# Optimization of Transfer Quality Factor of Limited-Size Coils for Series-Series Compensated Inductive Power Transfer System

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## Abstract

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## 1. Introduction

## 2. Problem Formulation

## 3. Optimization Procedure

**d**are taken as variables to solve the problem, the solution space will be very large, thus in this paper, we first analyze the variation law of the transfer quality factor of equally spaced coils with the number of turns and turn spacing. After obtaining the optimal number of turns, we optimize the turn spacing to further improve the transfer quality factor of the coils.

#### 3.1. Determination of the Number of Turns

#### 3.2. Optimization of the Distance between Adjacent Turn

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Curve of resistance with turn number N and the distance d between adjacent turn. (

**b**) Curve of M with turn number N and the distance d between adjacent turn.

**Figure 5.**(

**a**) Curve of transfer quality factor with turn number N and the distance d between adjacent turn. (

**b**) Transfer quality factor corresponding to the optimal number of turns ${N}_{opt}$ under different turn spacing d.

**Figure 7.**Schematic diagram of SUS principle.The red numbers in the figure are only used to illustrate the principle of this method.

Parameters | Symbol | Value |
---|---|---|

the working frequency | f | 85 kHz |

the minimum distance between adjacent turn | m | 1 mm |

the vertical distance between the two coils | ${Z}_{0}$ | 10 mm |

the maximum radius of the outermost turn of the coil | ${d}_{Nmax}$ | 200 mm |

the radius of the wire used to wind the coil | ${r}_{0}$ | $1.5$ mm |

f/kHz | Coil | N | d/mm | M/uH | $\mathit{R}/\mathbf{\Omega}$ | $\mathit{\omega}\mathit{M}/\mathit{R}\phantom{\rule{3.33333pt}{0ex}}\left({\mathit{T}}_{\mathit{Q}}\right)$ | ${\mathit{\eta}}_{\mathit{m}\mathit{a}\mathit{x}}$ |
---|---|---|---|---|---|---|---|

I (simulation) | 20 | 1 | 155.9 | 0.770 | 108.1 | 98.17% | |

II (simulation) | 14 | 5 | 59.2 | 0.205 | 154.1 | 98.71% | |

85 | III (simulation) | 14 | d | 59.6 | 0.204 | 156.0 | 98.73% |

I (measurement) | 20 | 1 | 154.0 | 0.751 | 109.5 | 98.19% | |

II (measurement) | 14 | 5 | 58.4 | 0.198 | 157.4 | 98.74% | |

III (measurement) | 14 | d | 59.1 | 0.195 | 161.8 | 98.77% |

f/kHz | Coil | ${\mathit{Z}}_{0}\phantom{\rule{3.33333pt}{0ex}}\left(\mathbf{mm}\right)$ | $\mathit{\omega}\mathit{M}\mathbf{/}\mathit{R}\phantom{\rule{3.33333pt}{0ex}}\mathbf{\left(}{\mathit{T}}_{\mathit{Q}}\mathbf{\right)}$ | ${\mathit{\eta}}_{\mathit{m}\mathit{a}\mathit{x}}$ |
---|---|---|---|---|

I (simulation) | 10 | 108.1 | 98.17% | |

I (simulation) | 20 | 105.9 | 98.13% | |

I (simulation) | 30 | 100.5 | 98.0% | |

III (simulation) | 10 | 156.0 | 98.73% | |

III (simulation) | 20 | 149.5 | 98.67% | |

III (simulation) | 30 | 140.3 | 98.58% | |

85 | I (measurement) | 10 | 109.5 | 98.19% |

I (measurement) | 20 | 106.7 | 98.14% | |

I (measurement) | 30 | 101.2 | 98.04% | |

III (measurement) | 10 | 161.8 | 98.77% | |

III (measurement) | 20 | 150.4 | 98.68% | |

III (measurement) | 30 | 142.1 | 98.60% |

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**MDPI and ACS Style**

Liu, P.; Gao, T.; Mao, Z.
Optimization of Transfer Quality Factor of Limited-Size Coils for Series-Series Compensated Inductive Power Transfer System. *Magnetochemistry* **2022**, *8*, 30.
https://doi.org/10.3390/magnetochemistry8030030

**AMA Style**

Liu P, Gao T, Mao Z.
Optimization of Transfer Quality Factor of Limited-Size Coils for Series-Series Compensated Inductive Power Transfer System. *Magnetochemistry*. 2022; 8(3):30.
https://doi.org/10.3390/magnetochemistry8030030

**Chicago/Turabian Style**

Liu, Peizhou, Tiande Gao, and Zhaoyong Mao.
2022. "Optimization of Transfer Quality Factor of Limited-Size Coils for Series-Series Compensated Inductive Power Transfer System" *Magnetochemistry* 8, no. 3: 30.
https://doi.org/10.3390/magnetochemistry8030030