A Hybrid Inductive Power Transfer System with High Misalignment Tolerance Using Double-DD Quadrature Pads

Abstract

Inductive power transfer (IPT) has been widely adopted as an efficient and convenient charging manner for both static and in-motion EVs. In this paper, a new hybrid topology is presented to improve the coupling tolerance under pad misalignment. The double inductor–capacitor–capacitor (LCC-LCC) network and series hybrid network combining the LCC-LCC topology and series-series (SS) topology are connected in parallel to provide better tolerance against self- and mutual inductance changes, particularly with a large Z-axis transmission distance. A double-DD quadrature pad (DD2Q) consists of a Q pad, and double orthogonal DD pads are analyzed in detail, which are employed to decouple the cross-mutual inductance. Moreover, a parametric design method based on the misalignment characteristics of the DD2Q pads is also proposed to maintain relatively constant power output. A 650-W hybrid topology with a fixed operating frequency of 85 kHz was built to verify the system’s feasibility. The size of the DD2Q pads was 280 mm × 280 mm, and the air gap was 100 mm. The results clearly show that the proposed hybrid topology can achieve a fluctuation within 5% in the output current with load varying from 100% full load to 25% light load conditions when the Z-axis transmission distance varies from 80 mm to 150 mm, and the maximum efficiency can reach 91% when the Z-axis transmission distance is 80 mm.

1. Introduction

An IPT system can deliver power over relatively large air gaps via magnetic couplings, including a high-frequency inverter, compensation topology, coupling coils, and charging circuits. An IPT system has the excellent advantages of safety with galvanic isolation [1], high reliability [2], and being environmentally friendly [3] compared with traditional conductive charging technology. Nowadays, the IPT system has been widely employed in powering electronic applications, such as low-power portable electronic devices, implantable medical instruments [4], electric vehicle (EV) charging [5], and autonomous underwater power supplies [6]. Much research has been conducted by numerous organizations, such as the Massachusetts Institute of Technology (MIT), Auckland University, Korea Advanced Institute of Science and Technology (KAIST), and Oak Ridge National Laboratory (ORNL).

The misalignments between the primary and secondary magnetic couplers can cause the variation of self-inductances and mutual inductances, which may in practice lead to a reduction in power transfer, instability of the system, and increased power losses. Aside from that, the equivalent load varies during the battery charging process [7]. Therefore, the goal of this paper is to design an IPT system with high misalignment tolerance and load-independent current output.

In order to improve the misalignment tolerance of the IPT system, some control schemes, such as increasing DC-DC conversion [8,9], phase shift control, and variable frequency control [10,11,12,13,14,15], have been proposed to modulate the output current or voltage. The additional DC-DC converter combines with MOSFET, the filter inductor and capacitor, and the driver circuit, which results in extra volume and cost and decreasing the system efficiency. The phase shift control and variable frequency control usually need a wireless communication device to collect the voltage and current signals of the secondary side to realize closed-loop control. However, wireless communications can be interrupted in highly magnetic conditions, which may result in instability of the IPT system. Moreover, phase shift control may not achieve ZVS under a wide range of loads, which increases the switching loss, and variable frequency control may result in bifurcation phenomena and decreasing the output power. Hence, in order to solve the above-mentioned defects, considerable efforts focus on proper magnetic coupler design [16,17,18,19,20,21], such as bipolar and double-D pads, tripolar pads, quadruple-D pads, and unsymmetrical pads, which can offer a relatively uniform magnetic distribution. For example, the quadruple-D pads are proposed in [16] to be tolerant to lateral misalignment, which consists double quadrature coils at the primary and secondary sides. Tripolar pads are proposed in [18] to improve the omnidirectional misalignment tolerance. However, these tripolar pads need to consist of three inverters at the primary side. That aside, unsymmetrical pads are presented in [19] to minimize the cost of copper and the size of the coil structure, adopting the method of concentrated magnetic flux to achieve misalignment tolerance. As an alternative method, hybrid topologies combining two different topologies with opposite output trends are implemented to maintain a stable output under misalignment conditions. A hybrid topology combines with LCC-LCC and SS topologies [20,21] to realize relatively constant power output within 50% Y-axis misalignment. In [22], LCC-S and S-LCC topologies are employed to tolerate 50% X-axis pad misalignment, where the primary sides are connected in parallel and the secondary sides are connected in series. Although the previous hybrid topologies are able to tolerate a pad’s special misalignment, as shown in Figure 1, the working range of misalignment tolerance is still narrow. Therefore, better misalignment tolerance, particularly with Z-axis tolerance for different EV class heights with a wider coupling variation range, is desired, which is identified as the research gap for this research.

This paper presents a new hybrid topology using DD2Q pads to achieve stable output power at a large vertical misalignment, and the main contributions of this article are summarized as follows:

(1)

This article proposes a new hybrid IPT system with high misalignment tolerance. The hybrid system consists of a series hybrid topology and LCC-LCC topology. The series hybrid topology and LCC-LCC topology are connected in parallel at the primary side and secondary side. The proposed approach can improve the output power compared with the single compensation topology and reduce the switch voltage stress. Moreover, the proposed hybrid IPT system can achieve a near load-independent current output.

(2)

DD2Q pads are used in the hybrid IPT system, which consist of a single-Q coil and double-DD coils. The size of the DD2Q pads is 280 mm × 280 mm, and the air gap is 100 mm. The double-DD coils are orthogonally placed, and the Q coil is placed in a centrally symmetric position, which can realize decoupling of the DD and Q coils on the same side of the primary and secondary sides. Therefore, the independent current output of the series hybrid topology and LCC-LCC topology can be achieved.

(3)

A parameter optimization method based on DD2Q mutual inductances is proposed to realize a relatively constant output current with high misalignment tolerance, which is able to simplify the control complexity. By using the monotonic decreasing characteristic of the series hybrid topology and monotonic increasing characteristic of the LCC-LCC topology to realize the complementary output of the two topologies, the output current is ensured to be relatively stable.

Specifically, the mathematical model of the proposed hybrid topology is systematically analyzed in Section 2. In Section 3, the mutual inductance characteristics of the DD2Q pads and the parameter optimization are presented. The experimental results are provided in Section 4 to verify the theoretical analysis. Finally, the conclusion is drawn in Section 5.

2. Theoretical Analysis

The circuit of the proposed hybrid IPT system is shown in Figure 2, which consists of a series hybrid topology and LCC-LCC topology. The high-frequency inverter combines with four MOSFETs (Q₁–Q₄). Inductor L₀ and capacitors C₀, C₁, and C₃ (L₇, C₂, C₄, and C₇) constitute the series hybrid topology, while inductor L₈ and capacitors C₅ and C₈ (L₉, C₆, and C₉) constitute the LCC-LCC compensation topology. The primary and secondary sides of the series hybrid topology and LCC-LCC topology are both connected in parallel, together forming the proposed hybrid topology. The main magnetic coupling between the coils is M₁₂, M₃₄, and M₅₆. The full-bridge rectifier comprises four diodes (D₁–D₄). Because the inductor L₀(L₇) and capacitor C₃(C₄) are connected in series in the proposed hybrid topology, and therefore they can be treated as a passive component, such as inductor L_e or capacitor C_e, which can be expressed as [16]

$$\{\begin{array}{l}j\omega L_{\mathrm{e}}=j\omega L_0+1/j\omega C_3, \mathrm{if} \omega L_0-1/\omega C_3 >0\\ 1/j\omega C_{\mathrm{e}}=j\omega L_0+1/j\omega C_3 \mathrm{if} \omega L_0-1/\omega C_3 <0\end{array}$$

(1)

The full-bridge rectifier is adopted in the secondary side, and thus the input voltage U_AB, the input current I_AB, and the equivalent resistance R_AB of the rectifier can be expressed as [8].

$$\{\begin{array}{l}{U}_{\mathrm{AB}}=\frac{2\sqrt{2}}{{\pi }^{}}{U}_{\mathrm{L}}\\ I_{\mathrm{AB}}=\frac{\pi \sqrt{2}}{4}{I}_{\mathrm{L}}\\ R_{\mathrm{AB}}=\frac{8}{{\pi }^2}{R}_{\mathrm{L}}\end{array}$$

(2)

2.1. Analysis of the Series Hybrid Topology

The circuit of the series hybrid topology is shown in Figure 3, where U_out is a high-frequency inverter output voltage. In order to minimize the VA rating of the power inverter, the compensation networks are tuned to the same resonant angular frequency ω. Thus, the resonant parameters should satisfy the following equations:

$$\{\begin{array}{l}{\omega }^2{L}_0{C}_0={\omega }^2{L}_1\frac{C_0{C}_1}{C_0+C_1}=1\\ {\omega }^2{L}_7{C}_7={\omega }^2{L}_2\frac{C_2{C}_7}{C_2+C_7}=1\\ {\omega }^2{L}_3{C}_3={\omega }^2{L}_4{C}_4=1\end{array}.$$

(3)

According to Kirchhoff’s voltage law, we can find

$$\left[\begin{array}{cccc}{Z}_{00}& Z_{01}& Z_{02}& Z_{03}\\ Z_{10}& Z_{11}& Z_{12}& Z_{13}\\ Z_{20}& Z_{21}& Z_{22}& Z_{23}\\ Z_{30}& Z_{31}& Z_{32}& Z_{33}\end{array}\right]\left[\begin{array}{c}{\dot{I}}_0\\ {\dot{I}}_1\\ {\dot{I}}_2\\ {\dot{I}}_3\end{array}\right]=\left[\begin{array}{c}{\dot{U}}_{\mathrm{out}}\\ 0\\ 0\\ 0\end{array}\right]$$

(4)

where $Z_{20}=j\omega M_{23}$$Z_{00}=j\omega L_0+{\left(j\omega C_0\right)}^{-1}+j\omega L_3+{\left(j\omega C_3\right)}^{-1}$, $Z_{01}=-{\left(j\omega C_0\right)}^{-1}+j\omega M_{13}$, $Z_{02}=-j\omega M_{23}$, $Z_{03}=j\omega M_{34}$, $Z_{10}=j\omega M_{13}-{\left(j\omega C_0\right)}^{-1}$, $Z_{11}=j\omega L_1+{\left(j\omega C_0\right)}^{-1}+{\left(j\omega C_1\right)}^{-1}$, $Z_{12}=-j\omega M_{12}$, $Z_{13}=j\omega M_{14}$, $Z_{21}=j\omega M_{12}$, $Z_{22}=j\omega L_2+{\left(j\omega C_2\right)}^{-1}+{\left(j\omega C_7\right)}^{-1}$, $Z_{23}={\left(j\omega C_7\right)}^{-1}+j\omega M_{24}$, $Z_{30}=j\omega M_{34}$, $Z_{31}=j\omega M_{14}$, $Z_{32}=-{\left(j\omega C_7\right)}^{-1}-j\omega M_{24}$, $Z_{33}=j\omega L_7+{\left(j\omega C_7\right)}^{-1}+j\omega L_4+{\left(j\omega C_4\right)}^{-1}+R_{\mathrm{AB}}$.

By designing proper coupling structures, which will be discussed in Section 3, the effects of the cross couplings (M₁₃, M₁₄, M₂₃, and M₂₄) on the output can be ignored. Hence, by solving Equation (4), the currents are expressed by

$$\{\begin{array}{l}{\dot{I}}_0=\frac{{\dot{U}}_{\mathrm{out}}}{{\omega }^2}\frac{M_{12}^2{R}_{\mathrm{AB}}}{{(L_0{L}_7+M_{12}{M}_{34})}^2}\\ {\dot{I}}_3=\frac{{\dot{U}}_{\mathrm{out}}}{j\omega }\frac{M_{12}}{L_0{L}_7+M_{12}{M}_{34}}\end{array}$$

(5)

According to Equation (5), the input equivalent impedance Z_in-series of the series hybrid system can be deduced to be

$$Z_{\text{in-series}}=\frac{{\omega }^2{\left(L_0{L}_7+M_{12}{M}_{34}\right)}^2}{M_{12}{}^2{R}_{\mathrm{AB}}}$$

(6)

According to Equations (5) and (6), the series hybrid topology can achieve zero phase angle (ZPA). Aside from that, the output current I₃ is related to the inverter output voltage U_out, resonant angular frequency ω, inductors L₀ and L₇, and mutual inductances M₁₂ and M₃₄. In order to achieve symmetry between the primary and secondary circuits, inductors L₀ and L₇ are usually assumed to be the same. The main mutual inductances M₁₂ and M₃₄ are assumed to have the linear trend with the air gap, which will be discussed in Section 3. Therefore, the output current of the series hybrid topology is shown in Figure 4, where all the related parameter values will be listed in

Table 1. Parameter values of the experimental platform.

Parameter	Value	Parameter	Value
f	85 kHz	C0	232.2 nF
L1	15.1 uH	C1	25.8 nF
L2	150.1 uH	C2	25.7 nF
L3	149.8 uH	C5	27.8 nF
L4	156.1 uH	C6	27.7 nF
L5	156.0 uH	C7	232.2 nF
L6	160.1 uH	C8	110.2 nF
L8	32.2 uH	C9	110.3 nF
L9	32.1 uH	E	70 V
Ce	25.1 nF

. It is obvious that the output current I₃ shows a downward concave parabolic trend with the decrease in the mutual inductance. Although the series hybrid topology has a certain misalignment tolerance, the operating range is still narrow.

2.2. Analysis of the LCC-LCC Topology

Figure 5 shows the LCC-LCC equivalent circuit, where U_out is also a high-frequency inverter output voltage. The compensation topology is tuned to the same resonant angular frequency ω. Therefore, the resonant tanks should satisfy the following equations:

$$\{\begin{array}{l}{\omega }^2{L}_8{C}_8={\omega }^2{L}_5\frac{C_5{C}_8}{C_5+C_8}=1\\ {\omega }^2{L}_9{C}_9={\omega }^2{L}_6\frac{C_6{C}_9}{C_6+C_9}=1\end{array}$$

(7)

According to Kirchhoff’s voltage law, we find

$$\left[\begin{array}{llll}{Z}_{00}\hfill & Z_{01}\hfill & 0\hfill & 0\hfill \\ Z_{10}\hfill & Z_{11}\hfill & Z_{12}\hfill & 0\hfill \\ 0\hfill & Z_{21}\hfill & Z_{22}\hfill & Z_{23}\hfill \\ 0\hfill & 0\hfill & Z_{32}\hfill & Z_{33}\hfill \end{array}\right]\left[\begin{array}{c}{\dot{I}}_4\\ {\dot{I}}_5\\ {\dot{I}}_6\\ {\dot{I}}_7\end{array}\right]=\left[\begin{array}{c}{\dot{U}}_{\mathrm{out}}\\ 0\\ 0\\ 0\end{array}\right]$$

(8)

where $Z_{00}=j\omega L_8+{\left(j\omega C_8\right)}^{-1}$, $Z_{01}=Z_{10}=-{\left(j\omega C_8\right)}^{-1}$, $Z_{11}={\left(j\omega C_8\right)}^{-1}+{\left(j\omega C_5\right)}^{-1}+j\omega L_5$, $Z_{12}=Z_{21}=-j\omega M_{56}$, $Z_{22}=j\omega L_6+{\left(j\omega C_6\right)}^{-1}+{\left(j\omega C_9\right)}^{-1}$, $Z_{23}=Z_{32}=-{\left(j\omega C_9\right)}^{-1}$, $Z_{33}=j\omega L_9+{\left(j\omega C_9\right)}^{-1}+R_{\mathrm{AB}}$.

By solving Equation (8), the currents are yielded as

$$\{\begin{array}{l}{\dot{I}}_4\text{=}\frac{M_{56}^2{\dot{U}}_{\text{out}}{R}_{\text{AB}}}{{\omega }^2{L}_8^2{L}_9^2}\\ {\dot{I}}_7\text{=}\frac{M_{56}{\dot{U}}_{\text{out}}}{j\omega L_8{L}_9}\end{array}$$

(9)

According to Equation (9), the output voltage of the inverter is also in the same phase with the current, which aids in maintaining ZVS across the entire operating region and improving the output efficiency of the system. The output current I₇ is related to the inverter output voltage U_out, resonant angular frequency ω, inductors L₈ and L₉, and mutual inductance M₅₆. In this paper, inductors L₈ and L₉ are also assumed to be the same. Therefore, the output current I₇ is shown in Figure 6, where all the related parameter values will be listed in Table 1. It is clear that the output current I₇ shows a monotonous downward trend with the decrease in the mutual inductance.

Therefore, the series hybrid compensation network and the LCC-LCC compensation network can be connected in parallel at the transmitter and the receiver, which is conductive to achieving a relatively constant power output with large misalignment.

2.3. Analysis of the Proposed Hybrid Topology

According to Equations (5) and (9), the total output current of the inverter is expressed by

$${\dot{I}}_{\mathrm{out}}={\dot{I}}_0+{\dot{I}}_4=\frac{{\dot{U}}_{\mathrm{out}}{R}_{\mathrm{AB}}}{{\omega }^2}(\frac{M_{12}^2}{{(L_0{L}_7+M_{12}{M}_{34})}^2}+\frac{M_{56}^2}{{(L_8{L}_9)}^2})$$

(10)

Then, the total input equivalent impedance of the proposed hybrid topology can be given by

$$Z_{\mathrm{in}}=\frac{{\dot{U}}_{\mathrm{out}}}{{\dot{I}}_{\mathrm{out}}}=\frac{{\omega }^2}{R_{\mathrm{AB}}}\frac{1}{\frac{M_{12}^2}{{(L_0{L}_7+M_{12}{M}_{34})}^2}+\frac{M_{56}^2}{{(L_8{L}_9)}^2}}$$

(11)

From Equations (10) and (11), the total input impedance of the proposed hybrid topology is purely resistant, which aids to improving the overall transmission efficiency.

According to the characteristics of the parallel circuit, the total output current of the proposed hybrid topology can be expressed as

$${\dot{I}}_{\mathrm{AB}}={\dot{I}}_3+{\dot{I}}_7=\frac{{\dot{U}}_{\mathrm{out}}}{j\omega }(\frac{M_{12}}{L_0{L}_7+M_{12}{M}_{34}}+\frac{M_{56}}{L_8{L}_9})$$

(12)

From Equation (12), the system can realize a load-independent current output. When misalignment occurs, the main mutual inductance M₁₂, M₃₄, and M₅₆ will drop at the same time. By designing appropriate compensating inductors L₀, L₇, L₈, and L₉, the constant current output can be realized in a certain range of misalignment.

3. Parametric Design of the Proposed Hybrid Topology

3.1. Misalignment Analysis of DD2Q Pads

As analyzed in Section 2, the expected coupling pad should have the following characteristics:

(1)

The expected coupling pad should consist of three transmitters and three receivers.

(2)

The cross mutual inductances are designed to be zero or small enough when misalignment occurs, and thus the proposed hybrid topology can realize a load-independent output.

Recently, the DDQ and DD coils have had anti-misalignment characteristics, which can realize decoupling in the X- and Z-axis to eliminate the influence of cross-coupling. However, these two coupling coil structures can only be applied to four-coil structures. Based on the DD coil and DDQ coil, the DD2Q coil structure is proposed in this paper, as shown in Figure 7. The DD2Q coils consist of a single-Q coil and double-DD coils, and there are three coils at both the transmitter and receiver sides. The size of the Q coil is 280 mm × 280 mm, the size of the DD coil is 280 mm × 280 mm, and the Z-axis transmission distance is 100 mm.

The misalignment between the primary and pick-up pads is unavoidable in the charging system, including the X-axis, Y-axis, Z-axis, and XY-axis. Therefore, Figure 8 shows the measured mutual inductances of the DD2Q pads with misalignment along the X-, Y-, Z-, and XY-axes separately.

Obviously, the main mutual inductances M₁₂, M₃₄, and M₅₆ and the cross-coupling mutual inductances vary significantly when X-axis, Y-axis, and XY-axis diagonal misalignments occur in Figure 8a,b,d. The reason for this is that non-orthogonal magnetic flux is coupled in the X-axis, Y-axis and XY-axis diagonal misalignments. The main mutual inductances M₁₂, M₃₄, and M₅₆ show a linear decreasing trend with the Z-axis transmission distance, and the cross-couplings are too small to be ignored, as shown in Figure 8c. Moreover, the main mutual inductances (M₃₄ and M₅₆) of the double orthogonal DD pads have the same change trend at the Z-axis transmission distance. Therefore, the proposed hybrid topology cannot provide a constant current output in the X-axis and Y-axis misalignments, as analyzed in Section 2. In many applications, such as cars, SUVs, and trucks, the X-axis and Y-axis misalignments can be adjusted by auxiliary devices for cars, such as a reversing camera and reversing radar, but the vertical air gap is hard to adjust. Hence, the DD2Q coils are fit for the proposed hybrid topology with a relatively constant current output, where the vertical direction changes dramatically.

3.2. Parametric Design Method

The design of compensation parameters is of great importance to realize a relatively constant output within the maximal misalignment. A parametric design method based on inductances L₀, L₇, L₈, and L₉ is presented to maintain the output current in a certain range of misalignment.

From Figure 8c, the relationship between M₁₂, M₃₄, and M₅₆ can be expressed by

$$\{\begin{array}{l}{M}_{56}=M_{34}\\ M_{34}=a{M}_{12}+b\end{array}$$

(13)

where a and b are coefficients and the calculated parameters a and b are 0.86 and −6.75 × 10⁻⁶, respectively, when the secondary pads move between 80 mm and 150 mm along the Z-axis transmission distance.

Thus, the total output current of the proposed hybrid topology is rewritten as

$$I_{\mathrm{AB}}=\frac{U_{\mathrm{out}}{M}_{12}}{\omega (L_0{L}_7+M_{12}(0.86M_{12}-6.75\times {10}^{-6}))}+\frac{U_{\mathrm{out}}(0.86M_{12}-6.75\times {10}^{-6})}{\omega L_8{L}_9}$$

(14)

According to Equation (14), we can obtain the current I_L of the load R_AB:

$$I_{\mathrm{L}}=\frac{4}{\pi \sqrt{2}}\frac{U_{\mathrm{out}}{M}_{12}}{\omega (L_0{L}_7+M_{12}(0.86M_{12}-6.75\times {10}^{-6}))}+\frac{4}{\pi \sqrt{2}}\frac{U_{\mathrm{out}}(0.86M_{12}-6.75\times {10}^{-6})}{\omega L_8{L}_9}$$

(15)

To simplify the complexity of multi-objective parameter design, inductances L₀ and L₇ are assumed to be equal, and inductance L₈ is also assumed to be equal with inductance L₉. Figure 8 shows that the output current I_L varies with different inductors L₀ and L₈. It can be found that the output current of the series hybrid topology shows a downward concave parabolic trend, while the output current of the LCC-LCC topology shows a monotonous downward trend with the decrease in M₁₂. Therefore, we used the monotonic decreasing characteristic of the LCC-S topology and monotonic increasing characteristic of the LCC-LCC topology to realize the complementary output of the two topologies and ensured the output current was relatively stable. In this article, an acceptable output current fluctuation ratio was limited within 5%, and the rated output current of the load R_AB was set to be 6 A. It is clear that the dashed line region in Figure 9 can satisfy the set requirement within an 80–150-mm Z-axis transmission distance. Thus, the values of L₀ and L₇ were both designed to be 15 uH, while L₈ and L₉ were both designed to be 32 uH. Finally, the resonant parameter value of the proposed hybrid topology could be obtained from Equations (1), (3), and (7).

4. Experimental Verifications

In order to verify the analysis of the proposed method, a 650-W hybrid IPT system was designed and implemented as illustrated Figure 10. The detailed parameters of the system are listed in Table 1. The inverter of the system operated with a fixed frequency and duty cycle control to demonstrate the performance of a constant current output with high misalignment tolerance.

The output current of the load is drawn in Figure 11, varying with a full load, half load, and quarter load under different Z-axis transmission distances. Within a 80–150-mm Z-axis transmission distance, the output current of the load was between 5.7 A and 6.3 A, which indicates that the output current variation was within 5% when the system worked in the full load and half load conditions. Aside from that, the output current of 4 Ω under the condition of a transmission distance between 110 mm and 130 mm was larger than 6.3 A, which was slightly over the limitation of 5%. Moreover, the output current climbed to the maximum at a 120-mm Z-axis transmission distance. This clearly demonstrates that the proposed hybrid topology with the parameter optimization process had high misalignment tolerance.

The experimental waveforms of U_out, I_out, U_L, and I_L with R_L = 17 Ω, 8.5 Ω, and 4 Ω are shown in Figure 12, Figure 13 and Figure 14 when the Z-axis transmission distance was 80 mm, 120 mm, and 150 mm, respectively. U_out and I_out are the inverter output voltage and current when the input DC power is 70 V, respectively.

Figure 12 illustrates the system operating at full load with R_L = 17 Ω. It is clear that ZVS could be achieved between an 80-mm and 150-mm Z-axis transmission distance, which could reduce the switching loss and improve the efficiency. Moreover, the output current was 5.84 A, 6.21 A, and 6.16 A, and the load output voltage was 99.30 V, 105.61 V, and 104.75 V, respectively. Hence, the fluctuation of the load current was within 5% when the variation of the Z-axis transmission distance was within 70%.

Figure 13 shows the system works at half load with R_L = 8.5 Ω. The load output current was 5.92 A, 6.25 A, and 6.18 A, and the load output voltage was 50.30 V, 53.38 V, and 52.35 V, which illustrated the current fluctuation to be 1.33%, 4.17%, and 3.0%, respectively, meeting the design requirements. That aside, the output voltage and current of the inverter were almost in phase, which indicates that soft switching could be achieved and decrease the switching losses.

Figure 14 shows the system operating in a light load conditions when the load was 25% against the fill load with R_L = 4 Ω. The load output current was 5.96 A, 6.42 A, and 6.23 A, and the load output voltage was 23.84 V, 25.68 V, and 24.92 V, which illustrated the current fluctuation to be 0.66%, 7%, and 3.8%, respectively. It is clear that the output current may slightly exceed the limitation of 5% under light load conditions.

Figure 15 clearly illustrates that there is an opposite trend of the output current I₃ of series hybrid topology and the output current I₇ of the LCC-LCC topology when the Z-axis transmission distance varied, and the RMS values of the output currents I₃ and I₇ had a slight deviation from the theoretical analysis in Section 2 due to the influence of parasitic resistance and parameter drift on the resonant parameters. Aside from that, the total output current I_AB of the proposed hybrid topology could almost remain stable. Moreover, there was a small phase angle between the output current of the series hybrid topology and LCC-LCC topology because the resonant parameters in the series hybrid topology and LCC-LCC topology operated in a weak inductive state.

Figure 16 shows the output power and efficiency along the Z-axis transmission distance. Figure 16a illustrates that the output power was relatively gentle and consistent with the variation curve of the load output current. The maximum output power was 650 W when the Z-axis transmission distance was 120 mm at full load with R_L = 17 Ω. Figure 16b shows that the efficiency varied with the load and misalignment, and the maximum efficiency could reach 91% with a full load at an 80-mm Z-axis transmission distance.

Some comparisons with traditional control schemes and existing hybrid topologies are listed in

Table 2. Comparison of traditional control schemes and existing hybrid topologies.

	[9]	[11]	[18]	[20]	[21]	[22]	This Work
Control	Additional DC-DC	Phase shift control	No	No	No	No	No
Number of inductors	1	0	2	2	0	2	2
Number of capacitors	4	2	6	6	6	6	10
Coupling coils	DD + BP	Q	QDQP	DD	DD	DDQ	DD2Q
Number of coils	3	2	4	4	4	4	6
Cost	High	Low	High	High	High	High	High
Size of coupling pad X * Y * Z (mm)	738 * 391 * 200	360 * 360 * 150	400 * 400 * 150	391 * 738 * 160	775 * 391 * 160	400 * 400 * 150	280 * 280 * 100
Misalignment tolerance (mm)	X:200 (27.5%)	X:140 (38.8%) Z:50 (33.3%)	X:150 (37.5%) Y:150 (37.5%) Z:55(36.6%)	X:160 (40.9%)	Y:160 (40.9%)	X:200 (50%)	Z:70 (70%)
Output characteristic	Constant voltage	Constant voltage	Constant voltage	Constant current	Constant current	Constant voltage	Constant current
Output fluctuation	\	\	5%	\	5%	5%	5%
Peak efficiency	\	90%	93.6%	91%	94%	93%	91%
Wireless communication	No	Yes	No	No	No	No	No

, which are made in terms of control, number of inductors and capacitors, coupling pads, misalignment tolerance, cost, output characteristic, etc. Compared with the traditional control schemes in [9,11], the proposed IPT system can realize a constant current output and misalignment tolerance without additional DC-DC converters and phase shift control, which can simplify the complicated controls. The topologies in [18,21,22] are named the “series hybrid topology”, while the topologies in [20] are named the “parallel hybrid topology”. These mentioned hybrid topologies all use four coils to transfer power. Aside from that, the number of inductors, capacitors and coupling pads and the cost of the hybrid topologies are higher than the traditional topologies with closed-loop controls. Moreover, the proposed hybrid topology has a wider misalignment tolerance compared with the four-coil hybrid topologies in [18] and [20,21,22], even though this topology has slightly more components than the other topologies. Thus, the proposed hybrid topology is superior to the traditional control schemes and other hybrid topologies in terms of misalignment tolerance.

5. Conclusions

A hybrid wireless charging system using DD2Q pads has been presented to improve the misalignment tolerance. The new proposed system, combined with the series hybrid topology and LCC-LCC topology, was studied based on the full mathematical model in the context, where the DD2Q pads consisted of a single-Q coil and orthogonal DD coils. The new pad geometry is able to decouple the cross-mutual inductances so as to realize the independent output of the two topologies. Moreover, a parameter optimization design method on the basis of the characteristics of the DD2Q pads is presented to maintain a stable output current and provide high misalignment tolerance in the Z-axis direction. A 650-W hybrid IPT system has been designed and implemented to verify the analysis of the proposed method. The experimental results validate that the proposed hybrid topology can maintain a relatively constant output current at 6 A when the Z-axis misalignment varies from −20 to +50 mm, and the output current fluctuation is within 5% when the load varies from 100% full load to 25% light load. In comparison with the conventional hybrid topology, the new proposed system showed a significant improvement in Z-axis misalignment tolerance, even though this topology has slightly more components. Moreover, the maximum efficiency can reach 91% when the Z-axis transmission distance is 80 mm.

In future research, a thorough economic analysis of the proposed method will be adopted to minimize the system cost, which consists of the number of inductors, capacitors, and coupling coils. That aside, the coupling coil structure should be improved to have better X-, Y-, and Z- misalignment tolerance.