# Research on Optimization of Horizontal Omnidirectional Misalignment Tolerance of WPT Based on Double D Coupler

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## Abstract

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## 1. Introduction

## 2. Theoretical Analysis of WPT

**U**

_{S}is the high-frequency input voltage source, R

_{tx}and R

_{rx}are the total resistances of the transmitting coils and receiving coils, respectively. R

_{L}is the resistive load. M is the mutual inductance. Normally, the output power P

_{out}of the system can be represented by

_{tx}, R

_{rx}and R

_{L}. Normally, if the load resistance and frequency remain fixed, the output power and efficiency are related to the coil equivalent internal resistance and M. Generally, the mutual inductance will change when the misalignment occurs, resulting in the fluctuation of efficiency and output power. Therefore, it is effective to stable the mutual inductance, which can suppress the variation of efficiency and output power.

## 3. Optimization of Circular DD Coupler WPT System

#### 3.1. Mutual Inductance Calculation of Non-Coaxial Circular Coils

_{1}and r

_{2}represent the radius of single transmitting coil and receiving coil, θ and φ are angle integral parameters. The horizontal distance of the center of non-coaxial circular coil is denoted as t, h is the separated gap, μ

_{0}is the vacuum permeability. The multi-turn wound spiral coil can be regarded as a series of coaxial circular coils. Thus, the mutual inductance between two multi-turn spiral coils can be considered as the superposition of mutual inductance between several circular coils. Figure 2 illustrates the half cross section of circular DD coils for intuitive presentation.

_{1}and R

_{2}represent the horizontal distance from the outermost coil to the center of the single coils, respectively. N

_{1}and N

_{2}represent the turns of the single circular transmitting and receiving coils respectively. d

_{w}represents the litz wire diameter.

_{tr}of the coupler is derived as:

_{ij}represents the mutual inductance between the ith transmitting coil and the jth receiving coil. Similarly, M

_{ij}* represents the mutual inductance between the ith transmitting coil and the j*th receiving coil. Also, M

_{i}*

_{j}represents the mutual inductance between the i*th transmitting coil and the jth receiving coil. M

_{i}*

_{j}* represents the mutual inductance between the i*th transmitting coil and the j*th receiving coil.

#### 3.2. Analysis of Antimisalignment Characteristics of DD Coupler

_{1}= 0.205 m, R

_{2}= 0.109 m, N

_{1}= 10, N

_{2}= 20, h = 0.15 m, d

_{w}= 2.5 mm. Where R

_{1}and R

_{2}represent the radius of the circular transmitting and receiving coils, respectively. h denotes the separation distance between the transmitting coils and receiving coils. Also, the electromagnetic simulation software Ansys Maxwell is employed to obtain the mutual inductance between transmitting and receiving of circular DD and rectangular DD coils, respectively. It should be noted that the rectangular DD coils share the identical circular size with the coils for the fair comparison. The finite element simulation models are shown in the Figure 3. Moreover, the maximum element length of mesh for each model is set as 5 mm.

_{rec}and M

_{tr1}denote mutual inductance between the receiving coils and rectangular coils and circular coils respectively. σ

_{rec}and σ

_{tr1}represent the misalignment tolerance of rectangular coils and circular coils, respectively.

_{tr2}is the mutual inductance between the compensation coils and the receiving coils. The values of M

_{tr1}and M

_{tr2}can be obtained from Equation (4). N

_{3}represents the turns of the single circular compensation coils. h

_{1}represents the distance between the compensation coils and the transmitting coils. R

_{3}is the radius of a single compensation coils. The above-mentioned parameters are chosen as the optimization factor to improve the anti-misalignment ability of the system. The mutual inductance M

_{tr}between the compound transmitting and receiving coils can be deduced as:

_{tr1}and M

_{tr2}will decrease simultaneously. Theoretically, the mutual inductance can be stable if the variation amplitude of ΔM

_{tr1}and ΔM

_{tr2}are the same. Therefore, the radius, the number of turns and the gap between primary transmitting coils and compensation coils are taken as the optimized variables to obtain high misalignment tolerance.

#### 3.3. Analysis on Optimization Strategy for Misalignment Tolerance of Circular DD Coils

_{3}for the improvement of the anti-misalignment ability. If the optimized R

_{3}still does not satisfy the desired misalignment tolerance, optimizing h

_{1}and N

_{3}should be considered. Note that the turns of the compensation coils and the gap between the compensation coils and the transmitting coils, limited by internal resistance and longitudinal space, should be appropriate. Then, the priority of the parameters optimization is defined as follows, optimizing R

_{3}> optimizing h

_{1}> optimizing N

_{3}. Meanwhile, the separated gap between compensation coils and primary transmitting coils is less than 1/3 of the maximum transmission gap. Denote a as the retention ratio of the original mutual inductance. χ

_{1}and χ

_{2}are denoted as the minimum and maximum misalignment tolerance in the X-axis. Similarly, set χ

_{3}and χ

_{4}as the initial values of the minimum and maximum misalignment tolerance in the Y-axis. The objective function can be written as follows:

_{i}and M

_{j}denote the mutual inductance of the right endpoint value of the ith interval when offset occurs in the X-axis and the Y-axis, respectively, where i, j = 1, 2, n. M

_{0}is mutual inductance when the system is well aligned. ${M}_{\mathrm{tr}1}^{\mathrm{min}}$ and ${M}_{\mathrm{tr}1}^{\mathrm{max}}$ represent the minimum and maximum mutual inductance of the original coupler without compensation coils respectively, when offset happens in the Y-axis direction. σ

_{i}and σ

_{j}are the misalignment tolerance in the X-axis and Y-axis respectively. χ

_{1}, χ

_{2}, χ

_{3}, χ

_{4}, n, a are the value of the established boundary conditions. Assume that χ

_{1}= χ

_{3}= 95%, χ

_{2}= χ

_{4}= 105%, n = 10, a = 80 mm. Based on the optimization method of compensation coils, shown in Figure 6, the optimized results are calculated as follows: R

_{3}= 86 mm, h

_{1}= 120 mm, and N

_{3}= 6. The M

_{tr}, M

_{tr1}and M

_{tr2}versus offset in all directions is illustrated in Figure 7 by numerical simulation.

_{tr}is relatively uniform, which verifies the strong misalignment tolerance of the optimized system. Finally, the simulation results indicate that the misalignment tolerance fluctuates from 85.5% to 104.3% within the maximum offset range of 0.1 m × 0.1 m. When the WPT system is equipped with magnetic cores, the optimization results of parameters on compensation coils are inferred as follows: R

_{3}= 103 mm, h

_{1}=105 mm, and N

_{3}= 7.

_{tr}, M

_{tr1}and M

_{tr2}by finite element analysis software is simulated, as shown in Figure 8.

_{tr}also shows basically uniform distribution, and the global misalignment tolerance ranges from 91% to 105%. To sum up, the optimization method proposed in this paper for the improvement of anti-misalignment ability can be applied to the case with or without magnetic cores.

## 4. Verification Experiment

**U**

_{s},

**I**

_{1},

**I**

_{2}and output voltage

**U**

_{out}are recorded by the oscilloscope Tektronix MSO54 as Figure 10 and Figure 11 shown. The efficiency can be derived by:

**U**

_{s}, while the efficiency is only related to the intrinsic parameters of the magnetic couplers. Hence, the specific efficiency and normalized output power offset characteristic curves versus the X-axis and Y-axis are plotted in Figure 12.

_{0}and η

_{1}are the efficiencies without and with compensation coils respectively, P

_{0}and P

_{1}are the output powers without and with compensation coils, respectively. As can be identified from Figure 12, the efficiency fluctuates from 85.5% to 85% when the antiparallel winding is adopted, while that of the primitive system changes significantly from 87.1% to 85.9%. Without compensation coils, the output power fluctuates in multiple-rate at 0.1-m misalignment. By contrast, the proposed system has a higher and basically more stable output power, which greatly reduces the impact of large power fluctuation on power electronic devices.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**The characteristic of DD couplers versus offset: (

**a**) circular DD coils; (

**b**) rectangular DD coils.

**Figure 10.**Experimental waveforms of

**U**

_{s},

**I**

_{1},

**I**

_{2}and

**U**

_{out}before compensation. Continuous waveform: (

**a**) 0.1-m offset in the Y-axis occurs first and then 0.1-m offset in the X-axis occurs. Stationary waveform: (

**b**) well aligned; (

**c**) 0.1-m offset in the X-axis and Y-axis occurs simultaneously.

**Figure 11.**Experimental waveforms of

**U**

_{s},

**I**

_{1},

**I**

_{2}and

**U**

_{out}after compensation. Continuous waveform: (

**a**) 0.1-m offset in the Y-axis occurs first and then 0.1-m offset in the X-axis occurs. Stationary waveform: (

**b**) well-aligned; (

**c**) 0.1-m offset in the X-axis and Y-axis occurs simultaneously.

Parameter | Value | Parameter | Value |
---|---|---|---|

L_{1} | Before compensation 315 μH After compensation 297 μH | L_{2} | 329 μH |

R_{1} | Before compensation 1.6 Ω After compensation 1.7 Ω | R_{2} | 1.7 Ω |

U_{S} | 20 V | R_{L} | 24 Ω |

f | 190 kHz |

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**MDPI and ACS Style**

Chi, F.; Wang, P.; Sun, C.; Wu, Y.; Dou, Z.; Xu, C.; Wang, S.; Wang, W.
Research on Optimization of Horizontal Omnidirectional Misalignment Tolerance of WPT Based on Double D Coupler. *Electronics* **2022**, *11*, 2163.
https://doi.org/10.3390/electronics11142163

**AMA Style**

Chi F, Wang P, Sun C, Wu Y, Dou Z, Xu C, Wang S, Wang W.
Research on Optimization of Horizontal Omnidirectional Misalignment Tolerance of WPT Based on Double D Coupler. *Electronics*. 2022; 11(14):2163.
https://doi.org/10.3390/electronics11142163

**Chicago/Turabian Style**

Chi, Fuhai, Pan Wang, Chenglong Sun, Yuming Wu, Zhenlan Dou, Chenjin Xu, Shuo Wang, and Wei Wang.
2022. "Research on Optimization of Horizontal Omnidirectional Misalignment Tolerance of WPT Based on Double D Coupler" *Electronics* 11, no. 14: 2163.
https://doi.org/10.3390/electronics11142163