Keywords Electric vehicle, Dynamic wireless power transfer, Efficiency maximization, Power control, Secondary-side control

Transcription

1 Dynamic Wireless ower Transfer System for lectric Vehicles to Simplify Groun Facilities - ower Control an fficiency Maximization on the Seconary Sie - Katsuhiro Hata, Takehiro Imura, an Yoichi Hori The University of Tokyo 5 5, Kashiwanoha, Kashiwa, Chiba, , Japan hone: , Fax: mail: hata@hflab.k.u-tokyo.ac.jp, imura@hori.k.u-toyko.ac.jp, hori@k.u-tokyo.ac.jp Abstract A ynamic wireless power transfer (WT) system for electric vehicles can exten their cruising istance an reuce the size of their energy storage system. ower control an efficiency maximization of WT are preferable to be controlle on the seconary sie because groun facilities of the ynamic charging system have to be simplifie. Although previous research has propose a seconary-sie simultaneous control of the maximum efficiency an the esire power, the battery charging current cannot be controlle irectly. In this paper, a novel seconary-sie control metho for power control an efficiency maximization is propose. The battery charging power is controlle by the DC- DC converter an the transmitting efficiency is maximize by Half Active Rectifier. These control strategies an the controller esign are propose base on the WT circuit analysis an the power converter moel. The effectiveness of the propose metho is verifie by simulation an experiment. I C R C m 2 R2 I 2 V 2 V 2 R ower source Transmitter an Receiver oa (a) quivalent circuit of magnetic resonant coupling. I C R C 2 R2 - m 2 - m I 2 Keywors lectric vehicle, Dynamic wireless power transfer, fficiency maximization, ower control, Seconary-sie control V m V 2 R I. INTRODUCTION lectric vehicles (Vs) have gathere attention for their highly environmental performance. Aitionally, their electric motors can achieve a high performance in motion control because of a faster torque response over internal combustion engines []. However, their limite mileage per charge, which are cause by a low energy ensity of their energy storage system, imposes the nee for a frequent an complicate charging on users. Wireless power transfer (WT) can mitigate complicate charging operations an enure the frequent charging. Aitionally, a ynamic WT system can provie electricity to Vs in motion. As a result, the cruising istance can be extene an the size of the energy storage system can be reuce [2 5]. However, groun facilities of the ynamic WT system, which are compose of power source, high-frequency inverters, transmitters, an so on, are applie to rugge roaways over long istances. Consequently, a feasible control strategy for the ynamic charging system is ifferent from a stationary charging system. In orer to simplify groun facilities, a seconary-sie control is preferable to a primary-sie control [6] or a ual-sie control [7]. Therefore, this paper focuses on the seconary-sie control without signal communication. Fig.. ower source Transmitter an Receiver (b) T type equivalent circuit. quivalent circuit of wireless power transfer system. oa revious research on the seconary-sie control has propose maximum efficiency control [8], [9] an power control []. Aitionally, efficiency an power can be controlle simultaneously using two power converters []. This control metho uses a DC-DC converter an Half Active Rectifier (HAR), which is a role as an AC-DC converter. The transmitting efficiency is maximize by the DC-DC converter an the transmitting power is controlle by the HAR. However, this metho cannot control battery charging power irectly. This paper proposes a novel seconary-sie control metho for power control an efficiency maximization. The propose metho irectly controls the battery charging current using the DC-DC converter. Because the DC link voltage becomes unstable [2], the propose metho stabilizes the DC link voltage using the HAR an maximize the transmitting efficiency by etermining the reference value of the DC link voltage.

2 Transmitting efficiency η η Chaging power [kw] Fig. 2. Transmitter an receiver coils. oa resistance R [Ω] TAB I. SCIFICATIONS OF COIS. Fig. 3. oa resistance vs. transmitting efficiency an charging power. rimary sie Seconary sie Resistance R, R 2.24 Ω.23 Ω Inuctance, 2 65 µh 65 µh Capacitance C, C 2 4 pf 4 pf Resonant frequency f, f 2 khz khz Outer iameter 44 mm Number of turns 5 turns Coil gap 3 mm Mutual inuctance m 37.8 µh Coupling coefficient k.65 Transmitting efficiency η η Chaging power [kw] II. WIRSS OWR TRANSFR VIA MAGNTIC RSONANC COUING A. Characteristics at resonance frequency This paper uses WT via magnetic resonance coupling [3], which is compensate by a series-series (SS) circuit topology. Fig. shows an equivalent circuit of the WT system [4]. The transmitter an receiver coils are connecte to the resonance capacitors in series. They are characterize by the self-inuctances, 2, the series-resonance capacitances C, C 2, an the internal resistances R, R 2, respectively. m is the mutual inuctance between the transmitter an the receiver. V is the RMS voltage of the power source an its angular frequency ω is the same as the resonance angular frequency of the transmitter an the receiver, which are expresse as follows: ω = C = 2 C 2. () The transmitter an the receiver that use in this stuy are shown in Fig. 2 an their specifications are escribe in TAB. I. When the loa resistance is R, the transmitting efficiency η an the transmitting power can be analyze by the circuit equation an they are obtaine as follows [5]: (ω m ) 2 R η = (R 2 + R ){R R 2 + R R + (ω m ) 2 } (2) (ω m ) 2 R = {R R 2 + R R + (ω m ) 2 } 2 V 2. (3) When the amplitue of V equals to V, Fig. 3 shows the loa resistance R versus the transmitting efficiency η an the charging power. Fig. 4. Seconary voltage V 2 [V] Seconary voltage vs. transmitting efficiency an charging power. B. Maximization of transmitting efficiency In orer to maximize the transmitting efficiency η, the loa resistance R shoul be optimize as follows [5]: { } (ω m ) R ηmax = R R 2. (4) R In a ynamic WT system for Vs, the mutual inuctance m changes epening on the motion of the vehicle. Therefore, R has to be controlle accoring to m. As a metho to control R, Seconary voltage control methos have been propose [8], [9]. In orer to obtain the optimal seconary voltage V 2ηmax, the seconary voltage V 2 versus the transmitting efficiency η an the charging power are epicte in Fig. 4. For efficiency maximization, V 2ηmax value is etermine as follows [8]: V 2ηmax = R2 R ω m R R 2 + (ω m ) 2 + R R 2 V. (5) In this stuy, the amplitue of the primary voltage V is fixe to simplify groun facilities. Then, if R is assume to be constant an given, m can be estimate from the seconary sie [9]. Therefore, efficiency maximization using seconary voltage control can be achieve base on seconarysie information, which are the seconary voltage V 2 an the seconary current I 2.

3 in I C R m R2 C 2 I 2 I c V S V 2 V 2 V c Cc S i r S 2 ower source Transmitter an receiver Half Active Rectifier DC-DC converter Battery Fig. 5. Circuit iagram of the wireless power transfer system. I c =, I c = V high V 2 V 2 = V c * V c V c C c C c V low t (a) Rectification moe (b) Short moe T rect T short Fig. 6. Operation moes of Half Active Rectifier. Fig. 7. Waveform of the DC link voltage. C. System configuration revious research on maximum efficiency control has propose using a ioe rectifier an a DC-DC converter on the seconary sie [8], [9]. However, this control cannot achieve the esire charging power because the seconary voltage V 2 is controlle for efficiency maximization. As a result, the charging power is etermine by V 2ηmax, which is given by eq. (5). In this paper, a seconary-sie simultaneous control metho of efficiency maximization an power control is propose. Fig. 5 shows the circuit iagram of the WT system for the simultaneous control. The ioe rectifier is replace with the HAR, which maximize the transmitting efficiency η. Then, the DC link voltage V c is regulate by the HAR to achieve eq. (5). Aitionally, the battery charging current I is controlle by the DC-DC converter. These control strategies are escribe further below. III. FFICINCY MAXIMIZATION BY HAF ACTIV RCTIFIR A. DC link voltage control The HAR is operate by two moes, which are shown in Fig. 6. In the rectification moe, the HAR is operate as the ioe rectifier. If the charging power is larger than the loa power, V c is increase. On the other han, the short moe is worke by turning on lower arm MOSFTs. Then, is cut-off an is supplie by the DC link capacitor. As a result, V c is ecrease in the short moe. Therefore, V c can be controlle by switching between the rectification moe an the short moe. In this paper, V c is controlle using hysteresis comparator [6]. The upper boun V high an the lower boun V low are efine as follows: V high = V c + V (6) V low = V c V, (7) where V c is the reference value of V c an V is the hysteresis ban. If V c becomes smaller than V low, the HAR is operate in the rectification moe. Aitionally, when V c becomes larger than V high, the HAR switches to the short moe. As shown in Fig. 7, V c is kept within the esire range. B. fficiency maximization In orer to achieve the maximum efficiency, V c has to be equal to, which is given as follows [8]: = R2 R ω m R R 2 + (ω m ) 2 + R R 2 V S. (8) Then, the transmitting efficiency η can be maximize uring the rectification moe. Meanwhile, losses in the short moe is small compare to losses in the rectification moe. This is because the seconary voltage V 2 is nearly equal to zero an the input power in is rastically ecrease in the short moe. In this paper, losses uring the short moe are assume to be negligible to losses uring the rectification moe.

4 S (t) r S 2 i i * + - FF controller quilibrium point calculation C I (z) FB controller + D + DC-DC converter i (a) Simplifie DC-DC converter i r i r Fig. 9. Block iagram of loa current control. Fig. 8. IV. (b) S :on, S 2 :off Circuit iagram of the DC-DC converter. (c) S :off, S 2 :on OWR CONTRO BY TH DC-DC CONVRTR A. Circuit configuration If the DC link voltage V c is regulate by the HAR, the circuit iagram of the DC-DC converter can be inicate as Fig. 8 (a). In this stuy, is use as the nominal value of the DC link voltage to simplify the DC-DC converter moel. is the battery voltage, is the inuctance of the reactor coil an r is the internal resistance of the reactor coil an the battery. In orer to achieve power control, the loa current i has to be controlle in battery charging. B. Moeling of the DC-DC converter This paper assumes that the DC-DC converter is operate in the continues conuction moe because the MOSFTs of the DC-DC converter are alternatively turne on an off. Therefore, the operation moes are expresse in Fig. 8 (b) an Fig. 8 (c). The plant moel of the DC-DC converter is obtaine by the state space averaging metho. From the circuit equation, the state equation of Fig.8 (b) is escribe as follows: t i (t) = r i (t) +. (9) Also, the state equation of Fig.8 (c) is expresse as follows: t i (t) = r i (t). () When (t) is efine as the uty cycle of the upper sie MOSFT S, the state space moel of the DC-DC converter is obtaine as follows: t i (t) = r i (t) + (t). () As the DC-DC converter is a non-linear system, it is linearize aroun an equilibrium point to apply the linear control theory on the controller esign. By efining I an D as the equilibrium point, i (t) an (t) are expresse as follows: i (t) = I + i (t) (2) (t) = D + (t), (3) where i (t) an (t) are the microscopic fluctuations aroun the equilibrium point. By substituting eq. (2) an eq. (3) in eq. (), the linearize DC-DC converter moel is obtaine as follows: t i (t) = r i (t) + (t). (4) Therefore, the transfer function from (s) to i (s) is given as follows: C. Controller esign i (s) = i (s) (s) = s + r. (5) Fig. 9 shows the block iagram of the loa current control. The feeforwar controller is the same as the equilibrium point calculation, which is given by the constraint equation of the DC-DC converter. Assuming i is the reference value of i, the equilibrium point I an D are obtaine as follows: I = i (6) D = + ri. (7) The feeback controller is esigne by the pole placement metho. As the plant moel of the DC-DC converter is expresse by the first-orer transfer function, we use a I controller C I (s), which is escribe as follow: C I (s) = sk + K I. (8) s If close loop poles are expresse by a multiple root ω c, the gains are obtaine as follows: K = 2ω c r (9) K I = ω c 2. (2) In orer to implement the iscretize controller C I (z), C I (s) is reesigne by Tustin transform.

5 DC link voltage V c [V] o Transmitting efficiency η.9.8 o Transmitting efficiency η Input power in [W] (a) DC link voltage V c (b) Transmitting efficiency η (c) Transmitting efficiency η (zoom) () Input power in Fig.. Simulation results of efficiency maximization by Half Active Rectifier DC link voltage V c [V] oa current I [A].5.5 oa current I [A].5.5 Duty cycle (FF+FB) D (FF) (a) DC link voltage V c (b) oa current I x -3 (c) oa current I (zoom) () Duty cycle Fig.. Simulation results of power control by the DC-DC converter with Half Active Rectifier. TAB II. SIMUATION AND XRIMNTA CONDITIONS. arameter Value ower source voltage V S 3 V Operating frequency f khz DC link voltage reference V c V Hysteresis ban V.5 V Battery voltage 2 V Reactor resistance r.5 Ω Reactor inuctance µh DC link capacitance C c 33 µf Carrier frequency f c 2 khz Fig. 2. Half Active Rectifier an DC-DC converter. V. SIMUATION Simulations are performe using MATAB Simlink Sim- owersystems. The circuit configuration is shown in Fig. 5. Simulation conitions are escribe in TAB II. The inverter supplies the transmitter with a square wave voltage. A. fficiency maximization by Half Active Rectifier In orer to verify the effectiveness of maximum efficiency control by the HAR, this simulation replace the DC-DC converter with a constant power loa, which is moele using controlle current source [2], inepenent of the power control performance by the DC-DC converter. The loa power was set to W. In case of without control, the HAR was operate in the rectification moe at all times. Fig. shows simulations results of efficiency maximization by the HAR. From Fig. (a) an (b) without control, the DC link voltage V c is unstable an eparts from the reference voltage, which maximize the transmitting efficiency η. On the other han, the HAR control using the hysteresis comparator can stabilize V c within the esire range an maximize η uring the rectification moe as shown in Fig. (c). Aitionally, Fig. () shows that the input power in is reuce uring the short moe. Therefore, it is verifie that efficiency maximization by the HAR is effective. B. ower control by the DC-DC converter with Half Active Rectifier. In this simulation, V c was regulate by the HAR an the loa current i was controlle by the DC-DC converter. The close loop poles of the loa current control were place at -3 ra/s (multiple root). The loa current reference i was change from.5 A to A at t = s. Simulation results of power control by the DC-DC converter with the HAR are shown in Fig.. The HAR can regulate V c within the esire range as shown in Fig. (a). The step response of i is shown in Fig. (b) an (c). The propose control achieves the fast response without steaystate errors. Fig. () shows the uty cycle of the DC-DC converter. The feeforwar controller upates the equilibrium

6 (FF+FB) DC link voltage V c [V] oa current i [A].5 oa current i [A].5 Duty cycle D (FF) (a) DC link voltage V c (b) oa current i (c) oa current i (zoom) () Duty cycle Fig. 3. xperimental results of power control by the DC-DC converter with Half Active Rectifier. point properly an the feeback controller compensates for the error of V c from the nominal voltage. From these results, the effectiveness of the propose metho is verifie. VI. XRIMNT The experiment was emonstrate using the experimental equipment. The HAR an the DC-DC converter are shown in Fig. 2. xperimental conitions are inicate in TAB II. The close loop poles of the loa current control were place at -3 ra/s (multiple root). The loa current reference i was change from A to.5 A at t = s. The feeback controller was worke from t = s. xperimental results are shown in Fig. 3. The DC link voltage V c keeps within the esire range as shown in Fig. 3 (a). As a result, the HAR with the hysteresis comparator are able to work properly. Fig. 3 (b) an (c) shows the loa current i. Although the steay-state error of i occurs before t = s ue to the moeling error of the DC-DC converter, it is suppresse by the feeback controller after t = s. Aitionally, the feeback controller also compensates for the parameter error of V c as shown in Fig. 3(). Therefore, the propose metho can achieve efficiency maximization using the HAR an power control by the DC-DC converter simultaneously. VII. CONCUSION This paper propose a simultaneous control metho of efficiency maximization by HAR an power control by a DC- DC converter. The HAR can regulate the DC link voltage using a hysteresis comparator an it can maximize the transmitting efficiency base on the WT circuit analysis. The DC-DC converter was moele uner the HAR control an a loa current feeback controller was esigne. The effectiveness of the propose metho is verifie by simulation an experiment. 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