An Active Shielding Control Method for a Wireless Power Transfer System under Misalignment Conditions

1. Mutual Inductance Analysis

Fig. 1 shows the geometry of the TX, RX, and SH coils under misalignment conditions. I, φ, and r refer to the current, phase, and radius of the coil, respectively. A misalignment condition is set for RX and SH coils, which moves in the x and y directions, increasing the distance from the TX coil. The RX and SH coils are located at a position moved by a and b on the x and y axes of the Cartesian coordinate. d_p-TX, d_p-RX, d_p-SH are the distances from the center of the TX, RX, and SH coils to point p (x_p, y_p, z_p), calculated by Eqs. (1) and (2). The angles between the z axes are expressed as θ_TX, θ_RX, and θ_SH. The magnetic field strength from each coil at point p can be calculated by Eq. (3), where ϑ = sin θ cosϕ cos θ [6].

Fig. 1

Geometry of TX, RX, and SH coils.

Fig. 2 shows the mutual inductance (M) variations of the RX and SH coils from the TX coil due to misalignments. M_TXRX is the M between the TX and RX coils, and M_TXSH is the M between the TX and SH coils. The TX and RX coils have identical radii of 95 mm, and the SH coil radius is 150 mm. The air gap between the TX and RX coils is 75 mm. The displacement of the RX and SH coils ranges from 0 to 40 mm in 10 mm steps on the x axis.

Fig. 2

Mutual variations according to the misalignment of the RX and SH coils: (a) M_TXRX and (b) M_TXSH.

Although the RX and SH coils have identical displacements, the variations of M_TXRX and M_TXSH differ because of the radius difference between the RX and SH coils.

M is determined by geometry, including the radius and distance of each coil. M between two coils is calculated using the Neumann formula according to Eq. (4) [13]. g is a distance between two coils, and M can be expressed in terms of the coupling coefficient (k) and the inductances of two coils determined by Eq. (5).

M between two coils decreases as misalignment occurs in the WPT system. In other words, the operation characteristics of the WPT system change under misalignment conditions due to M variations; therefore, this M variation should be considered to control the active shield system for high SP.

2. Power Transfer Efficiency Analysis

Fig. 3 shows the equivalent circuit of the WPT system, including the independent active shielding system. V_IN and V_SH are the voltage sources of the TX and SH system; S₁–S₈ are the MOSFETs for full-bridge inverters of TX and SH; and I_TX, I_RX, and I_SH are the currents of the TX, RX, and SH coils.

Fig. 3

Equivalent circuit of a WPT system with an active shielding system using an independent power source.

The TX and RX systems comprise inductance L, capacitance C, and resistance R, respectively; R_L is the load resistance. The SH system is composed of inductance and resistance without a resonant capacitor.

Based on Kirchhoff’s voltage law (KVL), the impedance of the circuit can be expressed by Eqs. (6)–(8). The impedance changes according to KVL because the M changes under misalignment conditions; consequently, the voltage and current characteristics can also vary.

Fig. 4 shows the current strengths and PTE variations according to k under identical load power (P_Load). The TX and RX coils have identical 150 mm radii, and the current strength of the TX coil is calculated while changing k from 0.05 to 0.3.

Fig. 4

Variation in the WPT system characteristics according to the coupling coefficient: (a) TX coil current strength and (b) PTE of the system.

Fig. 4(a) shows the variation in I_TX according to the k variation. The more k decreases, the more I_TX increases, meaning that power loss increases in terms of ohm loss I₂R under misalignment conditions. Furthermore, the required I_SH should be increased for high SP because of the increased I_TX, resulting in increased power loss in the SH system.

Fig. 4(b) shows the variations in the PTE of the system according to k variation. The decrease in k results in a decrease in the PTE. Decreasing k due to misalignment reduces the impedance of the circuit and changes the characteristics of the system to low voltage and high current. The high current characteristic has the effect of increasing the power loss at the coil.

Also, when the SH coil is applied to the WPT system, M_TXSH and M_RXSH should be considered. The magnetic field of the SH coil is out of phase with that of the TX and RX coils, which causes a decrease in the effective inductance of the TX and RX coils, as shown by Eq. (9). Consequently, the PTE decreases when applying the SH system. The PTE of the WPT system, including the active shielding system using an independent power source, can be calculated using Eq. (10).

3. Current and Phase Control of the Shielding System

Fig. 5 shows the front view of the WPT system, including the SH coil. To achieve high SP, the current applied to the SH coil should be determined, considering misalignment conditions. However, since the positions and designs of the three coils of TX, RX, and SH differ, the composite magnetic field in space varies depending on the positions, meaning that the shielding current and phase of the shielding coil depend on the target point p.

Fig. 5

Front view of the system under misalignment conditions for target point p.

Fig. 6(a) shows a magnetic vector diagram of the TX, RX, and SH coils in the alignment condition. The magnitude and phase of B_WPT is calculated by Eqs. (11) and (12) [6]. The maximum SP is obtained when the SH coil has an identical magnetic field strength and 180° of phase difference for the B_WPT; however, the magnetic field strengths of the TX and RX coils change under misalignment conditions.

Fig. 6

Phasor diagram of (a) alignment and misalignment conditions at (b) p1, (c) p2, and (d) p3.

Fig. 6(b)–6(d) show the magnetic flux density and phase changes according to the measurement point p under misalignment conditions. B_TX′, B_RX′, and B_WPT′ are the changed magnetic flux densities under misalignment conditions. The B_TX′ defined in Eq. (3) increases according to increased I_TX′, which is the TX coil current under misalignment conditions. I_TX′ increases by decreasing M_TXRX under misalignment conditions, as described in Section II-2. B_RX′ differs significantly depending on p because, although I_RX′ is identical to I_RX, the distance to point p differs. Compared to the alignment condition, B_RX′ increases at p1, is equal at p2, and decreases at p3.

According to Eq. (12), the changes in B_p-TX and B_p-RX cause a change in Φ_p–PWT. As the change occurs from p1 to p3, the distance from the RX coil increases; thus, B_p-RX decreases and B_p-TX becomes dominant. In this case, the φ_p–SH approaches the opposite direction of φ_p–TX as it goes from Fig. 6(b) to 6(d). Therefore, B_SH′ must be controlled according to the target point p and B_WPT′ to achieve high SP.

Assuming that the RX and SH coils are located at a point (a, b, z₁), as shown in Fig. 1, the distance between the TX and SH coils, g′, is calculated using Eq. (13). M_TXRX′ can then be calculated using Eq. (4) by substituting the distance g to g′. Since an identical P_Load is assumed, V_RX′ and I_RX′ are identical under the alignment condition, and I_TX′ can be calculated through M_TXRX according to Eq. (14). Thus, using the calculated I_TX′ and the known I_RX′, the magnetic field strengths B_TX′ and B_RX′ at point p can be calculated using Eq. (3). As a result, the magnitude and phase of the I_SH′ is determined based on the B_SH′ according to Eqs. (11) and (12).

1. Simulation and Experimental Setup

Fig. 7 shows the simulation and experimental model, and Fig. 8 shows the experimental setup. Also, Table 1 shows the electrical parameters of the WPT and SH coils, and P_Load and PTE before and after applying the SH coil. The TX and RX coils had outer and inner radii of 95 mm and 35 mm, respectively; the diameter of the wire was 4 mm. Ferrite plates with widths and lengths of 200 mm × 200 mm and heights of 4 mm were used for the TX and RX coils. The radius of the SH coil r_SH was 150 mm, and the number of turns was set to five. The operating frequency of the WPT system was 85 kHz, and R_L was 10.016 Ω. Also, the input voltage was adjusted to an identical P_Load of about 100 W for all measurements.

Fig. 7

Structures of the WPT system with a shielding system.

Fig. 8

Experimental setup.

Table 1

Specifications of the WPT system under alignment conditions at 85 kHz

Fig. 9 shows the alignment and misalignment conditions considered in the simulations and experiments: alignment, which is the condition in which the RX and SH coils are aligned on the z axis with the TX coil; and misalignment, meaning that the RX and SH coils are misaligned by 40 mm in both the x- and y-axis directions.

Fig. 9

Alignment conditions: (a) alignment and (b) misalignment.

Fig. 10 shows the measurement points (MPs) used to analyze SP. The MPs were set as the center and periphery of the system from MP1 to MP9 at distances of 15 cm above the RX coil.

Fig. 10

EMF measurement points.

The results according to the alignment and misalignment conditions were as follows: as misalignment occurred, I_TX increased. Regardless of the alignment condition, the P_Load was identical, so the I_RX did not change. However, when controlling for the misalignment condition, the I_SH increased, and the Φ_SH shifted close to the opposite direction of the TX, which was closer to −180°.

Table 2 shows the current strengths and phases of the TX, RX, and SH coils under alignment and misalignment conditions. For the misalignment conditions, the current strengths and phases were controlled. The shielding system control set the target point p as the center point of the alignment condition to evenly reduce all high magnetic fields at close ranges around the system.

Table 2

Current strengths and phases of the TX, RX, and SH coils

2. Simulation and Experimental Results

Fig. 11 shows the results of the simulations and experiments for the leakage magnetic field strength under alignment and misalignment conditions at nine different MPs when the SH coil was not applied. The magnetic field leakage increased when misalignment occurred. Under misalignment conditions, the leakage magnetic field strength around the locations where the RX coil was positioned (MPs 4, 5, 7, and 8) increased because the I_TX had increased for transferring identical P_Load against a decrease of M_TXRX.

Fig. 11

EMF simulation and experimental results for different MPs under alignment and misalignment conditions of a system without a SH coil.

Fig. 12(a) shows the simulation and experimental results for EMFs for the SH system under alignment conditions. The EMFs at all MPs decreased when the SH system was applied. In particular, since point p was selected as the center point for the alignment condition, the highest EMF reduction occurred at MP5, as shown in Fig. 12(a). The SP was calculated according to Eq. (15), and the average SP was the sum of the SPs from MP1–MP9 divided by 9. B_woSH and B_SH were the leakage magnetic field strengths before and after the application of the SH coil. The average SP under the alignment condition was 67.16%.

Fig. 12

EMF simulation and experimental results, with and without the SH coil, at different MPs under (a) alignment and (b) misalignment conditions.

Fig. 12(b) shows the simulation and experimental results for EMFs according to the SH system under misalignment conditions. Although EMF leakage decreased under misalignment conditions, the average SP was 49.22%—inferior to the alignment condition—because the current amplitude and phase of the SH coil were determined based on the alignment condition.

Fig. 13 shows the SP variations according to the active shielding control when misalignment occurred. The SP was improved by adding active shielding control under misalignment conditions. We confirmed that this improvement in SP occurred in all MPs, as well as at the target shielding point. The average SP of the controlled SH coil was 61.74%.

Fig. 13

EMF simulation and experimental results at different MPs under misalignment conditions: without SH coil, with SH coil, and with controlled SH coil.

Consequently, the average SP under misalignment conditions was increased from 49.22% to 61.74% by applying the proposed control method. This meant that 24.6% of the EMF leakage was additionally reduced by applying active shielding control for misalignment conditions.

Table 3 shows the PTE variations under misalignment conditions. P_in is the sum of the supplied power for TX and SH. The power transfer conditions for all measurements were 100 W transmission to R_L. As shown in Table 3, the proposed active shielding control method produced no additional PTE degradation, meaning that the SP could be improved without PTE degradation under misalignment conditions.

Table 3

PTE under misalignment conditions