# Comparison and Analysis of Electromagnetic Characteristics of Basic Structure of Wireless Power Coil for Permanent Magnet Motors in Electric Vehicles

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling and Analysis

_{R}and N

_{T}are the turns of the receiving and transmitting coils, respectively, I(t) is the current carried by the transmitting coil, dl is the micro-element on the wire, and r is the distance from the micro-element to one point in space.

#### 2.1. Derivation of Circular Coil Magnetic Flux Density

_{x}is the receiving coil, R

_{R}is the radius of R

_{x}, and the rest of the symbols are lengths or angles.

#### 2.2. Derivation of Square Coil Magnetic Flux Density

#### 2.3. Qualitative Analysis of Electromagnetic Properties

^{2}, according to (2) and (8), the normalized curve of the magnetic flux density can be obtained when the circular and square coils are used as the transmitting coils, respectively, as shown in Figure 10. In Figure 10, the horizontal axis is the horizontal distance from any point of constant height to the central axis of the transmitter coil. The height of the measuring point is 0.25 m from the coils. It can be seen from Figure 10 that the B value is higher inside the coils and gradually decreases outside the coils.

## 3. Numerical Simulations

#### 3.1. Normalized Coupling Coefficient Comparison

#### 3.2. Coupling Mutual Inductance Comparison

^{2}, 0.16 m

^{2}, and 0.25 m

^{2}of circular coupler, hybrid coupler, and square coupler, respectively. It can clearly be seen that the mutual inductance and coupling coefficient of the coupler with the circular loop are larger than that with the square loop.

_{1}, M

_{1}, and K

_{1,}respectively. The self-inductance of the square coil, the mutual inductance, and the coupling coefficient of the square coupler are set as L

_{2}, M

_{2}, and K

_{2}, respectively. The mutual inductance and the coupling coefficient of the hybrid coupler are set to M

_{3}and K

_{3}, respectively.

## 4. Experimental Validation

## 5. Discussion of the Electromagnetic Characteristics of Two Basic Coil Shapes

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Coil Type | Offset Resistance | Magnetic Leakage | Losses (nH) | Coefficient (%) |
---|---|---|---|---|

Flux pipe | better | larger | larger | 42 (offset) |

H | better | larger | larger | 90 |

DD | better | smaller | average | 95.66 |

DDQ | better | smaller | smaller | 95 |

BP | average | smaller | smaller | 92.85 |

Coil Type | Pacing (m) | Area (m ^{2}) | Mutual Inductance (nH) | Coupling Coefficient (%) |
---|---|---|---|---|

circular | 0.3 | 0.09 | 30 | 2.52 |

hybrid | 29 | 2.4 | ||

rectangular | 28 | 2.23 | ||

circular | 0.16 | 67.5 | 4.13 | |

hybrid | 66.9 | 3.94 | ||

rectangular | 65.5 | 3.75 | ||

circular | 0.25 | 120 | 5.62 | |

hybrid | 119.19 | 5.4 | ||

rectangular | 117.5 | 5.15 |

Coil Type | Pacing (m) | Area (m ^{2}) | Perimeter (m) | Outer Diameter (m) | Mutual Inductance (nH) | Coupling Coefficient (%) |
---|---|---|---|---|---|---|

circular | 0.3 | 0.09 | 1.06 | 0.34 | 30 | 2.52 |

hybrid | 29 | 2.4 | ||||

rectangular | 1.2 | 0.3 | 28 | 2.23 | ||

circular | 0.11 | 1.2 | 0.38 | 42.22 | 3.12 | |

hybrid | 34.95 | 2.69 | ||||

rectangular | 0.09 | 0.3 | 28 | 2.23 | ||

circular | 0.07 | 0.94 | 0.3 | 19.99 | 1.97 | |

hybrid | 23.7 | 2.1 | ||||

rectangular | 0.09 | 1.2 | 28 | 2.23 |

Coil Type | Pacing | Mutual Inductance | Coupling Coefficient |
---|---|---|---|

(mm) | (uH) | (%) | |

circular | 67.82 | 0.857 | 11.5 |

hybrid | 0.844 | 11.21 | |

rectangular | 0.735 | 9.66 | |

circular | 79.17 | 0.609 | 8.17 |

hybrid | 0.607 | 8.06 | |

rectangular | 0.593 | 7.8 | |

circular | 105.17 | 0.332 | 4.46 |

hybrid | 0.329 | 4.37 | |

rectangular | 0.326 | 4.29 |

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**MDPI and ACS Style**

Zhao, J.; Zhao, L.; Zou, Y.; Chen, T.
Comparison and Analysis of Electromagnetic Characteristics of Basic Structure of Wireless Power Coil for Permanent Magnet Motors in Electric Vehicles. *World Electr. Veh. J.* **2023**, *14*, 199.
https://doi.org/10.3390/wevj14080199

**AMA Style**

Zhao J, Zhao L, Zou Y, Chen T.
Comparison and Analysis of Electromagnetic Characteristics of Basic Structure of Wireless Power Coil for Permanent Magnet Motors in Electric Vehicles. *World Electric Vehicle Journal*. 2023; 14(8):199.
https://doi.org/10.3390/wevj14080199

**Chicago/Turabian Style**

Zhao, Junfeng, Lingyun Zhao, Yuwei Zou, and Tianjin Chen.
2023. "Comparison and Analysis of Electromagnetic Characteristics of Basic Structure of Wireless Power Coil for Permanent Magnet Motors in Electric Vehicles" *World Electric Vehicle Journal* 14, no. 8: 199.
https://doi.org/10.3390/wevj14080199