IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 6, JUNE

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1 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 6, JUNE Maximum Efficiency Tracking for Wireless Power Transfer Systems With Dynamic Coupling Coefficient Estimation Xin Dai, Member, IEEE, XiaofeiLi, Student Member, IEEE, Yanling Li, and Aiguo Patrick Hu, Senior Member, IEEE Abstract Maximum efficiency tracking is an important issue for wireless power transfer (WPT) system. Traditional maximum efficiency tracking method normally focuses on load impedance matching with fixed coupling condition. However, WPT system is a loosely coupling system, the coupling coefficient varies due to relative movement between the primary and secondary sides. Unknown to this variation may result in failure of the tracking. In this paper, a novel maximum efficiency tracking method is proposed with integrated dynamic coupling coefficient estimation. This method can take almost all requirements for maximum efficiency tracking into account including adaption for coupling coefficient and load variation, and output controllability. The tracking method is easy to implement because no additional circuitry or measurement is required. Experimental results have verified the correctness of the proposed coupling coefficient estimation method. And the maximum efficiency tracking results show the system can achieve a good performance against coupling coefficient and load variation with the proposed tracking method. Index Terms Coupling coefficient, impedance matching, maximum efficiency tracking, wireless power transfer (WPT). I. INTRODUCTION WIRELESS power transfer (WPT) technology is undergoing a rapid development in recent decades. Because it can provide electronic devices with more flexible and more convenient power supply, it has found a lot of applications in implantable biomedical device, cellphone wireless charging, electric vehicle (EV) charging, etc., [1] [9]. Maximum efficiency tracking is an important research topic for WPT systems. However, efficiency is a complex performance index related to many factors including load status, Manuscript received March 15, 2017; revised May 27, 2017; accepted July 11, Date of publication July 19, 2017; date of current version February 22, This work was supported in part by the research funds for the National Natural Science Foundation of China under Grant , in part by Chongqing International Science and Technology Cooperation Base Project under Grant CSTC2015GJHZ40001, and in part by the Fundamental Research Funds for the Central Universities ( CDJZR175510). Recommended for publication by Associate Editor M. Duffy. (Corresponding Author: Xin Dai.) X. Dai, X. Li, and Y. Li are with the School of Automation, Chongqing University, Chongqing , China ( toybear@vip.sina.com; @ qq.com; @qq.com). A. P. Hu is with the Department of Electrical and Computer Engineering, University of Auckland, Auckland 1142, New Zealand ( hu@ auckland.ac.nz). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TPEL coupling coefficient, operation frequency, and soft switching conditions [1] [3]. Therefore, it is relatively difficult to track the maximum power efficiency during system operation. Current research works on maximum efficiency tracking can be classified into three groups. 1) Due to load variations in system operation, impedance matching is the most commonly used method for converting dynamic load impedance to the optimal impedance point [1], [2], [6], [10] [13]. The passive impedance matching network uses inductor and capacitor network to realize the impedance conversion [11], [14]. The active impedance matching method uses a dc dc converter to match dynamic variation of the load impedance [6], [12], [15]. 2) In further research of maximum efficiency tracking, the output voltage control is considered [1] [3]. Li et al. [1] propose a closed-loop method by controlling the output voltage at the primary side. And an impedance matching network is adding at the secondary side to track the maximum power efficiency. 3) As the input power is directly related to the system efficiency, a method has been proposed in [2] and [3] by tracking the minimum input current instead of maximum efficiency. Since the output voltage is controlled to be constant, the minimum input power point is actually the maximum efficiency point. First group method mainly focuses on the load variation and impedance matching for the maximum efficiency tracking. The second group method integrates output control and load variation together, and the maximum efficiency tracking is achieved with output voltage control. The third group method achieves the maximum efficiency tracking by input power control, but the control direction is unknown in advance, so a trial-anderror approach needs to be taken, which can result in a long adjusting time when there is a load or coupling coefficient variation, and the system may oscillate under frequent variations. In the previous studies, few papers take coupling coefficient variation into consideration when tracking the maximum efficiency. Where as WPT system is a loosely coupling system, the coupling coefficient can vary drastically when there exists relative movement between primary and secondary sides [4], [16], [17]. The coupling coefficient variation will directly change the optimal maximum efficiency point, which may result in fail IEEE. 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2 5006 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 6, JUNE 2018 the high-frequency resonant current of primary and secondary sides, respectively. Assuming the system is fully resonant, i.e., the resonant frequency satisfies f = 1 / 2π Lp C p = 1 / 2π Ls C s, the power transferred from primary side to secondary side, i.e., the output power of R i can be expressed as Fig. 1. Typical SS topology WPT system. ure of the maximum efficiency tracking if it is not identified online. As far as the coupling coefficient estimation is concerned, few papers have reported some related works in WPT systems. Su et al. [4] propose a method to estimate the load and the coupling coefficient by switching capacitors, with the different steady-state equations, the two parameters can be obtained. However, the calculation of the two parameters needs to measure the resonant current at both the primary and secondary sides, which is difficult in practical operation. A method has been proposed in [5] and [18] to dynamically estimate the coupling coefficient, and only the secondary-side parameters are needed. However, the measurement of the true root mean square (RMS) value of the resonant and rectifier currents is difficult due to higher order harmonics, so the measurement may involve more complexity and uncertainty. Besides, the estimation of dynamic coupling coefficient using two instances is not appropriate. Chow and Chung [19] propose an estimation method of mutual inductance and load resistance; the equations are based only on one operating frequency, but the measurements of the amplitudes and phase shift of the resonant voltage and current are so difficult. From the above analysis, it can be seen that traditional coupling coefficient estimation method is not applicable for maximum efficiency tracking because of the additional detection circuit required, or difficulties in practical implementation. This paper proposes a novel maximum efficiency tracking method with dynamic coupling coefficient estimation. The main feature of this method is the coupling coefficient estimation that only utilizes the inherent maximum efficiency tracking circuit. This method can take almost all requirements for maximum efficiency tracking into account including adaption for coupling coefficient and load variation, and output controllability. II. CLOSED-LOOP MAXIMUM EFFICIENCY TRACKING OF WPT SYSTEM A. Optimal Load Conditions for Maximum Efficiency of WPT System A primary and secondary series (SS) resonant WPT system is taken as an example configuration for the study. Fig. 1 shows a typical SS topology, where u s is a high-frequency ac voltage source. L p, C p and L s, C s constitute the resonant network of primary and secondary sides, respectively. R p and R s are the internal resistances of L p and L s, respectively. M is the mutual inductance between the primary and secondary coils. R i is the load resistance of the resonant circuit. i p and i s are ω 2 M 2 U 2 s R i P = [ω 2 M 2 + R p (R s + R i )] 2 (1) where U s is the RMS value of the input power source u s, ω is the resonant angular frequency, and satisfies ω =2πf. The input power P in of the SS-type WPT system can be given by U 2 s (R i + R s ) P in = ω 2 M 2 + R p (R i + R s ). (2) Divide (2) by (1), the efficiency of the system can be derived as η = ω 2 M 2 R i (R s + R i )[ω 2 M 2 + R p (R s + R i )]. (3) By taking the derivative of (3) with respect to R i [20], [21], the optimal load condition based on maximizing the transfer efficiency can be obtained as { dη dr i =0 d 2 η dr i 2 < 0 R i η max = R s 1+(kQ) 2 (4) where k is the coupling coefficient that satisfies k = M / L p L s. Q is the quality factor defined as Q = Q p Q s. Q p and Q s are the quality factor of the primary and secondary resonant coils, respectively, and can be derived as Q p = ωl p/ Rp,Q s = ωl s / Rs. Substituting (4) into (3) results in the transferred maximum efficiency η max ω 2 M 2 R i η max η max = (R s + R i η max )[ω 2 M 2 + R p (R s + R i η max )]. (5) B. Impedance Matching for Maximum Efficiency Tracking Fig. 2 gives a typical topology for impedance matching. By using a front-end rectifier followed by a buck boost converter (it can be replaced by other dc dc converters such as Buck, Boost, Sepic, etc.), where D r1 D r4 constitute the full-bridge rectifier, C r is the output filter capacitor of the rectifier. S l and D l are the switch component and flyback diode of the buck boost converter, respectively. L l and C l are the inductance and the output capacitance of the buck boost converter, respectively. R i is the equivalent output resistance of the resonant circuit shown in Fig. 1, R r in is the equivalent input resistance of the rectifier, and R i equals to R r in. R r is the equivalent output resistance of the rectifier, R l in is the equivalent input resistance of the buck boost converter, and R r equals to R l in. R l is the load resistance, and U l and I l are the output dc voltage and dc

3 DAI et al.: MAXIMUM EFFICIENCY TRACKING FOR WIRELESS POWER TRANSFER SYSTEMS WITH DYNAMIC COUPLING 5007 Fig. 2. Typical impedance matching circuit. current of R l, respectively. U l in is the input dc voltage of the buck boost converter. As can be seen from Fig. 2, the equivalent impedance R i can be adjusted by changing the duty cycle of the buck boost converter. When R i equals to R i η max shown in (4), the maximum efficiency transfer of the system can be achieved. Assuming the buck boost converter operating at continuous current mode (CCM), the duty cycle should meet the following requirement: 2Ll R l f 2 d 2 1 (6) R l where d 2 and f 2 are the duty cycle and frequency of the buckboost converter, respectively. For the buck boost converter operating at CCM, the relationship between the input voltage U l in and output voltage U l under steady-state operation can be shown as U l = d 2 U l in. (7) 1 d 2 Assuming there is no power loss in the buck boost converter, the relationship between the input resistance R l in and the output resistance R l can be derived as ( ) 2 1 d2 R l in = R l. (8) Similarly, for the rectifier circuit, the relationship between the equivalent input resistance R r in (R i ) and the output resistance R r (R l in ) can be expressed as d 2 R i =R r in = 8 π 2 R l in. (9) In practice, the load R l may vary with time and the efficiency will change accordingly. But for the impedance matching circuit shown in Fig. 2, the maximum efficiency tracking can be achieved by changing d 2 to maintain R i equals to the optimal load resistance R i η max shown in (4), and the relationship between the optimal duty cycle d 2 and R l can be expressed as d 2 = 2 ( 2π R l R i η max 4R l ) π 2 R i η max 8R l. (10) C. Closed-Loop Output Voltage Control As mentioned in [1] and [3], a well-designed WPT system should guarantee the output voltage stability. When the coupling coefficient or the load resistance varies, a closed-loop control should be used to regulate the output voltage. In this paper, a buck boost converter is used to regulate the output voltage at the primary side. The topology is shown in Fig. 3, while the detailed circuit is shown in Fig. 4. U in is the input dc voltage. S i1 S i4 constitute the full-bridge inverter. S b, D b, L b, and C b constitute the primary-side buck boost converter. u s is the equivalent input voltage of the resonant circuit as shown in Fig. 1. u r in is the equivalent input voltage of the rectifier. Z s is the secondary-side loop impedance. Z ref is the reflected impedance from secondary side to primary side. As can be seen from Fig. 3, the output voltage information U l is transmitted to the primary side by wireless communication. And the primary-side controller can regulate the output voltage by changing the duty cycle d 1 of the primary-side buck boost converter. The primary-side controller also generates the pulse width modulation signal s 1 s 4 to control the inverter. The secondary-side controller adjusts the duty cycle d 2 of the secondary-side buck boost converter to track the maximum efficiency point. The load resistance R l can be detected by measuring the output dc voltage U l and current I l. The changing of the duty cycle d 1 to maintain the output voltage equals to the required U l req is achieved by a hysteretic control algorithm. Assume the tolerance band of the required voltage U l req is ± u l, the control scheme is to increase d 1 if U l is smaller than U l req u l ; or decrease d 1 when U l is larger than U l req + u l.andd 1 remains unchanged within the tolerance band. Till now, the maximum efficiency tracking with output voltage control schematic has been analyzed. And the output voltage control can be done when the load resistance or the coupling coefficient varies. However, the maximum efficiency tracking can be done only when the load resistance varies, since the maximum efficiency point varies when the coupling coefficient is change as shown in (4). In some applications such as dynamic EV charging, the coupling coefficient may vary when the EV is moved. So the dynamic coupling coefficient should be

4 5008 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 6, JUNE 2018 Fig. 3. Topology of WPT system ensures the maximum efficiency tracking and constant output voltage. Fig. 4. Main circuit of WPT system ensures the maximum efficiency tracking and constant output voltage. estimated in order to do the maximum efficiency tracking. In the following sections, the dynamic coupling coefficient estimation method by utilizing the maximum efficiency tracking schematic will be presented. And the novel maximum efficiency tracking process with the dynamic coupling coefficient estimation will be analyzed. III. INITIAL AND DYNAMIC COUPLING COEFFICIENT ESTIMATION As mentioned before, the prior information of the coupling coefficient needs to be estimated in order to do the maximum efficiency tracking. In this section, both the initial and dynamic coupling coefficient estimation is analyzed with the aid of Fig. 4. And the estimation method only utilizes the inherent maximum efficiency tracking circuit. A. Initial Coupling Coefficient Estimation According to (8) and (9), the secondary-side impedance Z s can be obtained as Z s = 8 ( ) 2 1 d2 π 2 R l + R s. (11) d 2 The RMS value U s of the input resonant circuit voltage u s can be derived as U s = U in 2 2d 1 π (1 d 1 ). (12) The RMS value I p of the primary resonant current i p can be derived as U s I p = (13) R p + Z ref where Z ref is the reflected impedance from secondary side to primary side, and it satisfies Z ref = ω2 M 2 / Zs. The RMS value U r in of the rectifier input voltage u r in can be derived as R r in U r in = ωmi p. (14) R r in + R s The input dc voltage U l in of the buck boost converter can then be obtained as 2πUr in U l in =. (15) 4 Then, the RMS value of the output dc voltage U l can be calculated as U l = d 2U l in = αωmu sz s 1 d 2 ω 2 M 2 (16) + R p Z s 2πRr in d 2 where α= The relationship between the coupling coefficient k and U l can be calculated according to (16) as k = αu sz s ± (αu s Z s ) 2 4R p U 2 l Z s. (17) 2ωU l Lp L s 4(R r in +R s )(1 d 2 ).

5 DAI et al.: MAXIMUM EFFICIENCY TRACKING FOR WIRELESS POWER TRANSFER SYSTEMS WITH DYNAMIC COUPLING 5009 Fig. 5. Flowchart of the whole tracking process. As can be seen from (17), calculation of k has two solutions based on one instance of output voltage U l. The estimation of k can be done only when we have two instances of the output voltage. The estimation process will be discussed in the following section. B. Dynamic Coupling Coefficient Estimation As mentioned before, the dynamic coupling coefficient should be estimated in order to realize the maximum efficiency tracking. The estimation method for initial coupling coefficient is not suitable for dynamic estimation case since two instances are needed. Thus, a dynamic coupling coefficient estimation method is proposed accordingly. As mentioned in Section II-C, d 1 is automatically adjusted to regulate the output voltage U l when the load resistance or the coupling coefficient varies. Assuming R l is unchanged, so the steady state d 1 must change when k is change. As shown in Fig. 3, the steady state d 1 is transmitted to the secondary side in real time. So the dynamic coupling coefficient can be estimated at the secondary side. With (12), (16), and the required output voltage is U l req, the relationship between the coupling coefficient k and d 1 can be derived as ( ) β k =f (d 1 )= ( 1+d 1 ) γd 1 + δd ξd 1 + ψ L p L s (18) where d 2 (i.e., the duty cycle of the secondary-side buck boost converter) is unchanged during the estimation process, ξ= U 2 l req R p (d 2 2 (2π 4 R s +16π 2 R l ) 32π 2 R l d 2 +16π 2 R l ), ψ =U 2 ( 2 l req R ( p d2 π 4 R s 8π 2 ) R l +16π 2 R l d 2 8π 2 ) R l, δ =U 2 ( 2 l req R ( p d2 π 4 R s 8π 2 ) R l +16π 2 R l d 2 8π 2 ) R l + U 2 2 s R ( l 16d d ), β = 1 U l req π 2 ωd 2, γ=4u s R l (1 d 2 ). Assuming d 1 is changed by d 1 (the previous value is d 1p ), k is changed by k (the previous value is k p ), the following relationship can be derived: [(k p +Δk) k p ] [( ) ] = f (d 1) d1 p +Δd 1 d1 p d 1. (19) d1 =d 1 p And then we can derive Δk = f (d 1) Δd 1 d 1. (20) d1 =d 1 p As the initial coupling coefficient k p can be obtained in the initialization process, shown in Section III-A, and the value of d 1 is recorded at the secondary side in real time. Hence, the latest coupling coefficient k l can be obtained by f (d 1 ) k l = k p +Δd 1 d 1. (21) d1 =d 1 p After the dynamic coupling coefficient is estimated, the maximum efficiency tracking can be achieved. The novel tracking process with dynamic coupling coefficient estimation will be presented in the following section. IV. MAXIMUM EFFICIENCY TRACKINGWITH DYNAMIC COUPLING COEFFICIENT ESTIMATION The flowchart of the novel maximum efficiency tracking process with dynamic coupling coefficient estimation is shown in Fig. 5. When the communication between the primary and secondary sides is established, the primary-side controller transmits the initialization order to the secondary side and maintains d 1 = d 1a. After choosing initial d 2 = d 2a, two results k 1a and k 2a can be obtained based on the detected output voltage U la by solving (17). Then choose d 2 = d 2b, another two results k 1b and k 2b can be obtained based on the detected output voltage U lb. The real initial coupling coefficient k p is obtained by averaging the closest two values among k 1a, k 2a, k 1b, and k 2b. Such an estimation process shown in Fig. 5 is just a simple

6 5010 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 6, JUNE 2018 TABLE I SYSTEM PARAMETERS Parameter Value Parameter Value L p μh L s μh R p 0.83 Ω R s 0.51 Ω C p nf C s nf L b 120 μh f 56.7 khz C b 470 μf L l 120 μh f khz C l 470 μf U in 60 V f khz U l req 30 V TABLE II SIMULATION RESULTS OF INITIAL COUPLING COEFFICIENT ESTIMATION d 2a d2b N/A N/A N/A N/A N/A N/A N/A Fig. 6. Detailed flowchart of the secondary-side tracking process. approach adopted in this research for proof of concept. In a practical design, k p can be determined while the output voltage is regulated. When the initial coupling coefficient k p is estimated, the secondary-side controller transmits the initialization complete information to the primary side. And then the primary-side controller automatically adjusts d 1 to regulate the output voltage U l, and transmits the steady state d 1 to the secondary-side controller. The secondary-side controller does the impedance detection, impedance matching, detecting the latest coupling coefficient k l, and transmitting the real time U l to the primary side. The detailed tracking process of the secondary-side controller is shown in Fig. 6. When R l is change, the duty cycle d 2 of the secondary-side buck boost converter will be adjusted to track the maximum efficiency point according to (10). Particularly, when R l is not change, but the steady state d 1 is change, then the dynamic coupling coefficient k l can be estimated. And then the system will go on the tracking process. V. ANALYSIS OF THE PROPOSED COUPLING COEFFICIENT ESTIMATION AND MAXIMUM EFFICIENCY TRACKING METHOD In this section, the proposed coupling coefficient estimation and maximum efficiency tracking method is verified by MATLAB/Simulink. A simulation circuit is built according to Fig. 4 with the parameters shown in Table I, where f 1, f 2, and f are the frequency of the primary- and secondary-side buck boost converters and the inverter. A. Analysis of the Initial Coupling Coefficient Estimation As mentioned in Section III-A, the initial coupling coefficient can be estimated by two instances. The estimation results are TABLE III SIMULATION RESULTS OF DYNAMIC COUPLING COEFFICIENT ESTIMATION Previous k p Reference k l Estimated k l Accuracy % % % % shown in Table II with different d 2a and d 2b (the value changes from 0.1 to 0.7). The reference coupling coefficient is It can be seen that the initial duty cycles (d 2a and d 2b )have very little effect on the final result of the estimated coupling coefficient, so it is not critical in selecting them in the beginning. B. Analysis of the Dynamic Coupling Coefficient Estimation As mentioned in Section III-B, the dynamic coupling coefficient estimation can be achieved when d 1 and the initial coupling coefficient k p are determined. Table III shows the dynamic estimation accuracy when k changes from and (the previous value k p ). It can be seen that the estimation accuracy is lower when the difference between k l and the previous k p is larger, this is because (21) is the equivalent linearization result, when the difference is larger, the error is bigger. C. Maximum Efficiency Tracking of the WPT System The d 1 and d 2 values to ensure the maximum efficiency tracking and constant output voltage when R l changes from 1 to 100 Ω are shown in Fig. 7, where the triangular symbol indicates d 1 while the plus sign (+) indicates d 2. The black, blue, and red curves are under k = 0.168, 0.109, and 0.08 conditions, respectively. It can be seen from Fig. 7, for a given coupling

7 DAI et al.: MAXIMUM EFFICIENCY TRACKING FOR WIRELESS POWER TRANSFER SYSTEMS WITH DYNAMIC COUPLING 5011 Fig. 7. d 1 and d 2 values to ensure the maximum efficiency tracking when R l changes from 1 to 100 Ω. coefficient k, when R l is larger, d 1 is getting smaller while d 2 is larger. This is because the output power is smaller when R l is larger (the output voltage U l is controlled to be unchanged in the tracking process), so d 1 is getting smaller to decrease the input power. As for d 2, it is getting larger to ensure that R i equals to R i η max when R l is larger. It can also be seen from Fig. 7, for a given load resistance R l, when k is larger, d 1 is getting larger while d 2 is smaller. VI. EXPERIMENTAL STUDIES OF THE PROPOSED COUPLING COEFFICIENT ESTIMATION AND MAXIMUM EFFICIENCY TRACKING METHOD To verify the proposed method, an experimental platform is built. The circuit is shown in Fig. 4, and the parameters are shown in Table I. Two FPGA chips (Altera Cyclone II EP2C5T144C8) are selected as the primary- and secondary-side controller. Two ARM chips (STM32F407) are selected to do the wireless communication. And the secondary-side ARM also detects the load resistance R l by measuring the dc voltage U l and current I l. In the experiment, both the coupling coefficient and load variation tests were carried out to verify the proposed maximum efficiency tracking method. A coupling mechanism is set up for air gap, i.e., coupling coefficient changing as shown Fig. 8. Load resistance variation tests are implemented by switching the relay array as shown in Fig. 9. A. Experimental Studies of the Coupling Coefficient Estimation As for the coupling coefficient variation, the air gap between the primary and secondary mechanism is varied from 5 to 25 cm. Fig. 8. Photo of the coupling mechanism. The load voltage U l and the initial coupling coefficient estimation results are shown in Fig. 10, where d 2a and d 2b are selected as 0.4 and 0.5, respectively. Fig. 10(a) shows the load voltage U la, U lb when d 2a =0.4andd 2b =0.5. Fig. 10(b) shows the initial coupling coefficient estimation results; the blue and red lines indicate the reference and the estimated values, respectively. As can be seen from Fig. 10(b), the initial coupling coefficient estimation values matched well with the reference values, so the feasibility of the estimation method is further verified by the experimental results.

8 5012 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 6, JUNE 2018 Fig. 9. Experimental platform. Fig. 10. Experimental results of load voltage U l and initial coupling coefficient estimation results. (a) Load voltage U la, U lb ; (b) initial coupling coefficient estimation results. TABLE IV EXPERIMENTAL RESULTS OF DYNAMIC COUPLING COEFFICIENT ESTIMATION Previous k p Reference k l Estimated k l Accuracy % % % % The dynamic coupling coefficient estimation results are shown in Table IV. The results show that the estimation accuracy is lower when the difference between the previous k p and k l is larger. Furthermore, the accuracy is smaller than the simulation results shown in Table III since the losses of the semiconductor devices in the experimental system and the calculation error. B. Experimental Results of the Proposed Maximum Efficiency Tracking Method The maximum efficiency tracking when there are coupling coefficient and load resistance variations is tested. Fig. 11 shows the tracking results when the coupling coefficient changes while Fig. 12 shows the tracking results when R l changes. Channels 1 and 2 are the output voltage U l and the current I l of R l, respectively. Channels 3 and 4 are the duty cycle d 1 and d 2 of the primary- and secondary-sides buck boost converter,

9 DAI et al.: MAXIMUM EFFICIENCY TRACKING FOR WIRELESS POWER TRANSFER SYSTEMS WITH DYNAMIC COUPLING 5013 Fig. 11. Maximum efficiency tracking when coupling coefficient change. Fig. 12. Maximum efficiency tracking when R l change. respectively (Using 0 1 V voltage indicate 0 100% of the duty cycle). As can be seen from Fig. 11, the coupling coefficient k changes from to The load resistance R l is 8 Ω. Since the changing of the coupling coefficient (the distance between the primary and secondary coils) is a manual work, so the coupling coefficient changes smoothly. The output voltage is getting larger when the coupling coefficient is smaller; the maximum overshot voltage is 17 V. It takes about 500 ms for d 1 to be decreased until the output voltage equals to the required voltage. And then the secondary-side controller detects the steady value d 1 and estimate the latest coupling coefficient (the total estimation time is about 100 ms). After the latest coupling coefficient is estimated, the optimal duty cycle d 2 is fed to the secondary buck boost converter. And then, d 1 is automatically adjusted until the output voltage equals to the required voltage once again, this process takes about 300 ms. Fig. 12 shows the tracking results when R l changes from 8 to 16 Ω and then back to 8 Ω. The coupling coefficient k is Since the load is changed by the switching of the relay, so the load changes instantaneously, the maximum overshot voltage is 15 V. It takes about 600 ms to track the maximum efficiency Fig. 13. Steady-state experimental values with different k and R l.(a)k = 0.109, R l =8Ω;(b)k =0.109, R l =16Ω;(c)k =0.168, R l =8Ω. when R l changes from 8 to 16 Ω, while 800 ms to track the maximum efficiency when R l changes from 16 to 8 Ω. The changing of d 1 and d 2 are the same with the above analysis, do not repeat them here. The steady-state values of Figs. 11 and 12 are shown in Fig. 13. Fig. 13(a) indicates the steady values when k = 0.109, R l = 8 Ω. Fig. 13(b) indicates the steady values when

10 5014 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 6, JUNE 2018 VII. CONCLUSION This paper proposes a novel maximum efficiency tracking method for WPT systems. Compared with traditional tracking methods, variation of coupling coefficient is taken into account. It is found that the increment information of duty cycle can reflect the change of coupling coefficient in the maximum efficiency tracking process. It is utilized for coupling coefficient estimation in the maximum efficiency tracking. This method is easy for implementation because it does not require any additional circuitry or measurement device other than the efficiency tracking circuits. In addition, the maximum efficiency tracking, output voltage control, and coupling coefficient estimation have been realized at the same time using the proposed method. Fig. 14. Experimental efficiency results with different coupling coefficients k and load resistance R l. TABLE V MAXIMUM EFFICIENCY RESULTS k R l Maximum Efficiency (Ideal) Maximum Efficiency (Experiment) Ω 91% 83% Ω 91% 82% Ω 94% 85% k =0.109, R l = 16 Ω. Fig. 13(c) indicates the steady values when k =0.168, R l = 8 Ω. Channels 1 and 2 are the output voltage U l and current I l of R l, respectively. Channels 3 and 4 are the drive voltage u 1 and u 2 of the primary- and secondary-sides buck boost converter, respectively. The Pos Width value of Channels 3 and 4 indicates the duty cycle d 1 and d 2. As can be seen from Fig. 13(a), (b) and (c), the output voltage is approximately equals to the required 30 V. By comparing Fig. 13(a) and (b), it can be seen that with the same coupling coefficient k, d 1 is getting smaller while d 2 is getting larger when R l is larger. Furthermore, it can be seen from Fig. 13(a) and (c) that with the same load resistance R l, d 1 is getting larger while d 2 is getting smaller when k is larger. These results match well with the simulation results shown in Fig. 7. Fig. 14 shows the experimental efficiency results when d 2 changes from 0.3 to 0.7 with different coupling coefficients k and load resistance R l. It can be seen from Fig. 14 that there is only one maximum point of efficiency for each set of k and R l. The maximum points (d 2 ) obtained by theoretical are consistent with the experimental results. Table V shows the tracked maximum efficiency results, where the ideal maximum efficiency is calculated by (5). It can be seen that with the larger of k, the maximum efficiency is larger, this is consistent with Fig. 14. It can also be seen that the experimental results are smaller than the ideal results since the losses of the semiconductor devices in the experimental system and the calculation error. ACKNOWLEDGMENT The authors would like to thank M. Y. Qin, F. Wu, and Y. C. Huang for providing the assistance to this paper. REFERENCES [1] H. C. Li, J. Li, K. P. Wang, W. J. Chen, and X. Yang, A maximum efficiency point tracking control scheme for wireless power transfer systems using magnetic resonant coupling, IEEE Trans. Power Electron., vol. 30, no. 7, pp , Jul [2] W. X. Zhong and S. Y. R. Hui, Maximum energy efficiency tracking for wireless power transfer systems, IEEE Trans. Power Electron., vol. 30, no. 7, pp , Jul [3] T. D. Yeo, D. Kwon, S. T. Khang, and J. W. Yu, Design of maximum efficiency tracking control scheme for closed-loop wireless power charging system employing series resonant tank, IEEE Trans. Power Electron., vol. 32, no. 1, pp , Jan [4] Y. G. Su, H. Y. Zhang, Z. H. Wang, A. P. Hu, L. Chen, and Y. Sun, Steady- State load identification method of inductive power transfer system based on switching capacitors, IEEE Trans. Power Electron., vol. 30, no. 11, pp , Nov [5] V. Jiwariyavej, T. Imura, and Y. Hori, Coupling coefficients estimation of wireless power transfer system via magnetic resonance coupling using information from either side of the system, IEEE J. Emerg. Sel. Topics Power Electron., vol. 3, no. 1, pp , Jun [6] M. Fu, H. Yin, X. Zhu, and C. Ma, Analysis and tracking of optimal load in wireless power transfer systems, IEEE Trans. Power Electron., vol.30, no. 7, pp , Aug [7] Y. Liu, A. P. Hu, and U. K. Madawala, Maximum power transfer and efficiency analysis of different inductive power transfer tuning topologies, in Proc. IEEE 10th Conf. Ind. Electron. Appl., 2015, pp [8] L. Q. Yuan, B. Y. Li, Y. M. Zhang, F. B. He, and K. N. Chen, Maximum efficiency point tracking of the wireless power transfer system for the battery charging in electric vehicles, in Proc. Elect. Mach. Syst., 2015, pp [9] W. H. Li, H. Zhao, J. J. Deng, S. Q. Li, and C. C. Mi, Comparison study on SS and double-sided LCC compensation topologies for Ev/Phev wireless chargers, IEEE Trans. Veh. Technol., vol. 65, no. 6, pp , Jun [10] K. Ogawa, N. Oodachi, S. Obayashi, and H. Shoki, A study of efficiency improvement of wireless power transfer by impedance matching, in Proc. Microw. Workshop Series Innovative Wireless Power Transmiss., 2012, pp [11] T. C. Beh, T. Imura, M. Kato, and Y. Hori, Basic study of improving efficiency of wireless power transfer via magnetic resonance coupling based on impedance matching, in Proc. Int. Symp. Ind. Electron., 2010, pp [12] M. Fu, C. Ma, and X. Zhu, A cascaded Boost-Buck converter for highefficiency wireless power transfer systems, IEEE Trans. Ind. Informat., vol. 10, no. 3, pp , Aug [13] T. C. Beh, T. Imura, M. Kato, and Y. Hori, Maximum efficiency control of wireless power transfer via magnetic resonant coupling considering dynamics of DC-DC converter for moving electric vehicles, in Proc. Appl. Power Electron. Conf. Expo., 2015, pp

11 DAI et al.: MAXIMUM EFFICIENCY TRACKING FOR WIRELESS POWER TRANSFER SYSTEMS WITH DYNAMIC COUPLING 5015 [14] Y. Lim, H. Tang, S. Lim, and J. Park, An adaptive impedance-matching network based on a novel capacitor matrix for wireless power transfer, IEEE Trans. Power Electron., vol. 29, no. 8, pp , Aug [15] Y. Huang, N. Shinohara, and T. Mitani, Theoretical analysis on DC-DC converter for impedance matching of a rectifying circuit in wireless power transfer, in Proc. Radio-Frequency Integr. Technol., 2015, pp [16] D. Kobayashi, T. Imura, and Y. Hori, Real-time coupling coefficient estimation and maximum efficiency control on dynamic wireless power transfer using secondary DC-DC converter, in Proc. IEEE Ind. Electron. Soc., 2015, pp [17] W. Zhang, J. C. WHite, A. M. Abraham, and C. C. Mi, Loosely coupled transformer structure and interoperability study for EV wireless charging systems, IEEE Trans. Power Electron., vol. 30, no. 11, pp , Nov [18] D. Kobayashi, T. Imura, and Y. Hori, Real-time coupling coefficient estimation and maximum efficiency control on dynamic wireless power transfer for electric vehicles, in Proc. IEEE PELS Workshop Emerging Technol., Wireless Power, 2015, pp [19] J. P. W. Chow and H. S. H. Chung, Use of primary-side information to perform online estimation of the secondary-side information and mutual inductance in wireless inductive link, in Proc. IEEE Appl. Power Electron. Conf. Expo., 2015, pp [20] M. Fu, T. Zhang, C. Ma, and X. Zhu, Efficiency and optimal loads analysis for multiple-receiver wireless power transfer systems, IEEE Trans. Microw. Theory Techn., vol. 63, no. 3, pp , Mar [21] T. Imura and Y. Hori, Unified theory of electromagnetic induction and magnetic resonant coupling, Elect. Eng. Japan, vol. 199, no. 2, pp , Apr Xin Dai (M 10) received the B.E. degree in industrial automation from Yuzhou University, Chongqing, China, in 2000, and the Ph.D. degree in control theory and control engineering from the College of Automation, Chongqing University, Chongqing, in In 2012, he was a Visiting Scholar with the University of Auckland, Auckland, New Zealand. He is currently a Professor with the College of Automation, Chongqing University. His current research interests include inductive power transfer technology and nonlinear dynamic behavior analysis of power electronics. Xiaofei Li (S 16) received the B.E. degree in automation in 2013 from the College of Automation, Chongqing University, Chongqing, China, where he is currently working toward the Ph.D. degree in control theory and control engineering. His research interests include modeling and control of wireless power transfer and power electronics. Yanling Li received the B.E. degree in industrial automation from Yuzhou University, Chongqing, China, in She is currently working toward the Ph.D. degree in control theory and control engineering in the College of Automation, Chongqing University, Chongqing, China. Her current research interests include wireless power transfer and advanced control technology in power electronics. Aiguo Patrick Hu (M 01 SM 07) received the B.E. and M.E. degrees in electrical engineering from Xian Jiaotong University, Xi an, China, in 1985 and 1988, respectively, and the Ph.D. degree in electrical and electronic engineering from the University of Auckland, Auckland, New Zealand, in He was a Lecturer, a Director of the China Italy Cooperative Technical Training Center in Xian, and the General Manager of a technical development company. Funded by Asian2000 Foundation, he stayed in the National University of Singapore for a semester as an exchange Postdoctoral Research Fellow. He is currently with the Department of Electrical and Computer Engineering, University of Auckland, and is the Head of research of PowerbyProxi, Ltd., Auckland, New Zealand. He holds 15 patents in wireless/contactless power transfer and microcomputer control technologies, published more than 200 peer-reviewed journal and conference papers, authored a monograph on wireless inductive power transfer technology, and contributed 4 book chapters. His research interests include wireless/contactless power transfer systems and application of power electronics in renewable energy systems.

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