A Compact and Coupling-Smooth Magnetic Coupler Design for AGV Wireless Charging Application

A compact magnetic coupler of inductive power transfer (IPT) system for automated guided vehicles (AGVs) is proposed in this paper, which consists of a double-D (DD) transmitter (Tx) and a compact dual-coil receiver (Rx). By overlapping between one coupling peak point and another coupling null point of two Rx coils, the Rx of the magnetic coupler achieves relatively small output voltage fluctuations, as well as minimizes its size. In addition, to eliminate cross-coupling of the dual-coil Rx, a mutual decoupling device composed of two lumped inductors is adopted, which possesses the same mutual inductance as the dual-coil Rx. Finally, based on the proposed magnetic coupler and its unique way of decoupling, a 3kW IPT system is constructed with 180mm<inline-formula> <tex-math notation="LaTeX">$\times 390$ </tex-math></inline-formula>mm Tx, 150mm<inline-formula> <tex-math notation="LaTeX">$\times 210$ </tex-math></inline-formula>mm Rx, 40mm air gap magnetic coupler, and inductor/capacitor/capacitor-series (LCC-S) based decoupling compensation network. The experimental results show that output voltage varies in proportion to the mutual inductance of Tx and Rx. The measured efficiency is 89.5% to 94.5% under the voltage range of 155V to 220V during the 90mm misalignment.


I. INTRODUCTION
Recently, inductive power transfer (IPT) technology has attracted substantial attention in the scientific and industrial communities. With its inherent advantages, such as safety, flexibility, convenience and competence in the wet environment [1], [2], IPT technology is widely employed in electric vehicles (EVs) [3], medical devices [4], consumer electronics [5], and underwater power supplies [6]. As a special EV, automated guided vehicle (AGV) is productive and flexible, can run 24/7, and have become an essential technology in the modern logistics and warehousing industry [7], [8]. To achieve a higher degree of automation and avoid electrical sparks caused by frequently manual plug-in/out actions, IPT-based wireless charging technology is inevitably adopted, instead of plug-in charging.
The associate editor coordinating the review of this manuscript and approving it for publication was Chi-Seng Lam . An IPT-based AGV wireless charging system is illustrated in Fig.1. The magnetic coupler composed of a transmitter (Tx) embedded under the ground, and a receiver (Rx) installed in the chassis of AGV, plays a crucial role in the wireless power transfer. Because of working indoors with relatively smooth road conditions, the chassis of AGV is usually several centimeters high [9]. However, the space of AGV's chassis is relatively narrow, which presents a challenge to magnetic coupler design [10], [11]. Nowadays, to ensure stable wireless power transmission, the study on the magnetic coupler with more competitive anti-misalignment ability and minimized pad size is still a challenge.
To obtain the most appropriate magnetic coupler, various coil structures have been considered for AGV IPT application. And a scheme with the circular Tx and Rx is proposed in [11]. By optimal selection of coil turns, the maximum coil efficiency achieves 98.9% at 40mm air gap for 2.5kW power delivery. However, the coupling coefficient (k) of the magnetic coupler in [11] has an 8% reduction in 20mm misalignment distance, which raises the rigorous positioning accuracy requirement to AGV. Compared to the circular magnetic coupler, k of square coils of the same size has a stable performance [12]. Aiming at higher efficiency and better anti-misalignment ability, Choi et al. [13] propose a square coil with aluminum-plate-integrated structure. However, the output power decreases approximately by 60% as the lateral misalignment changes from 0mm to 50mm at a 50mm air gap.
The above-mentioned circular and square geometries belong to non-polarized couplers [14]. In practice, the fundamental flux path height of these pads is roughly proportional to one-quarter of the pad diameter [15]. And the misalignment range must be within one-third of the half-side or radius of the coils, beyond which the mutual inductance will decrease rapidly [12]. To improve both anti-misalignment ability and power transmission distance which are limited by miniaturized coil size, multi-coil polarized couplers like double-D (DD) pad [15], bipolar (BP) pad [16], and double-D quadrature (DDQ) pad [14] have been proposed. [15] presents a DD pad, whose fundamental flux path height is approximately half the length of the pad, and able to provide a higher k for the magnetic coupler. Moreover, the effective working area of a DD pad is five times greater than that of a circular pad with a similar size and cost. However, coupling null still exists when the lateral misalignment reaches 34% of the pad length, which leads the system sensitive to misalignment. In [14], a magnetic coupler with DD pad Tx and DDQ pad Rx is developed to avoid the coupling null point and expand the anti-misalignment distance. However, the quadrature (Q) pad uses more copper which consequently increases the cost and energy losses.
To achieve a greater tolerance against lateral misalignment and higher efficiency, the BP pad is presented for AGV application in [16]. Composed of two identical and partially overlapping rectangle coils, the BP pad can achieve mutual decoupling by adjusting the overlapping area of two Rx coils. And voltage superposition is realized via independent Rx coils in series. Although coupling null point could be avoided by the superposition of Rx coils, the overlapping area between two Rx coils depends on the decoupling requirement, which reduces design degrees of freedom, and cannot achieve the optimal output power design. Actually, this magnetic coupler presents nearly 50% output power ripples under 100mm lateral misalignment in the absence of a followed boost converter.
Nevertheless, it is indispensable for a BP pad to realize decoupling, even though the structure design might be limited. And the existence of undesirable cross-coupling results in detuning the resonant circuits that significantly reduces the power transfer capability and efficiency [17]. To make the BP pad structure achieve a more compact size for Rx and smoother output power under misalignment, the traditional mutual decoupling scheme of adjusting coils overlapping may be abandoned to obtain greater design freedom.
At present, except for the method of positioning the coils to nullify the overall mutual flux generated by neighboring Rx coil such as BP pad or DDQ pad, three predominant methods are used for reducing cross-coupling or completely decoupling between the Rx coils. And these decoupling methods include: 1) Displacing the Rx coils far from each other [18], [19], [20]; 2) Using metal-insulator to reduce magnetic coupling [21]; 3) Retuning the compensation networks of receivers by reflecting reactance [22], [23].
When the size of the Rx is significantly smaller than the Tx, the coils of the different receivers can be relatively far apart to reduce cross-coupling, as the structure of the fourphase Rx adopted by Cui et al. [18]. In order to prevent the coupling between the Rx coils from affecting the output characteristics of the IPT system, the Rx coils are connected by parallel-series-parallel (PSP), and only two phases without cross-coupling are working at any time. However, this method requires the size of Tx or Rx to be large enough, which poses design challenges due to the limited space of the AGV chassis. A mutual decoupling scheme based on magnetic shielding is proposed by [21], which uses an aluminum sheet and two ferrite cores to decouple the four-coil IPT system into two independent dual-coil sub-systems. And the common magnetic flux between the dual-coil sub-systems is shielded by the ferrite and aluminum on the magnetic field to achieve the purpose of decoupling. In this way, the mutual inductance of coils in the same class can be increased while the mutual inductance of coils in different classes is decreased. However, the fatal limitation of the magnetic decoupling scheme is that it is only applicable to the overlapped multi-receiving coils, but for the coils in the same plane, such as the BP pad or DDQ pad, this method is not effective. Retuning the compensation network of the two Rx coils is a reliable way to mitigate the cross-coupling effect. Still it also requires a realtime adaptive matching compensation network to handle the load and positional changes between Tx and Rx. A similar approach is used in [19] and [20], where additional reactance is inserted in the resonant tanks of the receiver structure to compensate for cross-coupling. However, the variation of the load or the mutual inductance between any of the three coils would require retuning the compensation network by changing the capacitors used for matching [22]. This method is more meaningful in theory than in practice.
According to the above analysis, multi-coil Rx needs to be modeled again to acquire compact size and smooth output voltage characteristics during misalignment. In this paper, a DD Tx and a compact dual-coil Rx magnetic coupler collocation to independent decoupling method is applied to achieve size minimization, steadily and efficiently power transferring for AGV wireless charging system. The rest of this paper is organized as follows. In Section II, the magnetic coupler, which is composed of a DD pad Tx and a compact dual-coil Rx is analyzed. Section III presents the impact on output characteristics by cross-coupling of compact dual-coil Rx. And an innovative mutual decoupling method for Rx decoupling is introduced in Section IV. In Section V, an experimental prototype is established to verify the magnetic coupler design and decoupling scheme. Finally, Section VI concludes this article.

II. ANALYSIS OF THE DD PAD TX AND COMPACT DUAL-COIL RX
To generate a sufficiently high magnetic field under the requirement of minimal Tx size, a DD pad is applied in this paper. Compared with other multi-coil polarized transmitters like BP pad or DDQ pad, the DD pad is wound by a single wire, which means the decoupling link caused by the multicoil structure is omitted as well as the primary devices [24]. In order to obtain superior anti-misalignment ability, a dualcoil Rx consisting of two identical single-rectangle pads is analyzed. The proposed magnetic coupler and equivalent circuit model are shown in Fig.2, in which, w pa , l pa , w sa and l sa represent the width and length of Tx and Rx, respectively. And L P is the self-inductances of the Tx, while L S1 and L S2 are the self-inductances of Rx. The mutual inductances between the Tx and dual-coil receiver are denoted as M 1 and M 2 . Furthermore, M S is the cross-coupling inductance between two Rx coils. And the equivalent mutual inductance  M eq of the magnetic coupler could be expressed as: Usually, the windings of the coils along the outer sides are arranged in two-layer to ensure the transmission distance, while minimizing the size of the magnetic coupler by reducing the values of l pc , l sc , w pb and w sb .
In Fig. 3, the flux of DD pad Tx presents a parallel polarized feature and travels largely along the length of the pad, which allows the DD pad owns a higher fundamental flux path compared with the non-polarized coils. Before the design of the magnetic coupler, the magnetic field distribution which is generated by the Tx should be analyzed in the first place. As shown in Fig.3, the magnetic field generated by Tx can be decomposed into three dimensions along the x-axis, y-axis and z-axis (indicated as B x , B y , and B z ), respectively. Since the directions of B x , and B y are parallel to the receiver plane, the magnetic field B x and B y have no influence on the mutual flux linkage passing through the Rx [24].
To analyze the magnetic field B z on the Rx plane for the magnetic coupler without magnetic core quantitatively, finite element analysis (FEA) software ANSYS Maxwell has been used to simulate the field distribution. And the simulation result is shown in Fig. 4, and the normalized magnetic flux density along the z-axis B zn is defined as:  It can be obtained that the distribution of B zn is symmetrical around the center of the origin. The mutual flux linkage passing through the single-rectangle pad could be calculated by: where S indicates the effective flux area of the rectangle Rx, hence, the coupling null point will appear inevitably in the case when the center of the single-rectangle coil has zero misalignment along the y-axis from the origin. Fig.5 shows the effect of the width of Rx relative to Tx on the mutual inductance of the magnetic coupler structure. And the normalized mutual inductance M n between the DD Tx and single rectangle Rx is as follows: where M represents the mutual inductance between the DD Tx and single rectangle Rx. It should be noticed that the mutual inductance M of the magnetic coupler has no distinction on the positive and negative in number, as the difference in the direction of misalignment, the mutual inductance between the DD pad Tx and the single rectangle coil Rx is embodied in the difference of the dotted terminal. Actually, with the transposition of the y-axis misalignment, the dotted terminal of the magnetic coupler shifts. And it can be observed that the mutual inductance of DD pad Tx and single rectangle coil Rx increases rapidly while w sa < 0.5w pa , and the growth of M starts to slow when w sa > 0.5w pa . Thus, the width of single-rectangle coil values from 0.5 to 0.7 w pa is preferred. Obviously, the antimisalignment ability of the magnetic coupler is strengthened with w se growth. However, the coupling null point emerges when the rectangle Rx is aligned with DD pad Tx. To eliminate the coupling null point and improve the smoothness of M eq , the design of multi-coil Rx plays a crucial role.
In general, according to the superposition theory, complex magnetic couplers such as BP pads, DDQ pads, or other compound pads design Rx could be piled up by fundamental pads [12], [25], and the proposed Rx has no exception. The flux pattern for compact dual-coil Rx is shown in Fig.6. While: There is cross-coupling between the Rx coils. And the BP pad achieved decoupling by overlapping these two coils with specific overlapping areas to realize: However, the fixed overlapping area significantly decreases dual-coil Rx's degree of freedom. In most VOLUME 11, 2023   instances, the BP pad failed to implement the smoothest M eq between Tx and Rx. To find the optimal M eq for the magnetic coupler, a simulation is run to analyze the coupling characteristics of the magnetic coupler. Considering the AGV's relatively low chassis, the air gap of the magnetic coupler is determined to be 40mm. To acquire the sufficient height of magnetic field path, the Tx with the DD pad sized at w pa × l pa = 180mm × 390mm is modeled, the number of ferrite bar N F is set to 8, and the number of turns of Tx and Rx (N P and N S ) is set to 10. Referring to Fig.5, to obtain adequate M eq and anti-misalignment ability, the w sa / w pa is selected around 0.6. Thus, the single-rectangle pad size is chosen to w se × l sa = 115mm × 210mm. And l pa is set larger than l sa to acquire sufficient x-axis anti-misalignment ability (l x ). It can be expressed as: As shown in Fig.7, with the increase of w sd , the fluctuation of M eq tends to be stable in the y-axis misalignment. However, while w sd > 80mm, M eq in the case of misalignment is less than the maximum M eq , which causes M eq fluctuation to be larger. And while the overlapping area is constant, M S fluctuates very little in misalignment, which could be almost negligible. In order to improve the anti-misalignment ability and the stability of M eq during misalignment, the overlapping area is applied to make one Rx coil reaches the coupling highest point while the other coil is at the coupling null point. Moreover, the windings of the coils along the outer sides are arranged in two layers to reduce the size of the magnetic coupler further. The parameters of the magnetic coupler are listed in Table 1. And the magnetic coupler is constructed as shown in Fig.8.
From Fig.9, four special locations have been picked out for measurement. Y 0 is the position where Rx is exactly on top of Tx, and has no misalignment. Y 1 is the coupling peak point of receiving coil A and the coupling null point of receiving coil B, which, there is about 27mm y-axis misalignment distance. And it should be noted that the dotted terminal between the Tx and receiving coil B shifts while the y-axis misalignment goes through Y 1 . While Rx is on Y 2 , the mutual inductance of the two receiving coils is equal, and this point is about 63mm misalignment. Y 3 is the point at which Rx has a 100mm misalignment. And the variations of M S , L S1 , and L S2 are within 1µH during the misalignment, the coupling maximum point of M 1 occurs at the same position as the coupling null point of M 2 , which proves the feasibility of the proposed magnetic coupler.

III. ANALYSIS OF DD TX AND COMPACT DUAL-COIL RX BASED ON LCC-S COMPENSATION NETWORK
To improve the power factor of the IPT system and reduce reactive power loss, an inductor/capacitor/capacitor-series (LCC-S) compensation network [26], [27] is adopted in the proposed IPT system. With the constant current characteristic of the Tx coil as well as the constant voltage characteristic of output, the LCC-S compensation network allows Tx to produce a stable magnetic field and simplify the Rx side [28], [29]. In order to achieve output voltage superposition for more power, the compact Rx coils are connected in series. Fig.10 illustrates the proposed magnetic coupler with an LCC-S compensation network. The system consisted of a full bridge inverter on the primary side and two rectifiers on the secondary side, connected by a compensation inductance L 1 , a parallel compensation capacitance C 1 , and a series compensation capacitance C P , a loosely coupled transformer composed of L P , L S1 , and L S2 , and series compensation capacitances C S1 , C S2 . The DC voltage V in and V O are the corresponding input and output voltage. Where v ab , v ab1 , and v ab2 are the midpoint voltages of the inverter and rectifiers, respectively. The DC load R O could be equivalent to the sum of two AC loads of Rx circuits R eq . And R eq = R 1 + R 2 , where R 1 and R 2 present the AC load of each Rx circuit loop.
Considering fundamental harmonic analysis (FHA), Fig. 10 can be simplified to a linear circuit and in which, the voltage/current variable, e.g., v ab , v ab1 , v ab2 , i LP , i L1 , i LS1 and i LS2 , their fundamental components could be written asV ab ,V ab1 ,V ab2 ,İ LP ,İ L1 ,İ LS1 , andİ LS2 respectively. Similarly, V ab , V ab1 , V ab2 , I LP , I L1 , I LS1 , and I LS2 represent corresponding RMS value. The KVL equations of two Rx loops are established as follows: In the resonance state: where ω is the resonant angular frequency. When the crosscoupling exists between the Rx coils, the current of the Tx could be regarded as the excitation source, and the current of the two Rx coils are: Due to the series connection in the load circuit, I LS1 = I LS2 in the case both Rx coils are working together, and it can be inferred: From (9) to (11), the following equations are obtained: where κ = M 2 1 M 2 2 R 2 eq + ω 2 M 2 S (M 2 1 -M 2 2 ) 2 , and the output power could be expressed: where δ = (ωM 1 + ωM 2 ) 2 I 2 P /R O . It can be concluded from (13) that the existence of cross-coupling will destroy the resonance condition of the IPT system. In the case of the same I LP in the Rx, M S inevitably reduces the output voltage as well as output power.

IV. DECOUPLING METHOD FOR THE IPT SYSTEM
According to the analysis in section III, the output performance of the system is greatly affected by M S , so it is necessary to eliminate the cross-coupling by introducing the decoupling method. Distinguishing from the existing way, the decoupling method proposed in this article is to add an additional device between two receiving compensation networks, and counteract the mutual inductance between the Rx coils by generating opposite magnetic flux, so as to realize the decoupling. And the equivalent circuit is shown in Fig.11. As the decoupling devices, two lumped inductances L C1 and L C2 are integrated into one core, and the mutual inductance of L C1 and L C2 can be expressed as M C . According to KVL, each secondary circuit loop equation could be expressed as: As seen from the (14), in the case of M C = M S , the term of equationİ LS2 in receiving compensation network 1 will be eliminated, showing that L S1 receiving circuit will not be affected by the current in L S2 receiving circuit, so the same as the loop 2. Thus, the mutual decoupling of the two receiving circuit loops is achieved.
According to the proposed decoupling method, as M C is equal to M S , the value of the resonant capacitance C S1 and C S2 also needs to be re-matched to realize the resonance state VOLUME 11, 2023  of the IPT system. The conditions for the resonance of the two receiving circuit loops are as follows: With the Fourier transform, V ab and R eq can be expressed as: The currents of the IPT system are obtained: In the case where the two receiving circuits are decoupled, the output voltage and output power can be expressed as:  As shown in (18) to (20), the current of Tx and Rx, output voltage V O , and output power P O are no longer affected by M S , which proves the effectiveness of the decoupling method.
On account the combination of the dual-coil receivers and decoupling device can be equivalent to the uncoupled dualcoil receivers, the presented decoupling method is appropriate for any compensation network. Furthermore, the proposed decoupling method is also suitable for multi-coil structures both in Tx and Rx, as shown in Fig. 12. For the multi-coil situation, the multiple decoupling devices can be integrated into one or a few decoupling devices to improve the power density, which is unable to be achieved by traditional capacitive decoupling methods. At the same time, the decoupling device is incorporated into the compensation network to meet the condition of the receiving coils separated by a large distance.
Since the DD Tx is assumed to be embedded in the road, and the leakage flux intensity of DD Tx in the y-axis misalignment direction on the road is simulated and presented in Fig. 13. Compared with the leakage flux of 27 µT in ICNIRP2010 standard, the minimum safe distance of proposed magnetic coupler is about 150mm.

V. EXPERIMENT RESULTS
To verify the proposed magnetic coupler design and mutual decoupling solution, an experimental prototype based on the proposed magnetic coupler is established, as shown in Fig. 14. In addition, the measured self-inductances and mutual inductances after decoupling are demonstrated in Fig. 15, in which the cross-coupling M S could be eliminated completely by M C . The specific parameters of the experimental prototype are given in Table 2 and Table 3. In order to reduce the inductive reactance of the receivers, the decoupling device is wound into a closely coupled structure similar to a typical transformer.
Y 0 ∼Y 3 are the specific test points for the IPT system's output characteristics, and the waveforms of AC output voltages, as well as each Rx coil current before and after decoupling, are shown in Fig. 16∼19, and the experiments are arranged as follows: 1). In order to compare the output characteristics of the IPT system before and after decoupling, M C is replaced with a series compensation capacitance while the load R O is keeping constant to test the output characteristics under crosscoupling in four different positions along the y-axis.
2). To illustrate the performance of the decoupling solution, in this decoupling experiment, the output power P O is kept at 3kW by adjusting the resistance R O under the disturbance of misalignment.
Y 0 is the point where the Rx has no misalignment against Tx, and M 1 is equal to M 2 , as shown in Fig.16, the waveforms of v ab1 and v ab2 are in the same phase both decoupled and coupled. And the circuit works in resonance. VOLUME 11, 2023  However, while the Rx is misalignment, M 1 and M 2 are going to unbalance, which means the resonance state of the circuit is broken. Fig. 17(a) shows that v ab2 (i LS2 ) have 90 • phase in advance compared with v ab1 (i LS1 ). This is because Y 1 is the coupling null point of Rx coil L S2 , and v ab2 is generated by the i LS1 through cross-coupling M S between the Rx coils. After decoupling, the voltage induced in M C and the voltage induced in M S eliminated each other, so the v ab2 comes to zero. According to Fig.18, Y 2 is the point where M 1 is equal to M 2 . However, v ab1 and i LS1 have a 180 • phase differences compared with v ab2 and i LS2 . This is because the magnetic flux flowing through the Rx coil L S2 at Y 2 is reversed from that at Y 0 , resulting in the dotted terminal changing of the coil L S2 , so as the decoupling device.
As it can be obtained in Fig.19, the resonance characteristics of the IPT system are completely disturbed before decoupling. However, v ab1 and i LS1 start to have teeny incomplete reversal phase differences compared with v ab2 and i LS2 after decoupling, which is caused by the fluctuation of L S1 , L S2 , and M S at a sufficiently large misalignment distance.
As last, the output performance of the IPT system are shown in Fig.20. And Fig.20(a) shows the output voltage and the equivalent mutual inductance varying with the y-axis misalignment. As it could be obtained that M eq varies between 14.1µH to 19.5µH in 0∼90mm y-axis misalignment, while V O ranges from 155V to 220V. Fig.19(a) illustrates the fluctuations of V O and M eq are relatively stable and proportional to each other, which indicates that the coupling between the receivers is neutralized, thus verifying the effectiveness of the decoupling method and magnetic coupler design. As shown in Fig.20(b), the maximum and minimum efficiency of the system when the output power is 3kW are 94.5% and 89.5% in the designed misalignment range. In contrast, the output power and efficiency of the system are relatively lower with the same load condition when the Rx coils are not decoupled.
Thus, proving the improvement of the power and efficiency of the IPT system by this decoupling method.
In comparison with previously published magnetic couplers in Table 4, the proposed compact magnetic coupler can achieve relatively high peak efficiency and output power with reduced Rx size. This will not only meet the charging performance, but also significantly reduce the occupancy of the AGV chassis space by the IPT system. While compared with the self-decoupling coils, the proposed magnetic coupler accompanying with decoupling device has a more compact size for the receiver, and shows higher design freedom for the magnetic coupler. In addition, the proposed decoupling scheme is more flexible and has higher power density than the schemes in [18], [19], [20], and [21], and it is simpler in control when compared with [22] and [23].

VI. CONCLUSION
A magnetic coupler consists of a DD pad Tx and a compact dual-coil Rx, which pursues size and output power fluctuation minimization is proposed in this paper. The conclusion could be obtained through detailed magnetic circuit analysis and FEA simulation: By overlapping the Rx coils in a specific area, in which one coil reaches the coupling highest point, the other coil is at the coupling null point, thus, realizing stable wireless power transmission during the misalignment. And while the rectangle coils of the dualcoil Rx reach 0.5∼0.7 times of DD Tx's width, the magnetic coupler could achieve sufficient coupling. Moreover, to achieve mutual decoupling of Rx dual-coil, a decoupling method has been proposed, which uses two lumped inductors possessing the same mutual inductance as the Rx coils. Based on the proposed magnetic coupler design and decoupling method, an LCC-S compensated IPT system is established. The experimental results show that V O varies in proportion to mutual inductance M eq . The efficiency and output voltage range of 89.5% to 94.5% and 155V to 220V during the 90mm y-axis misalignment, while the output power is 3kW, shows the effectiveness of the decoupling method and magnetic coupler design.