm 70 200 Air gap distance lG/mm 70 Q coil turns in transmitter A NA 17 Q coil turns in transmitter A NA 17 Q coil turns in transmitter B N 17 Q coil turns in transmitter BB NB 17 Q coil turns in transmitter C NC 17 Q coil turns in transmitter C N 17 Q coil turns in receiver NR C 17 Relative position x/mm [0,1200] Q coil turns in receiver NR 17 Relative position x /mm [0,1200]

Energies 2017, 10, 45 4 of 12

H 40 Energies 2018, 11, 45 4 of 12 μ M / A1S

Energies 2017, 10, 45 c 4 of 12

n 30 M

a B1S t

a M

c C1S

u 2500

d M A2S

H 1400 M B2S

u μ

t M

/ M C2SA1S

c u

n 300 M M

a B1S t

a M

c C1S

u -120

0 20 40 60 80 100 M A2S

l 10 Location x of the receiver/cm M B2S a

u t M C2S u 0 Figure 3. SimulatedM mutual inductance between the receiver and transmitters. -10 0 20 40 60 80 100 Assuming that the amplitude of each coil current is equal. The relationship between I , I Location x of the receiver/cm TA TB and ITC can be expressed as: Figure 3 3.. SimulatedSimulated mutual mutual inductance inductance between the receiver and transmitters transmitters.. II   0  TAT 0 . . Assuming thatthat thethe amplitudeamplitude of of each each coil coil current current   is is equal. equal. The The relationship relationship between betweenITA ,IITATB, andITB . IITBT 0 120 (3) ITC can be expressed as:  and ITC can be expressed as: II.    240   TCT 0 ◦ ITA = IT0 0  . ∠ II   0 ◦ where IT0 is the RMS value of the current inITB theTAT= transmitterIT00 120 coil. The amplitude VS of the induced(3) . ∠     ◦ voltage can be expressed as: IIITCTBT= IT0 0∠120240 (3)  II   240 . VjMIjMIjMI  TCT 0 where IT0 is the RMS value of theSAS current TABS TBCS in TCthe transmitter coil. The amplitude VS of the induced voltage can be expressed as: 24 where IT0 is the RMS value of the current in the transmitterjj coil. The amplitude VS of the induced(4) jIMMeMe 33 voltage can be expressed as: . TASBSCS0  VS = |jωMAS ITA + jωMBS ITB + jωMCS ITC| (4) VjMIjMIjMI  j 2 j 4 F is the sum of all mutual inductances:SAS= TABS TBCS TC + 3 π + 3 π M jωIT0 MAS MBSe MCSe 24 jj (4) 2433 jIMMeMe jj FM is the sum of all mutual inductances:TASBSCS0 33 (5) FMMeMeMASBSCS j 2 π j 4 π FM = MAS + MBSe 3 + MCSe 3 (5) TFheM Equationis the sum (4) of shows all mutual that the inductances: amplitude of the induced voltage VS is related to FM directly, . when  and I are constant. 24 The EquationT0 (4) shows that the amplitude of thejj induced voltage VS is related to FM directly, 33 (5) FMMeMeMASBSCS whenTheω andmutualIT0 areinductances constant. against the location of the receiver and FM calculated by Equation (5) are shownThe mutual in Figure inductances 4. Large fluctuation against the locationof F exists of the with receiver the given and F Mparameters,calculated which by Equation will le (5)ad areto The Equation (4) shows that the amplitudeM of the induced voltage VS is related to FM directly, shown in Figure4. Large fluctuation of FM exists with the given parameters, which will lead to the thewhen fluctuation  and ofI the are induced constant. voltage. In order to alleviate the fluctuation of , overlapping is fluctuation of theT0 induced voltage. In order to alleviate the fluctuation of FM, overlapping is employed, employed, which is depicted in Figure 5. The overlap length is defined as L . whichThe is depictedmutual inductances in Figure5. Theagainst overlap the location length is of defined the receiver as LO and. FM calculatedO by Equation (5) are shown in Figure 4. Large fluctuation of F exists with the given parameters, which will lead to 50 M the fluctuation of the induced voltage. In order to alleviate the fluctuation of , overlapping is 40 M A1S L employed, which is depicted in Figure 5. The overlap length is definedM as O . 30 B1S M H C1S

μ 50

/ 20 M A2S

M M B2S 1400 MMC2SA1S MF 300 MB1S M

H C1S μ

-/ 1200 M A2S

0 20 40 60 80 100 M M B2S 10 x /cm M C2S F 0 FigureFigure 4 4.. ProcessedProcessed mutual mutual inductance inductance.. M -10 0 20 40 60 80 100 x /cm

Figure 4. Processed mutual inductance.

Energies 2017, 10, 45 5 of 12

Phase A Moving direction Phase B Phase C x Receiver Ferrite

Energies 2017, 10, 45 5 of 12 Energies 2018, 11, 45 25LO 5 of 12 Energies 2017, 10, 45 y 5 of 12 Phase A Moving direction x Phase B PhasePhase A C Movingx direction PhaseReceiver B PhaseFerrite C x Receiver L l Ferrite LO 25LO y L Figure 5. Illustration of the transmitters25O and receiver after overlapping. y x

From the Figure 6, the fluctuationx of FM varies as per the overlap of coils. It is of importance to

find the optimal overlap length to minimizeL the fluctuationl of . The variance DF()M is used to LO measure the fluctuation of , when the receiverL moves froml the second transmitter coils to the fifth LO transmitter coils. The variance of F with various overlapped length is calculated and shown in Figure 5. IllustrationM of the transmitters and receiver after overlapping . Figure 7. FigureFigure 5 5.. IllustrationIllustration of of the the transmitters transmitters and and receiver receiver after after overlapping overlapping..

From the Figure 6, the fluctuation of FM varies as per the overlap of coils. It is of importance to 50 From the Figure 6, the fluctuation of F varies as per the overlap of coils. It is of importance to find theFrom optimal the Figure overlap6, the length fluctuation to minimize of MFM thevaries fluctuation as per theof overlap. The ofvariance coils. ItDF is() ofM importance is used to to find the optimal overlap40 length to minimize the fluctuation of FM. The variance D(FM) is used findmeasure the optimal the fluctuation overlap of length , whento minimize the receiver the fluctuation moves from of the second. The variance transmitter DF() coilsM tois usedthe fifth to to measure the fluctuation of FM, when the receiver moves from the second transmitter coils to the LO  6cm measuretransmitter the coilsfluctuation. The variance of30 , when of FM the with receiver various moves overlapped from the secondlength istransmitter calculated coils and to shown the fifth in fifth transmitter coils. TheH variance of FM with various overlapped length is calculated and shown in

LO  9cm

μ / transmitterFigure 7. coils. The variance of F with various overlapped length is calculated and shown in

Figure7. M M LO  12cm

F 20

Figure 7. LO  15cm 50 10 50 40 0 40 20 40 60 80 100 L  6cm 30 x /cm O H LO  9cm

μ LO  6cm

30 H

M L  12cm Figure 6. The sum of mutual inductance with different overlappedLO  9cm length.

F 20 O

μ /

LO  15cm

M LO  12cm

F 20 10 DF()M is the square of the standard deviation of . As shown inL OFigure 15cm 7, varies with 10 the overlap proportion of the coil length, and the smallest variance occurs when LlO is about 0.45. 0 20 40 60 80 100 The calculated variance reaches the smallest x / valuecm when the overlap proportion is 0.445 from the 0 20 40 60 80 100 details of Figure 7. Meanwhile, the fluctuation x /cm of FM is the minimum, and the induced voltage is FigureFigure 6 6.. TheThe sum sum of of mutual mutual inductance inductance with with different different overlapped length length. . nearly uniform versus the variation of x . Figure 6. The sum of mutual inductance with different overlapped length. 18 DF()M is the square of the standard deviation of . As shown in Figure 7, varies with 16 DF() is the square of the standard0. deviation4 of . As shown in Figure 7, varies with the overlapM proportion of the coil length, and the smallest variance occurs when LlO is about 0.45. 14 0.3 theThe overlap calculated proportion variance of reaches the coil thelength, smallest and thevalue smallest when variance the overlap occurs proportion when Ll is 0.445 is about from 0.45. the

2 12 0.2 O H

Thedetails calculated of Figure variance 7. Meanwhile, reachesμ 10 the fluctuationsmallest value of FwhenM is thethe minimum,overlap proportion and the induced is 0.445 voltagefrom the is

/ 0.1

)

8 detailsnearly ofuniform Figure versus 7. Meanwhile, the variationF the fluctuationof x . of F is the minimum, and the induced voltage is

( 0 M

D 6 0.4 0.425 0.45 0.475 0.5 nearly uniform versus the variation18 of x . 4 1186 0.4 2 1164 0 00..43

2 11420.25 0.3 0.035.2 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

H 0.3

μ 10 LlO / 2 12 0.1 ) 0.2

H M

F μ

( 10

/ 0

0.1 ) Figure 7. Variance with various overlap proportion. FigureD 7. Variance0.4 with various overlap0.5 proportion.

0.425 0.45 0.475

M 6

( 0

D 64 0.4 0.425 0.45 0.475 0.5 D(FM) is the square of the42 standard deviation of FM. As shown in Figure7, D(FM) varies with 0 the overlap proportion of the2 coil length, and the smallest variance occurs when LO/l is about 0.45. 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 The calculated variance reaches0 the smallest value when the overlap proportion is 0.445 from the LlO 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 LlO Figure 7. Variance with various overlap proportion. Figure 7. Variance with various overlap proportion.

Energies 2017, 10, 45 6 of 12

Energies According20172018, ,1011, ,4 455 to the analysis, the induced voltage is dependent on the sum of all mutual66 of of 12 12 inductances. The fluctuation of F and the voltage can be reduced by overlapping three-phase According to the analysis, theM induced voltage is dependent on the sum of all mutual detailstransmitter of Figure coils.7. Meanwhile, the fluctuation of F is the minimum, and the induced voltage is inductances. The fluctuation of F and the voltageM can be reduced by overlapping three-phase nearlyThe uniform fluctuation versus of the variation is robustM of xto. the movement of the receiver along the x direction, but is transmitter coils. affectedAccording by the to misalignment the analysis, between the induced the voltagetransmitter is dependent coils and the on thereceiver sum ofcoil all along mutual the inductances. y direction The fluctuation of is robust to the movement of the receiver along the x direction, but is Theas shown fluctuation in Figure of FM 5.and Considering the voltage the can misalignment be reduced along by overlapping the y direction, three-phase the mutual transmitter inductance coils.s is affectedsimulatedThe by fluctuation theby misalignmentANSYS of Maxwell,FM is between robust and tothe the istransmitter calculated. movement coils The of theand calculated receiverthe receiver results along coil are the along shownx direction, the iny directionFigure but is8 asaffected shown by in theFigure misalignment 5. Considering between the misalignment the transmitter along coils the and ythe direction, receiver the coil mutual along inductance the y directions is where Ld i s indicates the lateral displacement of the receiver along the y direction. The mutual simulatedas shown inby Figure ANSYS5. ConsideringMaxwell, and the misalignment is calculated. along The thecalculatedy direction, results the are mutual shown inductances in Figure is8 inductances between the transmitters and the receiver will decrease with the increment of Ldis . The wheresimulated L by indicates ANSYS Maxwell, the lateral and displacementFM is calculated. of the The receiver calculated along results the are y showndirection. in Figure The 8 mutual where fluctuationd i s of is still constant, but smaller than that with no misalignment, when the receiver Ldis indicates the lateral displacement of the receiver along the y direction. The mutual inductances inductances between the transmitters and the receiver will decrease with the increment of Ldis . The betweenmoves along the transmitters the track. and the receiver will decrease with the increment of Ldis. The fluctuation fluctuation of is still constant, but smaller than that with no misalignment, when the receiver of FM is still constant, but smaller than that with no misalignment, when the receiver moves along 50 movesthe track. along the track. 40 50 30

H L  0cm

40 dis μ

/ 20 Ldis  5cm M

F 30 Ldis  10cm

H 10 Ldis  0cm μ

/ 20 Ldis  5cm

0 M

F L  10cm 1-010 dis 0 10 20 30 40 50 0 Location x of the receiver /cm -10 0 10 20 30 40 50 Figure 8. The sum of mutual inductance considering misalignment along the y direction. Location x of the receiver /cm

3. CircuitFigureFigure Analysis 8 8.. TheThe sum sum of of mutual mutual inductance inductance considering considering misalignment misalignment along along the the y direction. The circuit topology of the dynamic WPT system is shown in Figure 9. The input of the system 3.3. Circuit Circuit Analysis Analysis is a direct current (DC) source Vdc , which is connected to a three-phase full-bridge inverter to apply The circuit topology of the dynamic WPT system is shown in Figure 9. The input of the system threeThe high circuit-frequency topology ac voltage of the dynamic vPA , vPB WPT and systemvPC to the is shown resonant in Figurecircuit.9 The. The LCC input networks of the system [24,25] isis area a d direct irect chosen current current as the (DC) (DC) resonant sourc source e compensation VVdcdc ,, whichwhich isis topologies connectedconnected tofor a the three-phasethree transmitters.-phase full full-bridge- bridge Each transmitter inverter to to coilapply apply is three high-frequency ac voltage vPA, vPB and vPC to the resonant circuit. The LCC networks [24,25] threecompensated high-frequency independently. ac voltage TherevPA , v arePB transmitterand vPC to the coil resonant LTA ( LTB circuit., LTC ),The resonant LCC networks compensation [24,25] are chosen as the resonant compensation topologies for the transmitters. Each transmitter coil areinductors chosen asLPA the( L PB resonant, LPC ) , compensation and resonant capacitors topologies C forPA the( CPB transmitters., CPC ) and EachCTA ( C transmitterTB , CTC ) in coil each is is compensated independently. There are transmitter coil LTA(LTB, LTC), resonant compensation compensated independently. There are transmitter coil LTA ( LTB ,L LTC ), resonantC compensation inductorstransmitterLPA side.(LPB , ALPC series), and resonant resonant capacitorscompensation,CPA( C consistingPB, CPC) and of CTAS (andCTB , CSTC, ) is in adopted each transmitter on the inductors L ( L , L ), and resonant capacitors C ( C , C ) and C ( C , C ) in each side.receiver A series side.PA resonantMPBAS , MPC compensation,BS and MCS are consisting the mutual of L inductancesS andPA CPBS, is adopted betweenPC on theTA the transmitter receiverTB TC side. coils M andAS , transmitterMBS and M CS side.are A the series mutual resonant inductances compensation, between the consisting transmitter of coilsL and and receiverC , is adopted coil. MAB on, M theBC receiver coil. MAB , MBC and MCA are the mutual inductances betweenS the transmitterS coils. and MCA are the mutual inductances between the transmitter coils. receiver side. MAS , MBS and MCS are the mutual inductances between the transmitter coils and receiver coil. MAB , MBC and MCA are the mutual inductances between the transmitter coils. LPA CTA LTA CPA M AS

M CS L AB PA C M LPB TA L BS CTB TA M C CPA L AS LS D R Vdc C TB PB M M CA CS MAB vPA BC M v LLPB C BS PB PC TB M C R V vPC CTC LTB CS LS D dc CPB LTC CPC M CA M vPA BC vPB LPC M vPC CTC CS FigureFigure 9. 9.Schematic Schematic ofof thethe proposedproposedLTC system.system. CPC

The fundamental harmonics approximation method is used to analyze the circuit shown in Figure 9. Schematic of the proposed system. Figure 10. The inverter is regarded as ﬁrst-order harmonic voltage sources. RTA(RTB, RTC) and RS are the equivalent series resistors of the transmitter coil A (B, C) and the receiver coil respectively.

Energies 2017, 10, 45 7 of 12

The fundamental harmonics approximation method is used to analyze the circuit shown in

Figure 10. The inverter is regarded as first-order harmonic voltage sources. RTA ( RTB , RTC ) and RS areEnergies the 2018equivalent, 11, 45 series resistors of the transmitter coil A (B, C) and the receiver coil respectively.7 of 12

The rectifier and the dc load resistor R can be represented as an equivalent AC load resistor RL e q

[27]The, rectiﬁerwhich is and defined the dc as: load resistor R can be represented as an equivalent AC load resistor RLeq [27], which is deﬁned as: 8R R  8R R Leq = 2 (6(6)) Leq π2

iPA iTA

LPA v CTA L PA CPA TA

M AS RTA M AB CS iPB iTB iS RS L M PB C BS v TB L L R v PB CPB TB S Leq S M CA RTB M BC iPC iTC M CS LPC v CTC L PC CPC TC R TC Figure 10 10.. EquivalentEquivalent circuit circuit of the proposed system system..

Z ( Z , Z ) and Z ( Z , Z ) are the circuit impedance of the A (B, C)-phase in Z PA11(ZPBPB11, ZPCPC1 ) and ZPAPA2(ZPBPB22, ZPCPC22) are the circuit impedance of the A (B, C)-phase in Z transmitter side. The The circuit circuit impedance of receiver side is ZSS which which is is deﬁned defined as: as:  ZZ jPA L1 = j1ωL jPA C + 1/jωCPA  PA1 PA PA  Z  = 1/jωC + jωL + R + 1/jωC  PA2ZPA2 11 jTA C TA  j  L TA  R TATA  j  C PA PA     ZPB1 = jωLPB + 1/jωCPB  ZPB1  j L PB1 j C PB  = + + + ZPBZ2 1/11jω jC CTB  j ω LLTB  RRTB  j 1/ C jωCPB (7)   PB2 TB TB TB PB (7)   ZPC1 = jωLPC + 1/jωCPC  Z j L1 j C  Z  PC=11/jωC PC+ jωL PC + R + 1/jωC  PC2 TC TC TC PC  ZPC2 11 j C TC  j  L TC  R TC  j  C PC ZS = jωLS + RS + 1/jωCS + RLeq Z j L  R 1 j C  R  S S S S Leq Each transmitter circuit parameters of the three-phase dynamic charging system are the same. Thus,Each the relationshiptransmitter circuit is expressed parameters as: of the three-phase dynamic charging system are the same. Thus, the relationship is expressed as:  L = L = L  LLLPA PB PC  PAPBPC  CPA = CPB = CPC   CCCPAPBPC CTA = CTB = CTC (8) CCC  L TATBTC= L = L (8)  TA TB TC  LLL RTATATBTC= RTB = RTC  RRRTATBTC The values of CPA, CTA and CS are designed by:

The values of CPA , CTA and CS are designed by:  1 CPA = 2  ω LPA  1 CTA = 2 2 (9) ω [LTA−1/(ω CPA)]  1  CS = 2 ω LS

Energies 2018, 11, 45 8 of 12

Based on the Kirchhoff’s voltage law, the system can be expressed as:

.  .      I VPA ZPA1 −j/ωCPA 0 0 0 0 0 PA  .   0  − ITA    j/ωCPA ZPA2 0 jωMAB 0 jωMCA jωMAS  .   .     V  0 0 Z −j/ωC 0 0 0  IPB   PB   PB1 PB  .        0  = 0 jωMAB −j/ωCPB ZPB2 0 jωMBC jωMBS ITB (10)  .    .     −   VPC  0 0 0 0 ZPC1 j/ωCPC 0  IPC      .    0 jωM 0 jωM −j/ωC Z jωM    0   CA BC PC PC2 CS  ITC  .  0 jωMAS 0 jωMBS 0 jωMCS ZS 0 IS

The induced voltage in the receiver can be calculated from Equation (10) as:

. . VS= −RLeq × IS . . . 8R VPA MAS + VPB MBS + VPC MCS (11) = 2 LPA(8R + π RS) . . . where VPA, VPB and VPC are the output voltages of the three-phase inverter. The relationship between . . . VPA, VPB and VPC can be shown as: . . ( j 2 π VPB = VPAe 3 . . (12) j 4 π VPC = VPAe 3

By substituting Equation (12) into Equation (11), the induced voltage can be derived as:

. j 2 π j 4 π . 8RVPA MAS + MBSe 3 + MCSe 3 = VS 2 (13) LPA(8R + π RS) . Considering Equations (5) and (13), the output voltage VS is related to FM, when the R, LPA and . VPA are constant. Consequently, the fluctuation of output voltages reaches the minimum value with minimal fluctuation of FM. It should be noted that the angle frequency of the system is fixed and is equal to that of the inverter. Except for the generation of pulse width modulation (PWM) waves of the three-phase inverter, there’s no extra measurement circuit or control loop which is easy for implementation for practice.

4. Experimental Veriﬁcation A 500 W system is established to validate the proposed dynamic charging system as shown in Figure 11. All of the six transmitter coils have the same shape. Each transmitter coil with its compensation circuit is connected with a three-phase inverter in parallel. A square coil works as a receiver. The size and shape of each coil is identical as that described in Section2. Six transmitter coils share a three-phase inverter. The air gap distance in the dynamic charging system is 70 mm. The rectiﬁer and the compensation circuit of receiver coil are connected to a dc load resistor. The circuit parameters of the experimental system are listed in Table2. Energies 2017, 10, 45 9 of 12

Table 2. Parameters of the experiment system.

Parameters Value Parameters Value

f /kHz 200 RTB /Ω 0.15

Vdc /V 315 LPC /μH 50.29

Vo u t /V 72 CPC /nF 12.94

LO /cm 8.9 LTC /μH 119.47

LPA /μH 50.39 CTC /nF 15.32

CPA /nF 12.36 RTC /Ω 0.1

LTA /μH 120.1 LS /μH 110.53

CTA /nF 14.98 CS /nF 5.96

RTA /Ω 0.1 RS /Ω 0.18

LPB /μH 49.6 Maximum value of MAS /μH 37.68

CPB /nF 13.73 Maximum value of MBS /μH 38.1

L /μH 122.8 Maximum value of MCS /μH 38.55 Energies 2018, 11, 45 TB 9 of 12

CTB /nF 13.95 Output capacitor CD /μF 940

Figure 11. Experimental prototype. Figure 11. Experimental prototype.

A three-phase inverter is used to provide an ac excitation at the primary side. The oscilloscope Table 2. Parameters of the experiment system. Agilent DSO-X 3014T (KEYSIGHT TECHNOLOGIES, Beijing, China) is used to recording waveforms, and theParameters efficiency between Value dc source and Parameters dc load is gauged Valueby the power analyzer HIOKIPW6001 (HIOKI, Tokyo, Japan). When the receiver position x  644 mm, the stable f /kHz 200 RTB/Ω 0.15 waveforms of the output voltage v of the three-phase inverter, the output current i of the Vdc/V 315PC LPC/µH 50.29 PC Vout/V 72 CPC/nF 12.94 three-phase inverter, the input voltages urec and the input current iS of the rectifier are illustrated LO/cm 8.9 LTC/µH 119.47 in Figure 12. LPA/µH 50.39 CTC/nF 15.32 CPA/nF 12.36 RTC/Ω 0.1 LTA/µH 120.1 LS/µH 110.53 CTA/nF 14.98 CS/nF 5.96 RTA/Ω 0.1 RS/Ω 0.18 LPB/µH 49.6 Maximum value of MAS/µH 37.68 CPB/nF 13.73 Maximum value of MBS/µH 38.1 LTB/µH 122.8 Maximum value of MCS/µH 38.55 CTB/nF 13.95 Output capacitor CD/µF 940

A three-phase inverter is used to provide an ac excitation at the primary side. The oscilloscope Agilent DSO-X 3014T (Keysight Technologies, Beijing, China) is used to recording waveforms, and the efﬁciency between dc source and dc load is gauged by the power analyzer HIOKIPW6001 (HIOKI, Tokyo, Japan). When the receiver position x = 644 mm, the stable waveforms of the output voltage vPC of the three-phase inverter, the output current iPC of the three-phase inverter, the input voltages urec and the input current iS of the rectiﬁer are illustrated in Figure 12. EnergiesEnergies 20172018,, ,1011,, ,4 455 1010 of of 12 12

Energies 2017, 10, 45 10 of 12

)

v )

v v i

) PC PC

i v i )

v PC PC

i )

d v i i

/ PC PC

(

PC v

) urec i

) urec iS v

) S

)

i ) v u

i rec i

v S

)

(

rec

(

i rec u tt(2 s/div) t (2 s/div)

Figure 12.. Stable waveforms of the output voltages and currents of inverter and rectifier.. FigureFigure 12 12.. StableStable waveforms waveforms of of the the output output voltages voltages and and currents currents of of inverter inverter and and rectifier rectiﬁer.. In Figure 13a, L is aligned with transmitter coil L . M is much larger than M and In Figure 13a, LS is aligned with transmitter coil LTC . MCS is much larger than MAS and InIn Figure Figure 1313aa,, isLS aligned is aligned with with transmitter transmitter coil coilLTC .LTCMCS. MisCS much is much larger larger than thanMAS MandAS MandBS . M BS . Therefore, i PC is much larger than the other two, where iPA and i PB are almost equal. As the Therefore,BS iPC is muchPC larger than the other two, where iPA andPAiPB are almostPB equal. As the receiver MBS . Therefore, iPC is much larger than the other two, where i and iPB are almost equal. As the receiver moves to the transmitter coil L , the increases PA gradually and the i is gradually receivermoves to moves the transmitter to the transmitter coil LTA, the coili PALTAincreases, the gradually increases and gradually the iPC is and gradually the iPC reduced is gradually which receiver moves to the transmitter coil LTA , the increases gradually and the iPC is gradually reducedis shown which in Figure is shown 13b,c. in Figure 13b,c.

reduced which is shown in Figure 13b,c.

)

i ) i i i i i

) i i i i i i i PC PA PB PC )

i i PA i PB i i i i PA PB PC i d i i i PC v PA PC d PA PB PB

v PA PB PC

/ i

i i / i i i / i i i i i

/ PA PB PC PA PB PC /

A PA PB PC

(

i i t(2  s/div) t(2  s/div) t(2  s/div) (2 /div) t(2 ( sa/)div) t (sb) t(2 ( sc/)div) (a) (b) (c)

FigureFigure 13 13... MeasuredMeasured the the input input current current of inverter of inverter waveforms. waveforms. (a) Waveforms (a) Waveforms with withx  222x = mm222;;mm (b) ; Figure 13. Measured the input current of inverter waveforms. (a) Waveforms with x  222 mm ; (b) waveforms(b) waveforms with with x x259= 259 mm mm;;; (c ()c waveforms) waveforms with with xx=296mm296 mm... waveforms with x  259 mm ; (c) waveforms with x  296mm .

WhenWhen the the receiver receiver moves moves along along the the transmitters transmitters track, track, the the system system output output voltage voltage and and efficiency efficiency When the receiver moves along the transmitters track, the system output voltage and efficiency areare shown shown in in Figure Figure 14 14. The. The system system output output voltage voltage stays stays about about 72 V 72 with V with a fluctuation a fluctuation of ±3.05 of ±%3.05%.. The are shown in Figure 14. The system output voltage stays about 72 V with a fluctuation of ±3.05%. The highestThe highest system system efficiency efficiency between between the dc the source dc source and the and dc theload dc reaches load reaches up to 89.94% up to 89.94%and the and lowest the highest system efficiency between the dc source and the dc load reaches up to 89.94% and the lowest efficiencylowest efficiency is 86.67%. is 86.67%. In [28] In, the[28], system the system output output power power fluctuation fluctuation is is about about ±5.89%±5.89% with with a a load load efficiency is 86.67%. In [28], the system output power fluctuation is about ±5.89% with a load resistanceresistance of of 50 50Ω Ω, and, and the the maximum maximum of the of output the output power power is 230 W. is The 230 verificationW. The verification system’s maximum system’s resistance of 50 Ω, and the maximum of the output power is 230 W. The verification system’s maximumoutput power output is around power 120 is around W in [29 120]. TheW in maximum [29]. The maximum efficiency is efficiency 84% and is the 84% fluctuation and the fluctuation of power is maximum output power is around 120 W in [29]. The maximum efficiency is 84% and the fluctuation ofmore power than is ±more50%. than ±50%. of power is more than ±50%.

100 1 00 100 1 00

80 80

60 c

60 c V

f V

i /

60 c /

n V

i 90

out

90 e /

c out

n V

90 /

c out

% 40 y V 40

/ 40 % V 20 Voutout 20 V 20 Efoutf Eff 80 0 80 011 19 27 35 43 51 59 6780 11 19 27 35x /cm43 51 59 67 x /cm

FigureFigure 14 14... SystemSystem output output voltage voltage and and efficiency efﬁciency with with various various receiver receiver positions positions... Figure 14. System output voltage and efficiency with various receiver positions.

Energies 2018, 11, 45 11 of 12

5. Conclusions Aimed at reducing the voltage fluctuations in a dynamic WPT system, a three-phase dynamic charging system with two closely arranged overlapping transmitter coils to eliminate voltage dips between coils is proposed in this paper. The overlap length is optimized to reduce the fluctuation of the output voltage. The LCC-S compensation network is adopted in this paper. A 500 W output power dynamic charging system is set up to validate the proposed method. The experimental results show that the fluctuation of system output voltage is ±3.05%. The system’s highest efficiency from dc source to dc load reaches 89.94%.

Acknowledgments: This paper was supported by National Key R&D Program of China (2017YFB1201002), the National Natural Science Foundation of China under Grant (No. 51677155), the Sichuan Youth Science & Technology Foundation (No. 2016JQ0033), the Fundamental Research Funds for the Central Universities (No. 2682017QY01). Author Contributions: Ruikun Mai and Ling Fu designed the methodology and wrote the manuscript. Hongchao Li and Yeran Liu conceived and designed the experiments. Hongchao Li and Kunzhuo Zhou implemented the experiments. All authors contributed to improving the quality of the manuscript. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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