Design and Analysis of Platform Shielding for Wireless Charging Tram

The application of inductive power transmission system in trams makes trams get rid of the traditional overhead catenary, but the electromagnetic environment and safety problems brought by the inductive power transmission system also attract the public's attention. In this paper, the model of the wireless charging tram platform is built to analyze the electromagnetic environment when the tram stops at the platform. Then, the shielding shape of the platform is proposed. A mathematical model with the minimum shielding cost as the goal and the magnetic field and installation space as constraints, is proposed for the platform shielding model of wireless charging tram. The three-dimensional finite element simulation software is used to verify the designed platform shield. The results show that the designed platform shield can ensure the electromagnetic radiation at the platform reaches the standard, and the cost is low. The platform shielding scheme designed in this paper provides a theoretical basis for the establishment of electromagnetic protection measures in the practical application of the wireless charging tram.

SECTION I. Introduction

As a new type of urban transit vehicle, the wireless charging trams use inductive power transmission (IPT) technology for wireless power transmission, enabling the power supply system and the vehicle to transmit energy without pantograph and traction network. The IPT technology not only solves the disadvantages brought by the traditional contact power supply mode, such as easy loss, contact spark, carbon accumulation, difficult maintenance, high construction cost, but improves the safety, reliability and flexibility of vehicle operation [1]–​[3]. However, the application of IPT technology to urban rail transit vehicles inevitably brings electromagnetic radiation problems [4]–​[6]. As a place for passengers to wait for the tram, the platform of rail tram has the characteristics of dense personnel and large mobility, etc. Ensuring the electromagnetic safety at the platform can ensure the safety of the electromagnetic environment of passengers. Therefore, it is particularly important to analyze the electromagnetic environment at the platform of the wireless charging tram and conduct shielding design.

At present, domestic and foreign scholars’ research on electromagnetic environment of IPT system mainly includes: Reference [7] conducted electromagnetic safety assessment on IPT system, and found that the minimum safe distance between human model and IPT system is 12cm.Reference [8] constructed an electric vehicle chassis model, and obtained that the nearest safe distance between the body and the coil center is 0.8 meters. Reference [9] directly conducted electrical shielding on the coupling coil, effectively reducing the magnitude of magnetic field near the coupling area. In reference [10], Kim et al., from Korea institute of science and technology, proposed an active induction shielding scheme, which realized magnetic field shielding by introducing a resonant coil connected with compensating capacitor in series. Literature [11] compared and analyzed the three ways of coupling coil installing shield layer as a whole, lateral horizontal shield and lateral vertical shield, and considered that the horizontal shield mode was suitable for electric vehicle wireless charging system. According to the analysis, references [7], [8] analyzed the electromagnetic environment and gave the safe distance, but did not give the corresponding shielding scheme. In literature [9]–​[11], active or passive shielding schemes were adopted to focus on analyzing the influence of shielding on magnetic field distribution and system, and no shielding design was carried out.

Taking wireless charging trams using IPT technology as the application background, the model of the platform is built to analyze the electromagnetic environment when the tram stops at the platform. Shielding shape analysis and design are carried out for the platform of wireless charging tram. A mathematical model with magnetic field and installation space as constraints and minimum shielding cost as the goal is proposed. The relevant parameters of shielding body are designed. Then three - dimensional finite element simulation software is used to verify the shield. The results show that the designed platform shield can ensure that the electromagnetic radiation at the platform reaches the standard and the cost is the lowest. The platform shielding scheme designed in this paper provides a theoretical basis for the establishment of electromagnetic protection measures in the practical application of wireless charging tram.

SECTION II. Analysis of IPT Magnetic Field

In this paper, a two-coil coupling mechanism of inductive power transmission is adopted, and its circuit topology is shown in figure [12], [13].

In figure 1, the transmitting side excitation source is direct voltage source $U_{dc}$ . $S_{1}$ , $S_{2}$ , $S_{3}$ , $S_{4}$ are insulated-gate bipolar transistors that make up the high-frequency inverter circuit. $R_{1}$ and $R_{2}$ are the resistance of transmitting coil and receiving coil respectively. $L_{1}$ and $L_{2}$ are the self-equivalent inductance of transmitting coil and receiving coil respectively. $M$ is the mutual inductance between transmitting coil and receiving coil. $C_{1}$ and $C_{2}$ are the compensation capacitance of the transmitting side and the receiving side respectively. $D_{1}$ , $D_{2}$ , $D_{3}$ , $D_{4}$ are the diodes that make up the rectifier. $R_{L}$ is the load resistor on the receiving side. When the system works, the receiving coil and the transmitting coil are matched to the same resonant frequency through the compensation capacitors $C_{1}$ and $C_{2}$ . The inverter circuit generates high-frequency alternating current to supply energy for the transmitting coil. And then electromagnetic induction enables energy to be efficiently transmitted to the receiving coil. The current generated by the receiving coil is supplied to the load through the rectifying and filtering device, thereby realizing wireless power transmission of the entire system.

FIGURE 1.

Circuit topology diagram of IPT.

The simplification circuit is shown in figure 2 [14]. $R$ is the load resistance and $M$ is the mutual inductance between the transmitting coil and the receiving coil. $U_{1}$ is the alternating voltage source obtained after the direct voltage source passes through the full-bridge inverter.

FIGURE 2.

Simplification circuit of wireless power transmission system.

Under the sinusoidal steady-state operation of the alternating voltage source, the system is in a resonant state. The resonant frequency is $f$ , $\omega =2\pi f$ . The loop impedance $Z_{1}$ of the transmitting coil, the loop impedance $Z_{2}$ of the receiving coil are as follows: $$\begin{align*} Z_{1}=&\textrm {j}\omega L_{1} +\frac {1}{\textrm {j}\omega C_{1}}+R_{1} \tag{1}\\ Z_{2}=&\textrm {j}\omega L_{2} +\frac {1}{\textrm {j}\omega C_{2}}+R_{2}\tag{2}\end{align*}$$

According to Kirchhoff’s law and mutual inductance theory, the equation of transmitter loop and receiver loop can be listed as: $$\begin{align*} U_{1}=&Z_{1} I_{1} +\textrm {j}\omega MI_{2} \tag{3}\\ \textrm {j}\omega MI_{1} +\left ({{Z_{2} +R} }\right)I_{2}=&0\tag{4}\end{align*}$$

Then the coil current at transmitter end and the coil current at receiver end can be solved. $$\begin{align*} I_{1}=&\frac {U_{1} \left ({{Z_{2} +R} }\right)}{(\omega M)^{2}+Z_{1} \left ({{Z_{2} +R} }\right)} \tag{5}\\ I_{2}=&\frac {-\textrm {j}\omega MU_{1} \left ({{Z_{2} +R} }\right)}{(\omega M)^{2}+Z_{1} \left ({{Z_{2} +R} }\right)}\tag{6}\end{align*}$$

When the system resonates, there is $\textrm {j}\omega L_{1} +\raise 0.7ex\hbox {1} \!\mathord {\left /{ {\vphantom {1 {\textrm {j}\omega C_{1} }}}}\right. }\!\lower 0.7ex\hbox {${\textrm {j}\omega C_{1}}$}=0$ and $\textrm {j}\omega L_{2} +\raise 0.7ex\hbox {1} \!\mathord {\left /{ {\vphantom {1 {\textrm {j}\omega C_{2} }}}}\right. }\!\lower 0.7ex\hbox {${\textrm {j}\omega C_{2}}$}=0$ .

The working area of the coupling coil satisfies the magnetic quasi-static field condition [14]. After ignoring the term of displacement current density, according to Maxwell equation, the existence relation in the region where the system is in working state is equation (7). $$\begin{equation*} \begin{cases} \Omega & {\begin{cases} {\nabla \times \boldsymbol {H}=0} \\ {\nabla \times \boldsymbol {E}+\dfrac {\partial \boldsymbol {B}}{\partial t}=0} \\ {\nabla \bullet \boldsymbol {B}=0} \\ \end{cases}} \\ \Gamma & {\boldsymbol {n}\bullet \boldsymbol {B}=0} \\ {\Omega _{1}} & {\begin{cases} {\nabla \times \boldsymbol {H}=\sigma _{1} \boldsymbol {E}_{1} +\boldsymbol {J}_{1}} \\ {\nabla \times \boldsymbol {E}_{1} +\dfrac {\partial \boldsymbol {B}_{1}}{\partial t}=0} \\ {\nabla \bullet \boldsymbol {B}_{1} =0} \\ \end{cases}} \\ {\Gamma _{1}} & {\begin{cases} {\boldsymbol {n}_{1} \times (\boldsymbol {E}-\boldsymbol {E}_{1})=0} \\ {\boldsymbol {n}_{1} \bullet (\boldsymbol {B}-\boldsymbol {B}_{1})=0} \\ \end{cases}} \\ {\Omega _{2}} & {\begin{cases} {\nabla \times \boldsymbol {H}=\sigma _{2} \boldsymbol {E}_{2} +\boldsymbol {J}_{2}} \\ {\nabla \times \boldsymbol {E}_{2} +\dfrac {\partial \boldsymbol {B}_{2}}{\partial t}=0} \\ {\nabla \bullet \boldsymbol {B}_{2} =0} \\ \end{cases}} \\ {\Gamma _{2}} & {\begin{cases} {\boldsymbol {n}_{2} \times (\boldsymbol {E}-\boldsymbol {E}_{2})=0} \\ {\boldsymbol {n}_{2} \bullet (\boldsymbol {B}-\boldsymbol {B}_{2})=0} \\ \end{cases}} \\ \end{cases}\tag{7}\end{equation*}$$ where, $\boldsymbol{B}$ , $\boldsymbol{H}$ and $\boldsymbol{E}$ are respectively the magnetic induction intensity, magnetic field intensity and electric field intensity in the air. $\omega$ is angular frequency. $\boldsymbol{n}$ is its normal direction. $\sigma _{1}$ is the conductivity of the coil material. $\boldsymbol{H}_{\mathbf {1}}$ , $\boldsymbol{J}_{\mathbf {1}}$ , $\boldsymbol{E}_{\mathbf {1}}$ and $\boldsymbol{B}_{\mathbf {1}}$ are magnetic field intensity, current density, electric field intensity and magnetic induction intensity in the coil, while $\boldsymbol{B}_{\mathbf {2}}$ , $\boldsymbol{J}_{\mathbf {2}}$ , $\boldsymbol{H}_{\mathbf {2}}$ and $\boldsymbol{E}_{\mathbf {2}}$ are magnetic induction intensity, current density, magnetic field intensity and electric field intensity in the shielding material respectively. $\boldsymbol{n}_{\mathbf {2}}$ is its normal direction. $\sigma _{2}$ is the conductivity of the shielding material. $$\begin{equation*} \begin{cases} \Omega & {\nabla \times \left({\dfrac {1}{\mu }\nabla \times \boldsymbol {A}}\right)=0} \\ \Gamma & {\boldsymbol {n}\bullet \left({-\sigma \dfrac {\partial \boldsymbol {A}}{\partial t}-\sigma \nabla \varphi }\right)=0} \\ {\Omega _{1}} & {\begin{cases} {\nabla \times \left({\dfrac {1}{\mu _{1}}\nabla \times \boldsymbol {A}}\right)+\sigma _{1} \boldsymbol {A}=\boldsymbol {J}_{1} -\sigma _{1} \nabla \varphi _{1}} \\ {\nabla \bullet (-\sigma _{1} \boldsymbol {A}-\sigma _{1} \nabla \varphi _{1})=0} \\ \end{cases}} \\ {\Gamma _{1}} & {\begin{cases} {\boldsymbol {A} = \boldsymbol {A}_{1}} \\ {\dfrac {1}{\mu }\nabla \times \boldsymbol {A} \times \boldsymbol {n}=\dfrac {1}{\mu _{1}}\nabla \times \boldsymbol {A}_{1} \times \boldsymbol {n}_{1}} \\ \end{cases}} \\ {\Omega _{2}} & {\begin{cases} {\nabla \times \left({\dfrac {1}{\mu _{2}}\nabla \times \boldsymbol {A}}\right)+\sigma _{2} \boldsymbol {A}=\boldsymbol {J}_{2} -\sigma _{2} \nabla \varphi _{2}} \\ {\nabla \bullet (-\sigma _{2} \boldsymbol {A}-\sigma _{2} \nabla \varphi _{2})=0} \\ \end{cases}} \\ {\Gamma _{2}} & {\begin{cases} {\boldsymbol {A}=\boldsymbol {A}_{2}} \\ {\dfrac {1}{\mu }\nabla \times \boldsymbol {A}\times \boldsymbol {n}=\dfrac {1}{\mu _{2}}\nabla \times \boldsymbol {A}_{2} \times \boldsymbol {n}_{2}} \\ \end{cases}} \\ \end{cases}\tag{8}\end{equation*}$$

For convenience of calculation, magnetic vector $\boldsymbol{A}$ and scalar potential function $\varphi$ are introduced. In the analysis, the boundary conditions in different domains are homogeneous boundary conditions. Considering the coulomb specification [15], [16], the convergence conditions on the interface of the solution domain is equation (8).

Where, $\mu$ represents the permeability of corresponding materials in the domain. $\boldsymbol{n}_{\mathbf {1}}$ and $\boldsymbol{n}_{\mathbf {2}}$ are unit normal vectors on the interface between coil and air, and between magnetic shielding material and air, respectively.

According to equations (5) and (6), the current density in the coil $\boldsymbol{J}_{\mathbf {1}}$ can be obtained. The eddy current density in the shielded conductor $\boldsymbol{J}_{\mathbf {2}}$ is $$\begin{equation*} \nabla ^{2}\boldsymbol {J}_{2} =\sigma \mu \frac {\partial \boldsymbol {J}_{2}}{\partial t}\tag{9}\end{equation*}$$

The magnetic vector $\boldsymbol {A}$ and scalar potential function $\varphi$ are $$\begin{align*} \begin{cases} \boldsymbol {A}=\dfrac {\mu }{4\pi }\int _{V} {\dfrac {\boldsymbol {J}}{R} dV} \\[0.5pc] \varphi =\dfrac {1}{4\pi \varepsilon }\int _{V} {\dfrac {\rho }{R} dV} \\ \end{cases}\tag{10}\end{align*}$$

Based on the above principle, the magnetic vector $\boldsymbol {A}$ and scalar potential $\varphi$ functions are solved by finite element method. Magnetic field parameters such as magnetic induction intensity, magnetic field intensity and electric field intensity are obtained. Then verify the effectiveness of platform shielding measures.

SECTION III. Analysis of Shielding at Platform

In order to ensure the safety of the electromagnetic environment at the platform, according to the specification for electromagnetic radiation issued by the international commission on non-ionizing radiation protection (ICNIRP) [17], the electromagnetic waves in the frequency range of 3–150kHz are mostly used for wireless charging. The electromagnetic parameters of the electromagnetic radiation standard without human body are given in table 1.

TABLE 1 ICNIRP 3–150khz Electromagnetic Radiation Standard

Therefore, the electric field intensity at the platform should not exceed 83V/m, the magnetic field intensity should not exceed 21A/m, and the magnetic flux density should not exceed 0.025mT. The influence of magnetic field intensity at the platform is far greater than that of electric field intensity. Therefore, this paper mainly analyzes the magnetic field intensity, that is, the magnetic field intensity is less than or equal to 21 A/m, and the electromagnetic environment is safe.

The electromagnetic shielding design of the platform includes the electromagnetic shielding design of the coupling coil and the electromagnetic shielding design of the platform. As the carrier of induced energy transmission, the coupling coil is the source of electromagnetic radiation. Therefore, electromagnetic shielding of the coupling coil can reduce the electromagnetic radiation from the source.

A. Analisis of Different Coil Structure

Coil shapes commonly used in inductive power transmission systems include circular, rectangular, and combined (DD) coils. Electromagnetic analysis was carried out on the three shape coils, and the distribution of magnetic field intensity was shown in figure 3.

FIGURE 3.

Magnetization field intensity distribution of different coil structures in XZ plane.

It can be seen from the figure that the magnetic field intensity of the combined (DD) coil at the center of the coil is significantly greater than that of the circle and rectangle, which is not conducive to reducing electromagnetic radiation. Moreover, combination (DD) winding is complex and costly, so it is not suitable for wireless charging trains. The circular coil has direction consistency but offset tolerance is poorer, so it is not suitable for wireless charging trains. The rectangular winding is easy to ensure the evenness of air gap magnetic field, which is suitable for trains moving in only one direction. Therefore the wireless charging tram is equipped with rectangular coil.

Since the receiving coil is located below the vehicle body, the wireless charging tram adopts aluminum as the vehicle body material, which has a good shielding effect on the receiving coil, so there is no need to carry out shielding design at the receiving coil. However, due to the strong magnetic field near the transmitting coil, the eddy current loss of the shielding body is large, which increases the wear of the shielding body and affects the service life [21], [22]. Therefore, the cost performance of shielding in the measurement of transmitting coil is low. To sum up, although shielding the coil directly can fundamentally solve the electromagnetic radiation, it has disadvantages such as low cost performance and high loss. Moreover, research shows that [18], [19] shielding the coil will reduce system efficiency and influence system parameters. Therefore, this paper directly designs shielding for the platform itself.

B. The Model of Platform

According to the size of the wireless charging tram, the relevant parameters of the platform for the unconnected current train are obtained as shown in table 2.

TABLE 2 The Parameters of Electromagnetic Coupling Mechanism

The above parameters are used to build the model of the wireless charging tram, as shown in figure 4 when the train stops at the platform. According to the characteristics of trams, a rectangular coil structure with long transmitting coil and short receiving coil is selected. The undercarriage space configuration scheme of the wireless charging tram is shown in figure 5.

FIGURE 4.

Platform model of train stop.

FIGURE 5.

The undercarriage space configuration scheme of the wireless charging tram.

C. Analysis and Design of Platform Shielding Shape

The wireless charging tram adopts the segmented wireless power supply mode. If the tram does not run to the platform, there will be no power supply on the ground, which will not generate electromagnetic radiation at the platform. When the tram stops at the platform, the coil will supply power, which may generate electromagnetic radiation at the platform. In order to analyze the electromagnetic influence at the platform, the electromagnetic environment at the platform is analyzed and calculated according to the principle in section II. In figure 4, position A is the cut plane of the XZ plane at the edge of the platform, and position B is the cut plane of the upper surface of the platform. Positions A and B are selected for analysis. The distribution of magnetic field intensity is shown in figure 6.

FIGURE 6.

Magnetic field distribution of the platform.

For the convenience of description, the platform near the side of the vehicle is called the inside of the platform. At position A, the magnetic field strength decreases gradually with the increase of X-axis coordinate. and the magnetic field strength decreases gradually with the increase of Z-axis coordinate. The magnetic field intensity is greater than 21A/m in the range of 0.8m from the inside of the platform in the direction of X axis and 2.2m from the bottom of the platform in the direction of Z axis. According to the requirements of the international commission on non-ionizing radiation protection (ICNIRP) on magnetic field intensity, the electromagnetic radiation within this range exceeds the standard. At position B, the magnetic field strength decreases with the increase of the X-axis. In the direction of Y-axis, the magnetic field intensity on both sides of the platform is relatively large, while the magnetic field intensity on the middle part is small. This is because the aluminum car body can generate shielding effect when the train stops at the platform. Due to the existence of bogie and other metals, the magnetic field strength of the inner part of the platform is relatively large. The magnetic field intensity is greater than 21A/m within the range of 1.2m from the inner side of the platform in the direction of X axis. According to the requirements of the international commission on non-ionizing radiation protection (ICNIRP) on magnetic field intensity, the electromagnetic radiation within this range exceeds the standard. Therefore, do not take other shielding measures only rely on aluminum car body shielding, there is electromagnetic radiation at the platform exceed the standard.

Through the above analysis, it is proposed that “” type shielding is used. The relevant dimensions of shielding body are shown in figure 7, and the red part in the figure is the shielding body.

FIGURE 7.

Shape and position of the shield.

SECTION IV. Analysis of Electromagnetic Shielding Parameters

As a place for passengers to wait for the tram, the platform has the characteristics of dense and large flow of people, so the electromagnetic environment at the platform must be guaranteed to be safe. It is found that when the tram is parked at the platform without electromagnetic protection, there is excessive electromagnetic radiation at the platform, which cannot guarantee the safety of the electromagnetic environment for passengers [17]. Therefore, it is necessary to design the electromagnetic shielding structure of the platform. After determining the shape of the shield, it is necessary to analyze the shielding material, shielding body thickness and related structural parameters of the shield.

A. Analisis of Shielding Material

In physics, the main parameters to describe the electromagnetic properties of metal shielding materials include permeability and conductivity. Metal shielding materials can be divided into two categories according to the different permeability. The first type is non-ferromagnetic metal, which has high conductivity and can shield the magnetic field by eddy current effect. The second category is ferromagnetic metals, which use their high permeability to guide and change the system’s spatial magnetic field to achieve electromagnetic shielding.

In order to analyze the shielding efficiency of metal, a simple model is built, as shown in figure 8. In the figure, the coil is located in the plane XOY and the shield is located in the plane YZ with the X = 0.5m.

FIGURE 8.

Shielding effect analysis model.

The shielding effect of materials is commonly expressed as shielding efficiency SE. and its calculation formula is [19] $$\begin{equation*} SE=20\log \frac {H_{1} \left ({{x_{0},y_{0},z_{0}} }\right)}{H_{2} \left ({{x_{0},y_{0},z_{0}} }\right)}\textrm {dB}\tag{11}\end{equation*}$$ where, $H_{1}$ is the magnetic field intensity at the point P (x₀, y₀, z₀) without shielding, and $H_{2}$ is the magnetic field intensity at the point P (x₀, y₀, z₀) with shielding.

The magnetic field intensity H1 at the time point P(x₀, y₀, z₀) without shielding body is only generated by coil excitation. According to Biot-Savart law, the magnetic field intensity is $$\begin{equation*} \boldsymbol {H}_{1} =\frac {\boldsymbol {B}_{1}}{\mu _{0}}=\frac {1}{\mu _{0}}\int {d\boldsymbol {B}_{1} =\int {\frac {I\boldsymbol {dl}\times \boldsymbol {r}}{4\pi r ^{2}}}}\tag{12}\end{equation*}$$

After shielding, eddy currents will be generated in the shielding body which is excited by the changing magnetic field of the coupling coil. The eddy current density can be obtained from formula (9). The magnetic field intensity generated by the eddy current in the conductor in the air is $$\begin{equation*} \begin{cases} \boldsymbol {A}_{21} =\dfrac {\mu _{0}}{4\pi }\int _{V} {\dfrac {\boldsymbol {J}}{R} dV} \\ \boldsymbol {H}_{21} =\dfrac {1}{\mu _{0}}\nabla \times \boldsymbol {A}_{21} \\ \end{cases}\tag{13}\end{equation*}$$ where $R$ is the distance from the field point to the elementary charge. After shielding, the magnetic field intensity at points P (x₀, y₀, z₀) is composed of the magnetic field of the coil and the eddy current magnetic field of the shielded conductor. The magnetic field strength is $$\begin{equation*} \boldsymbol {H}_{2} = \boldsymbol {H}_{1} + \boldsymbol {H}_{21} =\int {\frac {I\boldsymbol {dl}\times \boldsymbol {r}}{4\pi r^{3}}} +\frac {1}{\mu _{0}}\nabla \times \boldsymbol {A}_{21}\tag{14}\end{equation*}$$

The magnetic field intensity at point P(x₀ = 1m and y₀ = z₀ = 0m) is calculated to obtain the shielding efficiency of the metal shielding body. The results are shown in table 3.

TABLE 3 Common Metal Shielding Material Parameters

As can be seen from the table, the shielding effect varies with the material’s permeability and conductivity. Aluminum has the highest electromagnetic shielding efficiency and the best shielding effect. Therefore, aluminum is chosen as the shielding material in this paper.

B. Analisis of Shielding Thickness

Electromagnetic shielding utilizes the electromagnetic field generated by the eddy current in the conductor to resist the external electromagnetic field so as to realize the shielding of a given area. Studies have shown that [11], the thickness of the shielding body should be close to 3~6 times the penetration depth of the shielding material in order to achieve effective shielding effect. The formula of penetration depth and shield thickness $d$ is as follows. $$\begin{align*} \alpha=&\sqrt {\frac {2}{\omega \mu \sigma }} \tag{15}\\ d\approx&2\pi \alpha\tag{16}\end{align*}$$

When the frequency is 30kHz, the penetration depth of the aluminum plate is 0.47mm. Therefore, in order to achieve effective shielding effect, the thickness of the aluminum plate is about 2.96mm. Considering the manufacturing technology, the thickness of the shielding aluminum plate is 3mm.

C. Structural Parameter Optimization of the Shield

Through the above analysis, this paper chooses 3mm thick aluminum plate as the shielding body for magnetic field shielding. Then, the relevant parameters of the shielding body will be optimized.

1) Shielding Body Parameter Design Optimization Objective

Considering aesthetics, convenience and other factors, the length of the shielding body $L$ is equal to the length of the platform. The shielding body thickness is 3mm. The shielding volume is $$\begin{equation*} V=6\times 10^{3} b(a-c)+3\times 10^{3} Lc\tag{17}\end{equation*}$$

In the shielding design, in addition to achieving the purpose of electromagnetic shielding, the cost should also be considered. $$\begin{equation*} S=mV\rho\tag{18}\end{equation*}$$ where, $m$ is the unit price (yuan /kg) of aluminum, the density (kg/$\text{m}^{3}$ ) of aluminum, and $V$ is the shielding volume (m³). The unit price of aluminum alloy is considered to remain unchanged for a period of time, so to achieve the minimum shielding cost, the minimum shielding volume is required. Based on the above analysis, this paper takes the minimum shielding cost as the goal of shielding parameter optimization.

2) Shielding Body Parameters Design Constraints

In order to clarify the exceeding range of electromagnetic radiation, line segments X₁ and X₃ are drawn along the X-axis at the edge and center of the platform surface to observe the magnetic field distribution in the horizontal direction on the platform surface. Draw line segments X₂ and X₄ along the Z axis at the inside edge and center of the platform to observe the magnetic field distribution in the upper space of the platform. Draw line segment X₅ along the Y axis on the inside edge of the platform to observe the magnetic field distribution of the column and the moving direction of the platform. The positions and directions of line segments X₁, X₂, X₃, X₄ and X₅ are shown in figure 7. According to the regulations on electromagnetic radiation issued by the international commission on non-ionizing radiation protection (ICNIRP) [17], in order to ensure that the electromagnetic environment at the platform will not affect passengers, the magnetic field intensity at the platform should be less than or equal to 21A/m. $$\begin{equation*} \begin{cases} {H_{X_{1}} \le 21} \\ {H_{X_{2}} \le 21} \\ {H_{X_{3}} \le 21} \\ {H_{X_{4}} \le 21} \\ {H_{X_{5}} \le 21} \\ \end{cases}\tag{19}\end{equation*}$$

The space between the platform and the unnetted train is limited, so the installation space will restrict the relevant parameters of the shield. $$\begin{equation*} \begin{cases} {a\ge 0} \\ {0\le b\le 20000} \\ {c\ge 0} \\ \end{cases}\tag{20}\end{equation*}$$

Based on the above analysis, the mathematical model for parameter optimization of platform shielding with the minimum shielding cost as the optimization target and the magnetic field and installation space as constraints can be described by the following formula: $$\begin{equation*} \begin{cases} {\min (S)} \\ {s.t.\begin{cases} {H_{X_{1}} \le 21} \\ {H_{X_{2}} \le 21} \\ {H_{X_{3}} \le 21} \\ {H_{X_{4}} \le 21} \\ {H_{X_{5}} \le 21} \\ {a\ge 0} \\ {0\le b\le 20000} \\ {c\ge 0} \\ \end{cases}} \\ \end{cases}\tag{21}\end{equation*}$$

3) Shielding Body Parameter Design Optimization Process

Due to meet the conditions of shield parameters array is very much, so shielding parameters need to be optimized. The specific process is: the initial array of shield structure parameters is determined according to vehicle structure parameters and platform related parameters. Verify that the initial array satisfies the constraint condition. An array that does not satisfy the constraint will be thrown out. Then the shielding parameters were changed according to the fixed step size. The array with sufficient constraints will be compared with the previous group, and the array with smaller shielding structure parameters will be retained for comparison with the next group. Finally, an optimal set of shielding parameters is obtained. The optimization flow chart is shown in figure 9. According to the above shielding body design and optimization methods, the relevant parameters of the shielding body are a = 2.85m, b = 3.3m and c = 0.8mm.

FIGURE 9.

Flow chart for optimizing shielding parameters.

SECTION V. System Simulation

Wirelessly charged trams use rectangular coils, S-S compensation topology. The related parameters of coupling coil and system are shown in table 4.

TABLE 4 The Parameters of Electromagnetic Coupling Mechanism

The system simulation model based on Matlab is built by using the system parameters in the table, and the simulation results are shown in figure 10. The simulation results show that the voltage in the transmitting coil and receiving coil is the square wave with amplitude of 750V, and the current is the sine wave with effective value of 445A.

FIGURE 10.

Transmitter coil and receiver coil voltage and current waveform.

The train platform model and the shielding body of optimal design in the figure 8 were imported into Maxwell for three-dimensional modeling and simulation analysis. Positions A and B were selected in the simulation to obtain the spatial magnetic field distribution of the platform after the shielding material was added, as shown in figure 11.To determine the intensity of electromagnetic radiation, calculate the magnetic field intensity at the positions of line segments X₁, X₂, X₃, X₄ and X₅, and obtain the distribution curve of magnetic field intensity as shown in figure 12. The magnetic field intensity distribution on the platform is shown in the figure 13.

FIGURE 11.

Magnetic field intensity distribution in XZ plane and XY plane.

FIGURE 12.

Distribution curve of magnetic field intensity.

FIGURE 13.

Distribution curve of magnetic field intensity.

As can be seen from the figure, the magnetic field intensity at the platform after shielding measures is less than 21A/m, meeting the requirements of ICNIRP2010 electromagnetic standard. It shows that the designed shielding scheme can effectively shield the platform.

To verify the cost of shielding measures, the cost of different shielding measures is calculated. The unit price of aluminum is 15 yuan /kg, and the results are shown in table 5.

TABLE 5 Shielding Cost

According to the calculation, the selected shielding parameters a = 2.85m, b = 3.3m and c = 0.8m can make the magnetic field intensity at the platform reach the standard and the cost is the lowest. Simulation and calculation results verify the effectiveness of the shielding scheme.

SECTION VI. Conclusion

With the application of inductive power transmission technology to the non-contact tram, its electromagnetic environment and safety problems have been widely concerned. High-power transmission will affect the environment, equipment and human body. In this paper, a mathematical model with magnetic field and installation space constraints, aiming at the minimum shielding cost, is proposed for the platform model of the wireless charging tram. Then, the simulation model of the platform is built to analyze the electromagnetic environment after shielding at the platform when the tram stops at the platform. The results show that the designed platform shield can ensure the electromagnetic radiation at the platform reaches the standard and the cost is low. The platform shielding scheme mentioned in this paper provides a theoretical basis for the establishment of electromagnetic protection measures in the practical application of the wireless charging tram.