# Core Loss Analysis and Modeling of a Magnetic Coupling System in WPT for EVs

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Distribution of Magnetic Flux Density in the Disk Core

_{p}= 12 A, the receiver winding current I

_{s}= 18 A and the phase-shift = 0°.

## 3. Analysis and Modeling of Core Loss

#### 3.1. Modeling of Magnetic Flux Density Distribution

#### 3.2. Theoretical Calculation Method of Magnetic Flux Density Model Parameters

_{max}in Formula (1) is determined, the magnetic flux density distribution inside the disk core can be obtained. However, Bm

_{max}needs to be determined by the magnetic field distribution characteristics of the magnetic coupling system. The magnetic-field line distribution schematic diagram of the magnetic coupling system is shown in Figure 5, where the air gap diffusion effect exists at the inner radius and the outer radius of the magnetic core and the air gap diffusion flux loop is approximately a semicircle [29].

_{core}is formed by the magnetic core and air closure and the other φ

_{air}is formed by the air closure. Where s

_{0}is the distance between the two magnetic cores, s

_{1}is the distance between the outer edge of the air gap diffusion magnetic flux and the inner radius of the magnetic core, and s

_{2}is the distance between the outer edge of the air gap diffusion magnetic flux and the center of the winding. The expression of each parameter is:

_{p}and that the initial phase angle of the receiver winding current is zero, according to the constant-linkage theorem on the transmitter:

_{1core}is the flux linkage formed by the magnetic core and air closure and φ

_{1air}is the flux linkage formed by the air closure on the transmitter.

_{1core}formed by the magnetic core and air closure on the transmitter can be expressed as:

_{1}(i) is the relative position of the i-th turn coil center of the transmitter winding, the expression is:

_{1air}formed by the air closure in the s

_{2}area, this paper ignored the influence of the core thickness and adopted the magnetic-field distribution of the method of images model to obtain the magnetic-field distribution of the magnetic coupling system. The equivalent model of the method of images was established as shown in Figure 6.

_{p-0}generates a primary mirror current group with the current amplitude I

_{p-1}under the action of the transmitter core; the source current and the primary mirror current group will generate a secondary mirror current group with the current amplitude of I

_{p-2}and a third mirror current group with the current amplitude of I

_{p-3}under the action of the receiver core, and the second mirror current group and the third mirror current group will generate a fourth mirror current group and a fifth mirror current group under the action of the transmitter core. Similarly, the alternating reflections of the two magnetic core planes produce an infinite set of mirror current groups. In the same way, for the receiver winding current, the alternating reflections of the two magnetic core planes also produce an infinite set of mirror current groups.

_{m}to the source current I

_{o}is a function with the core plane width, coil diameter and transmission distance:

_{0}and d

_{0}are the core plane width and coil diameter, respectively; y is the vertical position of the magnetic-field test.

_{p-k}and I

_{s-k}, respectively. When the thickness of the magnetic core is ignored and the plane of the transmitter core is Z = 0, the axial height of each transmitter mirror current group and receiver mirror current group can be expressed as:

_{2}and the axial height s

_{0}/2, taking the i-th turn of the k-th transmitter mirror current group and the receiver mirror current group, as an example. According to the method of magnetic vector potential, the mutual inductance magnetic flux generated in the load coil can be expressed as:

_{air}can be got by Formula (14):

_{1air}formed by air closure on the transmitter can be expressed as:

_{2core}(Bm

_{2max}) is the flux linkage formed by the magnetic core and air closure on the receiver; R

_{2}(i) is the relative position of the i-th turn coil center of the receiver winding; and φ

_{2air}is the flux linkage formed by air closure on the receiver.

_{p}= 12 A, the receiver winding current I

_{s}= 18 A and phase-shift = 0°.

_{2}area, and smaller than the magnetic flux density of simulation in the A

_{1}area. The core loss is mainly determined by the A

_{2}area, where the magnetic flux density is relatively large. The maximum absolute value of the relative error of the magnetic flux density Bm

_{1}in the A

_{2}area is 2.57%; the relative error of the core loss determined by the relative error of the Bm

_{1}is 5.97%.

_{2}area, while it is opposite in the A

_{1}area. On the whole, the relative error of the overall core loss becomes smaller.

#### 3.3. Core Loss Modeling

_{core}is the core loss of magnetic component; f is frequency; V

_{e}is the volume of the magnetic component; k, α, and β are the empirical parameters obtained from the experimental measurement. Formula (21) is suitable for applications where the core loss is at a certain frequency and magnetic flux density of the magnetic component.

_{0}; the distance between the inner radius and the outer radius of the winding is w

_{0}. The magnetic core is equally divided into n circle sheets along the radial direction as shown in Figure 8.

## 4. Simulation and Verification

_{p}= 4 A, I

_{s}= 8 A, phase-shift = 35°. The core loss at a given operating point is obtained under FEA simulation, as shown in Figure 9. In the same way, the core loss under different coil currents and different current phase-shift can also be obtained by FEA simulation. The core losses obtained by the theoretical model and FEA simulation are compared at different operating points, and then the results are drawn in the same figure by Mathcad15 software.

_{p}= 12 A.

## 5. Conclusions

- The magnetic flux density inside the disk core through each radial circle sheet core is different; consequently, the average magnetic flux density cannot be used to calculate the overall core loss because of the non-linear core loss characteristic of the magnetic core.
- In the core loss calculation, the distribution of the magnetic flux density in the core needs to be taken into consideration. According to FEA simulation results, the mathematical model of the distribution of magnetic flux density is established. This model can be described as a quadratic function in which the parameters are extracted from the magnetic-field distribution of the magnetic coupling system.
- In order to build the disk core loss model of the WPT system, the disk core is divided into several circle sheets. In each circle sheet, the magnetic flux density can be seen to be the same and the core loss can be calculated by the Steinmetz formula. Combining the model of the distribution of magnetic flux density inside the magnetic core, the disk core loss model of the WPT system is proposed.
- The FEA simulation results show that the magnetic core loss calculated by the proposed model has good accuracy. This core loss model can provide an easier way to calculate the disk core loss of the WPT system than the FEA simulation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The distribution of magnetic flux density inside the transmitter core and the receiver core.

**Figure 3.**The distribution of magnetic flux density inside the transmitter core. (

**a**) The distribution of magnetic flux density versus R-axis; (

**b**) The distribution of magnetic flux density versus Z-axis.

**Figure 5.**The schematic diagram of the magnetic field line distribution in the magnetic coupling system.

**Figure 6.**The method of images equivalent model. (

**a**) The magnetic coupling system model; (

**b**) The method of images model of transmitter winding current; (

**c**) The method of images model of receiver winding current.

**Figure 7.**The magnetic flux density distribution inside the disk core obtained by theoretical calculation and simulation. (

**a**) Transmitter core; (

**b**) Receiver core.

**Figure 10.**The core losses of the disk core obtained by theoretical calculation and simulation under different winding currents. (

**a**) Transmitter core; (

**b**) Receiver core.

**Figure 11.**The core losses of the disk core obtained by theoretical calculation and simulation under different current phase differences. (

**a**) Transmitter core; (

**b**) Receiver core.

Magnetic Coupling System Model Parameters | Parameters and Setup | |
---|---|---|

The inner and outer radius of the winding | R_{win} = 100 mm | R_{wout} = 250 mm |

The inner and outer radius of the core | R_{cin} = 70 mm | R_{cout} = 280 mm |

Coil diameter and core thickness | d_{0} = 4.2 mm | b_{0} = 100 mm |

Turns of transmitter winding and receiver winding | N_{p} = 23 turns | N_{s} = 18 turns |

Transmitter winding current and receiver winding current | I_{p} = 12 A | I_{s} = 18 A |

Core material | Philips-3C96 | |

Boundary conditions | Balloon border | |

The transmission distance between coils | h_{0} = 50 mm |

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**MDPI and ACS Style**

Chen, Q.; Fan, F.; Wang, J.; Chen, W.
Core Loss Analysis and Modeling of a Magnetic Coupling System in WPT for EVs. *World Electr. Veh. J.* **2021**, *12*, 198.
https://doi.org/10.3390/wevj12040198

**AMA Style**

Chen Q, Fan F, Wang J, Chen W.
Core Loss Analysis and Modeling of a Magnetic Coupling System in WPT for EVs. *World Electric Vehicle Journal*. 2021; 12(4):198.
https://doi.org/10.3390/wevj12040198

**Chicago/Turabian Style**

Chen, Qingbin, Feng Fan, Jinshuai Wang, and Wei Chen.
2021. "Core Loss Analysis and Modeling of a Magnetic Coupling System in WPT for EVs" *World Electric Vehicle Journal* 12, no. 4: 198.
https://doi.org/10.3390/wevj12040198