dynamic wireless power transfer system for...
TRANSCRIPT
Dynamic Wireless Power Transfer System forElectric Vehicles to Simplify Ground Facilities- Power Control and Efficiency Maximization
on the Secondary Side -
Katsuhiro Hata, Takehiro Imura, and Yoichi HoriThe University of Tokyo
5–1–5, Kashiwanoha, Kashiwa, Chiba, 277–8561, JapanPhone: +81-4-7136-3881, Fax: 81-4-7136-3881
Email: [email protected], [email protected], [email protected]
Abstract—A dynamic wireless power transfer (WPT) systemfor electric vehicles can extend their cruising distance and reducethe size of their energy storage system. Power control andefficiency maximization of WPT are preferable to be controlled onthe secondary side because ground facilities of the dynamic charg-ing system have to be simplified. Although previous research hasproposed a secondary-side simultaneous control of the maximumefficiency and the desired power, the battery charging currentcannot be controlled directly. In this paper, a novel secondary-sidecontrol method for power control and efficiency maximization isproposed. The battery charging power is controlled by the DC-DC converter and the transmitting efficiency is maximized byHalf Active Rectifier. These control strategies and the controllerdesign are proposed based on the WPT circuit analysis and thepower converter model. The effectiveness of the proposed methodis verified by simulation and experiment.
Keywords—Electric vehicle, Dynamic wireless power transfer,Efficiency maximization, Power control, Secondary-side control
I. INTRODUCTION
Electric vehicles (EVs) have gathered attention for theirhighly environmental performance. Additionally, their electricmotors can achieve a high performance in motion controlbecause of a faster torque response over internal combustionengines [1]. However, their limited mileage per charge, whichare caused by a low energy density of their energy storagesystem, imposes the need for a frequent and complicatedcharging on users.
Wireless power transfer (WPT) can mitigate complicatedcharging operations and endure the frequent charging. Addi-tionally, a dynamic WPT system can provide electricity to EVsin motion. As a result, the cruising distance can be extendedand the size of the energy storage system can be reduced [2–5]. However, ground facilities of the dynamic WPT system,which are composed of power source, high-frequency inverters,transmitters, and so on, are applied to rugged roadways overlong distances. Consequently, a feasible control strategy forthe dynamic charging system is different from a stationarycharging system. In order to simplify ground facilities, asecondary-side control is preferable to a primary-side control[6] or a dual-side control [7]. Therefore, this paper focuses onthe secondary-side control without signal communication.
RLV1
Power source Load
V2
I1
I2
C1
C2
R2
L2
R1
L1
Lm
Transmitter and Receiver
(a) Equivalent circuit of magnetic resonant coupling.
RL
V1
Power source Load
V2
I1 I
2
C1
C2R
2R1 L
1-L
m
Lm
Transmitter and Receiver
L2-L
m
(b) T–type equivalent circuit.
Fig. 1. Equivalent circuit of wireless power transfer system.
Previous research on the secondary-side control has pro-posed maximum efficiency control [8], [9] and power control[10]. Additionally, efficiency and power can be controlledsimultaneously using two power converters [11]. This controlmethod uses a DC-DC converter and Half Active Rectifier(HAR), which is a role as an AC-DC converter. The trans-mitting efficiency is maximized by the DC-DC converter andthe transmitting power is controlled by the HAR. However,this method cannot control battery charging power directly.
This paper proposes a novel secondary-side control methodfor power control and efficiency maximization. The proposedmethod directly controls the battery charging current using theDC-DC converter. Because the DC link voltage becomes unsta-ble [12], the proposed method stabilizes the DC link voltageusing the HAR and maximize the transmitting efficiency bydetermining the reference value of the DC link voltage.
Fig. 2. Transmitter and receiver coils.
TABLE I. SPECIFICATIONS OF COILS.
Primary side Secondary side
Resistance R1, R2 1.24 Ω 1.23 Ω
Inductance L1, L2 615 µH 615 µHCapacitance C1, C2 4000 pF 4000 pF
Resonant frequency f1, f2 101 kHz 101 kHz
Outer diameter 440 mm
Number of turns 50 turns
Coil gap 300 mm
Mutual inductance Lm 37.8 µH
Coupling coefficient k 0.0615
II. WIRELESS POWER TRANSFER VIA MAGNETICRESONANCE COUPLING
A. Characteristics at resonance frequency
This paper uses WPT via magnetic resonance coupling[13], which is compensated by a series-series (SS) circuittopology. Fig. 1 shows an equivalent circuit of the WPT system[14]. The transmitter and receiver coils are connected to theresonance capacitors in series. They are characterized by theself-inductances L1, L2, the series-resonance capacitances C1,C2, and the internal resistances R1, R2, respectively. Lm is themutual inductance between the transmitter and the receiver.V1 is the RMS voltage of the power source and its angularfrequency ω0 is the same as the resonance angular frequencyof the transmitter and the receiver, which are expressed asfollows:
ω0 =1√L1C1
=1√L2C2
. (1)
The transmitter and the receiver that used in this study areshown in Fig. 2 and their specifications are described inTABLE. I.
When the load resistance is RL, the transmitting efficiencyη and the transmitting power P can be analyzed by the circuitequation and they are obtained as follows [15]:
η =(ω0Lm)2RL
(R2 +RL)R1R2 +R1RL + (ω0Lm)2(2)
P =(ω0Lm)2RL
R1R2 +R1RL + (ω0Lm)22V1
2. (3)
When the amplitude of V1 equals to 100 V, Fig. 3 shows theload resistance RL versus the transmitting efficiency η and thecharging power P .
0
0.5
1
1.5
2
2.5
0
0.2
0.4
0.6
0.8
1
1 10 100 1000 10000
Ch
ag
ing
po
we
r P
[k
W]
Tra
nsm
itti
ng
eff
icie
ncy
η
Load resistance RL
[Ω]
η
P
Fig. 3. Load resistance vs. transmitting efficiency and charging power.
0
0.5
1
1.5
2
2.5
0
0.2
0.4
0.6
0.8
1
1 10 100 1000 10000
Ch
ag
ing
po
we
r P
[k
W]
Tra
nsm
itti
ng
eff
icie
ncy
η
Secondary voltage V2
[V]
η
P
Fig. 4. Secondary voltage vs. transmitting efficiency and charging power.
B. Maximization of transmitting efficiency
In order to maximize the transmitting efficiency η, the loadresistance RL should be optimized as follows [15]:
RLηmax =
√R2
(ω0Lm)2
R1+R2
. (4)
In a dynamic WPT system for EVs, the mutual inductance Lm
changes depending on the motion of the vehicle. Therefore, RL
has to be controlled according to Lm.
As a method to control RL, Secondary voltage controlmethods have been proposed [8], [9]. In order to obtain theoptimal secondary voltage V2ηmax, the secondary voltage V2
versus the transmitting efficiency η and the charging power Pare depicted in Fig. 4. For efficiency maximization, V2ηmax
value is determined as follows [8]:
V2ηmax =
√R2
R1
ω0Lm√R1R2 + (ω0Lm)2 +
√R1R2
V1. (5)
In this study, the amplitude of the primary voltage V1 isfixed to simplify ground facilities. Then, if R1 is assumedto be constant and given, Lm can be estimated from thesecondary side [9]. Therefore, efficiency maximization usingsecondary voltage control can be achieved based on secondary-side information, which are the secondary voltage V2 and thesecondary current I2.
Idc
LmC
1C
2R2
L2
R1
L1V
1
Power source Transmitter and receiver
V2
I1 I2
VS Cdc
PPin
L r
DC-DC converter Battery
E
PL
S1
S2
dVdc
Half Active Rectifier
iL
Fig. 5. Circuit diagram of the wireless power transfer system.
Idc
Cdc
Vdc
V2
PL
P
(a) Rectification mode
Cdc
P = 0, Idc
= 0
Vdc
V2 = 0
PL
(b) Short mode
Fig. 6. Operation modes of Half Active Rectifier.
C. System configuration
Previous research on maximum efficiency control has pro-posed using a diode rectifier and a DC-DC converter on thesecondary side [8], [9]. However, this control cannot achievethe desired charging power because the secondary voltageV2 is controlled for efficiency maximization. As a result, thecharging power P is determined by V2ηmax, which is given byeq. (5).
In this paper, a secondary-side simultaneous controlmethod of efficiency maximization and power control is pro-posed. Fig. 5 shows the circuit diagram of the WPT systemfor the simultaneous control. The diode rectifier is replacedwith the HAR, which maximize the transmitting efficiency η.Then, the DC link voltage Vdc is regulated by the HAR toachieve eq. (5). Additionally, the battery charging current ILis controlled by the DC-DC converter. These control strategiesare described further below.
III. EFFICIENCY MAXIMIZATION BY HALF ACTIVERECTIFIER
A. DC link voltage control
The HAR is operated by two modes, which are shownin Fig. 6. In the rectification mode, the HAR is operated asthe diode rectifier. If the charging power P is larger than theload power PL, Vdc is increased. On the other hand, the shortmode is worked by turning on lower arm MOSFETs. Then, Pis cut-off and PL is supplied by the DC link capacitor. As a
Vhigh
Vlow
Vdc
*
≈ ≈ ≈ ≈
t
Tshort
Trect
Fig. 7. Waveform of the DC link voltage.
result, Vdc is decreased in the short mode. Therefore, Vdc canbe controlled by switching between the rectification mode andthe short mode. In this paper, Vdc is controlled using hysteresiscomparator [16].
The upper bound Vhigh and the lower bound Vlow aredefined as follows:
Vhigh = Vdc∗ +∆V (6)
Vlow = Vdc∗ −∆V, (7)
where Vdc∗ is the reference value of Vdc and ∆V is the
hysteresis band. If Vdc becomes smaller than Vlow, the HARis operated in the rectification mode. Additionally, when Vdc
becomes larger than Vhigh, the HAR switches to the shortmode. As shown in Fig. 7, Vdc is kept within the desired range.
B. Efficiency maximization
In order to achieve the maximum efficiency, Vdc∗ has to
be equal to Vdcηmax, which is given as follows [8]:
Vdcηmax =
√R2
R1
ω0Lm√R1R2 + (ω0Lm)2 +
√R1R2
VS . (8)
Then, the transmitting efficiency η can be maximized duringthe rectification mode. Meanwhile, losses in the short modeis small compared to losses in the rectification mode. This isbecause the secondary voltage V2 is nearly equal to zero andthe input power Pin is drastically decreased in the short mode.In this paper, losses during the short mode are assumed to benegligible to losses during the rectification mode.
Vdcηmax
L r
E
d(t)
PL
iL
S1
S2
(a) Simplified DC-DC converter
L riL
Vdcηmax
E
(b) S1:on, S2:off
L riL
EVdcηmax
(c) S1:off, S2:on
Fig. 8. Circuit diagram of the DC-DC converter.
IV. POWER CONTROL BY THE DC-DC CONVERTER
A. Circuit configuration
If the DC link voltage Vdc is regulated by the HAR, thecircuit diagram of the DC-DC converter can be indicated asFig. 8 (a). In this study, Vdcηmax is used as the nominal value ofthe DC link voltage to simplify the DC-DC converter model.E is the battery voltage, L is the inductance of the reactorcoil and r is the internal resistance of the reactor coil and thebattery. In order to achieve power control, the load current iLhas to be controlled in battery charging.
B. Modeling of the DC-DC converter
This paper assumes that the DC-DC converter is operatedin the continues conduction mode because the MOSFETsof the DC-DC converter are alternatively turned on and off.Therefore, the operation modes are expressed in Fig. 8 (b)and Fig. 8 (c).
The plant model of the DC-DC converter is obtained bythe state space averaging method. From the circuit equation,the state equation of Fig.8 (b) is described as follows:
d
dtiL(t) = − r
LiL(t)−
1
LE +
1
LVdcηmax. (9)
Also, the state equation of Fig.8 (c) is expressed as follows:
d
dtiL(t) = − r
LiL(t)−
1
LE. (10)
When d(t) is defined as the duty cycle of the upper sideMOSFET S1, the state space model of the DC-DC converteris obtained as follows:
d
dtiL(t) = − r
LiL(t)−
1
LE +
Vdcηmax
Ld(t). (11)
As the DC-DC converter is a non-linear system, it islinearized around an equilibrium point to apply the linearcontrol theory on the controller design. By defining IL and
CPI (z) DC-DC converteriL
* iL
D
∆d
+-
+
+
Equilibrium point
calculation
FF controller
FB controller
Vdcηmax
Fig. 9. Block diagram of load current control.
D as the equilibrium point, iL(t) and d(t) are expressed asfollows:
iL(t) = IL +∆iL(t) (12)d(t) = D +∆d(t), (13)
where ∆iL(t) and ∆d(t) are the microscopic fluctuationsaround the equilibrium point. By substituting eq. (12) andeq. (13) in eq. (11), the linearized DC-DC converter modelis obtained as follows:
d
dt∆iL(t) = − r
L∆iL(t) +
Vdcηmax
L∆d(t). (14)
Therefore, the transfer function from ∆d(s) to ∆iL(s) is givenas follows:
∆Pi(s) =∆iL(s)
∆d(s)=
Vdcηmax
Ls+ r. (15)
C. Controller design
Fig. 9 shows the block diagram of the load current control.The feedforward controller is the same as the equilibrium pointcalculation, which is given by the constraint equation of theDC-DC converter. Assuming iL
∗ is the reference value of iL,the equilibrium point IL and D are obtained as follows:
IL = iL∗ (16)
D =E + rILVdcηmax
. (17)
The feedback controller is designed by the pole placementmethod. As the plant model of the DC-DC converter isexpressed by the first-order transfer function, we use a PIcontroller CPI(s), which is described as follow:
CPI(s) =sKP +KI
s. (18)
If closed loop poles are expressed by a multiple root ωc, thegains are obtained as follows:
KP =2Lωc − r
Vdcηmax(19)
KI =Lωc
2
Vdcηmax. (20)
In order to implement the discretized controller CPI(z),CPI(s) is redesigned by Tustin transform.
0 0.05 0.1 0.15 0.220
40
60
80
Time [s]
DC
lin
k voltage
Vdc [
V]
w/
w/o
(a) DC link voltage Vdc
0 0.05 0.1 0.15 0.20.7
0.8
0.9
1
Time [s]
Tra
nsm
itting e
ffic
iency η
w/
w/o
(b) Transmitting efficiency η
0 0.01 0.02 0.03 0.04 0.050.7
0.8
0.9
1
Time [s]
Tra
nsm
itting e
ffic
iency η
w/
(c) Transmitting efficiency η (zoom)
0 0.01 0.02 0.03 0.04 0.050
10
20
30
40
Time [s]
Input
pow
er
Pin [
W]
w/
(d) Input power Pin
Fig. 10. Simulation results of efficiency maximization by Half Active Rectifier
-0.02 -0.01 0 0.01 0.02 0.0327.5
28
28.5
29
29.5
Time [s]
DC
lin
k voltage
Vdc [
V]
(a) DC link voltage Vdc
-0.02 -0.01 0 0.01 0.02 0.030
0.5
1
1.5
Time [s]
Load c
urr
ent
I L [
A]
(b) Load current IL
-1 0 1 2 3 4
x 10-3
0
0.5
1
1.5
Time [s]
Load c
urr
ent
I L [
A]
(c) Load current IL (zoom)
-0.02 -0.01 0 0.01 0.02 0.030.4
0.45
0.5
0.55
Time [s]
Duty
cycle
d (FF+FB)
D (FF)
(d) Duty cycle d
Fig. 11. Simulation results of power control by the DC-DC converter with Half Active Rectifier.
TABLE II. SIMULATION AND EXPERIMENTAL CONDITIONS.
Parameter Value
Power source voltage VS 30 V
Operating frequency f0 101 kHz
DC link voltage reference Vdc∗ 28.38 V
Hysteresis band ∆V 0.5 V
Battery voltage E 12 V
Reactor resistance r 0.5 Ω
Reactor inductance L 1000 µH
DC link capacitance Cdc 3300 µF
Carrier frequency fc 20 kHz
V. SIMULATION
Simulations are performed using MATLAB Simlink Sim-PowerSystems. The circuit configuration is shown in Fig. 5.Simulation conditions are described in TABLE II. The invertersupplies the transmitter with a square wave voltage.
A. Efficiency maximization by Half Active Rectifier
In order to verify the effectiveness of maximum efficiencycontrol by the HAR, this simulation replaced the DC-DCconverter with a constant power load, which is modeledusing controlled current source [12], independent of the powercontrol performance by the DC-DC converter. The load powerPL was set to 10 W. In case of without control, the HAR wasoperated in the rectification mode at all times.
Fig. 10 shows simulations results of efficiency maximiza-tion by the HAR. From Fig. 10 (a) and (b) without control, theDC link voltage Vdc is unstable and departs from the referencevoltage Vdcηmax, which maximize the transmitting efficiencyη. On the other hand, the HAR control using the hysteresiscomparator can stabilize Vdc within the desired range and
Fig. 12. Half Active Rectifier and DC-DC converter.
maximize η during the rectification mode as shown in Fig.10 (c). Additionally, Fig. 10 (d) shows that the input powerPin is reduced during the short mode. Therefore, it is verifiedthat efficiency maximization by the HAR is effective.
B. Power control by the DC-DC converter with Half ActiveRectifier.
In this simulation, Vdc was regulated by the HAR and theload current iL was controlled by the DC-DC converter. Theclosed loop poles of the load current control were placed at-3000 rad/s (multiple root). The load current reference iL
∗ waschanged from 0.5 A to 1 A at t = 0 s.
Simulation results of power control by the DC-DC con-verter with the HAR are shown in Fig. 11. The HAR canregulate Vdc within the desired range as shown in Fig. 11 (a).The step response of iL is shown in Fig. 11 (b) and (c). Theproposed control achieves the fast response without steady-state errors. Fig. 11 (d) shows the duty cycle of the DC-DCconverter. The feedforward controller updates the equilibrium
27.5
28
28.5
29
29.5
-0.05 0 0.05 0.1 0.15
DC
lin
k v
olt
ag
e V
dc
[V]
Time [s]
(a) DC link voltage Vdc
-0.5
0
0.5
1
1.5
-0.05 0 0.05 0.1 0.15
Lo
ad
cu
rre
nt
i L[A
]
Time [s]
(b) Load current iL
-0.5
0
0.5
1
1.5
-0.005 0 0.005 0.01 0.015
Lo
ad
cu
rre
nt
iL
[A]
Time [s]
(c) Load current iL (zoom)
0.4
0.42
0.44
0.46
0.48
0.5
-0.05 0 0.05 0.1 0.15
Du
ty c
ycl
e
Time [s]
d (FF+FB)
D (FF)
(d) Duty cycle d
Fig. 13. Experimental results of power control by the DC-DC converter with Half Active Rectifier.
point properly and the feedback controller compensates for theerror of Vdc from the nominal voltage Vdcηmax. From theseresults, the effectiveness of the proposed method is verified.
VI. EXPERIMENT
The experiment was demonstrated using the experimentalequipment. The HAR and the DC-DC converter are shown inFig. 12. Experimental conditions are indicated in TABLE II.The closed loop poles of the load current control were placedat -300 rad/s (multiple root). The load current reference iL
∗
was changed from 0 A to 0.5 A at t = 0 s. The feedbackcontroller was worked from t = 0 s.
Experimental results are shown in Fig. 13. The DC linkvoltage Vdc keeps within the desired range as shown in Fig.13 (a). As a result, the HAR with the hysteresis comparatorare able to work properly. Fig. 13 (b) and (c) shows the loadcurrent iL. Although the steady-state error of iL occurs beforet = 0 s due to the modeling error of the DC-DC converter,it is suppressed by the feedback controller after t = 0 s.Additionally, the feedback controller also compensates for theparameter error of Vdc as shown in Fig. 13(d). Therefore,the proposed method can achieve efficiency maximizationusing the HAR and power control by the DC-DC convertersimultaneously.
VII. CONCLUSION
This paper proposed a simultaneous control method ofefficiency maximization by HAR and power control by a DC-DC converter. The HAR can regulate the DC link voltage usinga hysteresis comparator and it can maximize the transmittingefficiency based on the WPT circuit analysis. The DC-DCconverter was modeled under the HAR control and a loadcurrent feedback controller was designed. The effectiveness ofthe proposed method is verified by simulation and experiment.
Future works are to propose efficiency maximization con-sidering losses during the short mode of the HAR and toimplement a high power prototype for EV applications.
REFERENCES
[1] Y. Hori, “Future vehicle driven by electricity and control-research onfour-wheel-motored “UOT electric march II”,” IEEE Transactions onIndustrial Electronics, vol. 51, no. 5, pp. 954–962, Oct. 2004.
[2] S. Chopra and P. Bauer, “Driving range extension of EV with on-road contactless power transfer—a case study,” IEEE Transactions onIndustrial Electronics, vol. 60, no. 1, pp. 329–338, Jul. 2013.
[3] J. Shin, S. Shin, Y. Kim, S. Ahn, S. Lee, G. Jung, S. Jeon, and D.Cho, “Design and implementation of shaped magnetic-resonance-basedwireless power transfer system for roadway-powered moving electricvehicles,” IEEE Transactions on Industrial Electronics, vol. 61, no. 3,pp. 1179–1192, Mar. 2014.
[4] K. Lee, Z. Pantic, and S. M. Lukic, “Reflexive Field Containment inDynamic Inductive Power Transfer Systems,” IEEE Transactions onIndustrial Electronics, vol. 29, no. 9, pp. 4592–4602, Sep. 2014.
[5] L. Chen, G. R. Nagendra, J. T. Boys, and G. A. Covic, “Double-coupledsystems for IPT roadway applications,” IEEE Journal of Emerging andSelected Topics in Power Electronics, vol. 3, no.1, pp. 37–49, Mar. 2015.
[6] J. M. Miller, O. C. Onar, and M. Chinthavali, “Primary-side power flowcontrol of wireless power transfer for electric vehicle charging,” IEEEJournal of Emerging and Selected Topics in Power Electronics, vol. 3,no.1, pp. 147–162, Mar. 2015.
[7] H. H. Wu, A. Gilchrist, K. D. Sealy, and D. Bronson, “A high efficiency5 kW inductive charger for EVs using dual side control,” IEEE Transac-tions on Industrial Informatics, vol. 8, no. 3, pp. 585–595, Aug. 2012.
[8] M. Kato, T. Imura, and Y. Hori, “Study on maximize efficiency bysecondary side control using DC-DC converter in wireless power transfervia magnetic resonant coupling,” in Proc. The 27th International ElectricVehicle Symposium and Exhibition (EVS), 2013, pp. 1–5.
[9] D. Kobayashi, T. Imura, and Y. Hori, “Real-time coupling coefficientestimation and maximum efficiency control on dynamic wireless powertransfer for electric vehicles,” in Proc. IEEE PELS Workshop on Emerg-ing Technologies; Wireless Power, 2015, pp. 1–6.
[10] S. Li and C.C. Mi, “Wireless power transfer for electric vehicleapplications,” IEEE Journal of Emerging and Selected Topics in PowerElectronics, vol. 3, no.1, pp. 4–17, Mar. 2015.
[11] G. Lovison, M. Sato, T. Imura, and Y. Hori, “Secondary-side-onlysimultaneous power and efficiency control for two converters in wirelesspower transfer system,” in 41st Annual Conference of the IEEE IndustrialElectronics Society (IECON), 2015, pp. 4824–4829.
[12] D. Gunji, T. Imura, H. Fujimoto, “Stability analysis of constant powerload and load voltage control method for wireless in-wheel motor,” inProc. The 9th International Conference on Power Electronics - ECCEAsia (ICPE), 2015, pp. 1–6.
[13] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, andM. Soljacic, “Wireless power transfer via strongly coupled magneticresonance,” Science Express on 7 June 2007, vol. 317, no. 5834, pp.83–86, Jun. 2007.
[14] T. Imura and Y. Hori, “Maximizing air gap and efficiency of magneticresonant coupling for wireless power transfer using equivalent circuit andNeumann formula,” IEEE Transactions on Industrial Electronics, vol. 58,no. 10, pp. 4746–4752, Oct. 2011.
[15] M. Kato, T. Imura, and Y. Hori, “New characteristics analysis con-sidering transmission distance and load variation in wireless powertransfer via magnetic resonant coupling,” in IEEE 34th InternationalTelecommunications Energy Conference (INTELEC), 2012, pp. 1–5.
[16] D. Gunji, T. Imura, and H. Fujimoto, “Basic study of transmittingpower control method without signal communication for wireless in-wheel motor via magnetic resonance coupling,” in Proc. The IEEE/IESInternational Conference on Mechatronics (ICM), 2015, pp. 313–318.