Dynamic Wireless Power Transfer System for Electric Vehicles to Simplify Ground Facilities-Real-time Power Control and Efficiency Maximization -

This paper focuses on dynamic wireless power transfer for electric vehicles and proposes a vehicle-side control method for real-time power control and efficiency maximization. The proposed control strategy and controller design are presented based on a real-time estimation of the mutual inductance between a transmitter and a receiver. Simulations and experiments demonstrate that the proposed method can achieve the maximum efficiency and the desired power simultaneously.


Introduction
Wireless power transfer (WPT) is one of the hottest research topic in transportation applications [1,2].In particular, a dynamic wireless power transfer (DWPT) system for electric vehicles (EVs) has gathered attention to extend the cruising distance of EVs and to reduce the size of the energy storage system [3]- [6].Its ground facilities are mainly composed of power source, high-frequency inverters, transmitters, and so on.As they are applied to rugged roadways over long distances, power control and efficiency maximization of wireless charging are desirable to be achieved on the vehicle side without signal communication.
Although previous research has proposed simultaneous control methods of power control and efficiency maximization on the vehicle side [7,8], they have not been applied to the DWPT system.For maximizing the transmitting efficiency in the DWPT system, the mutual inductance between a transmitter and a receiver has to be estimated from the vehicle side.In this paper, an estimation method considering the vehicle-side control is proposed and applied to the simultaneous power and efficiency control.The effectiveness of the proposed method is verified by simulations and experiments.

Wireless Power Transfer via Magnetic Resonance Coupling 2.1 Circuit analysis
The transmitter and the receiver coils are shown in Figure 1.They are compensated by resonance capacitors for WPT via magnetic resonance coupling [9], which can achieve a highly efficient mid-range transmission and robustness to misalignment.In this paper, a series-series (SS) compensated circuit topology is used and its circuit diagram is shown in Figure 2

Power source
Load  resistances R 1 , R 2 , respectively.L m is the mutual inductance between the transmitter and the receiver.These parameters are expressed in Table 1.If power source angular frequency is designed as follows:

Transmitter and Receiver
the transmitting efficiency η and the transmitting power P can be obtained as follows [11]: where V 1 is the RMS value of the primary voltage and R L is the load resistance.When V 1 equals to 100 V, η and P are expressed in Figure 3.In order to maximize the transmitting efficiency η, R L has to be given as follows [11]: Then, the transmitting power P is determined by R Lηmax .As a result, the desired power cannot be achieved only using R L optimization when the transmitting efficiency η is maximized.

System configuration
In order to achieve the maximum efficiency and the desired power simultaneously, the vehicle is equipped with two power converters, i.e.Half Active Rectifier (HAR) and the DC-DC converter [7,8].The circuit diagram of the DWPT system is shown in Figure 4.The ground facility consists of voltage source V S and an inverter, which generates a square wave voltage with resonance angular frequency ω 0 .The transmitting power P is rectified by the HAR and the charging power P L is controlled by the DC-DC converter.These control strategies and controller design methods are described below.

Power Source
Transmitter and Receiver

DC link voltage control
The HAR regulates the DC link voltage V dc for efficiency maximization.V dc control is achieved using two operation modes of HAR, which are shown in Figure 5 [12].When the lower arm MOSFETs are off-state, HAR is operated as the rectification mode.If the MOSFETs are turned on, HAR becomes the short mode and the receiver is shorted.Assuming the transmitting power P is larger than the load power P L , V dc is increased during the rectification mode.On the other hand, V dc is decreased during the short mode because P is cut-off and P L is supplied by the DC link capacitor.Therefore, the waveform of V dc can be depicted in Figure 6.If the upper bound V high and the lower bound V low are defined as follows: where V dc * is the reference value of the DC link voltage and ∆V is the hysteresis band, V dc is kept within the desired range.

Efficiency maximization
In order to maximize the transmitting efficiency, the load resistance R L , which is expressed in Figure 2, has to satisfy eq. ( 4) during the rectification mode.If V dc * is given as follows: R L is equated to R Lηmax and the transmitting efficiency η can be maximized [13].
On the other hand, during the short mode, the transmitting power P is drastically deceased because R L is minimized.As a result, losses during the short mode are assumed to be negligible to losses during the rectification mode in this paper.Therefore, V dc * is determined only by V dcηmax .

Mutual inductance estimation
For tracking the maximum efficiency in the DWPT system, the mutual inductance L m has to be estimated to obtain V dcηmax only using the vehicle-side information.From the circuit equations of the DWPT system, the estimation equation of L m can be given as follows [14]: Although eq. ( 8) has two solutions, the solution with a positive sign is used in this paper.Assuming the RMS primary voltage V 1 is constant and given to simplify ground facilities, L m can be estimated from the vehicle side.The RMS secondary voltage V 2 and the RMS secondary current I 2 are calculated from the DC link voltage V dc and the rectified DC current I dc using Fourier series expansions.
In order to reduce the estimation error due to the sensor noise, recursive least square (RLS) filter is applied.From eq. ( 8), output y[i] and regressor φ[i] are determined as follows: ) RLS filter is used to estimate L m statistically by updating Lm [i], y[i] and φ[i] with following equations.
In order to use the effective values for the estimation, the RLS filter updates Lm [i], y[i] and φ[i] only during the rectification mode of the HAR.If the HAR is operated as the short mode, I dc equals to 0 and the estimated value becomes incorrect.Therefore, the RLS filter has to be improved according to the operation mode of the HAR.
4 Power Control by the DC-DC converter

Modeling of the DC-DC converter
The DC-DC converter controls the load current i L for battery charging.Assuming the DC link voltage V dc is controlled to V dcηmax by the HAR, the circuit diagram of the DC-DC converter can be expressed in Figure 7 (a).E is the battery voltage, L is the inductance of the reactor coil and r is the internal resistance of the reactor coil and the battery.In this paper, the DC-DC converter model is obtained by the state space averaging method.Assuming the DC-DC converter is operated in the continuous conduction mode, its circuit diagram in each switching modes is expressed in Figure 7 (b) and (c).From the circuit equation, the state equation of Figure 7 (b) is given as follows: Also, the state equation of Figure 7 (c) is described as follows: When d(t) is defined as the duty cycle of the upper arm MOSFET S 1 , the state space model of the DC-DC converter is obtained as follows: In order to apply the linear control theory to the controller design, this model is linearized around an equilibrium point.When I L and D are defined as the equilibrium point, i L (t) and d(t) are expressed as follows: where ∆i L (t) and ∆d(t) are the microscopic fluctuations around the equilibrium point.By substituting eq. ( 15) and eq.( 16) in eq. ( 14), the linearized DC-DC converter model is given as follows: Therefore, the transfer function from ∆d(s) to ∆i L (s) is obtained as follows:

Controller design
Figure 8 shows the block diagram of the proposed control.The feedforward controller is the same as the equilibrium point calculation, which is given by the constraint of the DC-DC converter.From Vdcηmax , which is calculated from Lm , and the reference value of the load current i L * , the equilibrium point is obtained as follows:   The feedback controller is designed by the pole placement method.As ∆P i (s) is the first-order system, we apply a PI controller C P I (s), which is expressed as follows: If closed loop poles are given by a multiple root ω cl , the gains are obtained as follows: In this paper, V dcηmax and the gains are calculated by assuming the nominal value of L m is 30 µH.
5 Simulation and Experiment

Experimental setup
The experimental setup is shown in Figure 9.The system configuration is the same as Figure 4.The receiver is driven by the motor to simulate motion of the vehicle.The inverter is operated only while the receiver is above the transmitter to prevent huge power losses.Simulation and experimental conditions are expressed in Table 2.The forgetting factor λ of the RLS filter was set to 0.95 and the estimated mutual inductance Lm was updated only during the rectification mode of the HAR.The reference value of the DC link voltage Vdcηmax was calculated from Lm and the reference value of the load current i L * was set to 1.0 A.

Simulation
In the simulations, the change in L m was simulated by a sine wave.Its minimum and maximum values were set to 20 µH and 40 µH.   Figure 10 shows the simulation results without the proposed control.In this simulation, the HAR was operated as only the rectification mode and the duty cycle d of the DC-DC converter was equated to 0.95.From Figure 10 (b), Lm is closely matched with the actual L m .However, the transmitting efficiency η is decreased from the maximum efficiency because the DC link voltage V dc cannot be regulated to V dcηmax .Furthermore, the load current i L cannot be controlled to i L * .Figure 11 shows the simulation results with the proposed control.The closed loop poles of the proposed control were placed at -2000 rad/s.Although L m was estimated only during the rectification mode of the HAR, Lm accords with the actual L m as shown in Figure 11 (b).From Figure 11 (c) and (d), V dc is regulated around V dcηmax and η is maximized during the rectification mode.In addition, Figure 11 (e) indicates that the load current control can be achieved.

Experiment
In the experiments, the receiver was driven at 10 km/h and Lm was compared to the actual L m , which was measured by an LCR meter (NF Corp., ZM2371).The DC to DC efficiency η dc includes not only the transmitting efficiency but also the converter efficiency because it was measured by the DC voltages and currents on each sides.Therefore, improvement of system efficiency is verified in the experiments.
Figure 12 shows the experimental results without the proposed control.The HAR and the DC-DC converter were operated at the same condition as the simulation without control.From Figure 12 (b), Lm and the actual L m are closely matched.Although Lm has a short-time delay, Vdcηmax is near by the actual V dcηmax as shown Figure 12 (c).However, the transmitting efficiency cannot be maximized because V dc is not regulated to V dcηmax .Furthermore, Figure 12 (e) indicates that i L cannot be controlled unless the proposed control is applied.
In the case of with control, the DC-DC converter started power control when V dc reached V dcηmax .The closed loop poles of the proposed control were placed at -1000 rad/s.Figure 13 shows the experimental results with the proposed control.Although the error of Lm is larger than without control, V dc can be controlled around V dcηmax as shown in Figure 13 (c).From Figure 13 (d), η dc during the rectification mode of the HAR is increased compared to without control.In addition, Figure 13 (e) shows that i L can be controlled to i L * .If the closed loop poles of the proposed control are optimized, it is possible to suppress the current ripple due to the fluctuation of V dc .

Conclusion
This paper proposed a simultaneous control method of real-time power control and efficiency maximization based on improved mutual inductance estimation from the vehicle side.Its control strategy and controller design methods were presented.The effectiveness of the proposed method was verified by the simulations and the experiments.Future works are to propose an efficiency maximization method considering losses during the short mode of HAR and to design an optimal controller for the proposed control.Furthermore, the proposed method is implemented to an actual DWPT system using an EV.
[10].The transmitter and the receiver are characterized by the inductances L 1 , L 2 , the series-resonance capacitances C 1 , C 2 , and the internal EVS29 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 1 20 cmᡒ20 cm Receiver 20 cmᡒ40 cm Transmitter

Figure 4 :
Figure 4: Circuit diagram of the DWPT system.

Figure 5 :
Figure 5: Operation modes of Half Active Rectifier.

Figure 6 :
Figure 6: Waveform of the DC link voltage.

Figure 7 :
Figure 7: Circuit diagram of the DC-DC converter.
Whole picture of the DWPT system.(b) Half Active Rectifier and the DC-DC converter.

Figure 10 :
Figure 10: Simulation results without the proposed control.

Figure 11 :
Figure 11: Simulation results with the proposed control.

Figure 12 :
Figure 12: Experimental results without the proposed control.

Figure 13 :
Figure 13: Experimental results with the proposed control.

Table 1 :
Parameters of Coils.

Table 2 :
Simulation and experimental conditions.
c 20 kHz DC link capacitance C dc 2000 µF