# A Double Helix Flux Pipe-Based Inductive Link for Wireless Charging of Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Double Helix Flux Pipe-Based Inductive Link

#### 2.1. IPT System Using SS Topology

_{X}coil) and the secondary coil (R

_{X}coil) are loosely coupled. The compensation capacitors are generally used for compensating the leakage inductance. The compensation networks can be classified into four types: the series-series (SS), parallel-parallel (PP), series-parallel (SP), and parallel-series (PS) types. Source compensation is used to reduce the reactive power on the transmitter side [11,14], and receiver compensation is used to maximize the power transfer and efficiency. The features of the compensation networks are listed in Table 1 [15,16]. From Table 1, we can see that the primary capacitance of the SS topology has a constant value, regardless of the coupling coefficient and load conditions. On the other hand, the capacitances in SP topology vary when the coupling coefficient changes. For PS and PP topology, the capacitances depend on both the coupling coefficient and load conditions. The type of compensation network can be selected using the specific application requirements for the IPT system [17,18,19,20,21]. The series-series (SS) compensation topology is suitable for charging EV battery because the capacitance on the primary side is independent of the load and magnetic coupling coefficient [22,23].

_{0}L

_{S}/R

_{S}. When the inductances of T

_{X}coil and R

_{X}coil are L

_{P}and L

_{S}, respectively, the compensation capacitance at the primary side and secondary side can be expressed as follows:

_{T}of the inductive link is calculated by Equation (3).

_{P}, R

_{S}, and M are the T

_{X}coil resistance, R

_{X}coil resistance, and mutual inductance between the two coils, respectively. In addition, the quality factors of the T

_{X}coil Q

_{P}and R

_{X}coil Q

_{S}can be expressed as follows:

_{X}coil and R

_{X}coil are connected to the compensation capacitors in series. When the capacitors are added to the primary side and secondary side, the system resonates, and the power transferred to the load increases. If the currents through the T

_{X}coil and the R

_{X}coil are I

_{P}and I

_{S}, respectively, the output power is written as follows:

_{P}/R

_{S}= (1+k

^{2}Q

_{P}Q

_{S})

^{1/2}, and it can be expressed as follows:

_{X}coil and the R

_{X}coil, and the larger the coupling coefficient, the higher the efficiency.

#### 2.2. Flux Pipe for IPT System

_{X}coils for flux pipe-based inductive link. The ideal solenoid coil for the flux pipe can be used to simplify modeling, but it is not an accurate model because it requires a turn-to-turn pitch when the solenoid coil is actually manufactured. The helix model, on the other hand, is relatively accurate compared to the ideal solenoid because it takes into account the turn-to-turn pitch that can occur during production. In this paper, we set the helix angle of the coil to 45° and all other specifications such as the winding turns and coil sizes. The double helix coil is in two layers, of which the tilted angle θ is 45° to form cross configuration. The inner layer and outer layer are connected in series.

_{X}pad. In addition, the DD coil was designed to have the same number of turns within the same width and length, and Litz wire with 200 strands at 2.2 mm diameter was used for both the T

_{X}coil and the R

_{X}coil. The litz wire is used by most engineers and researchers for the two coils of wireless power transfer systems. [30,31,32]. Compensation capacitors connected in series with the coils on the secondary and primary sides were calculated using Equation (2).

## 3. Characteristics Analysis

#### 3.1. Coupling Coefficient Between Two Coils

_{X}coil, and the change in the coupling coefficient according to misalignment in the x, y, and z axis directions was simulated. Figure 6 shows the variation of the coupling coefficient with the size of misalignment in each direction. Here, misalignment in the z direction indicates misalignment in the gap direction between the R

_{X}coil and the T

_{X}pad, and x and y directions indicate lateral misalignment in the axial direction and the width direction of the coil, respectively.

#### 3.2. Power Transfer Efficiency of IPT System

_{X}pad. On the other hand, the most suitable inductive link for the IPT system was the double helix flux pipe type in terms of the maximum power transfer efficiency and their reduction rate.

## 4. Discussion

## 5. Conclusion

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**The simulation results of magnetic distributions according to inductive link type. (

**a**) Ideal flux pipe, (

**b**) helix flux pipe, (

**c**) double helix flux pipe, and (

**d**) planar coil.

**Figure 6.**The coupling coefficient according to the misalignment: (

**a**) x direction misalignment, (

**b**) y direction misalignment, (

**c**) z direction misalignment.

**Figure 7.**The maximum power transfer efficiency according to the misalignment: (

**a**) x direction misalignment, (

**b**) y direction misalignment, (

**c**) z direction misalignment.

Type | Primary Capacitance, C_{P} | Secondary Capacitance, C_{S} | Load Resistance, R_{L} |
---|---|---|---|

SS topology | $\frac{{C}_{R}{L}_{R}}{{L}_{T}}$ | $\frac{1}{{\omega}_{0}^{2}{L}_{R}}$ | $\frac{{\omega}_{0}{L}_{R}}{{Q}_{R}}$ |

PP topology | $\frac{{C}_{R}{L}_{R}}{{L}_{T}}\xb7\frac{1-{k}^{2}}{{Q}_{R}^{2}{k}^{4}+1-{k}^{2}}$ | $\frac{1}{{\omega}_{0}^{2}{L}_{R}}$ | ${\omega}_{0}{L}_{R}{Q}_{R}$ |

SP topology | $\frac{{C}_{R}{L}_{R}}{{L}_{T}}\xb7\frac{1}{1-{k}^{2}}$ | $\frac{1}{{\omega}_{0}^{2}{L}_{R}}$ | ${\omega}_{0}{L}_{R}{Q}_{R}$ |

PS topology | $\frac{{C}_{R}{L}_{R}}{{L}_{T}}\xb7\frac{1}{{Q}_{R}^{2}{k}^{4}+1}$ | $\frac{1}{{\omega}_{0}^{2}{L}_{R}}$ | $\frac{{\omega}_{0}{L}_{R}}{{Q}_{R}}$ |

Parameter | Type I | Type II | Type III | Type IV |
---|---|---|---|---|

R_{X} coil topology | Ideal solenoid | Helix | Double Helix | Planar (Double D) |

Winding Turns of R_{X} coil | 20 | 20 | 20 (inner 10/outer 10) | 20 (10 × 2 EA) |

Helix angle | 0° | 45° | ±45° | N/A |

Coil size (width × length) | 100 × 80 mm | 100 × 80 mm | 100 × 80 mm | 100 × 80 mm |

R_{X} coil Inductance, L_{S} | 6.37 μH | 7.62 μH | 7.53 μH | 8.89 μH |

Compensation capacitor, C_{S} at secondary side | 550.25 nF | 459.69 nF | 465.50 nF | 394.23 nF |

Quality factor, Q_{S} @ 85 kHz | 149.7 | 169.5 | 159.5 | 328.2 |

T_{X} coil topology | Solenoid with ferrite core | Planar (Double D) with ferrite core | ||

Winding Turns of T_{X} coil | 30 | 30 (15 × 2EA) | ||

Coil size (width × length) | 100 × 90 mm | 100 × 90 mm | ||

Ferrite core size (width × length) | 100 × 110 mm | 5 × 110 mm × (7 EA) | ||

T_{X} pad inductance, L_{P} | 145.81 μH | 38.73 μH | ||

Compensation capacitor, C_{P} at primary side | 24.04 nF | 90.52 nF | ||

Output power, P_{OUT} | 1 kW | 1 kW | 1.6 kW | 400 W |

Gap distance | 20 mm | |||

Litz wire dia. | 2.2 mm | |||

Litz wire strands | 200 |

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**MDPI and ACS Style**

Hwang, Y.J.; Kim, J.M.
A Double Helix Flux Pipe-Based Inductive Link for Wireless Charging of Electric Vehicles. *World Electr. Veh. J.* **2020**, *11*, 33.
https://doi.org/10.3390/wevj11020033

**AMA Style**

Hwang YJ, Kim JM.
A Double Helix Flux Pipe-Based Inductive Link for Wireless Charging of Electric Vehicles. *World Electric Vehicle Journal*. 2020; 11(2):33.
https://doi.org/10.3390/wevj11020033

**Chicago/Turabian Style**

Hwang, Young Jin, and Jong Myung Kim.
2020. "A Double Helix Flux Pipe-Based Inductive Link for Wireless Charging of Electric Vehicles" *World Electric Vehicle Journal* 11, no. 2: 33.
https://doi.org/10.3390/wevj11020033