# Quadruple-U Auxiliary Structure-Based Receiving Coil Positioning System for Electric Vehicle Wireless Charger

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- A quadruple-U auxiliary structure with cruciform distribution was designed without changing the magnetic coupler;
- (2)
- The magnetic field variation was studied when the proposed quadruple-U auxiliary structure was introduced into the typical magnetic coupler, of which the transmitting coil and the receiving coil are rectangular;
- (3)
- A corresponding positioning approach based on the quadruple-U auxiliary structure was proposed to assist in the vehicle entering the effective charging area.

## 2. Auxiliary Structure and Performance

#### 2.1. Quadruple-U Auxiliary Structure

_{R1}is defined as the mutual inductance between the U1 coil and the receiving coil. A similar notation applies to the mutual inductances M

_{R2}, M

_{R3}, and M

_{R4}.

_{R-U}) varies with the misalignment position of the receiving coil under the condition that the system is in the positioning and guidance process. It can be seen that the numerical values of M

_{R-U}appear the trend as a wavy pattern; that is, M

_{R-U}reaches a maximum at ΔY = ±100 mm and approximately zero at ΔY = 0 mm. Meanwhile, its misalignment sensitivity is satisfactory. The reason is that the U-shaped coil can be regarded as a bipolar coil, while the receiver coil is a unipolar coil. Hence, the mutual inductance between them will present the maximum when the receiver coil is located directly above the two structural endpoints of the U-shaped coil and present approximate zero when it is located directly above the structure center of the U-shaped coil, for they are decoupled from each other.

#### 2.2. Optimization of the Structural Parameters

_{1}, outer height, h

_{1}, outer width, w

_{1}, endpoint length, w

_{2}, inner height, h

_{2}, and inner length, l

_{2}. Moreover, we achieved parameter optimization by relying on the following set conditions: the overall dimensions of the primary and the secondary coils and corresponding ferrite are 300 mm × 300 mm, and the transfer distance is 160 mm.

_{R1}, varies with each crucial parameter when the receiving coil is only misaligned in the Y-axis, with the step being 50 mm. As a whole, M

_{R1}changes under the influence of any parameter, which is consistent with the trend shown in Figure 2.

_{1}, M

_{R1}is proportional to l

_{1}, and M

_{R1}reaches a minimum at ΔY = 0.5l

_{1}. While the variation of M

_{R1}, with the change of l

_{1}when ΔY > 0.5l

_{1}, is not obvious enough. Meanwhile, considering the identifiable range of the U-shaped coil should be enhanced as far as possible under the limitation of the available space, we selected l

_{1}= 200 mm, eventually. In addition, due to the cruciform distribution of the quadruple-U auxiliary structure, one endpoint of each U-shaped coil near the center of the quadruple-U structure will be coupled with the other U-shaped coils, resulting in the variation not being completely symmetric. In order to analyze the influence of h

_{1}on M

_{R1}, h

_{1}− h

_{2}= 10 mm was set in this simulation process. As shown in Figure 4b, M

_{R1}is proportional to h

_{1}, and the numerical value of M

_{R1}under the two conditions of h

_{1}= 60 mm and h

_{1}= 70 mm changes little when ΔY is within 50 mm~100 mm. Therefore, we picked h

_{1}as equal to 60 mm. Furthermore, in order to simplify the production of the U-shaped coils, we set the parameters w

_{1}= w

_{2}and optimized them synchronously; the simulation results are shown in Figure 4c. It can be indicated that M

_{R1}is also proportional to w

_{1}and w

_{2}, while w

_{1}= w

_{2}= 15 mm and w

_{1}= w

_{2}= 20 mm have little influence on the variation of M

_{R1}when ΔY = 0~100 mm. Thus, w

_{1}= w

_{2}= 15 mm was determined. At last, the variation between M

_{R1}and h

_{2}is exhibited in Figure 4d, and it can be seen that even if h

_{2}changes, it has little effect on M

_{R1}. Therefore, h

_{2}= 50 mm was selected to reduce the volume of the ferrite.

## 3. WPT System Based on the Quadruple-U Auxiliary Structure

#### 3.1. Positioning System Model

_{1}–S

_{4}is the switch of the full-bridge inverter circuit, and D

_{1}–D

_{4}is the diode of the rectifier circuit. L

_{R}, L

_{U1}, L

_{U2}, L

_{U3}, and L

_{U4}represent the inductance of the receiving coil and the four auxiliary coils. C

_{R}, C

_{U1}, C

_{U2}, C

_{U3}, and C

_{U4}represent the resonant capacitor in the series of the corresponding inductance. L

_{1}, L

_{2}, L

_{3}, L

_{4}, and C

_{1}, C

_{2}, C

_{3}, and C

_{U4}are the other compensating inductances and compensating capacitances, respectively, in the LCC resonant circuit at the transmitting side. M

_{R1}, M

_{R2}, M

_{R3}, and M

_{R4}are the mutual inductances between each U-shaped coil and the reserving coil. Moreover, due to the method that four U-shaped coils worked independently was adopted to avoid the influence of the complex cross-coupling situation on the system, the other mutual inductances, such as between one U-shaped coil and another, M

_{12}, M

_{13}, M

_{14}, M

_{23}, M

_{24}, and M

_{34}are not shown.

#### 3.2. Calculation of Mutual Inductance

_{R-U}represents the mutual inductance between the receiving coil and U-shaped coil, μ

_{0}is the vacuum permeability, and dl

_{1}and dl

_{2}indicate the line elements of the corresponding loop [22].

_{a11-b11}as an example, the coordinates of any point on the side of a

_{11}can be expressed as A(x

_{1}, y

_{1}, 0), and any point on b

_{11}is described as B(x

_{2}+ Δx, y

_{2}+ Δy, z

_{1}). Thus, the relative position of the two points can be obtained:

_{a11-b11}between a

_{11}and b

_{11}is:

_{U}, and that in the rectangular coil is d

_{R}. The U-shaped coil can be divided into three parts, that is the left vertical sub-coil (20 turns), the lower horizontal sub-coil (60 turns), the right vertical sub-coil (20 turns), and the mutual inductance between the three parts of the U-shaped coil, and the receiving coil is, respectively, expressed as M

_{1(R-U)}, M

_{2(R-U)}, and M

_{3(R-U)}. On the basis of it, the overall mutual inductance can be subdivided into the sum of the mutual inductance between each sub-coil and the receiving coil.

_{1}y

_{1}z

_{1}is established at the vertex center of the vertical sub-coil on the left of the U-shaped coil. Any point on the side of a

_{n1}can be expressed as A(x

_{1}, y

_{1}, n·d

_{U}+ n·r − d

_{U}− r), where n ∈ [1,20], and any point on the side of b

_{k1}is B(x’

_{1}, y’

_{1}+ k·d

_{R}+ k·r − d

_{R}− r, z

_{1}), where k ∈ [1,20]. Thus, the mutual inductance between a

_{n1}and b

_{n1}M

_{1(an1-bk1)}can be obtained.

_{k1}, respectively [27], can be written as:

_{R-U}can be obtained as follow:

## 4. Positioning Approach

#### 4.1. Mutual Inductance Analysis under Different Misalignment

_{R1}, M

_{R2}, M

_{R3}, and M

_{R4}, with ΔX and ΔY, is shown in Figure 9. It can be seen that once the receiving coil is aligned with the quadruple-U auxiliary structure, the coupling degree between the receiving coil and the four U-shaped coils is the same so that the corresponding mutual inductances satisfy the relationship that MR1 = MR2 = MR3 = MR4, while if the receiving coil is in a certain misalignment, the numerical value of the corresponding four mutual inductances is different; that is, MR1 ≠ MR2 ≠ MR3 ≠ MR4. This is due to the four different coupling degrees caused by the different relative positions between the receiving coil and each U-shaped coil. Meanwhile, take the structure center of each U-shaped coil as the origin, the direction perpendicular to the coil is the X-axis, and the direction horizontal to the coil is the Y-axis, establishing the corresponding four coordinates. We can find that the overall variation of the four mutual inductances is consistent.

_{R1}, and the load voltage V

_{O1}. When the receiving coil is misaligned, the load voltage can be obtained, and it will correspond to the unique mutual inductance, M

_{R1}. According to the variation of M

_{R1}, all of the possible misaligned positions of the receiving coil can be summarized as a specific trajectory in the plane of XOY when the M

_{R1}keeps constant, which means that a certain M

_{R1}will correspond to countless kinds of receiving coil misalignment cases. Figure 10 is the schematic diagram of the specific trajectory mentioned above.

#### 4.2. Positioning Approach

- Precise Positioning. Through the coupling relationship between the receiving coil and the three or four U-coils, the misalignment position can be determined quickly and accurately. Then the driver decides whether they need to correct the vehicle by using the feedback of the misalignment position.
- Fuzzy Positioning. Through these coupling relationships, only the possible positions in the general area of the receiving coil offset can be predicted. Then, the driver corrects the vehicle into the precise positioning area by using the feedback of the deduced position or area.

## 5. Experimental Validation

#### 5.1. Verification of Mutual Inductance

_{R1}, M

_{R2}, M

_{R3}, and M

_{R4}vary with the misalignment of the receiving coil just by measuring each mutual inductance in a certain quadrant of the XOY plane when the receiving coil is misaligned. Hence, an array of 7 × 9 typical positions within the identifiable range that abut the aligned position of each U-shaped coil was measured. The experimental results of the four mutual inductances in the misalignment cases are shown in Figure 15a–d.

_{R1}, presents a variation of gradually increasing to the maximum and then decreasing with ΔY, and there is an inverse relationship between M

_{R1}and ΔX, which are consistent with the variation obtained by the simulation. In addition, according to the symmetry of the magnetic field of the U1 coil shown in Figure 9, we can deduce that when ΔX ∈ [−300 mm, 0 mm] and ΔY ∈ [−300 mm, 100 mm], the variation of M

_{R1}with ΔY is consistent with that in Figure 15a, while the variation of M

_{R1}with ΔX is opposite of that in Figure 15a. Therefore, combining the symmetry of the structure and the test results, we can indicate that there exists a symmetry among the four mutual inductions, M

_{R1}, M

_{R2}, M

_{R3}, and M

_{R4}. Moreover, the numerical value of the measured mutual inductances is slightly smaller than those in the simulations, and the deviations are less than 10%. The tiny differences are caused by the ferrite of the U-shaped coil being composed of a few ferrites with different sizes overlapping and splicing together.

#### 5.2. Verification of Load Voltage

#### 5.3. Positioning Results

_{O1}, V

_{O2}, V

_{O3}, and V

_{O4}were measured when the four U-shaped coils worked independently, and the intersection point coordinates were deduced after obtaining the most matched information by retrieving these load voltages from the database. As shown in Figure 14, the proposed positioning method based on the special quadruple-U auxiliary structure exhibits a wide positioning range and high positioning accuracy. On the one hand, among the 6 × 6 and 4 × 7 tested positions, all of them were accurate to within 10 mm. On the other hand, combined with the symmetry of the auxiliary structure and the obtained identifiable range within ΔX ∈ [−300 mm, 0 mm]∩ΔY ∈ [−300 mm, 300 mm], we can conclude that the overall identifiable range of the designed auxiliary structure is ΔX ∈ [−300 mm, 300 mm]∩ΔY ∈ [−300 mm, 300 mm].

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Structure of the quadruple-U auxiliary device. (

**a**) The overall view. (

**b**) The structure of the U-shaped coil.

**Figure 2.**Magnetic field variations of the DD coil and the U-shaped coil. (

**a**) DD coil. (

**b**) U-shaped coil.

**Figure 4.**Optimization of the structural parameters. (

**a**) is the optimization of l

_{1}. (

**b**) is the optimization of h

_{1}. (

**c**) is the optimization of w

_{1}and w

_{2}. (

**d**) is the optimization of h

_{2}.

**Figure 7.**Relative position of U-shaped coil and rectangular receiving coil. (

**a**) Relative position between two single-turn coils. (

**b**) Relative position between U-shaped coil and rectangular coil.

**Figure 8.**Structural parameters of the receiving coil and the U-shaped coil. (

**a**) Parameters of the receiving coil. (

**b**) Parameters of the U-shaped coil.

**Figure 17.**Positioning results in typical positions. (

**a**) The moving step of the receiving coil is 20 mm. (

**b**) The moving step of the receiving coil is 100 mm.

Method | Advantage | Disadvantage |
---|---|---|

Use sensor | Simplify the positioning process | Increase the cost |

Use the coil’s parameters | High positioning accuracy | Lack of applicability |

Use new magnetic coupler | Satisfactory accuracy | Lack of practicality |

Place the auxiliary coil on the secondary side | Satisfactory accuracy | Change the receiving coil |

Place the auxiliary coil on the primary side | Satisfactory accuracy | Change the primary-side |

Coil | Induction Range (about the Aligned Position) | Induction Range (Avoid the Aligned Position) |
---|---|---|

U1 | −300 mm < ΔX < 300 mm, −300 mm < ΔY < 100 mm | −300 mm < ΔX < 300 mm, 100 mm < ΔY < 500 mm |

U2 | −100 mm < ΔX < 300 mm, −300 mm < ΔY < 300 mm | −500 mm < ΔX < −100 mm, −300 mm < ΔY < 300 mm |

U3 | −300 mm < ΔX < 300 mm, −100 mm < ΔY < 300 mm | −300 mm < ΔX < 300 mm, −500 mm < ΔY < −100 mm |

U4 | −300 mm < ΔX < 100 mm, −300 mm < ΔY < 300 mm | 100 mm < ΔX < 500 mm, −300 mm < ΔY < 300 mm |

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

MCU | TMS320F28335 | C_{1} | 126.5/nF | C_{3} | 126.5/nF |

S_{1}–S_{4} | SiHB33N60EF | L_{U2} | 722.8/μH | L_{U4} | 717.6/μH |

D_{1}–D_{4} | IDW20G65C5 | L_{2} | 20.4/μH | L_{4} | 20.4/μH |

L_{R} | 409.5/μH | C_{U2} | 2.87/nF | C_{U4} | 4.4/nF |

C_{R} | 7.7/nF | C_{2} | 126.5/nF | C_{4} | 126.5/nF |

L_{U1} | 720.1/μH | L_{U3} | 718.7/μH | C_{O} | 220/μF |

L_{1} | 20.4/μH | L_{3} | 20.4/μH | R | 5000/Ω |

C_{U1} | 4.2/nF | C_{U3} | 4.3/nF | f_{O} | 95/kHz |

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## Share and Cite

**MDPI and ACS Style**

Li, C.; Yang, Y.; Cao, G.
Quadruple-U Auxiliary Structure-Based Receiving Coil Positioning System for Electric Vehicle Wireless Charger. *World Electr. Veh. J.* **2023**, *14*, 115.
https://doi.org/10.3390/wevj14050115

**AMA Style**

Li C, Yang Y, Cao G.
Quadruple-U Auxiliary Structure-Based Receiving Coil Positioning System for Electric Vehicle Wireless Charger. *World Electric Vehicle Journal*. 2023; 14(5):115.
https://doi.org/10.3390/wevj14050115

**Chicago/Turabian Style**

Li, Chuan, Yi Yang, and Guimei Cao.
2023. "Quadruple-U Auxiliary Structure-Based Receiving Coil Positioning System for Electric Vehicle Wireless Charger" *World Electric Vehicle Journal* 14, no. 5: 115.
https://doi.org/10.3390/wevj14050115