Article A High Efficiency Charging Strategy for a Supercapacitor Using a Wireless Power Transfer System Based on Inductor/Capacitor/Capacitor (LCC) Compensation Topology
Yuyu Geng *, Bin Li, Zhongping Yang, Fei Lin and Hu Sun School of Electrical Engineering, Beijing Jiaotong University, No. 3 Shangyuancun, Beijing 100044, China; [email protected] (B.L.); [email protected] (Z.Y.); fl[email protected] (F.L.); [email protected] (H.S.) * Correspondence: [email protected]; Tel.: +86-1520-1315-752
Academic Editor: Hongjian Sun Received: 14 October 2016; Accepted: 12 January 2017; Published: 21 January 2017
Abstract: In the application of rail transit vehicles, when using typical wireless power transfer (WPT) systems with series–series (SS) compensation supply power for supercapacitors, the output current is in an approximately inverse relationship with the duty cycle in a wide range. This renders the typical buck circuit control inappropriate. In order to help resolve the above issues, this paper designs inductor/capacitor/capacitor (LCC) compensation with new compensation parameters, which can achieve an adjustable quasi-constant voltage from the input of the inverter to the output of the rectifier. In addition, the two-port network method is used to analyze the resonant compensation circuit. The analysis shows that LCC compensation is more suitable for the WPT system using the supercapacitor as the energy storage device. In the case of LCC compensation topology combined with the charging characteristics of the supercapacitor, an efficient charging strategy is designed, namely first constant current charging, followed by constant power charging. Based on the analysis of LCC compensation, the system has an optimal load, by which the system works at the maximum efficiency point. Combined with the characteristics of the constant voltage output, the system can maintain high efficiency in the constant power stage by making constant output power the same as the optimal power point. Finally, the above design is verified through experiments.
Keywords: wireless power transfer; inductor/capacitor/capacitor (LCC) compensation; supercapacitor load; quasi-constant voltage gain; charging strategy
1. Introduction Wireless power transfer (WPT) systems have been widely developed for applications to rail transit vehicles because they avoid direct electrical connection, which can help eliminate the danger of electrical sparks and provide automatic power supply [1–4]. In recent years, some initiatives (Bombardier´s PRIMOVE and South Korea´s KAIST) have introduced the WPT technology power supply mode combined with the energy storage-type tram [5,6] to provide more convenient and safe traffic vehicles. Such vehicles do not require a large number of energy storage devices, and this can help make the vehicle more lightweight. In addition, the WPT system renders the power supply safer and more reliable, thus reducing the influence of environmental conditions. For this type of WPT system applied in rail transit vehicles, a three-phase rectifier is used to convert the grid alternating current (AC) to the direct current (DC) bus voltage. The primary-side coil is typically fed with a high-frequency AC current, which is converted via a single-phase inverter, and generates an AC magnetic flux linkage. Then, a secondary-side coil will induce an AC current to supply power to the load. The electrical equipment requires a small DC voltage and/or a current
Energies 2017, 10, 135; doi:10.3390/en10010135 www.mdpi.com/journal/energies Energies 2017,, 1010,, 135135 2 of 17 supply power to the load. The electrical equipment requires a small DC voltage and/or a current ripple, anan AC/DC AC/DC rectifier, rectifier, and and a DC/DC a DC/DC converter converter consisting consisting of a regulation of a regulation circuit, whichcircuit, is which typically is connectedtypically connected between itbetween and the it load. and Thethe load. topology The topology is displayed is displayed in Figure 1in. Figure 1.
Figure 1. Wireless power transfer (WPT) system configurationconfiguration in rail transit vehicles.vehicles.
In the WPT system, resonance compensation design is an important method by which suitable In the WPT system, resonance compensation design is an important method by which suitable characteristics of the system may be achieved, such as constant voltage or constant current. Authors characteristics of the system may be achieved, such as constant voltage or constant current. Authors in [7] propose a series-parallel/series (SPS) compensation topology which can ensure that the load in [7] propose a series-parallel/series (SPS) compensation topology which can ensure that the load stabilizes the active power even if there is alignment error in the coupling coils, while the input stabilizes the active power even if there is alignment error in the coupling coils, while the input resistance of the inverter is much higher. In [8], the characteristics of SS compensation and PS resistance of the inverter is much higher. In [8], the characteristics of SS compensation and PS compensation are analyzed, and a method is proposed to improve the efficiency in the full range by compensation are analyzed, and a method is proposed to improve the efficiency in the full range switching compensation. Other resonant compensations, such as inductor/capacitor/inductor (LCL), by switching compensation. Other resonant compensations, such as inductor/capacitor/inductor and inductor/capacitor/capacitor/inductor (LCCL), are found in [9–11]. These papers focus on (LCL), and inductor/capacitor/capacitor/inductor (LCCL), are found in [9–11]. These papers focus on improving performance indicators such as system efficiency, transfer power level and so on, and improving performance indicators such as system efficiency, transfer power level and so on, and give give the corresponding resonant compensation design criteria. Authors of [12,13] describe how to the corresponding resonant compensation design criteria. Authors of [12,13] describe how to achieve achieve resonant compensation design to obtain a soft switching inverter. For the battery load, the resonant compensation design to obtain a soft switching inverter. For the battery load, the system system efficiency, transfer power and voltage gain are analyzed under the condition of SS efficiency, transfer power and voltage gain are analyzed under the condition of SS compensation [14,15]. compensation [14,15]. The above research focuses on the resistance or battery load, but the energy storage device is The above research focuses on the resistance or battery load, but the energy storage device is typically a supercapacitor, so as to meet the demand of fast charging. There has been no further typically a supercapacitor, so as to meet the demand of fast charging. There has been no further research on resonant compensation considering the WPT system with a supercapacitor as the load. research on resonant compensation considering the WPT system with a supercapacitor as the load. Considering the supercapacitor to be the load of the WPT system, and adding buck circuit to Considering the supercapacitor to be the load of the WPT system, and adding buck circuit to control the charging current, it is hoped that the DC voltage after the secondary-side rectifier is constant control the charging current, it is hoped that the DC voltage after the secondary-side rectifier is so as to easily control the output power. The typical series–series (SS) compensation method [16,17] constant so as to easily control the output power. The typical series–series (SS) compensation is unable to meet such requirements. The compensation structures which have constant voltage method [16,17] is unable to meet such requirements. The compensation structures which have output are the series/parallel (SP) compensation [18], LCL compensation [9] and the secondary-side constant voltage output are the series/parallel (SP) compensation [18], LCL compensation [9] and controlled rectifier [14]. However, the SP compensation voltage gain is too high, while the LCL the secondary-side controlled rectifier [14]. However, the SP compensation voltage gain is too high, compensation voltage gain is too low for high power level WPT systems, and the controllable rectifier while the LCL compensation voltage gain is too low for high power level WPT systems, and the renders the control too complex. In order to resolve these issues, this paper presents a compensation controllable rectifier renders the control too complex. In order to resolve these issues, this paper structure which includes primary-side LCC compensation and the secondary-side series compensation presents a compensation structure which includes primary-side LCC compensation and the (known as LCC compensation), and gives the design of the compensation parameters. This LCC secondary-side series compensation (known as LCC compensation), and gives the design of the compensation can achieve adjustable quasi-constant voltage output to make input voltage of the compensation parameters. This LCC compensation can achieve adjustable quasi-constant voltage secondary buck circuit work at the constant value. The primary side and secondary side of WPT output to make input voltage of the secondary buck circuit work at the constant value. The primary system can be separated structures, and this can therefore reduce the information interaction between side and secondary side of WPT system can be separated structures, and this can therefore reduce the primary side and secondary side. In addition, combined with the charging requirements of the the information interaction between the primary side and secondary side. In addition, combined supercapacitor, an efficient charging strategy is proposed to allow the WPT system to work in optimal with the charging requirements of the supercapacitor, an efficient charging strategy is proposed to efficiency conditions. allow the WPT system to work in optimal efficiency conditions. The organization of this paper is as follows: The model and analysis or the WPT system is shown The organization of this paper is as follows: The model and analysis or the WPT system is in Section2. The problems of SS compensation are given and the LCC compensation analysis is shown in Section 2. The problems of SS compensation are given and the LCC compensation analysis carried out. Next, Section3 proposes the supercapacitor charging strategy using the WPT system, is carried out. Next, Section 3 proposes the supercapacitor charging strategy using the WPT system, and system efficiency is given. In Section4, an experimental prototype is fabricated to achieve the and system efficiency is given. In Section 4, an experimental prototype is fabricated to achieve the WPT system power supply for the supercapacitor (SC), and to verify the theory correctness of the LCC WPT system power supply for the supercapacitor (SC), and to verify the theory correctness of the
Energies 2017, 10, 135 3 of 17 Energies 2017, 10, 135 3 of 17 LCC compensation topology and feasibility of the supercapacitor charging strategy. Finally, compensationconclusions are topology given. and feasibility of the supercapacitor charging strategy. Finally, conclusions are given. 2. Model and Analysis of the WPT System 2. Model and Analysis of the WPT System 2.1. Mode of SS Compensation Cascade Buck Circuit 2.1. Mode of SS Compensation Cascade Buck Circuit In the application of rail transit, the bidirectional DC/DC converter is used to realize the functionIn the of application charging/discharging of rail transit, an the bidirectionalSC. The bidirectional DC/DC converter DC/DC isis used equivalent to realize to the the function buck ofconverter charging/discharging when charging an for SC. Thean SC. bidirectional When us DC/DCing a WPT is equivalent system that to the adopts buck converterthe typical when SS chargingcompensation for an SC.mode When supplying using a WPTpower system to an thatSC, adoptsthe buck the converter typical SS will compensation cascade after mode the supplying rectifier, powerand the to ansystem SC, thecan buck be converterdefined as will the cascade SS compensa after thetion rectifier, cascade and buck the system circuit can mode be defined as shown as the in SSFigure compensation 2. cascade buck circuit mode as shown in Figure2.
Figure 2. Series–series (SS) compensation cascade buck circuit mode. Figure 2. Series–series (SS) compensation cascade buck circuit mode.
TheThe systemsystem consistsconsists ofof DCDC busbus voltage,voltage, anan inverterinverter (working(working atat tenstens ofof kHz),kHz), thethe primary-primary- andand secondary-side coils, a rectifier, a buck converter and a load, where U is the DC bus voltage, UL/IL secondary-side coils, a rectifier, a buck converter and a load, where Ud d is the DC bus voltage, UL/IL is the load voltage/current, Uin/Iin is the input voltage and current of the coupling coils, Uout is the is the load voltage/current, Uin/Iin is the input voltage and current of the coupling coils, Uout is the output voltage of the coupling coils, IP and IS are the root-mean-square (RMS) values of the primary- output voltage of the coupling coils, IP and IS are the root-mean-square (RMS) values of the and secondary-side currents, respectively, and U is the DC voltage after rectifier. T1–T4 are the primary- and secondary-side currents, respectively,d2 and Ud2 is the DC voltage after rectifier. T1–T4 full-bridge semiconductor switches, D1–D4 are the rectifier diodes, RP (RS), LP (LS) and CP (CS) are the are the full-bridge semiconductor switches, D1–D4 are the rectifier diodes, RP (RS), LP (LS) and CP (CS) primaryare the primary (secondary) (secondary) side coil resistance,side coil resistance, inductance inductance and series compensationand series compensation capacitors respectively, capacitors Mrespectively,is the mutual M inductanceis the mutual of theinductance primary- of and the secondary-side primary- and coils,secondary-side and C and Lcoils,are theand DC C and side L filter are inductor and capacitor, respectively. Finally, T5/D5 is the semiconductor switch and diode of the buck the DC side filter inductor and capacitor, respectively. Finally, T5/D5 is the semiconductor switch converter, and RL is the load resistance. and diode of the buck converter, and RL is the load resistance. InIn orderorder to to simplify simplify the analysisthe analysis of the transferof the characteristicstransfer characteristics of the system, of the SSsystem, compensation the SS WPTcompensation system may WPT be arrangedsystem may as shown be arranged in Figure as3 show. Accordingn in Figure to Kirchhoff’s 3. According voltage to Kirchhoff's law, the following voltage equationslaw, the following are obtained: equations are obtained: . . . U =I R 1+ 1 + jωL − jωMI =++−in P P jωCPωωP S . UIRin. P P jLjMI P S . . (1) jCω 1 Uout = −ISRS + P + jωLS + jωMIP = ISReq jωCS (1) =− +1 +ωω + = UIRout S S jLjMIIR S P S eq The operating frequency ω is the angularω frequency of the high frequency inverter, IP and IS are jCS the primary and secondary side current. Based on the working principle of the rectifier and buck circuit,The the operating relationship frequency between ω is the the outputangular equivalent frequency resistanceof the high of frequency coupling inverter, coils (Req IP) and I loadS are resistancethe primary (R Land) is achievedsecondary as side follows, current. Based on the working principle of the rectifier and buck circuit, the relationship between the output√ equivalent resistance of coupling coils (Req) and load U 2 2U /π 8 U /D 8 resistance (RL) is achieved as= follows,out = d2√ = L = Req 2 2 2 RL (2) IS πId2/2 2 π DIL π D UU22 π 88UD R ==out d2 =L = R eqπ ππ222 L (2) where D is the duty cycle of the buckIDISL circuit.Id2 22 D
where D is the duty cycle of the buck circuit.
Energies 2017, 10, 135 4 of 17
In order to reduce the power converter volt-ampere (VA) rating and improve the transfer EnergiesefficiencyEnergies2017 2017 ,of,10 10 ,the, 135 135 system [19], the compensation capacitance parameters are determined by Formula44 ofof 1717 (3) in the SS compensation topology. In order to reduce the power converter volt-ampere (VA) rating and improve the transfer ==ωω22 efficiencyIn order of tothe reduce system the [19], power the converter compensation1 volt-ampereLCP capacitancePSS (VA) LC ratingparameters and improve are determined the transfer by efficiency Formula(3) of(3) the in systemthe SS compensation [19], the compensation topology. capacitance parameters are determined by Formula (3) in the SS compensation topology. ==ωω22 1 2 LCP PSS2 LC (3) 1 = ω LPCP = ω LSCS (3)
Figure 3. SS compensation equivalent circuit.
The secondary side current IS can be calculated according to Formulas (1) and (3): FigureFigure 3.3. SSSS compensationcompensation equivalentequivalent circuit.circuit. ωMU = in IS 8 2 TheThe secondarysecondary sideside currentcurrentI ISS cancan bebe calculatedcalculated++ accordingaccording()ω toto FormulasFormulas (1)(1) andand (3):(3): (4) 22RRRLSP M π D ωMU = ωMUinin I=S IS 2 (4) According to the relationship of the8 8parameters++ of input/output()ω 2 voltage and current of (4)the 2 222 RLRRR+LSPRS RP + (ω MM) rectifier and buck circuit, the load currentππ DcanD be determined as follows: AccordingAccording to to the the relationship relationship22 of theof parametersthe parameters of input/outputω MUof input/output voltage voltage and current and current of the rectifier of the II== in andrectifier buck and circuit, buck the circuit, load currenttheLS load can current be determined can be determined as follows: as follows: πD πD 2 22 (5) √ R RM++()ω RR PSπ PL 2222 22 ωωMUin D IL II===IS = h in i √ (5) LSπD π√D 2 2 2 πD πD RPRS + (ωM)2 +22RPRL (5) When Uin and M are fixed values, the2 2 relationshipR RM++()ω betweenπ D RRand IL is as shown in Figure 4. The parameters of SS compensation are22 shownPS in Table 1. It πcanD be PL found that when the D is When U and M are fixed values, the relationship between D and IL is as shown in Figure4. gradually increased,in the IL first increases and then decreases, and the maximum value of IL is The parametersWhen Uin and of SS M compensation are fixed values, are shown the relationship in Table1. It between can be found D and that IL whenis as shown the D isin gradually Figure 4. obtained when the critical value of Db is equal to that shown in Formula (6). RP is a relatively low increased,The parameters the IL firstof SS increases compensation and then are decreases, shown in and Table the maximum1. It can be value found of IthatL is obtainedwhen the when D is value, thus the critical value of Db is very small. In a large range of Db < D < 1, the load current IL gradually increased, the IL first increases and then decreases, and the maximum value of IL is theand critical duty cycle value D of presentDb is equal an approximate to that shown inverse in Formula proportion (6). RofP isthe a variation. relatively lowThe value,mode of thus the the SS obtained when the critical value of Db is equal to that shown in Formula (6). RP is a relatively low criticalcompensation value of cascadeDb is very buck small. circuit In ais large different range offromDb 300 200 250 150 200 100 22 RR 150 PL 50 π + ()ω 2 RRPS M 100 0 0 0.1220.2 RR0.3PL 0.4 0.5 0.6 0.7 0.8 0.9 1 50 π + ()ω 2 RRPS M Figure 4. The relationship between D and I . 0 Figure 4. The relationship between D and ILL. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 4. The relationship between D and IL. Energies 2017, 10, 135 5 of 17 Energies 2017, 10, 135 5 of 17 TableTable 1. 1.Experiment Experiment platform parameters. parameters. SymbolsSymbols Note Note Value Value Ubus DC bus voltage 100 V Ubus DC bus voltage 100 V f f OperatingOperating frequency frequency 58 kHz 58 kHz LPLP Primary-sidePrimary-side coil coil inductance inductance 167.6 167.6 μHµ H RPRP Primary-sidePrimary-side coil coil self-resistance self-resistance 0.19 0.19 Ω Ω CPCP Primary-sidePrimary-side series series compensation compensation capacitor capacitor 44.42 44.42 nF nF L Secondary-side coil inductance 169.7 µH SLS Secondary-side coil inductance 169.7 μH RS Secondary-side coil self-resistance 0.27 Ω RS Secondary-side coil self-resistance 0.27 Ω CS Secondary-side series compensation capacitor 44.39 nF MCS Secondary-side Mutualseries compensation inductance capacitor 44.39 29.2 nFµ H LM MutualFilter inductance inductance 29.2 2.5μH mH L Filter inductance 2.5 mH UsingUsing Formula Formula (7), (7), it canit can be be found found thatthat the reason for for this this is isthat that the the variations variations of duty of dutycycle cycleD D will resultwill result in the in the change change of of the the output output voltage voltage ofof the rectifier rectifier UUd2d2, and, and is thus is thus inversely inversely proportional proportional 2 to D . 2 to D . √ s 2 2 R R D = P L (6) b 22 RRPL 2 D = π R R + (ωM ) b π P S+ ()ω 2 (6) RRPS M ωMUinRL Ud2 = h ωMU R i √ (7) =πD2 in L2 2 2 U d2 √ R R + (ωM) + R R 2 π2 2 P S π P L D ++()ω 2 22 (7) RRP SPL M RR In order to allow the input voltage22 of the secondary buckπ circuit to work at the constant value, the secondary-sideIn order to allow voltage the needs input voltage to be constant of the secondar or nearlyy buck constant. circuit Theto work primary at the sideconstant and value, secondary sidethe of WPTsecondary-side system arevoltage expected needs to be be constant separated or nearly structures, constant. therefore The primary interaction side and ofsecondary information betweenside theof WPT primary system side are and expected secondary to be sideseparate cand be structures, reduced. therefore interaction of information betweenConsidering the primary the above side factors,and secondary this paper side redesignscan be reduced. the LCC resonance compensation topology to achieve theConsidering constant the output above voltage factors, characteristics this paper rede ofsigns the the buck LCC circuit. resonance compensation topology to achieve the constant output voltage characteristics of the buck circuit. 2.2. LCC Compensation Topology Analysis 2.2. LCC Compensation Topology Analysis In view of the above problems, this paper proposes a compensation topology. The mode by In view of the above problems, this paper proposes a compensation topology. The mode by which the primary side provides LCC compensation and secondary side provides series compensation which the primary side provides LCC compensation and secondary side provides series has thecompensation characteristic has ofthe quasi characteristic constant of voltage quasi constant output, voltage which output, can allow which the can buck allow circuit the tobuck use the traditionalcircuit to control use the method. traditional In control addition, method. this mode In addition, has adjustable this mode voltagehas adjustable gain and voltage is suitable gain and for the applicationis suitable of for a high the application power WPT of a system. high power WPT system. FigureFigure5 shows 5 shows the the principle principle of of the the resonant resonant compensationcompensation topology. topology. Resonant Resonant inductance inductance Lr Lr and capacitorand capacitorCr areCr are additional additional elements elements comparedcompared with with SS SS resonant resonant compensation compensation mode, mode, RLr isR theLr is the self-resistanceself-resistance of L ofr. Lr. FigureFigure 5. 5.LCC LCC compensationcompensation equivalent equivalent circuit. circuit. According to the principle of the circuit, the secondary-side coil parameters are converted to According to the principle of the circuit, the secondary-side coil parameters are converted to the the primary-side system, as shown in Figure 6a, ZRE is the reaction impedance. The secondary side primary-side system, as shown in Figure6a, Z is the reaction impedance. The secondary side is is series resonant compensation method, so the REreaction impedance ZRE can be calculated as follows, series resonant compensation method, so the reaction impedance ZRE can be calculated as follows, ω2 M2 ZRE = (8) Req + RS Energies 2017, 10, 135 6 of 17 Energies 2017, 10, 135 6 of 17 ω 22 = M ZRE (8) Energies 2017, 10, 135 22+ 6 of 17 RRωeqM S Z = RE + (8) RReq S U Uin in Uω Uin j inLr ω j Lr Figure 6. Equivalent transformation of LCC compensation. Figure 6. Equivalent transformation of LCC compensation. To achieve constant output voltage of the receiving side, it is necessary to meet the To achieve constant output voltage of the receiving side, it is necessary to meet the requirement requirement that the primary-side coil current is constant. Then, in the case of secondary-side series that theTo primary-sideachieve constant coil current output is constant.voltage Then,of the in re theceiving case of side, secondary-side it is necessary series compensation,to meet the compensation, the constant voltage output can be achieved. According to the Norton theorem, LLC therequirement constant voltagethat the outputprimary-side can be coil achieved. current According is constant. to Then, the Norton in the theorem,case of secondary-side LLC compensation series compensation circuit can be equivalent to that shown in Figure 6b. Therefore, in the case of circuitcompensation, can be equivalent the constant to that voltage shown output in Figure can be6b. achieved. Therefore, According in the case to of the constant-voltage-source Norton theorem, LLC constant-voltage-source input, the constant-current-source can be obtained by series inductor Lr. If input,compensation the constant-current-source circuit can be equivalent can be obtained to that byshown series in inductor Figure L6b.r. If Therefore, the parallel in compensation the case of the parallel compensation capacitor Cr is resonant with Lr, the constant current characteristic of the capacitorconstant-voltage-sourceC is resonant withinput,L the, the constant-curre constant currentnt-source characteristic can be obtained of the primary-side by series inductor coil can Lr. be If primary-sider coil can be achieved.r As shown in Figure 6b. The constant current value of the achieved.the parallel As compensation shown in Figure capacitor6b. The C constantr is resonant current with value Lr, ofthe the constant primary-side current coils characteristic can be obtained of the primary-side coils can be obtained when the self-resistance of inductance is ignored: whenprimary-side the self-resistance coil can be of inductanceachieved. As is ignored:shown in Figure 6b. The constant current value of the primary-side coils can be obtained when the self-resistanceU of inductance is ignored: I = in P ωUin (9) = Lr IP Uin (9) IP = ωLr (9) ωL The values of LS, CS, Cr and Lr are given by the followingr formula The values of LS, CS, Cr and Lr are given by the following formula The values of LS, CS, Cr and Lr are given1 by the following formula ==L CLC ω1 2 rr SS (10) 1 = = 2 ==LrCr LSCS (10) ω 2 LrrCLC SS (10) To reduce the power converter VA rating,ω the primary-side capacitor is typically tuned so that To reduce the power converter VA rating, the primary-side capacitor is typically tuned so that the the inputTo reduce voltage the and power current converter is in zero-phase VA rating, un theder prim certainary-side coupling capacitor and isload typically conditions, tuned and so thatthe input voltage and current is in zero-phase under certain coupling and load conditions, and the value valuethe input of the voltage capacitor and C currentP is determined is in zero-phase by the following under certain formula: coupling and load conditions, and the of the capacitor CP is determined by the following formula: value of the capacitor CP is determinedω by the following11 formula:= jLP ++ 0 (11) jCωω jC 111P 1 r jωωLP + + == 0 (11) jLP ++ 0 (11) jωjCωωCP j jCωCr According to (10) and (11), CP can be determined:P r According to (10) and (11), C can be determined: According to (10) and (11), CPP can be determined:1 C = P ω2 ()− (12) LL1P1 r CP == (12) CP 22 (12) ωω (()LLLP −− Lr) Next, the two-port network theory [19] is introducedP r to analyze the equivalent circuit of the primaryNext,Next, side, the and two-porttwo-port the system network has theory constant-volta [[19]19] is introducedintroducedge-source input to analyzeanalyze as shown thethe equivalentequivalent in Figure 7, circuit where ofof U thetheRE primaryand IRE are side, the and voltage the system and current has constant-voltage-source of the reactance resistance. input as shown in Figure7, where URE and primary side, and the system has constant-voltage-source input as shown in Figure 7, where URE IRE are the voltage and current of the reactance resistance. and IRE are the voltage and current of the reactance resistance. Iin IRE Iin IRE Uin U RE Uin U RE Figure 7. Two port network of LCC compensation. Figure 7. Two port network of LCC compensation. As the input type of LCCFigure compensation 7. Two port networksystem ofis a LCC voltage compensation. source, a two-port network [21] can be expressedAs the input as follows: type of LCC compensation system is a voltage source, a two-port network [21] can As the input type of LCC compensation system is a voltage source, a two-port network [21] can be expressed as follows: be expressed as follows: " . # " #" . # Uin Z11 Z12 Iin . = . (13) Z Z URE 21 22 IRE Energies 2017, 10, 135 7 of 17 where . Uin 1 Z11 = . | . = RLr + jωLr + (14) IRE=0 jωC Iin r . Uin 1 Z12 = . | . = (15) Iin=0 jωC IRE r . URE 1 Z21 = . | . = (16) IRE=0 jωC Iin r . URE 1 1 Z22 = . | . = RP + jωLP + + (17) Iin=0 jωC jωC IRE P r When the parameters satisfy the compensation requirements of (10) and (12), Equations (14)–(17) can be simplified as follows: h iT h iT Z11 Z12 Z21 Z22 = RLr jωLr jωLr RP (18) Therefore, the output and input voltage gain of the two-port network is: URE Z21ZRE ωLrZRE G = = = (19) U ( + ) − 2 Uin Z11 ZRE Z22 Z12Z21 RLr(ZRE + RP) + (ωLr) The voltage gain of the output of the coupling coil to the reactance resistance can be calculated as: . jωMIP + × Req R Uout RS Req eq = . = (20) URE I × Z ωM P R It can be concluded that the voltage gain from the output of the inverter to the output of the coupling coil is as follows: 2 Req ω MLr Uout Uout URE RS+Req HU = = = (21) Uin URE Uin (ωM)2 2 R + R + (ωLr) Lr RS+Req P Under the condition of ignoring the self-resistance of the coils and the resonant inductance, the voltage gain (HU) can be simplified as: M HU ≈ (22) Lr HU can be approximated as the ratio of M and Lr, and when the equivalent resistance Req changes, Uout can be maintained as a quasi-constant state. In addition, when the duty cycle of the buck circuit is changed, the secondary-side DC bus voltage Ud2 will remain in the quasi-constant state. Furthermore, if M is determined, then the voltage gain of the system can be adjusted by the appropriate choice of the Lr value. According to the parameters shown in Table1, Figure8 shows the comparison of the voltage gain between the SS compensation and LCC compensation. It can be found that the LCC topology has a more stable voltage gain even if the load changes. EnergiesEnergies2017 2017, 10, 10, 135, 135 88 of of 17 17 3 2.5 2 1.5 1 0.5 SS LCC 0 0 5 10 15 20 25 30 FigureFigure 8. 8.The The comparison comparison of of the the voltage voltage gain gain between between SS SS and and LCC LCC compensation. compensation. The output current of the inverter Iin and primary-side coil current IP can be calculated The output current of the inverter I and primary-side coil current I can be calculated according according to the characteristics of the twoin port network, P to the characteristics of the two port network, U I = in in U 2 = ()ωLRRin ()+ Iin rSeq2 (23) + (ωLr) (R +Req) RLr 2 S RLr +()ω 2 ++() (ωMRRRM) +RPPS(RS+Req) eq U = Uinin IPI=P 2 2 (24) RLr RP RLr(ω()ωM) RRLr P+ RMLr + ωLr (24) ωLr ++ωLr(R +Req) ωL ω ω S + r Lr LRrS() R eq Ignoring the self-resistance of the coils and the resonant inductance, (23) and (24) can be simplified as follows:Ignoring the self-resistance of the coils and the resonant inductance, (23) and (24) can be M2 simplified as follows: ≈ Iin Uin 2 (25) Lr Req M 2 IU≈ in inUin 2 (25) IP ≈ LreqR (26) ωLr U When the parking error causes the decreaseI ≈ of thein mutual inductance, the output current of P ω (26) the inverter will reduce according to Equation (25), whichLr ensures the safe operation of the system. When the inverter output voltage Uin is fixed, the current flow through the primary-side coil IP has a When the parking error causes the decrease of the mutual inductance, the output current of the quasi-constant current characteristic according to Equation (26) which is consistent with Equation (9). inverter will reduce according to Equation (25), which ensures the safe operation of the system. The quasi-steady characteristic of IP leads to the primary coil magnetic field stability which guarantees When the inverter output voltage Uin is fixed, the current flow through the primary-side coil IP has a the transmission of electrical energy. This also proves that the LCC compensation topology has better quasi-constant current characteristic according to Equation (26) which is consistent with Equation fault tolerance ability and is more suitable for application in rail transit. (9). The quasi-steady characteristic of IP leads to the primary coil magnetic field stability which 3.guarantees Supercapacitor the transmission Charging Strategy of electrical Using WPTenergy System. This also proves that the LCC compensation topology has better fault tolerance ability and is more suitable for application in rail transit. 3.1. Characteristics Analysis of Super Capacitor Load 3. Supercapacitor Charging Strategy Using WPT System The supercapacitor is typically used as the energy storage device in rail transit vehicles due to its advantage of high power density, and the equivalent circuit of the supercapacitor can be seen in Figure9. 3.1. Characteristics Analysis of Super Capacitor Load When the WPT system charges for the supercapacitor, the voltage and current of supercapacitor will changeThe in realsupercapacitor time due to is the typically charging used process. as the This energy paper storage adopts device an equivalent in rail transit variable vehicles resistance due to RitsL to advantage represent of the high supercapacitor. power density, The and relationship the equivalent between circuit them of can the be supercapacitor determined as can follows: be seen in Figure 9. When the WPT system charges for the supercapacitor, the voltage and current of U supercapacitor will change in real time Rdue= to SCthe charging process. This paper adopts(27) an L I equivalent variable resistance RL to represent the SCsupercapacitor. The relationship between them can be determined as follows: U = SC RL (27) I SC Energies 2017, 10, 135 9 of 17 The instantaneous equivalent load value RL is the ratio of the supercapacitor voltage and the Energies 2017, 10, 135 9 of 17 charging current. The instantaneous equivalent load value RL is the ratio of the supercapacitor voltage and the Energies 2017, 10, 135 9 of 17 charging current. Figure 9. Simplified equivalent model of the supercapacitor. The use of supercapacitorFigure 9. Simplified is typically equivalent based modelon the of thecharge supercapacitor. and discharge curve. The most Figure 9. Simplified equivalent model of the supercapacitor. common method is constant current charging at the beginning, followed by adopting low charging currentThe charging instantaneoususe of supercapacitor to the equivalentrated voltage is loadtypically when value basedtheRL supercapacitoris on the the ratio charge of the reaches and supercapacitor discharge rated voltage. curve. voltage This The and papermost the chargingcommonconsiders current.method the constant is constant power current charge chargingto the rated at thevoltage. beginning, The charging followed curve by adopting is shown lowin Figure charging 10. currentTheThe charging usecharging of supercapacitor to process the rated will is voltagehave typically an wheneffect based theon on thesupercapacitor the characteristics charge and dischargereaches of the ratedWPT curve. system.voltage. The most Considering This common paper methodconsidersthe supercapacitor´s is the constant constant current charging power charging charge features, to at thethis the rated beginning,paper vo proposesltage. followed The a chargingnew by segmented adopting curve is lowcharging shown charging in strategy Figure current 10.for chargingthe supercapacitorThe tocharging the rated process using voltage the willwhen LCC have thecompensation-m an supercapacitor effect on theode characteristics reaches WPT ratedsystem. voltage.of theThe WPT following This system. paper subsection considersConsidering will the constanttheprovide supercapacitor´s an power introduction. charge charging to the rated features, voltage. this Thepaper charging proposes curve a new is shown segmented in Figure charging 10. strategy for the supercapacitor using the LCC compensation-mode WPT system. The following subsection will provide an introduction. FigureFigure 10.10. Supercapacitor (SC)(SC) chargingcharging method.method. 3.2. Segmented Charging Strategy The charging process willFigure have 10. an Supercapacitor effect on the (SC) characteristics charging method. of the WPT system. Considering the supercapacitorThe supercapacitor´s charging charging features, process this is paper divided proposes into two a new stages, segmented namely chargingthe constant strategy current for the3.2.and supercapacitorSegmented constant powerCharging using stage. Strategy the In LCC the compensation-modeconstant current stage, WPT the system. LCC compensation The following mode subsection can ensure will provide an introduction. that theThe output supercapacitor voltage of charging the rectifier process remains is divided constant, into which two signifiesstages, namely that the the input constant voltage current of the buck converter is constant. Therefore, the constant charging current of the supercapacitor is easily 3.2.and Segmentedconstant power Charging stage. Strategy In the constant current stage, the LCC compensation mode can ensure thatachieved the output by controlling voltage of the the buck rectifier circuit, remains and constant,the control which method signifies can usethat PIthe control input voltage to adjust of the buckdutyThe cycleconverter supercapacitor of the is buck constant. circuit. charging Therefore, This process is consistent the is constant divided with intocharging the twotypi stages,cal current control namely of of the the thesupercapacitor buck constant circuit. current is easily and constantachievedWhen powerby the controlling supercapacitor stage. In the the buck constant voltage circuit, increases current and stage,the to thecontrol the reference LCC method compensation voltage can use value PI mode UcontrolSC* at can the to ensure adjustend of that the thedutyconstant output cycle current voltageof the buckcharging, of the circuit. rectifier it willThis remainsenter is consistent the constant, constant with which thepower typi signifies chargingcal control that stage. theof the input The buck system voltage circuit. efficiency of the buck is convertermore important is constant. when Therefore, USC is in the constantrange from charging the reference current voltage of the supercapacitor USC* to the rated is easily voltage achieved UMAX, When the supercapacitor voltage increases to the reference voltage value USC* at the end of the byconstantas controllingthe charging current the powercharging, buck circuit,is greater. it will and enter This the controltheprovides constant method a constant power can usecharging power PI control charging stage. to The adjust strategy system the dutybased efficiency cycle on the ofis theLCC buck compensation circuit. This method is consistent to maintain with the a high typical charging control efficiency of the buck of the circuit. WPT system. more important when USC is in the range from the reference voltage USC* to the rated voltage UMAX, as theWhenThe charging current the supercapacitor power gain of is the greater. two voltage port This network increases provides is todetermined a the constant reference aspower follows: voltage charging value strategyUSC* at thebased end on of the constant current charging, it will enter the constant power charging stage. The system efficiency is LCC compensation method to maintain aIZ high charging efficiencyω L of the WPT system. more important when USC is in theG range==RE from the reference21 = voltage r USC* to the rated voltage UMAX, The current gain of the two portI network is determined++ as follows: (28) as the charging power is greater. This providesIZZZRin a RE constant22 power RE charging P strategy based on the LCC compensation method to maintain a highIZ charging efficiencyω of L the WPT system. ==RE21 = r When the system is under theG Iresonance and when the converter (including inverter, rectifier(28) The current gain of the two port networkIZZZR is determined++ as follows: and buck converter) losses are ignored thein system RE efficiency22 RE expression P can be obtained: IRE Z21 ωLr When the system is underG the= resonance= RR and when= the converter (including inverter, rectifier(28) I UI RE RE eq eq η =⋅ Iin ZRE + Z =⋅22GGZRE + RP and buck converter) losses are ignored the system++ efficiencyUI expression can be obtained: (29) UIin in R eq R S R eq R S When the system is under the resonanceUI andRR when the converter (including inverter, rectifier and η =⋅RE RE eq =⋅GG eq buck converter) losses are ignored the system efficiency++ expressionUI can be obtained: (29) UIin in R eq R S R eq R S URE IRE Req Req η = · = GU GI · (29) Uin Iin Req + RS Req + RS Energies 2017, 10, 135 10 of 17 Energies 2017, 10, 135 10 of 17 According to the formula of GU and GI, the system efficiency based on LLC compensation can be expressed as follows: According to the formula of GU and GI, the system efficiency based on LLC compensation can be R expressed as follows: ω 422ML eq r ()RR+ 2 η = Seq 224 2 2 Req (30) ()ωωMMRω M()Lr 2 2 +++(RS+LrReq) ()ω η = RRRLPLrPr (30) RR++2 RR2 (ωMSeq) (ωM) SeqRLr 2 + R + R R + (ωLr) RS+Req P RS+Req Lr P Considering the system parameters listed in Table 1, the relationship between η and Req is shownConsidering in Figure the11 systemaccording parameters to (30). In listed the inprocess Table 1of, the the relationship equivalent betweenload Req graduallyη and Req increases.is shown inThe Figure system 11 according efficiency to will (30). first In theincrease, process then of the de equivalentcrease, which load isR similareq gradually with increases.the SS compensation The system efficiencymode. If the will output first increase, equivalent then resistance decrease, of which the coupling is similar coil with is the the optimal SS compensation load Ropt, the mode. system If thecan outputmaintain equivalent the efficient resistance operation, of the coupling namely coilReq is= theRopt optimal, and then load Rtheopt , thesystem system achieves can maintain maximum the efficientefficiency. operation, namely Req = Ropt, and then the system achieves maximum efficiency. 100 90 80 70 0 20 40 60 80 100 Figure 11. The relationship between η and Req. Figure 11. The relationship between η and Req. By differentiating η with respect to Req and equating the differential function to zero, By differentiating η with respect to Req and equating the differential function to zero, ∂η = 0 ∂ηR (31) eq= 0 (31) Req The optimum value Ropt for maximum efficiency can be obtained as follows: The optimum value Ropt for maximum efficiency can be obtained as follows: ()ωωω222+++ () () MRRMRLRRRRP S Lr r S P S Lr Rv = uopt h 2 ih 2 2 2 i (32) u (ωM) + RPRS RLRR(ωM()ω) RLr+ + (ωLr) RS + RPRSRLr u Pr PLr Ropt = (32) t h 2 i RP (ωLr) + RPRLr As the self-resistance (RP, RS, RLr) is further decreased, the reactance (ωM, ωLr), Ropt can be simplified as shown in (33), As the self-resistance (RP, RS, RLr) is further decreased, the reactance (ωM, ωLr), Ropt can be simplified as shown in (33), 4 ()ωMR R 2 RMv≈+Lr S ()ω optu 42 (33) u (ω()ωMLR) R RRP ≈ t rPLr + S ( )2 Ropt 2 ωM (33) (ωLr) RP RP When the load RL changes, it is found that the duty cycle of the buck circuit can be adjusted to makeWhen Req = theRoptload accordingRL changes, to Formula it is found (2) which that thecan duty ensure cycle that of the the system buck circuit has been can beworking adjusted at the to makemaximumReq = Refficiencyopt according point. to In Formula order to (2) simplify which canthe control ensure thatdifficulty the system in the hasactual been control, working combined at the maximumwith Formula efficiency (22) the point. optimal In order load to control simplify can the be control converted difficulty to optimal in the actualpower control,control. combinedWhen the withoutput Formula power (22)of system the optimal is the constant load control Popt, the can maximum be converted efficiency to optimal of the power system control. based on When the LCC the outputcompensation power of structure system iscan the be constant obtained:Popt , the maximum efficiency of the system based on the LCC compensation structure can be obtained: UU222 =≈outM in Popt 2 (34) 2 2 2 URoptMLr UR opt = out ≈ in Popt 2 (34) Ropt Lr Ropt Energies 2017, 10, 135 11 of 17 Energies 2017, 10, 135 11 of 17 Based on the above analysis, an efficientefficient charging strategy for the supercapacitor is designed combined with the WPT system, as shown in Figure 1212.. The supercapacitor voltage and current are detected in real time,time, andand ifif thethe supercapacitorsupercapacitor voltagevoltageU USCSC isis smallersmaller thanthan thethe referencereferencevoltage voltageU USCSC*,*, the buck circuit is controlledcontrolled under the constantconstant current charging model. When the super capacitor voltage USC isis greater greater than than the the USC** instruction, instruction, then then the the product product of of the the super capacitor voltage and current is calculated as the supercapacitor chargingcharging power, andand thethe constantconstant powerpower referencereference PPSCSC* is used to adjust the buck circuit duty cycle D toto achieveachieve constantconstant powerpower charging.charging. Figure 12. Charging strategy for supercapacitor. Figure 12. Charging strategy for supercapacitor. In order toto satisfysatisfy thethe output output requirements requirements of of the the system system and and maintain maintain high high system system efficiency, efficiency, the thetraditional traditional methods methods are basedare based on dual-side on dual-side control, control, namely namely the inverter the inverter and DC/DC and DC/DC which which adjust adjustthe efficiency the efficiency and the outputand the power output respectively. power re Thisspectively. method This skillfully method uses skillfully the characteristics uses the characteristicsof LCC constant of voltageLCC constant output, voltage further output, combined further with thecombined requirements with the of therequirements supercapacitor of the´s supercapacitor´sconstant power supply constant to designpower ansupply efficient to design charging an strategy.efficient Tocharging a certain strategy. extent, To system a certain efficiency extent, is systemimproved, efficiency and the is complicated improved, an duald the side complicated control is avoided, dual side which control can is prove avoided, the stable which operation can prove of the stable WPT system. operation of the WPT system. 4. Experiment Verification 4. Experiment Verification 4.1. Setup of Experiment 4.1. Setup of Experiment In order to verify the constant voltage characteristics of LCC compensation mode and feasibility In order to verify the constant voltage characteristics of LCC compensation mode and of the proposed charging strategy, a WPT system experimental prototype is fabricated, and shown in feasibility of the proposed charging strategy, a WPT system experimental prototype is fabricated, Figure 13. The topology of the WPT system using SC as a load is similar to that shown in Figure2, and shown in Figure 13. The topology of the WPT system using SC as a load is similar to that but the SS compensation is replaced by LCC compensation. The parameters are consistent with those shown in Figure 2, but the SS compensation is replaced by LCC compensation. The parameters are in Table2. consistent with those in Table 2. Energies 2017, 10, 135 12 of 17 Energies 2017, 10, 135 Table 2. Experiment platform parameters. 12 of 17 Symbols Note Value Table 2. Experiment platform parameters. Ubus DC bus voltage 100 V f Operating frequency 58 kHz Symbols Note Value LP Primary-side coil inductance 167.6 μH U RP bus Primary-side coil self-resistance/DC bus voltage 0.19 100 Ω V f Operating frequency 58 kHz CP Primary-side series compensation capacitor 54.7 nF LP Primary-side coil inductance 167.6 µH LR Primary-side series compensation inductance 33.4μH RP Primary-side coil self-resistance/ 0.19 Ω RLr CP Primary-side seriesPrimary-side compensation series compensation self-resistance capacitor 0.1 54.7 Ω nF CR LR Primary-sidePrimary-side parallel compensation series compensation capacitor inductance 0.25 33.4 μFµ H RLr Primary-side series compensation self-resistance 0.1 Ω LS Secondary-side coil inductance 169.7 μH CR Primary-side parallel compensation capacitor 0.25 µF RS Secondary-side coil self-resistance 0.27 Ω LS Secondary-side coil inductance 169.7 µH CS RS Secondary-side seriesSecondary-side compensation coil self-resistance capacitor 44.39 0.27 nFΩ M CS Secondary-sideMutual inductance series compensation capacitor 29.2 44.39 μH nF L M Filter inductanceMutual inductance 2.5 29.2 mHµ H L Filter inductance 2.5 mH The SanRex three-phase bridge DF100AA160 (Osaka, Japan) is used to convert the grid alternatingThe SanRex current three-phase (AC) to direct bridge current DF100AA160 (DC). (Osaka,CREE SiC Japan) MOSFET is used C2M0080120D to convert the grid(Durham, alternating NC, currentUSA) is (AC)adopted to direct as the current active (DC). switch CREE of inverter SiC MOSFET (DC/AC) C2M0080120D on the 58 kHz (Durham, switching NC, frequency. USA) is adopted CREE asSiC the SBD active C4D20120D switch of inverter(Durham, (DC/AC) NC, USA) on theis used 58 kHz as switchingthe anti-parallel frequency. diode CREE of the SiC inverter SBD C4D20120D (DC/AC) (Durham,and the switch NC, USA) of the is usedrectifier as the(AC/DC). anti-parallel The transmitter diode of the and inverter receiver (DC/AC) inductors and are the circular switch of coils the rectifierwith a single (AC/DC). layer and The a transmitter turn number and of receiver 18, comp inductorsosed of tightly-wound are circular coils litz with wires a singlewith a layerdiameter and aof turn 3 mm. number The external of 18, composed diameter of coil tightly-wound is 40 cm and litz the wires gap withbetween a diameter the transmitter of 3 mm. and The receiver external is diameter15 cm. The of coilinductor is 40 cmand andcapacitor the gap are between chosen theunder transmitter the resonance and receiver for both is 15the cm. transmitter The inductor and andreceiver, capacitor and arethe chosen resonant under frequency the resonance is same for bothas the the transmitteroperating frequency and receiver, for and improving the resonant the frequencyefficiency isand same reducing as the operatingthe VA frequencyrating of forthe improvingWPT system. the efficiencyThe SC andvoltage, reducing charging the VA current, rating oftransmitter the WPT and system. receiver The AC SC voltage,currents chargingand voltages current, are tested transmitter usingand a Tektronic receiver ACDPO3034 currents Digital and voltagesPhosphor are Oscilloscope tested using (Beaverton a Tektronic, OR, DPO3034 USA). Digital Based Phosphoron the test Oscilloscope results, the (Beaverton, transmitting OR, power, USA). Basedreceiving on thepower test results,and transfer the transmitting efficiency power,are calc receivingulated using power MATLAB and transfer software efficiency according are calculated to the usingdefinition MATLAB of power. software according to the definition of power. The supercapacitor charging processprocess isis asas follows.follows. First, constant currentcurrent ((IISCSC*)*) charging is performed until the supercapacitorsupercapacitor voltagevoltage increasesincreases toto thethe referencereference voltagevoltage ((UUSCSC*), thethe IISCSC** is is 12 A and thetheU USCSC** isis 50 50 V. V. Then, Then, when when the supercapacitorthe supercapacitor voltage voltage is greater is greater than U SCthan*, the USC charging*, the charging process changesprocess tochanges constant to powerconstant charging, power and charging, the power and reference the powerPSC* isreference 600 W. ThePSC* capacitance is 600 W. of The the supercapacitorcapacitance of the is 18 supercapacitor F. is 18 F. Figure 13. Cont. Energies 2017, 10, 135 13 of 17 Energies 2017, 10, 135 13 of 17 Energies 2017, 10, 135 13 of 17 Figure 13. Demo SC-load wireless power transfer (WPT) system (up) and each part (down). 4.2. Setup of Experiment When supercapacitor charging adopts an efficient charging strategy, the inverter output voltage and current waveform are as shown in Figure 14 under the mode of the constant power. It can be seen that the phase of inverter output voltage is ahead of the current phase. This is because the above theoretical analysis is based on the fundamental waveform, however the output of the inverter isFigure a square 13. Demo wave SC-load at three wireless times power and has transfer higher (WPT) harmonics, system ( upthus) and there each is part only (down a light). phase difference of the voltage and current. This also enables the system to achieve zero voltage switching (ZVS).4.2. Setup of Experiment Figure 15 shows the waveform of the secondary-side DC bus voltage Ud2 during the When supercapacitorsupercapacitor charging charging adopts adopts an efficientan efficient charging charging strategy, strategy, the inverter the inverter output voltageoutput supercapacitor charging process. It was found that the amplitude of Ud2 decreased from 100 V to 83 voltage and current waveform are as shown in Figure 14 under the mode of the constant power. It V,and which current is because waveform with are the as shownincrease in of Figure the ou14tput under power, the mode the DC of thebus constant voltage power.decreases, It can and be seencan be that seen the that phase the of phase inverter of inverter output voltage output isvolt aheadage ofis ahead the current of the phase. current This phase. is because This is the because above during the constant power process Ud2 is constant. Thus, the voltage gain HU can maintain a the above theoretical analysis is based on the fundamental waveform, however the output of the quasi-steadytheoretical analysis state. Since is based the voltage on the fundamentalgain is approximately waveform, 1 (corresponding however the output to the of ratio the invertervalue of isM a squareinverter wave is a square at three wave times at and three has times higher and harmonics, has higher thus harmonics, there is only thus a light there phase is only difference a light phase of the and Lr) this verifies the accuracy of the analysis. voltagedifference and of current. the voltage This and also current. enables This the system also en toables achieve the system zero voltage to achieve switching zero voltage (ZVS). switching (ZVS). Figure 15 shows the waveform of the secondary-side DC bus voltage20 Ud2 during the supercapacitor charging100 process. It was found that the amplitude of Ud2 decreased from 100 V to 83 V, which is because with the increase of the output power, the DC bus voltage decreases, and 10 during the constant power50 process Ud2 is constant. Thus, the voltage gain HU can maintain a quasi-steady state. Since the voltage gain is approximately 1 (corresponding to the ratio value of M 0 0 and Lr) this verifies the accuracy of the analysis. -50 -10 20 -100100 -20 10 50 FigureFigure 14. 14. OutputOutput0 voltage( voltage(uuinin) )and and current( current(iiniin) )of of the the inverter inverter in in constant constant power power0 mode. mode. Figure 15 shows-50 the waveform of the secondary-side DC bus voltage U during the -10 d2 supercapacitor charging process. It was found that the amplitude of Ud2 decreased from 100 V to 83 V, which is because with-100 the increase of the output power, the DC bus voltage decreases, and during the -20 constant power process Ud2 is constant. Thus, the voltage gain HU can maintain a quasi-steady state. Since the voltage gain is approximately 1 (corresponding to the ratio value of M and Lr) this verifies the accuracy of the analysis. Figure 14. Output voltage(uin) and current(iin) of the inverter in constant power mode. EnergiesEnergies 2017 2017, ,10 10, ,135 135 1414 of of 17 17 120120 100100 Energies 2017 10 Energies 2017, , 10, 135, 135 1414 of of 17 17 8080 1206060 1004040 802020 00 6000 2020 4040 6060 8080 100100 120120 40 20FigureFigure 15. 15. DC DC Voltage Voltage of of rectifier rectifier at at secondary secondary side side 0 FigureFigure 1616 representsrepresents thethe0 waveformswaveforms20 40ofof thethe supercapacitorsupercapacitor60 80 charging100charging120 current,current, chargingcharging voltagevoltage andand chargingcharging power.power. TheThe constantconstant chargingcharging powerpower isis 593593 W,W, whichwhich isis essentiallyessentially inin agreementagreement withwith referencereference powerpower PPSCSC*.*. AccordingAccording toto thethe outputoutput voltagevoltage andand currentcurrent ofof thethe inverterinverter asas shownshown inin thethe FigureFigure 15. 15.DC DC Voltage Voltage of of rectifier rectifier at at secondary secondary side. side FigureFigure 14,14, thethe inverterinverter outputoutput activeactive powerpower ((PPinin)) isis obtainedobtained asas shownshown inin FigureFigure 17.17. TheThe constantconstant powerpowerFigure P Pinin is is 16675 675 represents W. W. the waveforms of the supercapacitor charging current, charging voltage Figure 16 represents the waveforms of the supercapacitor charging current, charging voltage and chargingTheThe variation variation power. of of Thethe the coupling couplingconstant system chargingsystem efficiency efficiency power is of of 593 the the W, charging charging which processis process essentially is is shown shown in agreement in in Figure Figure 18. with18. It It andcan charging be found power. that during The constant constant charging current powercharging, is 593 the W, efficiency which is will essentially increase in and agreement the maximum with referencecan be found power that P SCduring*. According constant to currentthe output chargi voltageng, the and efficiency current willof the increase inverter and as theshown maximum in the referenceefficiency power will bePSC obtained*. According with to constant the output power voltage charging. and current That is of because the inverter the optimal as shown power in the is Figureefficiency 14, willthe inverterbe obtained output with active constant power power (Pin) ischarging. obtained That as shown is because in Figure the optimal17. The powerconstant is Figureobtained. 14, the The inverter experimental output active results power are almost (Pin) is obtainedthe same aswith shown the incalculation Figure 17 .results The constant in accordance power powerobtained. Pin isThe 675 experimental W. results are almost the same with the calculation results in accordance P is 675 W. withinwithThe Equation Equation variation (30), (30), of and and the the thecoupling maximum maximum system efficiency efficiency efficiency is is about aboutof the 95%. 95%.charging process is shown in Figure 18. It can be found that during 20constant20 current charging, the efficiency will increase and the maximum efficiency will be obtained1010 with constant power charging. That is because the optimal power is obtained. The experimental results are almost the same with the calculation results in accordance 00 with Equation (30), and the100100 maximum efficiency is about 95%. 205050 10 00 8008000 100 400400 50 00 00 2020 4040 6060 8080 100100 120120 0 800 Figure 16. Voltage, current and power of supercapacitor. Figure400Figure 16. 16.Voltage, Voltage, current current and and power power of of supercapacitor. supercapacitor. 0 7007000 20 40 60 80 100 120 600600 Figure 16. Voltage, current and power of supercapacitor. 500500 400400 700 300300 600 200200 500 100100 400 00 300 200 FigureFigureFigure 17. 17. 17.Output Output Output power power power of of of the the the inverter inverter inverter at at at constant constant constant power power power mode. mode. mode. 100 The variation of the coupling0 system efficiency of the charging process is shown in Figure 18. It can be found that during constant current charging, the efficiency will increase and the maximum efficiency will be obtainedFigure 17. with Output constant power power of the inverter charging. at constant That is power because mode. the optimal power is obtained. The experimental results are almost the same with the calculation results in accordance with Equation (30), and the maximum efficiency is about 95%. Energies 2017, 10, 135 15 of 17 Energies 2017, 10, 135 1 15 of 17 Energies 2017, 10, 135 15 of 17 0.95 1 0.9 Calculation η 0.95 Experiment 0.85 0.9 Calculation 0.8 η Experiment 0.85 0.75 0 20 40 60 80 100 120 0.8 0.75 Figure 18. Calculation0 20and experimental40 results60 of80 the coupling100 coils120 efficiency. According to the experimental results, the overall efficiency of the inverter to the supercapacitorFigure (includingFigure 18. 18.Calculation Calculation the efficiency and and experimental experimentalof the rectifier results results and of of thethe thecoupling buck coupling circuit) coils coils efficiency. was efficiency. found to be 87.8% in the constant power stage as shown in Figure 19. Overall efficiency can be maintained at the maximumAccordingAccording efficiency to theto point. experimentalthe experimental results, results, the overall the efficiency overall ofefficiency the inverter of tothe the inverter supercapacitor to the (includingsupercapacitorThe experimental the efficiency (including results of thethe rectifierefficiencyverify andthe of thecorrectnessthe buckrectifier circuit) ofand the wasthe theoretical buck found circuit) to bederivation 87.8%was found in theof to constantthe be LCC87.8% powercompensationin the stage constant as WPT shownpower system, instage Figure and as theshown 19 efficient. Overallin Figure segmen efficiency 19.ted Overall charging can efficiency be strategy maintained can is performedbe at maintained the maximum using at the the efficiencyexperiments.maximum point. efficiency point. The experimental results verify the correctness of the theoretical derivation of the LCC compensation WPT system, and the efficient segmented charging strategy is performed using the 0.9 experiments. 0.8 0.9 η 0.7 0.8 0.6 η 0.7 0.5 0 20 40 60 80 100 120 0.6 0.5 FigureFigure 19.019. ExperimentalExperimental20 results40results ofof60 thethe overalloverall80 systemsystem100 efficiency.efficiency.120 5. ConclusionsThe experimental results verify the correctness of the theoretical derivation of the LCC Figure 19. Experimental results of the overall system efficiency. compensationThis paper WPT presents system, a and new the compensation efficient segmented mode chargingwhich strategyincludes isprimary-side performed usingLCC the experiments. compensation5. Conclusions and secondary-side series compensation, and is based on the deficiency of the typical mode of SS compensation cascade buck circuit. In this manner, the WPT system can achieve 5. Conclusions adjustableThis quasi-constantpaper presents voltage a new output, compensation which renders mode the buckwhich circuit includes control primary-side method easier LCC to usecompensation andThis more paper reliable. presentsand secondary-side This a new allows compensation theseries design compensation mode method which of, and includesthe iscompensation based primary-side on the deficiencyparameters LCC compensation of to the achieve typical andadjustablemode secondary-side of voltageSS compensation gain. series Based compensation, cascade on this buck LCC and circuit. compensation is based In this on the manner,topology, deficiency the an WPT ofefficient the system typical supercapacitor can mode achieve of SSsegmentedadjustable compensation charging quasi-constant cascade strategy buck voltage is proposed, circuit. output, In namely thiswhich manner, firerstnders constant the the WPT buck current system circuit charging cancontrol achieve and method then adjustable constant easier to quasi-constantpoweruse and charging, more voltage reliable. and the output, This system allows which can rendersthebe operateddesign the buckme effithodciently circuit of the controlat acompensation constant method po easierwer parameters stage. to use Finally, and to achieve more the reliable.theoryadjustable correctness This voltage allows of the gain.the design LCC Based compensation method on this of theLCC compensationtopology compensation and feasibility parameters topology, of to the achievean supercapacitor efficient adjustable supercapacitor charging voltage gain.strategysegmented Based are verified oncharging this LCCthrough strategy compensation experiments. is proposed, topology, namely an first efficient constant supercapacitor current charging segmented and then charging constant strategypowerIn future ischarging, proposed, works, and namely thethe constantsystem first constant can power be operated currentcharging charging effi processciently and will at thena be constant constantoptimized po powerwer further stage. charging, to Finally, improve and the theoveralltheory system system correctness can efficiency. be operated of the For LCC efficiently example, compensation atthe a losses constant topology of the power converter and stage. feasibility will Finally, be of considered, the the supercapacitor theory such correctness as thecharging loss of themodelstrategy LCC of compensation rectifierare verified and through buck topology converter. experiments. and feasibility The charging of the time supercapacitor of the constant charging current strategy charging areverified process throughwill beIn designed experiments. future works, under thethe conditioconstantn powerthat the charging charging processrequirements will be ha optimizedve been satisfied, further such to improve as the chargingoverallIn future systemtime works, and efficiency. energy. the constant For example, power charging the losses process of the willconverter be optimized will be considered, further to improve such as overall the loss systemmodel efficiency. of rectifier For and example, buck converter. the losses The of the charging converter time will of be the considered, constant current such as charging the loss modelprocess Acknowledgments: Thanks for Fuji Electric Co., Ltd. support the IGBT devices and Nippon Chemi-con ofwill rectifier be designed and buck under converter. the conditio The chargingn that the time charging of the requirements constant current have charging been satisfied, process such will as be the Corporationcharging time for supplying and energy. the supe rcapacitor for the experiments. Acknowledgments: Thanks for Fuji Electric Co., Ltd. support the IGBT devices and Nippon Chemi-con Corporation for supplying the supercapacitor for the experiments. Energies 2017, 10, 135 16 of 17 designed under the condition that the charging requirements have been satisfied, such as the charging time and energy. Acknowledgments: Thanks for Fuji Electric Co., Ltd. support the IGBT devices and Nippon Chemi-con Corporation for supplying the supercapacitor for the experiments. Author Contributions: Fei Lin contributed to the conception of the study, Yuyu Geng and Bin Li contributed significantly to analysis and manuscript preparation, Zhongping Yang helped perform the analysis with constructive discussions and Hu Sun provided experimental assistance. Conflicts of Interest: The authors declare no conflict of interest. References 1. Covic, G.A.; Boys, J.T. Modern trends in inductive power transfer for transportation applications. IEEE J. Emerg. Sel. Top. Power Electron. 2013, 1, 28–41. 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Wireless Power Transfer for Electric Vehicle Applications. IEEE J. Emerg. Sel. Top. Power Electron. 2015, 3, 4–17. © 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).