High Misalignment Tolerance in Efficiency of WPT System with Movable Intermediate Coil and Adjustable Frequency

Offsets between the primary and secondary coils of loosely coupled transformers (LCT) are attributable to the efficiency decline of the wireless power transfer (WPT) system. To improve the misalignment tolerance of efficiency in WPT system, this paper presents a LCT system with a movable intermediate coil and adjustable system frequency, which can promote the efficiency of the WPT system under misalignment condition. First, the influences of the position and compensation parameter of intermediate coil on the system efficiency during migration are summarized. The optimal compensation parameter and optimal position selection method of intermediate coil are proposed. Then, the influence of frequency on system efficiency is studied, and the detailed control strategy of intermediate coil’s position and system frequency is proposed. A 3-kW prototype WPT with the proposed three-coil LCT is manufactured and experimental validations are also performed. The results show that the efficiency declines of three-coil LCT with the proposed control strategy is 1.8% when the lateral offsets reach 300mm, namely 43% of the outer diameter of coil.


I. INTRODUCTION
Owing to the rapid growth of the electric vehicle (EV) industry, obvious momentum in research of energy storage system charging was witnessed in the last few years [1]. Among the feasible charging solutions are the wireless power transfer (WPT) systems [2]- [4]. Although the performance of these WPTs can meet the efficiency requirements at certain occasions, the efficiencies of the WPT system witness an obvious decline when the primary and secondary coils are misaligned. The suppression of system efficiency decline is equivalent to the strength of the misalignment tolerance of efficiency under offset conditions. Various approaches were proposed for achieving higher misalignment tolerance of the WPT efficiency [5]- [8]. These methods can be divided into the following categories: 1) loosely coupled transformer (LCT) design; 2) compensation topology design; and 3) control methods.
As for the optimal design of LCT, a double D-shaped (DD) coil and a DD-quadrature (DDQ) coil with additional orthogonal coil were proposed on the primary side [9] and the EV side [10], respectively, for improving the misalignment tolerance of WPT's efficiency. However, considering that the DDQ coil increases the use of wires, the bipolar pad (BP) coil partially overlapping DD coils was proposed in [11]. In addition, it is revealed that the square coil is more suitable for WPT application [12]. In [13], a flux pipe coupler was designed which has a significantly improved flux path. In [14], Quad-D-quadrature (QDQ) was proposed to improve the misalignment performance.
The number of turns and the quality factors of coils were also optimized [13]. It was also verified that I/N -type core can improve the lateral misalignment tolerance of the dynamic WPT's efficiency [14]. Moreover, to further improve the system's efficiency, several methods were proposed, such as the nonlinear thickness ferrite core [15], field-type ferrite core [2], non-linear ferrite core [16], EE/CC-type ferrite core [17], multi-coil LCT [18][19][20], etc.
Furthermore, a compensation topology named L/C was adopted to improve the efficiency of WPT [21]. Reviewing six types of compensation topologies, the series-series (SS) and series-parallel (SP) compensation circuits were presented for efficiency improvement in [22]. However, the double-sided inductor-capacitor-capacitor compensation, which is LCC topology, is less sensitive to mistuning than other topologies [23]. Therefore, it can be used to improve the misalignment tolerance of WPT's efficiency. To obtain the higher misalignment tolerance of efficiency, a variable inductor (VI) was inserted in the primary circuit for compensating the additional reactance [24]. However, the volume of WPT was increased. Moreover, a design considering compensation capacitor was proposed in [25], and the lateral misalignment tolerance was extended to 44.3% of the coupler's size. The above measures can improve the misalignment tolerance of efficiency to some extent, but they adopted a more complex structure, compensating topology, and even complex control strategy.
A third coil is used to reversely connect with the primary coil in [26], improving the misalignment tolerance in both xand y-directions. The application of passive intermediate coil in WPT system is also widely studied. In [27], a WPT system with an intermediate coil is analyzed, and an optimal design method is proposed for high system efficiency. Therefore, three coil system with an additional coil can improve the misalignment tolerance of efficiency. In the application of electric vehicle wireless charging, the primary coil is fixed on the ground and the secondary coil is installed on vehicle. When the secondary coil is not aligned, only the intermediate coil without power cable can be move freely. In addition, compared with two-coil system, the intermediate coil can get rid of the restriction of the power cable. However, when the secondary coil is not aligned with the primary coil, the influence of a movable intermediate coil on the misalignment tolerance has not been studied.
To improve the misalignment tolerance of the WPT's efficiency with a simple structure or simple control strategy, a novel LCT with intermediate coil and control strategy of intermediate coil's position and system frequency is proposed. First, the characteristics of the intermediate coil's compensation parameter are analyzed. Furthermore, the influences of the intermediate coil's position and system frequency on the system efficiency during migration are studied, and a detailed control strategy of the intermediate coil's position and system frequency is proposed. Finally, the effect to promote misalignment tolerance of the proposed control strategy in this paper is verified on a 3-kW LCT.

A. EQUIVALENT CIRCUIT MODELING OF TWO-COIL LCT
The equivalent circuit model of the two-coil LCT with series-series (SS) compensation is shown in Fig.1, where U p is the high-frequency supply; L p and L s are the selfinductances of the primary and secondary coils, respectively; R p and R s are the resistances of the coils, respectively; C p and C s are the compensation capacitance of the coils; respectively, M ps is the mutual inductance between the primary and secondary coils, and R eq is the equivalent resistance of the load.
According to the equivalent circuit and Kirchhoff's law, the equations of the output power and efficiency of the resonant two-coil LCT are represented in (1)  (2)

B. EQUIVALENT CIRCUIT MODELING OF THREE-COIL LCT
The equivalent circuit model of the three-coil LCT is shown in Fig.2 According to (9), (10), and (11), output power and the efficiency of three-coil LCT can be deduced as (12) . . . .

III. PROPOSED THREE-COIL LCT WITH MOVEABLE INTERMEDIATE COIL
The higher misalignment tolerance of system efficiency of LCT means lower decline of the efficiency under misalignment condition. Consequently, enhancing the efficiency of LCT when the offset reaches the maximum value should be considered during the design of LCT. To study how to improve misalignment tolerance of efficiency by virtue of movable intermediate coil, the influence of compensation parameter and physical position of the intermediate coil on efficiency are studied in this section, and the results are compared with two-coil WPT. This paper focuses on the influence of compensation parameter and physical position of the intermediate coil and proposing an adjustment strategy consequently. Therefore, the parameters of primary coil, secondary coil and intermediate coil are assumed to be known, and the corresponding optimization of coils is not described in this paper. To study the difference between three-coil LCT and two-coil LCT, and the influence of position and compensation parameter of intermediate coil on system efficiency, two-coil LCT and three-coil LCT are modeled in finite element simulation software, as shown in Fig. 3. The outer diameter of the intermediate coil is set to be the same as that of the primary and secondary coil, and the detailed parameters are given in Table I. The adopted structure of three-coil LCT is shown in Fig.  3. The intermediate coil is placed slightly above the primary coil to facilitate its movement, and the intermediate coil can be removed to get a two-coil LCT as a contrast. The distance between primary and secondary coils is fixed at 200 mm, and the distance between primary and intermediate coils is fixed at 30 mm. The above structure is modeled in the finite element simulation software to calculate the performance of WPTs, and the parameters of three-coil LCT and two-coil LCT are listed in Table I.

A. ANALYSIS OF INTERMEDIATE COIL'S MPENSATION PARAMETER
For two-coil WPT system, S/S compensation is widely used for its simple structure and excellent performance. The maximum efficiency can be achieved when the compensation parameter satisfies the following formula, which means the circuit is under resonant condition.
Substituting the parameters of two-coil LCT in Table I, the efficiency can be calculated to be 95.42%. For more intuitive comparison, the primary and secondary compensation parameters of the three-coil LCT are set to be the same as that of two-coil LCT. Then, the influence of intermediate coil's compensation parameter on system efficiency is shown in Fig. 4. To compare with the resonant capacitance parameter, the independent variable is set as the ratio of the intermediate coil's compensation parameter to the resonant capacitance parameter. As can be concluded from Fig. 4, when the resonant capacitance parameter of intermediate is adopted the system efficiency isn't the highest point, and it's even lower than the efficiency of two-coil LCT.
Ci/Cires Efficiency Three-coil system Two-coil system  The above discussion of intermediate coil's compensation parameter is on the premise that the receiving coil is aligned. Therefore, based on the above discussion, the intermediate coil's compensation is set to be C iopt . Then, two-coil system, three-coil system with C i =C ires , and threecoil system with C i =C iopt under misalignment condition are simulated. The simulated efficiency results are shown in Fig. 5. It is evident that the efficiency of three-coil system with C i =C iopt is still higher than two-coil system and threecoil system with C i =C ires . In addition, when the receiving coil at the maximum offset 300mm, the efficiency decline of three-coil system with C i =C iopt is also the smallest.

B. ANALYSIS OF LCT SYSTEM WITH A MOVABLE INTERMEDIATE COIL
In a three-coil LCT system without magnetic core, the change of intermediate coil's position mainly affects the coupling coefficient between intermediate coil and primary or secondary coils. Firstly, the influence of coupling coefficient between intermediate coil and primary or secondary coils on system efficiency is studied. When the inductance parameters and mutual inductance between primary and secondary coil in Table Ⅰ is adopted, the variation of the efficiency of three-coil LCT with k pi and k is is given in Fig. 6, where k ps is the coupling coefficient between the primary and the secondary coil, k pi is the coupling coefficient between the primary and the intermediate coil, and k is is the coupling coefficient between the intermediate and secondary coil. To observe the influence of k pi and k is on system efficiency more intuitively, the top view of Fig. 6 is shown in Fig. 7. The darkest red area in Fig. 7 shows the collection of (k is , k pi ) that can make the system efficiency reach the maximum with different k is .

Efficiency(%)
kpi kis However, the collection of (k is , k pi ) that can make the system efficiency reach the maximum value may not be obtained by adjusting the position of intermediate coil. Therefore, to simplify the analysis and make the conclusion more feasible, the influence of the position of intermediate coil on system efficiency under different misalignment of secondary coil will be studied next. It's worth noting that only the horizontal offset will be considered in this paper. Through finite element simulation, the efficiency of LCT system under different misalignment of secondary and intermediate coils can be obtained as shown in Fig. 8, where X s and X i represent offset of secondary and intermediate coils respectively. It can be concluded from Fig. 8 that there is an optimal position of intermediate coil to maximize system efficiency under different misalignment of secondary coil. In addition, the optimal position of intermediate coil X iopt isn't the same as the position of secondary coil, but is slightly less than X s . Then, based on the data in Fig. 8, the optimal positions of intermediate coil at different X s are sorted out, as shown in Fig. 9. It's evident that the relationship between X iopt and X s is iopt s /2 XX  . According to the position relationship of X s and X iopt in Fig. 9, the system efficiency of three-coil system with adjusted X i = X iopt is shown in Fig. 10. Compared with three-coil system with fixed X i =0mm, the decrease of system efficiency under misalignment condition is obviously reduced. When the secondary coil is offset by 300mm, the distribution of flux density with fixed and optimal position of intermediate coil is shown in Fig. 11. By adjusting the position of the intermediate coil under the misalignment condition, the magnetic flux coupling between the transmitter and receiver is greatly enhanced, so the movable intermediate coil can enhance the misalignment tolerance.

C. ANALYSIS OF THE INFLUENCE OF ADJUSTABLE SYSTEM FREQUENCY
The compensation capacitance parameter of the intermediate coil is selected as the optimal value when the secondary coil and the intermediate coil are both aligned. However, when the secondary coil is offset and the position the intermediate coil is adjusted accordingly, the optimal compensation parameter changes, and the compensation capacitance needs to be adjusted accordingly to maximize the efficiency. Considering the difficulty of adjusting capacitance parameter in the actual system, the adjustable system frequency is adopted in this paper.
According to the previous analysis, the optimal position of intermediate coil is 150mm, while the offset of secondary coil is 300mm. With the above cases, the effect of variable frequency on the system efficiency is analyzed, as shown in Fig. 11. It's evident that the highest efficiency is realized when the frequency deviates from the rated frequency. Therefore, the misalignment tolerance of efficiency can be further improved by adjusting system frequency to improve the efficiency when the secondary coil is not aligned.

C. CONTROL STRATEGY OF LCT SYSTEM WITH MOVABLE INTERMEDIATE COIL AND ADJUSTABLE FREQUENCY
According to the above analysis, when the secondary coil is not aligned, the position of intermediate coil and system frequency both affect the system efficiency. By adjusting the position of the intermediate coil and system frequency, the system efficiency under different misalignment condition can be maximized. The flowchart of detailed control strategy is shown in Fig. 12, including position adjustment control and frequency tracking control.
Firstly, the position of secondary coil is detected and the initial frequency is set as 85-kHz. Then, the position of intermediate coil is adjusted to half of the offset position of the secondary coil, according to Section Ⅲ. B. The frequency tracking procedure is performed subsequently to maximize the system efficiency.

A. PROTOTYPE AND EXPERIMENTAL SETUP
To validate the feasibility of the proposed control strategy for the LCT with movable intermediate coil and adjusted frequency, a prototype of WPT system is manufactured and shown in Fig. 14. The parameters of the prototype are shown in Table II. The test platform includes DC power supply, high frequency inverter with adjustable switching frequency, a three-coil LCT, three compensating capacitor banks made by film capacitors, and non-inductive load resistor.
The LCT consist of three layers coils which wound by the Litz wire with a radius of 6.5 mm, the size of the primary and secondary coils is 700×700 mm, the size of the intermediate coil is also 700×700 mm. The distance between primary and secondary coils is fixed at 200mm, and the distance between primary and intermediate coils is fixed at 30mm, which is same as the air gap distance in simulation.
The physical parameters of the test rig are measured by the impedance analyzer and the circuit parameters of the test rig are measured by the precise power analyzer.

B. COMPARISON BETWEEN THE TWO-COIL AND THREE-COIL LCT
In the experimental verification, the advantage of three-coil LCT in improving the misalignment tolerance of efficiency is compared with two-coil LCT. After selecting the compensation parameter of intermediate coil according to the method mentioned above, the efficiency of two-coil and three-coil LCT under the alignment condition are tested by using the high precise power analyzer, as shown in Fig. 14.
It can be seen that the efficiency of three-coil LCT is higher than two-coil LCT when the output power is both 3 kW.
Then, the variations of the efficiency of two-coil and threecoil LCT with lateral offset are shown in Fig. 15. It can be concluded that. 1) With the increase of lateral offset, the efficiency of two-coil and three-coil LCT both decreases.
2) At different offset positions, the efficiency of the three-coil system is higher than that of the two-coil system. With the increase of lateral offset, the effect of intermediate coil in improving efficiency is increasing.

C. COMPARISON BETWEEN THREE-COIL LCT WITH AND WITHOUT CONTROL STRATEGY
Based on the comparison of three-coil and two-coil LCT above, the control strategy of intermediate coil's position and system frequency proposed in this paper is verified. During the experiment, when the secondary coil is offset laterally, the position of intermediate coil and system frequency are adjusted. According to the simulation analysis above, the optimal position of intermediate coil is half of X s , and the adjustment of position intermediate coil and system follows the process in Fig. 12. The lateral offsets of secondary coil are obtained directly from the scale on coils. By using the high precise power analyzer, with movable intermediate coil at optimal position and adjusted system frequency, the efficiency of three-coil LCT under misalignment condition is measured and shown in Fig. 16, and the measured waveforms when lateral offset reaches 300mm are shown in Fig. 17. Channel 3 measures the input voltage/current of primary coil, and the channel 4 measures the output voltage/current of secondary coil. It's evident that the efficiency of three-coil LCT can be further improved under the misalignment condition. When the lateral offset of secondary coil reaches 300mm, the efficiency of three-coil LCT can be improve by 3.3% compared with two-coil LCT. It can be concluded that.
1) Comparing to the three-coil LCT with intermediate coil at fixed position, when the lateral offset is no more than 100mm, the effect of moveable intermediate coil in improving efficiency is not obvious.
2) When the lateral offset is more than 100mm, with the increase of lateral offset, the effect of moveable intermediate coil in improving efficiency is increasing.

V．CONCLUSIONS
To improve the misalignment tolerance of efficiency of WPT system, this study proposed a three-coil LCT with movable intermediate coil and adjustable frequency. Main conclusions are as follows.
1) The influence of the intermediate coil's compensation parameter on the efficiency of three-coil LCT is studied and compared with the efficiency of two-coil LCT. Afterward, the efficiency of three-coil LCT with optimized intermediate coil's compensation parameter under misalignment condition is compared with the twocoil LCT.
2) Then, the influence of the position of the intermediate coil and system frequency on the efficiency of LCT with lateral offset was studied, and a control strategy of the intermediate coil's position and system frequency was proposed to promote the misalignment tolerance of efficiency.
3) A 3-kW prototype WPT with three-coil LCT was designed and manufactured, and the effectiveness of the proposed control strategy for system efficiency was also verified. Experimental results showed that the proposed strategy can effectively suppress the efficiency decline, improving the misalignment tolerance of WPT.