# The Impact of Coil Position and Number on Wireless System Performance for Electric Vehicle Recharging

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## Abstract

**:**

## 1. Introduction

## 2. Electric Vehicle (EV), Hybrid Electric Vehicle (HEV), and Wireless Recharge Architectures

#### 2.1. Hybrid and Pure EV in the Literature

#### 2.2. The Wireless Charging System

## 3. Different Topologies

## 4. Modeling of the Wireless Charging System: One or Two Coil Receivers

#### 4.1. Wireless Charging System with a Simple Receiver Coil

_{1}and V

_{2}the input and output voltages of this IPT [13].

_{1}. Here, ${R}_{L}$ represents a serial resistive load. It is used to quantify the final expression of the global yield value, as shown in Equation (7). Expression (1) shows the power consumption formula if a resistive load is connected, considering the mutual inductance parameter in the function of the primary current [28].

_{p}or C

_{s}must be evaluated under a null imaginary part of Z

_{1}. The corresponding equation of the related capacitance can then be expressed, as seen in Equation (5).

_{2}and R

_{1}are the secondary and primary sides’ internal impedance, respectively. When the charging system is definite, the load and the internal impedance are constant. It can be concluded that the system efficiency is only related to mutual inductance between the primary and the secondary side coils. The condition for achieving optimal efficiency can be deduced from Equation (7). The highest possible efficiency can be achieved if $\frac{{R}_{p}\left({R}_{s}+{R}_{L}\right)}{{\omega}^{2}{M}^{2}}$ tends to 0. As a result:

#### 4.2. Wireless Charging System with Multiple Receiver Coils

## 5. Impacts of Coil Position and Receiver Coil Number on the WPT Performance

#### 5.1. Transmitter/Receiver Coil: Design and Parameters

#### 5.2. One Transmitter and One Receiver Coil: Magnetic Field Zones

_{p}and L

_{s}, respectively. But their relative position affects too. Mathematically, the mutual inductance M can be expressed, as seen in Equation (13).

#### 5.3. One Transmitter and Two Receivers Coils: Magnetic Field Zones

## 6. Experimental Validation

## 7. One and Two Coils Receivers’ Specifications

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

IPT | Inductive Power Transfer |

EV | Electric Vehicles |

HEV | Hybrid Electric Vehicle |

HF | High-Frequency |

AFE | Active Front End |

WPT | Wireless Power Transfer |

SWC | Static Wireless Charging system |

FEM | Finite Element Method |

FEA | Finite Element Analysis |

M | Mutual inductance (H) |

ω | Oscillation angular frequency (rad/sec) |

k | Coupling coefficient |

L_{s} | Secondary inductance (H) |

L_{p} | Primary inductance (H) |

Z_{p} | Primary impedance (Ω) |

Zs | Secondary impedance (Ω) |

I_{p} | Primary current (A) |

I_{s} | Secondary current (A) |

V_{p} | Primary voltage (V) |

V_{s} | Second voltage (V) |

I_{1} | Source current (A) |

I_{2} | Load current (A) |

C_{s} | Secondary capacitance (F) |

C_{p} | Primary capacitance (F) |

P_{s} | Secondary power (W) |

P_{p} | Primary Power (W) |

L_{a} | Primary leakage inductance (H) |

L_{b} | Secondary leakage inductance (H) |

R_{L} | Load (Ω) |

η | The efficiency of the power transfer (%) |

Z_{1} | The global impedance of the primary coil (Ω) |

V_{1} | Source voltage (V) |

R_{s} | Secondary resistance (Ω) |

R_{p} | Primary resistance (Ω) |

n | Number of receiver coils |

D | Distance between the receiver middle and the transmitter middle |

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**Figure 5.**Wireless power transfer design for two receiver coils: (

**a**) high magnetic field zone, (

**b**) medium magnetic field with one receiver, (

**c**) medium magnetic field with two receivers.

**Figure 8.**Coil model: (

**a**) Coupling coefficient versus the gap variation, (

**b**) mutual inductance versus the gap variation.

**Figure 11.**(

**a**) Coupling coefficient for each receiver coil proportionally to the transmitter position, (

**b**) Mutual inductance for only one receiver coil, and the totally mutual inductance for two receivers coil proportionally to the coil transmitter position.

**Table 1.**Internal parameters of transmitter and receiver coils according to the compensation topology form.

Features | Series-Series (SS) | Series-Parallel (SP) | Parallel-Series (PS) | Parallel-Parallel (PP) |
---|---|---|---|---|

Primary capacitor | $\frac{1}{{\omega}^{2}\xb7{L}_{P}}$ | $\frac{1}{{\omega}^{2}\xb7\left({L}_{P}-\frac{{M}^{2}}{{L}_{s}}\right)}$ | $\frac{1}{{\omega}^{2}\xb7\left({L}_{P}-\frac{{\omega}^{2}\xb7{M}^{4}}{{L}_{P}\xb7{R}_{load}}\right)}$ | $\frac{1}{{\omega}^{2}\xb7\left(\left({L}_{P}-\frac{{M}^{2}}{{L}_{s}}\right)+\frac{\frac{{M}^{4}}{{L}_{s}^{4}}\xb7{R}_{load}^{2}}{{\omega}^{2}\xb7\left({L}_{P}-\frac{{M}^{2}}{{L}_{s}}\right)}\right)}$ |

Secondary capacitor | $\frac{1}{{\omega}^{2}\xb7{L}_{s}}$ | $\frac{1}{{\omega}^{2}\xb7{L}_{s}}$ | $\frac{1}{{\omega}^{2}\xb7{L}_{s}}$ | $\frac{1}{{\omega}^{2}\xb7{L}_{s}}$ |

Load | $\frac{\omega \xb7{L}_{s}}{{Q}_{s}}$ | $\omega \xb7{L}_{s}\xb7{Q}_{s}$ | $\frac{\omega \xb7{L}_{s}}{{Q}_{s}}$ | $\omega \xb7{L}_{s}\xb7{Q}_{s}$ |

_{load}represents the resistance load on the secondary coil.

Designation | Used Choice |
---|---|

Coil material | Copper |

Polygon Segments | 4 |

Polygon Radius | 1 mm |

Start Helix Radius | 20 mm |

Radius Change | 2.05 mm |

Pitch | 0 |

Turns | 10 |

Segments Per Tum | 36 |

Right-Handed | 1 |

Distance (mm) | Power Transfer | Efficiency | $\mathit{M}\mathit{a}{\mathit{x}}_{\mathit{e}\mathit{f}\mathit{f}}$ | $\mathit{M}\mathit{a}{\mathit{x}}_{\mathit{p}\mathit{o}\mathit{w}}$ | $\mathit{A}{\mathit{v}}_{\mathit{p}\mathit{o}\mathit{w}}$ | |
---|---|---|---|---|---|---|

Simple receiver coil | −200 | 0.3 kw | 10% | 92% | 4.9 kw | 2.34 kw |

−100 | 1.9 kw | 54% | ||||

−50 | 3.6 kw | 78% | ||||

0 | 4.9 kw | 92% | ||||

50 | 3.5 kw | 77% | ||||

100 | 1.9 kw | 54% | ||||

200 | 0.3 kw | 10% | ||||

Multiple receiver coils | −300 | 0.5 kw | 12% | 96% | 5.1 kw | 3.95 kw |

−250 | 3.7 | 79% | ||||

−200 | 4.8 | 87% | ||||

−100 | 4.9 | 88% | ||||

−50 | 5.1 kw | 96% | ||||

0 | 5.2 kw | 96% | ||||

50 | 5.2 kw | 95% | ||||

100 | 5 kw | 90% | ||||

200 | 4.9 kw | 88% | ||||

250 | 3.7 kw | 79% | ||||

300 | 0.5 kw | 12% |

Coil diameter | 50 cm |

Distance between coil | 150 cm |

Width of winding “w” | 21 cm |

Average winding radius “r” | 14.5 cm |

Number of turns “N” | 15 Turns |

Specifications | One Coil Receiver | Two Coils Receivers |
---|---|---|

Maximum Quantity of the given current | 140 A | 280 A |

Quantity of the losses power | 10% of the rated total power | 20% of the rated total power |

Additive weight on the vehicle | +10 kg on the vehicle weight | +20 kg on the vehicle weight |

Electronic complexity | medium | high |

Needed recharge time in stopped mode * | 8 h | 6 h |

Needed recharge time in motion mode *^{,1} | 50 h | 26 h |

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**MDPI and ACS Style**

Mohamed, N.; Aymen, F.; Issam, Z.; Bajaj, M.; Ghoneim, S.S.M.; Ahmed, M.
The Impact of Coil Position and Number on Wireless System Performance for Electric Vehicle Recharging. *Sensors* **2021**, *21*, 4343.
https://doi.org/10.3390/s21134343

**AMA Style**

Mohamed N, Aymen F, Issam Z, Bajaj M, Ghoneim SSM, Ahmed M.
The Impact of Coil Position and Number on Wireless System Performance for Electric Vehicle Recharging. *Sensors*. 2021; 21(13):4343.
https://doi.org/10.3390/s21134343

**Chicago/Turabian Style**

Mohamed, Naoui, Flah Aymen, Zaafouri Issam, Mohit Bajaj, Sherif S. M. Ghoneim, and Mahrous Ahmed.
2021. "The Impact of Coil Position and Number on Wireless System Performance for Electric Vehicle Recharging" *Sensors* 21, no. 13: 4343.
https://doi.org/10.3390/s21134343