Magnetic shielding structure optimization design for wireless power transmission coil

Based on electromagnetic field transformation, wireless power transmission (WPT) technology can transmit energy through non-contact method. In some specific application situations such as medical implantable devices, electric vehicles and sensors etc., WPT technology has unparalleled advantages over the traditional tail energy transfer.^1–5 However, the practical application of WPT technology is currently limited by the contradiction between over meters-scale power transmitting distance and coil volume and weight constrains, such as in the field of implanted device and unmanned aerial vehicles.^6,7 The performance of WPT is normally evaluated by energy transmission efficiency and other electromagnetic influence index during the transmission process.

In order to improve the performance of WPT, the related researches have mainly focused on two aspects. On the one hand, the body of the WPT was studied, such as the coil structure optimization and the source structure design.^8–11 At present, related researches are predominantly focused on two aspects in order to improve the system performance of WPT. The first aspect concentrates on internal parameters design, such as coil structure optimization and the source structure redesign while the second research direction pays more attention to external materials addition, for example, the magnetic shielding material.^12–16 The first aspect has been widely studied,^17–19 and it is difficult to further improve the performance of WPT. On the other hand, special materials are not always effective for performance improvement and some of the materials have specific using requirements.^20–22 As for the shielding structure, researchers generally depend on experimental experience without adequate theoretical support. There are no specific or comprehensive shielding structure design scheme published so far.^23–26 

In this paper, a novel magnetic shielding structure was proposed based on the electromagnetic field theory, with inclusion of detail coil magnetic flux linkage theoretical calculation and the characteristics of the magnetic flux linkage trend. The shielding structure was gradually optimized in the process under consideration of performance stability, practical feasibility and manufacture convenience. And then a complete design procedure of the new shielding structure is summarized at length. Through the joint simulation of ANSYS Maxwell and ANSYS Simplorer and comparative analysis, the new shielding structure was verified possessing the optimal transmission efficiency when compared with the traditional shielding structure. Furthermore, for the example presented, the weight of the new shielding structure is decreased by approximately 41%. Finally, the experimental evaluation verifies the advantages and rationality correctness of the new shielding structure. In the  appendix, the new shielding structure was operated for wireless car charging, whose results proves that the design can meet the requirements of the maximum magnetic field distribution of human body human safety through ANSYS Maxwell and ANSYS Simplorer field-circuit co-simulation, when the man is at the closest distance between the man and the coil.

In the WPT system, the coupling coefficient k and the quality factor Q of the winding were both related to the power losses and thus related to the energy transmission efficiency of the system. It was found that a power loss is inversely proportional to the product of kQ, indicating that the energy efficiency η is proportional to the kQ product.^27,28 For the WPT system with two coils, we have

It can be seen that when the coils of a WPT system have been fixed, the angular frequency and the coil resistance are invariant at a certain operating frequency, which means that the power transfer efficiency is only related to the coupling coefficient.

When the magnetic shielding structure is added to the coil to restrain the trend of the magnetic flux linkage, it can improve the performance of the coil on two aspects. On the one hand, the mutual inductance coefficient between the two coils is consolidated. On the other hand, the leakage of the magnetic field is reduced. To calculate the coil magnetic flux linkage, Fig. 1(a) shows a single-turn circular coil, whose inner radius is R₁, outer radius is R₂, average radius is b and circular section radius is a. In the plane of the circular coil, P is a point inside the circular coil, point Q is on the circular coil, the distance between point P and point Q is R. When the average radius b is much larger than a, the circular coil can be simplified as shown in Fig. 1(b). α is the included angle between the link line of point P and point O and the link line of point Q and point O. r is the length of line PO, from the point P to the center O of the circular coil, and I is the current flowing through the circular coil.

According to Biot Savart law, the tiny current-carrying line element $Idl→$ generates the magnetic induction intensity $dB→$ at a certain point in infinite space. The mathematical expression is²⁹ 

The magnetic flux of the circular area is

When the helix coil structure with n-turn is tightly wound, it is equivalent to be constructed by a number of single-turn circular coils with increasing radius, thus the magnetic flux linkage of the n-turn helix coil is

Where, Φ_n is the magnetic flux linkage passing through the area of coil n.

Because the material with high permeability is usually used for the coil shielding structure, which is much higher than that of the air, it can be assumed that all the magnetic induction line on the side of the shielding material passes through the shielding material. When a circular shielding structure is used for the helix coil, suppose the saturation magnetic induction intensity is expressed as B_m, and take 20% of the saturation magnetic induction intensity as the margin, the thickness of the shielding material with the distance r from the center of the circle is h, we have

When the magnetic linkage of the helix coil and shielding material saturation induction density are invariant, the distance r to the center is inversely correlated with the thickness h of the shielding materials. The relevant schematic diagram is shown in Fig. 2.

From Fig. 2, it can be found the farther away from the center, the thinner the thickness is. Therefore, the thickness of the circular shielding structure edge h_ext and the initial radius of the helix coil h_int all can be calculated, when the internal radius R_int and the external radius R_ext are known after the helix has been selected.

The magnetic field is a passive field, and the magnetic induction line must form a closed path. When the magnetic induction line enter into the shielding structure from the edge and get out of it from the center, the cross-sectional area of the outlet needs to meet

So the outlet radius of the magnetic induction line of the shielding structure R_out and the corresponding thickness of the shielding structure h_out also can be calculated.

When the helix coil and shielding material are determined, the exit circular radius can be calculated by (6). So merge (5) and (6), we have

It is sure that he central outlet radius must be less than that of the helix coil. Fig. 3 shown the relevant graphics according to (7). It can be found when the shielding structure radius r is invariant, the thickness h of the shielding structure central outlet decreases gradually with the increase of export center radius R. The shielding structure exit thickness h increases with the increase of the shielding structure radius r when the shielding structure exit radius R is determined.

When designing the shield structure, the shielding structure should cover one side of the coil. In order to reduce the volume of the whole coil, the protruding part does not exceed or slightly higher than the other side of the coil height. In this paper, the protruding part is just the same as the other side of the coil, that is

If h_max > h_out, which means the saturation induction density of the shielding material is too low to meet the requirement, the shielding material has to re-select and the parameters have to recalculate.

When h_max < h_out, the maximum thickness of shielding structure is h_max. The relationship curve of the distance from the center and the corresponding thickness was plotted according to (7), as shown in Fig. 4. 2a is the coil thickness and D is the distance between the coil and the shielding structure.

It can be concluded from Fig. 4 that the cross-section curve of the shielding structure is

Plot the curve of the curved shield structure model, whose cross section is in consistent with (9), as shown in Fig. 5.

The shielding structure model shown in Fig. 5 was bulit based on the theoretical calculation. It is a challenge to manufacture this structure on the production process in practical application. According to the thought of equivalent area, the same thickness R_int of the fan type shielding structure was used under the shield structure cross-sectional area unchanged when the distance r from the center range from R_int to R_ext. When the distance r within the range of R_max ≤ r ≤ R_int, the outline of the shield structure can be expressed by a linear equation $h=hmax−hintRmax−Rintr+hint$ instead of (9), as shown in Fig. 6. The Fan-shaped shielding structure model was built shown in Fig. 7.

The shielding structures shown in Fig. 5 and Fig. 7 require that the enter direction of the magnetic lines generated by the coil should be paralleled with the coil plane. However, the enter direction of most of the magnetic lines is perpendicular to the coil plane. So a guide portion of the magnetic induction lines is added to optimize the structure design at the edge of the shielding structure, as shown in Fig. 8.

By summarizing the design of the shielding structure, the whole design process of the new shielding structure is shown in Fig. 9.

The parameters of the helix coil are shown in Table I.

According the parameter of Table I, the geometric model of the helix coil is built shown in Fig. 10.

The magnetic flux linkage of the area surrounded by the helix coil can be calculated when the current is 10A.

The selected shielding material is MnZn ferrite from TDK, whose parameters are shown in Table II.

Based on the parameters of the shielding material and the total magnetic flux linkage of the coil, it can be calculated the relationship between the distance r from the center and the thickness h of the shielding structure.

Therefore, the thickness of the circular shielding structure edge and the initial radius of the helix coil are h_ext ≈ 1.794(mm), h_int ≈ 2.870(mm). The outlet radius of the magnetic induction line of the shielding structure is R_out ≈ 18.560(mm), and the corresponding thickness of the shielding structure is h_out = 9.280(mm).

Due to h_max = max(h_int,h_ext) + D + 2a = 5.87(mm) < h_out, the maximum thickness of shielding structure is h_max based on the Fig. 4. The models of the coil with different shielding structure are built shown in Fig. 11. The improved fan-shaped shielding structures with different angles are built to study which angle is better, and it will be studied and verified in section IV.

For the helix coil shown in Fig. 10, the flat plate shielding structure is the most common of those shown in Fig. 10,^19,20 the weight of it is

And the weight of the improved fan-shaped shield structure is

Contrast (12) and (13), we have

It is can be found that the weight of the improved fan-shaped shield structure is reduced by about 41% compared with the common shielding structure.

Firstly, in the eddy current of ANSYS Maxwell the simulation frequency is set to 100kHz. The magnetic field distributions of the coils with different shielding structure shown in Fig. 11 are shown in Fig. 12. It can be found that there is a strong magnetic field distribution in the non-effective transmission area (the area out of two coils) without the shielding structure. But there is still a large portion of magnetic field excluded in energy transfer. The coil with shielding structure can reduce the divergence of magnetic field in the non-effective energy transmission area, and concentrate more magnetic flux to transmit energy at a targeted direction. Among them, the coil 4 with 4 rectangular shielding structure has the weakest binding force to the magnetic field, while the coil with the improved shielding structure with edge has the strongest binding force and the least external magnetic field leakage.

Fig. 13 shows that the coil with the shielding structure with edge improved has a higher self-inductance, mutual inductance and coupling coefficient than the other shielding structures or the coil without shielding structure. Among them, the coil with improved fan-shaped shielding structure with acute angle edge has the highest mutual inductance of about 11.788uH. According to (1), a conclusion can be drawn that the transmission efficiency is related to the mutual inductance when the WPT coil is determined. Therefore it can be concluded that the coil with the improved fan-shaped shielding structure with acute angle edge has the highest transmission efficiency.

From Fig. 14, when the resonant frequency of coils all were set to 100kHz with compensation capacitor, the amplitude of input sinusoidal current source is 14.14A through a matched capacitance and the coil with the improved shielding structure with edge receives the maximum current amplitude. Among them, the received current amplitude, about 5.72A, of the coil with the improved fan-shaped shielding structure with acute angle edge is higher than the other two improved shielding structure, which further verifies that the coil with the improved fan-shaped shielding structure with acute angle edge has the highest transmission efficiency.

Based on the previous theory and simulation analyses, the corresponding experimental platform is built. The comparison of the coil without shielding structure, with circular shielding structure and with the improved fan-shaped shielding structure with acute angle edge is carried out in experiments. The coil, the circular shielding structure and the fan-shaped shielding structure with acute angle edge are shown in Fig. 15.

From Fig. 16, the coil with the improved fan-shaped shielding structure with acute angle edge receive more current than the other two coils in the same scale of resources, which corresponds to the former theoretical analyses and simulation verifications. The feasibility and advantages of this new WPT coil shielding structure are verified once again.

In this paper, we have proposed a new type design method of a WPT coil shielding structure based on the magnetic field characteristics of a helix coil. The whole design process was deduced and summarized. A helix coil shielding structure was built with a specific example to verify the new shielding structure is the best. From the simulation and experiment, it can be concluded that the new shielding structure not only has the stronger binding force for the magnetic field and increases the transmitting efficiency, but can reduce the magnetic field leakage and improve security in the process of WPT. Compared with the flat plate shielding structure, the weight of the new shielding structure is reduced by about 41%, which bring down the cost of material and the weight of the whole coil. It contributes to application expansion of WPT in some special field.

This work was supported in part by the National Natural Science Foundation of China (Grant Number 51507114) and in part by the Natural Science Foundation of Hubei Province (Grant Number 2014CFB272).

To test the practical application effect of the coil with the improved fan-shaped shielding structure with acute angle edge, it is used in the wireless charging for electric vehicles. The coil size used in electric vehicles is 600mm*600mm, but the former used coil size is 200mm*200mm. Therefore, the car model and the human body model are reduced by 3 times equally. In the worst case, where the man lying on the side of the car, the distance, which is 600mm (the distance is reduced 3 times to 200mm in simulations), between the human body and the coil structure is the shortest, as shown in Fig. 17.

When the input current amplitude is 14.14A and the frequency is 100kHz, the simulation results are shown in Fig. 18.

As shown in Fig. 18, during the process of electric vehicle wireless charging, the closest distance from human breast to coil edge is about 750mm (the distance is 250mm in simulations) when the person is in the worst case. And the maximum magnetic field distribution of human body, about 1.69e-5T, also appeared here, which is far lower than the standard of human safety requirements (relative to the earth static magnetic field about 4.5 e-5T).