# Wireless Power Transfer Positioning System with Wide Range Direction-Guided Based on Symmetrical Triple-U Auxiliary Pad

^{*}

## Abstract

**:**

## 1. Introduction

## 2. WPT Positioning System Based on Triple-U Positioning Auxiliary Pad

#### 2.1. Positioning System Model

**V**

_{O1},

**V**

_{O2},

**V**

_{O3}are collected in real-time and used as the positioning signals. On the one hand, when the primary pad and secondary pad are aligned, the secondary pad will be in the center of the triple-U auxiliary pad, which indicates that the mutual inductances between the secondary pad and each U pad M

_{U1P-SP}, M

_{U2P-SP}, M

_{U3P-SP}are zero, thus, the corresponding output voltages

**V**

_{O1},

**V**

_{O2},

**V**

_{O3}are zero too. On the other hand, when the primary pad and secondary pad are misaligned, the mutual inductance M

_{U1P-SP}, M

_{U2P-SP}, M

_{U3P-SP}and corresponding output voltages

**V**

_{O1},

**V**

_{O2},

**V**

_{O3}will be different; therefore, positioning can be realized by identifying the trajectory of the three load output voltages.

#### 2.2. Mathematical Model Analysis

_{U1P-PP}, M

_{U2P-PP}, M

_{U3P-PP}are the mutual inductance between the primary pad and the three U pads, respectively; M

_{U1P-SP}, M

_{U2P-SP}, M

_{U3P-SP}are the mutual inductance between the secondary pad and the three U pads, respectively; M

_{PP-SP}represents the mutual inductance between the primary pad and secondary pad, R and Req are the load and equivalent load, respectively; C

_{O}represents the filter capacitor,

**V**

_{1},

**V**

_{2},

**V**

_{3}, and

**V**

_{O1},

**V**

_{O2},

**V**

_{O3}are the input voltages and load output voltages under the three U pads U1P, U2P, U3P work, respectively.

_{p1}, L

_{1}, L

_{2}, L

_{3}, and combining with (1), it can be concluded from Kirchhoff’s law that the relevant current is:

_{1}are determined, the output current I

_{S}and the corresponding load output voltage V

_{O1}are positively proportional to the mutual inductance between U pad and secondary pad.

_{C}is the heat loss of the control circuit.

## 3. Triple-U Positioning Auxiliary Pad

#### 3.1. Comparison and Selection of Auxiliary Pad

_{3}, Figure 5 shows the mutual inductance M between the double-D pad (DDP) and U pad (UP) to the secondary pad (SP), denoted as M

_{DDP-SP}and M

_{UP-SP}, respectively, vary with the offset distance ΔY and gap distance d. We can see that the M

_{DDP-}

_{SP}and M

_{UP-SP}are inversely proportional to the gap distance d and increases first and then drops down with ΔY. Although when d = 120 to d = 150, the M

_{DDP-SP}change obviously than M

_{UP-SP}, when d = 200 to d = 300, the variation degree of M

_{DDP-SP}and M

_{UP-SP}are similar and the offset sensitivity is inferior. Therefore, according to the mutual inductance M

_{DDP-SP}variation in Figure 5a, the range of magnetic field corresponding to the U pad is wider than that of the DD pad. In addition, considering the structural limitation of the positioning auxiliary pad, the U pad is better than the DD pad.

_{CP-SP}, varies with the horizontal offset as shown in Figure 5b. When the same copper consumption and gap distance d adopted by the couplers, it can be seen that CP has the same upward offset sensitivity of all parties, but the range is limited, while the U pad has a better tolerance range and sensitivity when the offset occurs.

#### 3.2. Structure of Triple-U Positioning Auxiliary Pad

_{UP-SP}between the U pad and the secondary pad shown in Figure 5b, it can be known that the obtained M

_{UP-SP}at a certain moment will correspond to various horizontal offset situations, and under these situations, if we project the secondary pad’s center O to the plane centered on the U pad, two trajectories with axisymmetric distribution will be formed, which is described as the equivalent mutual inductance feature trajectory. Figure 6a shows the auxiliary structure is composed of one U pad; however, the detection blind spot trajectory is in the form of two axisymmetric circles, which hardly realize the positioning. Figure 6b shows the auxiliary structure is composed of two U pads, and the detection blind spot is the two intersection points of the circular trajectories corresponding to the two U pads, respectively, and it is difficult to identify the specific position. Two kinds of positioning auxiliary structures using three U pads are, respectively, shown in Figure 6c,d; likewise, using four U pads are, respectively, shown in Figure 6e,f. Although all of these structures can realize the positioning of the secondary pad, structures shown in Figure 6c,e need to modify the primary pad, and the control of the structure shown in Figure 6f is more complex than the structure shown in Figure 6d. Thus, we picked the structure shown in Figure 6d that is distributed on the periphery of the primary pad in a rotationally symmetric form as the auxiliary pad of the WPT system.

## 4. Positioning Algorithm Based on Feature Trajectory

#### 4.1. Equivalent Mutual Inductance Feature Trajectory Corresponding to U Pad

_{U1P-SP}with horizontal offset when the gap distance d = 120 mm is shown in Figure 7. M

_{U1P-SP}is the mutual inductance between U1P and secondary pad; the X

_{1}O

_{1}Y

_{1}shown in Figure 7 is the sub-coordinate centered on U1P. It can be seen that in any quadrant of the X

_{1}O

_{1}Y

_{1}plane, M

_{U1P-SP}will increase and then drop down with the offset of ΔY, and gradually decrease with the offset of ΔX; meanwhile, the value is approximately zero when the secondary pad is located on the X-axis. Due to the spatial distribution characteristics of the triple-U auxiliary pad, M

_{U1P-SP}, M

_{U2P-SP}and M

_{U3P-SP}generally show a rotation symmetry variation of 120°. Therefore, when the primary pad is aligned with the secondary pad, there is decoupling between the secondary pad and each U pad, which is M

_{U1P-SP}= M

_{U2P-SP}= M

_{U3P-SP}= 0. Moreover, when the primary pad and secondary pad are in misalignment, the mutual inductances are different, that is, M

_{U1P-SP}≠ M

_{U2P-SP}≠ M

_{U3P-SP}.

_{U1P-SP}at a certain moment will correspond to the various horizontal offset situations between the primary pad and secondary pad, under these situations, if we project the secondary pad’s center O to the sub-coordinate X

_{1}O

_{1}Y

_{1}centered on the U pad, two trajectories with axisymmetric distribution will be formed, which is represented as the equivalent mutual inductance feature trajectory. As shown in Figure 8, when the projection of the secondary pad’s structure center O is located on the feature trajectory of equivalent mutual inductance, M

_{U1P-SP}is consistent in this case. Moreover, for the sake of a simpler description, we define the corresponding equivalent mutual inductance trajectories of U1P, U2P and U3P to be A, B, and C, respectively.

#### 4.2. Guidance of Optimal Direction under Dynamic Movement

_{O2}and V

_{O3}can be detected based on U2P and U3P working, respectively. If V

_{O2}> V

_{O3}, the secondary pad is located in the second quadrant of the XOY plane centered on the triple-U pad structure; if V

_{O2}< V

_{O3}, it is in the third quadrant. The equivalent mutual inductance feature trajectories B and C are obtained relying on V

_{O2}and V

_{O3}if B and C intersect at two points, which represents the secondary pad structure center O and exist in two suspicious positions (x

_{1}, y

_{1}) and (x

_{2}, y

_{2}), so the suspect guidance trajectory can be generated according to the position with further distance and then feed back to the driver. On the one hand, the driver modified the position in real-time according to the guidance trajectory B and C, on the other hand, the corresponding output voltage V

_{O2}and V

_{O3}are detected by MCU in real time to correct the guidance trajectory B and C. Until the load output voltage V

_{O1}under U1P working is detected by MCU, which represents that the vehicle has entered the precise positioning area and the specific position (x, y) can be obtained to precisely modify the guidance trajectory until the vehicle is in the optimal charging area. The guidance of optimal direction under a dynamic trajectory is shown in Figure 9.

#### 4.3. Positioning Algorithm Based on Feature Trajectory

_{O1}, V

_{O2}and V

_{O3}in real time. Then the equivalent mutual inductance feature trajectories A, B and C are obtained based on V

_{O1}, V

_{O2}and V

_{O3}, which are used to determine the current optimal guidance trajectory and judge whether the vehicle is in the precise positioning area. Lastly, feeding back the guidance trajectory to the driver to modify the current position.

_{O1}under U1P working is detected by MCU, at this time, there is a unique intersection point (x, y) between the trajectories A, B, and C, from which the vehicle’s specific position (x, y) can be obtained.

## 5. Experimental Validation

#### 5.1. Mutual Inductance and Load Output Voltage Verification of U Pad

_{U1P-SP}, M

_{U2P-SP}, M

_{U3P-SP}between each U pad and secondary pad variation on corresponding load output voltage V

_{O1}, V

_{O2}and V

_{O3}, we measured the value of V

_{O1}, V

_{O2}and V

_{O3}under typical positions; the results are shown in Figure 12. Meanwhile, for a more intuitive expression of the corresponding load output voltage variation under the three U pads working, respectively, we defined the sub-coordinate X

_{1}O

_{1}Y

_{1}, X

_{2}O

_{2}Y

_{2}, and X

_{3}O

_{3}Y

_{3}, which centered on the corresponding U pad. It can be concluded that the corresponding load output voltage variation of each U pad is consistent with its mutual inductance variation of it. Meanwhile, due to U1P being separate from the ferrite in the primary pad and the other two pads partially coinciding with the ferrite of the primary pad in space, the value of V

_{O1}is smaller than V

_{O2}and V

_{O3}at these positions, while the variation of V

_{O2}and V

_{O3}is similar.

#### 5.2. Mutual Inductance and Output Voltage Verification of Typical Coupler with Triple-U Pad

_{U1P-SP}, M

_{U2P-SP}, M

_{U3P-SP}, V

_{O1}, V

_{O2}and V

_{O3}under the horizontal offset of the XOY plane centered on the triple-U auxiliary pad are shown in Figure 13. On the one hand, the maximum relative errors of M

_{U1P-SP}, M

_{U2P-SP}, M

_{U3P-SP}between the measurement and simulation are 9.28%, 9.79%, 9.86%, the minimum relative errors are zero, and the average relative errors are 2.51%, 5.58%, 4.78%. On the other hand, the maximum relative errors of V

_{O1}, V

_{O2}, V

_{O3}between the measurement and simulation are 9.48%, 9.73%, 9.75%, the minimum relative errors are zero, and the average relative errors are 3.38%, 4.77%, 4.55%. Thus, we can conclude that the measurement of these mutual inductances and load output voltages are consistent with the expected variation, so the proposed triple-U auxiliary pad could be perfectly applied in the positioning and guidance of vehicles.

#### 5.3. Verification of Optimal Direction Guidance

_{O2}> V

_{O3}. Firstly, when a vehicle comes into the recognizable range, the three U pads work, respectively, and V

_{O1}= 0 V, V

_{O2}= 14.5 V, V

_{O3}= 11 V are detected in the initial state, so there are blind spots in the secondary pad’s position at this time, and the suspicious position points (−200 mm, 50 mm) and (−190 mm, 30 mm) are obtained by curve fitting. Then the guidance trajectory of the current position is defined, relying on the further point (−200 mm, 50 mm), which is used for modifying the current parking position. During the secondary pad movement, the V

_{O1}is detected, that is, V

_{O1}≠ 0 V, which indicates that the secondary pad has entered the precise positioning area; we measured the values of V

_{O1}, V

_{O2}and V

_{O3}which are, respectively, 0.2 V, 12.03 V, 13.3 V. Therefore, the guidance trajectory is modified in real time according to the dynamic position of the secondary pad until it is aligned with the primary pad.

_{O2}< V

_{O3}. When the vehicle drives into the recognizable range, we get the parameters of the corresponding load output voltage that V

_{O1}= 0 V, V

_{O2}= 12.86 V, V

_{O3}= 13 V, and the suspicious position points (−220 mm, −80 mm) and (−160 mm, 20 mm) are obtained by analyzing the corresponding mutual inductance feature trajectory and fitting with the database. Then the guidance trajectory of the current position is defined relying on (−220 mm, 80 mm) to modify the current parking position. Once V

_{O1}≠ 0 V is detected, the correct position of the secondary pad is determined, and then the guidance trajectory is modified according to the precise position of the secondary pad until it is aligned with the primary pad.

_{O2}≈ V

_{O3}. Similarly, when the vehicle drives into the recognizable range, we get the parameters of load output voltage that V

_{O1}= 0 V, V

_{O2}= 13.5 V, V

_{O3}= 13.47 V, and then the suspicious position points (−210 mm, 0 mm) and (−180 mm, 0 mm) are obtained by analyzing the corresponding mutual inductance feature trajectory and fitting with the database. Then guidance trajectory of the current position is defined relying on (−210 mm, 0 mm) to correct the current parking position. The three load output voltages satisfy V

_{O1}= V

_{O2}= V

_{O3}= 0 V, which represents the secondary pad being aligned with the primary pad.

#### 5.4. Positioning Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Comparison on M

_{DDP-SP}, M

_{UP-SP}, M

_{CP-SP.}(

**a**) shows the comparison between MUP-SP and MDDP-SP, when the situation that the power secondary pad is rectangular and the length of the U pad and DD pad are the same, (

**b**) shows the comparison between MUP-SP and MCP-SP, when the situation that the power secondary pad is rectangular and the copper consumption of the U pad and the circular pad are the same.

**Figure 6.**Physical models in different spatial distribution. (

**a**) represents the structure composed of one U coil, (

**b**) represents the structure composed of two U coils, (

**c**,

**d**) represent the structures composed of three U coil respectively, (

**e**,

**f**) represent the structures composed of four U coil respectively.

**Figure 13.**Measurements of M

_{U1P}-

_{SP}, M

_{U2P}-

_{SP}, M

_{U3P}-

_{SP}, V

_{O1}, V

_{O2}and V

_{O3}under different misalignment. (

**a**–

**c**) represent the measurement results of M

_{U1P}-

_{SP}, M

_{U2P}-

_{SP}and M

_{U3P}-

_{SP}, under the three U coils work respectively; (

**d**–

**f**) represent the measurement results of V

_{O1}, V

_{O2}and V

_{O3}, under the three U coils work respectively.

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

MCU | TMS320F28335 | L_{U2}/μH | 1354 | C_{2}/nF | 114 |

S_{1}-S_{4} | SiHB33N60EF | L_{3}/μH | 20.4 | C_{U2}/μF | 2.1 |

D_{1}-D_{4} | IDW20G65C5 | L_{U3}/μH | 1361 | C_{3}/nF | 114 |

L_{p1}/μH | 54 | L_{S}/μH | 383 | C_{U3}/μF | 2.1 |

L_{P}/μH | 409.5 | C_{p1}/nF | 51.5 | C_{S}/nF | 7.7 |

L_{1}/μH | 20.4 | C_{P}/nF | 8.3 | C_{O}/μF | 220 |

L_{U1}/μH | 1195 | C_{1}/nF | 114 | R/Ω | 5000 |

L_{2}/μH | 20.4 | C_{U1}/nF | 2.5 | f_{O}/kHz | 95 kHz |

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

Camera | 22 mm | Simplicity | Sensitive to obstructions |

Triple-coil [25] | 15 mm | Reduced the excitation current | Reconstruct EV structure |

Proposed pad | 10 mm | Maintain EV structure, adapt to different magnetic couplers and EV models | Requires additional ferrite |

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## Share and Cite

**MDPI and ACS Style**

Yang, Y.; Cao, G.; Zhang, G.; Xie, S.
Wireless Power Transfer Positioning System with Wide Range Direction-Guided Based on Symmetrical Triple-U Auxiliary Pad. *World Electr. Veh. J.* **2022**, *13*, 140.
https://doi.org/10.3390/wevj13080140

**AMA Style**

Yang Y, Cao G, Zhang G, Xie S.
Wireless Power Transfer Positioning System with Wide Range Direction-Guided Based on Symmetrical Triple-U Auxiliary Pad. *World Electric Vehicle Journal*. 2022; 13(8):140.
https://doi.org/10.3390/wevj13080140

**Chicago/Turabian Style**

Yang, Yi, Guimei Cao, Ge Zhang, and Shiyun Xie.
2022. "Wireless Power Transfer Positioning System with Wide Range Direction-Guided Based on Symmetrical Triple-U Auxiliary Pad" *World Electric Vehicle Journal* 13, no. 8: 140.
https://doi.org/10.3390/wevj13080140