# Inductive Power Transmission System for Electric Car Charging Phase: Modeling plus Frequency Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Wireless Charging System Presentation and Modelisation

#### 2.1. The Position of the Frequency Controller

#### 2.2. Model of the Wireless Charging System

#### 2.2.1. Static Modeling

_{1}and V

_{2}as it is in Equation (6) [23]. The mutual inductance coupling model can be depicted from Equation (1), as it is in relation with the impedance formulation [22].

_{r}is the reflected impedance from the secondary to the primary, and it is expressed in Equation (3).

_{s}is the secondary impedance part which depends on the selected compensation topology and then the current flowing in the secondary winding is in Equation (4).

_{1}being the primary current, I

_{2}is the secondary current. The primary and secondary inductance and capacitance are presented by (C

_{1}, C

_{2}), (L

_{1}, L

_{2}).

_{1}, P

_{1}as the primary voltage and power, V

_{2}, P

_{2}are the secondary voltage and power.

#### 2.2.2. Dynamic Modeling

_{t}. k is the percentage of the obtained flux in the secondary coil is given by Equation (8).

_{t}” is the energy transfer time. The vehicle speed will affect the quantity of the received flux and power as the secondary coil is in movement. The transmitted time between the two coils is seen in Equation (9) The flux transferred is related to numerous characteristics such as the distances among coils (noted by “D

_{coil}”) and the vehicle (noted by “V

_{s}> 0”) [24]. We note that even though the vehicle speed is high, the coming output power from the wireless generator is minima as the inverse for the lowest rate.

_{s}> 0.

_{s})is the relation between the static model and the dynamic model we observe that V

_{2}in the dynamic model according to T

_{t}and T

_{t}= f (V

_{s}).

_{2}” is the Resistance of the secondary coil.

## 3. Results and Discussion

^{−3}%, 8.7 × 10

^{−3}%, 50 kHz, or more the gain estimate is 9.9 × 10

^{−3}%, 10 × 10

^{−3}%.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

M | Mutual inductance (H) |

ω | Oscillation angular frequency (rad/s) |

k | Magnetic coupling constant |

L_{2} | Secondary inductance (H) |

L_{1} | Primary inductance (H) |

Z_{2} | Primary impedance (Ω) |

Z_{s} | Secondary impedance (Ω) |

I_{1} | Primary current (A) |

I_{2} | Secondary current (A) |

V_{1} | Primary voltage (V) |

V_{2} | Secondary voltage (V) |

N | Number of turns |

${\mu}_{0}$ | Magnetic constant |

L | Inductance (H) |

P_{1} | Primary power |

P_{2} | Secondary power |

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**Figure 1.**Wireless charging system: (

**a**) Block diagram of the wireless power transfer; (

**b**) Simplified diagram of the wireless transfer system.

**Figure 4.**(

**a**) The effect of speed on the time required for energy to be transferred; (

**b**) Input and output voltage of each coil receiver and transmitter.

**Figure 5.**Magnetic flux in relation to the resonance frequency: (

**a**) 10 kHz; (

**b**) 30 kHz; (

**c**) 50 kHz; (

**d**) 65 kHz.

Drive Battery | Lithium-ion |

Coil diameter (cm) | 50 |

Distance between coil (cm) | 150 |

Test frequency (kHz) | (10; 30; 50; 65) |

Self-Inductance, Lp = Ls | (37 μH 140 μH) |

SS compensation capacitance, Cp = Cs | [95 nF 0.37 μF] |

Frequency | The Energy Gain for 3 s × 10^{−3} | The Energy Gain for 10 h |
---|---|---|

10 kHz | 48.5% | 9.7% |

30 kHz | 86.5% | 17.3% |

50 Khz | 99.1% | 19.82% |

65 kHz | 100% | 20.01% |

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**MDPI and ACS Style**

Mohamed, N.; Aymen, F.; Alqarni, M.
Inductive Power Transmission System for Electric Car Charging Phase: Modeling plus Frequency Analysis. *World Electr. Veh. J.* **2021**, *12*, 267.
https://doi.org/10.3390/wevj12040267

**AMA Style**

Mohamed N, Aymen F, Alqarni M.
Inductive Power Transmission System for Electric Car Charging Phase: Modeling plus Frequency Analysis. *World Electric Vehicle Journal*. 2021; 12(4):267.
https://doi.org/10.3390/wevj12040267

**Chicago/Turabian Style**

Mohamed, Naoui, Flah Aymen, and Mohammed Alqarni.
2021. "Inductive Power Transmission System for Electric Car Charging Phase: Modeling plus Frequency Analysis" *World Electric Vehicle Journal* 12, no. 4: 267.
https://doi.org/10.3390/wevj12040267