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A Multireceiver Wireless Power Supply System with Power Equalization in Stereoscopic Space

With the rapid development of wireless power transfer (WPT) technology, the traditional single-transceiver WPT system has become more and more advanced; however, it is still difficult to meet its extensive application requirements. Aiming at the wireless charging of mobile phones in public places, electric vehicles (EVs) in multistorey garages, and electronic shelf labels (ESLs) in supermarket merchandise shelves, a multireceiver wireless power supply system with power equalization is proposed. The condition of power equalization is derived according to the equivalent circuit of the proposed WPT system, and the received power can be equally maintained by adjusting the transceiver loop resistance when the total load number or transmission distance changes. A simulation model is established to evaluate the electromagnetic environment of the proposed WPT system, and the results comply with the electromagnetic safety of the ICNIRP-2018 guidelines. Finally, the experimental results show that the power differential rate that meets the power equalization condition is 13 to 17% lower than that of the unsatisfied rate, which verifies the effectiveness of the proposed system in terms of power equalization.


Introduction
In recent years, wireless power transfer (WPT) technology has attracted widespread attention and research due to its safe and convenient characteristics [1,2]. At present, the technology has been successfully used in consumer electronics, electric vehicles, implantable devices, etc., [3][4][5].
With the rapid development of WPT technology, the ordinary single-transceiver system has been relatively widespread, but it is still difficult to meet its wide application requirements [6]. For a multireceiver WPT system with loads, the distribution and control of received power is the focus of this research [7]. By designing a nonuniform gap thickness between the transmitter and the receiver at a specific location, the uniformity of the induced power of multiple receivers can be improved [8]. On the other hand, it is necessary to maximize system efficiency while meeting the power requirements of each load [9]. However, external factors, such as changes in transmission distance and load, may lead to the power received becoming unstable, which will cause great damage to the electrical equipment. To solve this problem, researchers have studied various techniques.
The series energy storage battery in the WPT system is designed with a voltage equalizer using a voltage multiplier, which can achieve single-switch voltage equalization without feedback control [10]. Based on the automatic frequency tracing technique, the problem of frequency shifts when the load number changes can be solved [11]. By periodically short-circuiting the receiver coil closest to the transmitter coil, the magnetic flux of the remote receiver coil can be controlled to equalize the received power among all receiver coils [12]. Auxiliary circuits, including band-pass and/or band-stop circuits, are proposed to be incorporated into receiver circuits and optional relay circuits to facilitate the selection and enhancement of wireless power transmission to designated loads [13].
Efforts to improve the efficiency of multiple receivers are productive in the field of active equalizers, such as switched capacitors, converters based on the transformer, and so on [14,15]. Through the reconfigurable shape of the modular WPT array system, multiple power flow paths are provided in the space between the transmitter and the receiver, thereby improving the reliability of power transmission [16]. However, circuits using these components, or the various control techniques, usually have issues of complexity which will intensify further when more receivers are added in the WPT system [17].
At the same time, various standards for WPT technology have been released to standardize designs applied in different fields, from developers such as SAE J2954-(R) for EVs [18] and Qi standard for mobile devices [19]. Moreover, electromagnetic radiation around the WPT system cannot be ignored during the working period. As such, the International Commission on Non-Ionizing Radiation Protection (ICNIRP), the American National Standards Institute (ANSI), and the Institute of Electrical and Electronics Engineers (IEEE) worked on many standards to give a reference to limit magnetics, such as the ICNIRP-2010 Guidelines, the ICNIRP-2018 Guidelines, IEEE Std C95.3 TM -2002, IEEE Std C95.1 TM -2005, etc. [20][21][22][23].
In this paper, we propose a stereoscopic space wireless power transfer (WPT) system, and present a method by adjusting the loop resistances of transmitter and relay transmitter coils to satisfy the condition of power equalization under different transmission distances or load numbers. The proposed method is more efficient, convenient, and economic in keeping power equalization of all loads in stereoscopic space, especially when there exist many loads. Only the resistances of transmitter and relay transmitter coils are adjusted to achieve power equalization, instead of redesigning all receiver coils. A simulation model is built to study the H-field intensity around the WPT system compared with the ICNIRP-2018 guidelines. Furthermore, experimental verification is also carried out to validate the feasibility of the proposed scheme.

Proposed Structure and Power Equalization
A block diagram of this paper is shown in Figure 1.   Planar spiral coils are widely used in wireless power transfer systems. In order to study the magnetic flux of receiver coils and the mutual inductance between transmitter and receiver coils, a theoretical calculation model is established, as shown in Figure 2, including single-turn transmitter and receiver coils.
Electronics 2021, 10, x FOR PEER REVIEW Planar spiral coils are widely used in wireless power transfer systems. In study the magnetic flux of receiver coils and the mutual inductance between tra and receiver coils, a theoretical calculation model is established, as shown in F including single-turn transmitter and receiver coils.
where μ0 is the vacuum permeability, l1 and l2 are the length of each turn, dl1 an the infinitesimal of l, and r12 is the distance of dl1 and dl2. Then,


Assuming that the transmitter current is ITX, the magnetic flux on the receive be obtained by the following formula: Single-turn transmitter and receiver coils at any spatial location.
According to the Niemann formula, the mutual inductance between two coils can be expressed as: where µ 0 is the vacuum permeability, l 1 and l 2 are the length of each turn, dl 1 and dl 2 are the infinitesimal of l, and r 12 is the distance of dl 1 and dl 2 . Then, For the planar spiral coil: Assuming that the transmitter current is I TX , the magnetic flux on the receiver coil can be obtained by the following formula: By setting parameter values reasonably, the relationship between magnetic flux Φ and transmission distance h can be obtained according to (3) and (4).
As shown in Figure 3, Φ will decrease sharply when h increases, so it is challenging to sustain enough output power for receiver coils at different heights simultaneously, unless input current is added to increase the input power, which will contribute to the high power As shown in Figure 3, Φ will decrease sharply when h increases, so it is challenging to sustain enough output power for receiver coils at different heights simultaneously, unless input current is added to increase the input power, which will contribute to the high power supplied by the front-end driver and cause potential safety hazards. More often, it is difficult to put into practice. To solve the problem mentioned above, a new type of WPT system, with multiple receiver coils at different layers in stereoscopic space, is proposed. The proposed structure diagram is shown in Figure 4. TX1 represents the transmitter coil, while TX2 to TXk represent the relay transmitter coils of each layer. Receiver coils, RX, are symmetrically placed on TX. All RXs will acquire the same transmission power by configuring corresponding parameters properly. According to the coupling mechanism of the stereoscopic space wireless power transfer system with multilayers, the corresponding equivalent circuit diagram can be obtained, as shown in Figure 5. To solve the problem mentioned above, a new type of WPT system, with multiple receiver coils at different layers in stereoscopic space, is proposed. The proposed structure diagram is shown in Figure 4. TX1 represents the transmitter coil, while TX2 to TXk represent the relay transmitter coils of each layer. Receiver coils, RX, are symmetrically placed on TX. All RXs will acquire the same transmission power by configuring corresponding parameters properly.
power supplied by the front-end driver and cause potential safety hazards. More is difficult to put into practice. To solve the problem mentioned above, a new type of WPT system, with receiver coils at different layers in stereoscopic space, is proposed. The proposed s diagram is shown in Figure 4. TX1 represents the transmitter coil, while TX2 to T resent the relay transmitter coils of each layer. Receiver coils, RX, are symmetricall on TX. All RXs will acquire the same transmission power by configuring corres parameters properly. According to the coupling mechanism of the stereoscopic space wireless pow fer system with multilayers, the corresponding equivalent circuit diagram can tained, as shown in Figure 5. According to the coupling mechanism of the stereoscopic space wireless power transfer system with multilayers, the corresponding equivalent circuit diagram can be obtained, as shown in Figure 5. The Kirchhoff Voltage Laws (KVL) equations for the first layer of the transmitter coil, for each layer of the relay transmitter coil, and for the receiver coils are listed, respectively, as follows: where Us represents the input voltage; ω is the angular frequency; ITXk represents the current passing through TX of the kth layer; IRXkp represents the current in the pth RX of the kth layer; RTXk, LTXk and CTXk, respectively, represent the resistance, inductance and series resonant capacitance of the TX loop of the kth layer; Rkp, Lkp and Ckp, respectively, represent the resistance, inductance and series resonant capacitance of pth RX loop of the kth layer; Mk(k−1) represents mutual inductance between the kth layer and (k − 1)th layer TX; and Mkkp represents mutual inductance between the kth layer TX and pth RX of the same layer.
In fact, there are many mutual inductances in (5) that can be ignored, such as the mutual inductance between different RXs, the mutual inductance between TX and RX of different layers, etc. Thus, Z will be a sparse matrix, and, in Section 3 (Table 1), we will quantitatively calculate these mutual inductance values to show that they can be ignored.
We can assume that the RXs of the same layer are identical and evenly distributed on the TX. The mutual inductance between each RX and TX is equal. Since all loops are resonant, the currents in all RXs of each layer are also equal. Considering the first two layers and the first RX, the following equations can be obtained: where RTX1 and RTX2 represent the resistance of the TX loop on the first and the second layer, Ra1 and Rb1 are the resistance of the first RX loop on the first and the second layer, M1a1 represents mutual inductance between the first TX and the first RX on the first layer, The Kirchhoff Voltage Laws (KVL) equations for the first layer of the transmitter coil, for each layer of the relay transmitter coil, and for the receiver coils are listed, respectively, as follows: where U s represents the input voltage; ω is the angular frequency; I TXk represents the current passing through TX of the kth layer; I RXkp represents the current in the pth RX of the kth layer; R TXk , L TXk and C TXk, respectively, represent the resistance, inductance and series resonant capacitance of the TX loop of the kth layer; R kp , L kp and C kp, respectively, represent the resistance, inductance and series resonant capacitance of pth RX loop of the kth layer; M k(k−1) represents mutual inductance between the kth layer and (k − 1)th layer TX; and M kkp represents mutual inductance between the kth layer TX and pth RX of the same layer.
In fact, there are many mutual inductances in (5) that can be ignored, such as the mutual inductance between different RXs, the mutual inductance between TX and RX of different layers, etc. Thus, Z will be a sparse matrix, and, in Section 3 (Table 1), we will quantitatively calculate these mutual inductance values to show that they can be ignored. We can assume that the RXs of the same layer are identical and evenly distributed on the TX. The mutual inductance between each RX and TX is equal. Since all loops are Electronics 2021, 10, 713 6 of 15 resonant, the currents in all RXs of each layer are also equal. Considering the first two layers and the first RX, the following equations can be obtained: where R TX1 and R TX2 represent the resistance of the TX loop on the first and the second layer, R a1 and R b1 are the resistance of the first RX loop on the first and the second layer, M 1a1 represents mutual inductance between the first TX and the first RX on the first layer, while M 2b1 is mutual inductance between the second TX and the first RX on the second layer, M 12 represents mutual inductance between the first TX and the second TX, m and n are the total number of RX on the first layer and the second layer, respectively. I TX1 , I TX2 , I RX1 and I RX2 are the current in TX1, TX2, RX1, and RX2, respectively, which can be expressed by: The total output power of the WPT system P and the transmission efficiency η can be calculated by (8) and (9), respectively.

P= mI
In order to equalize I RX1 and I RX2 , M 12 should satisfy: We can also obtain that I TX1 = I TX2 as (10) is valid. According to (3) and (10), we can distribute the RX if TX is determined, or the TX can be determined if RX is known. We will discuss this further in the next section.

System Design and Analysis
The size parameters of the WPT system were designed according to the actual size of mobile phone wireless chargers, as shown in Table 1, where N represents the turn number of TX or RX, D min and D max are the inner diameter and outer diameter, respectively, the coils are tightly wound with the turn spacing D ≈ a, and a is wire diameter.
We set the input voltage at U s = 50 V and the resonance frequency at f = 200 kHz. In Table 1, the TX (RX) resistances of different layers are equal to R T (R R ), and the mutual inductance of TX and RX in the same layers are equal to M. As such, the equalization condition (10) can be simplified as: Assuming the equalization condition is always satisfied, the relationship between I TX1 (I TX2 ), I RX1 (I RX2 ) and the RX number m, n can be figured according to (7) and (11); the relationship between the output power P, the transmission efficiency of η and m, n can also be figured according to (8) and (9), respectively, where the change in relationship between P and I RX is the same. Given this, only one of the diagrams needs to be made, as shown in Figure 6. We set the input voltage at Us = 50 V and the resonance frequency at f = 200 kHz. In Table 1, the TX (RX) resistances of different layers are equal to RT (RR), and the mutual inductance of TX and RX in the same layers are equal to M. As such, the equalization condition (10) can be simplified as: Assuming the equalization condition is always satisfied, the relationship between ITX1 (ITX2), IRX1 (IRX2) and the RX number m, n can be figured according to (7) and (11); the relationship between the output power P, the transmission efficiency of η and m, n can also be figured according to (8) and (9), respectively, where the change in relationship between P and IRX is the same. Given this, only one of the diagrams needs to be made, as shown in Figure 6. We can conclude from Figure 6 that, as m or n increase, ITX, IRX (P) will decrease accordingly, while η will be improved. The number of RX on the first layer m or the second layer n can be limited according to the specific requirements of TX currents, load currents, transmission power, or transmission efficiency.
According to (11) and the parameters listed in Table 1, the relationship between M12 and the number of RX on second layer n is shown in Figure 7. M12, which satisfies the power equalization condition, is proportional to the number of RX on the second layer n. The relationship between M12 and h can be obtained using (3) and the parameters in Table  1, as Figure 8 shows. We can conclude from Figure 6 that, as m or n increase, I TX , I RX (P) will decrease accordingly, while η will be improved. The number of RX on the first layer m or the second layer n can be limited according to the specific requirements of TX currents, load currents, transmission power, or transmission efficiency.
According to (11) and the parameters listed in Table 1, the relationship between M 12 and the number of RX on second layer n is shown in Figure 7. M 12 , which satisfies the power equalization condition, is proportional to the number of RX on the second layer n. The relationship between M 12 and h can be obtained using (3) and the parameters in Table 1, as Figure 8 shows.

A. Example of the Known h and the Unknown m, n
Assuming h = 37 cm, the mutual inductance between TX1 and TX2 M12 can also be calculated as 48 μH, according to (3). The number of RX on the second layer n should be 3 to meet the equalization condition, as Figure 7 shows.
To achieve a design requirement for mobile phone wireless charging with transmission power P ≥ 19 W and transfer efficiency η ≥ 92%, the number of RX on the first layer

A. Example of the Known h and the Unknown m, n
Assuming h = 37 cm, the mutual inductance between TX1 and TX2 M12 can also be calculated as 48 μH, according to (3). The number of RX on the second layer n should be 3 to meet the equalization condition, as Figure 7 shows.
To achieve a design requirement for mobile phone wireless charging with transmission power P ≥ 19 W and transfer efficiency η ≥ 92%, the number of RX on the first layer

A. Example of the Known h and the Unknown m, n
Assuming h = 37 cm, the mutual inductance between TX1 and TX2 M 12 can also be calculated as 48 µH, according to (3). The number of RX on the second layer n should be 3 to meet the equalization condition, as Figure 7 shows.
To achieve a design requirement for mobile phone wireless charging with transmission power P ≥ 19 W and transfer efficiency η ≥ 92%, the number of RX on the first layer m can be limited to 3, according to (8) and (9). Then we can calculate that I TX1 = 0.415 A, I TX2 = 0.415 A, I RX1 = 1.632 A, I RX2 = 1.632 A.

B. Example of the Known m, n and the Unknown h
Assuming m = n = 4, the mutual inductance between TX1 and TX2 M 12 can also be calculated as 62.8 µH, according to (3). This means the transmission distance should be 32.2 cm to satisfy the relationship between M 12 and h, as Figure 8 shows. We can calculate that I TX1 = 0.317 A, I TX2 = 0.317 A, I RX1 = 1.247 A, I RX2 = 1.247 A.
In practical applications, when transmission distance or load number are unknown, we can satisfy the power equalization condition by adjusting the TX resistance with an impedance matching network. If the TX coil is offset (angular or horizontal), the mutual inductance between the TXs will be changed according to (3). Correspondingly, the parameters in (11) must be adjusted to meet the power equalization condition. The implementation flowchart of adjusting the internal resistance value of transmitter coil loop and relay transmitter coil loop, according to different load numbers and transmission distances, is shown in Figure 9. calculated as 62.8 μH, according to (3). This means the transmission distance should b 32.2 cm to satisfy the relationship between M12 and h, as Figure 8 shows. We can calculat that ITX1 = 0.317 A, ITX2 = 0.317 A, IRX1 = 1.247 A, IRX2 = 1.247 A.
In practical applications, when transmission distance or load number are unknown we can satisfy the power equalization condition by adjusting the TX resistance with a impedance matching network. If the TX coil is offset (angular or horizontal), the mutua inductance between the TXs will be changed according to (3). Correspondingly, the pa rameters in (11) must be adjusted to meet the power equalization condition. The imple mentation flowchart of adjusting the internal resistance value of transmitter coil loop an relay transmitter coil loop, according to different load numbers and transmission dis tances, is shown in Figure 9.

Electromagnetic Field Simulation
Using the parameters in Table 1, we can set the operating frequency f to 200 kHz an the transmission distance h to 32.2 cm. Taking the worst situation into consideration, th input voltage Us is raised to 100 V, which will cause the currents in TX1 and TX2 to in crease to 0.63 A, and the currents in all RXs to increase to 2.49 A. The simulation model i shown in Figure 10a, and the entire H-field intensity distribution is provided in Figur 10b.

Electromagnetic Field Simulation
Using the parameters in Table 1, we can set the operating frequency f to 200 kHz and the transmission distance h to 32.2 cm. Taking the worst situation into consideration, the input voltage U s is raised to 100 V, which will cause the currents in TX1 and TX2 to increase to 0.63 A, and the currents in all RXs to increase to 2.49 A. The simulation model is shown in Figure 10a, and the entire H-field intensity distribution is provided in Figure 10b.
To visualize the magnetic field distribution around the WPT system, we study the Hfield strength along two lines in Figure 10b. The simulation results are shown in Figure 11, where "I" represents the H-field intensity distribution in the horizontal direction, "II" represents that in vertical direction, while "III" represents the reference level according to ICNIRP-2018 [21].
To visualize the magnetic field distribution around the WPT system, we study the Hfield strength along two lines in Figure 10b. The simulation results are shown in Figure  11, where "I" represents the H-field intensity distribution in the horizontal direction, "II" represents that in vertical direction, while "III" represents the reference level according to ICNIRP-2018 [21].  The H-field strength along line "II" clearly shows a strong magnetic field distribution to RX and TX. However, the H-field strength along line "I" (4 cm away from the TX edge) is always below the reference level, which reflects the fact that the WPT system does no harm to people nearby, even in a worst-case scenario. Therefore, the WPT system exhibits a good performance in an electromagnetic environment.

Experimental Verification
As shown in Figure 12, an experimental prototype was established, according to the parameters in Table 1, to verify the feasibility of the proposed structure and the correctness of the power equalization condition. The TX side was connected to a high-frequency AC power supply by a phase-shifted, full-bridge inverter; the working frequency was 200 To visualize the magnetic field distribution around the WPT system, we study the Hfield strength along two lines in Figure 10b. The simulation results are shown in Figure  11, where "I" represents the H-field intensity distribution in the horizontal direction, "II" represents that in vertical direction, while "III" represents the reference level according to ICNIRP-2018 [21].  The H-field strength along line "II" clearly shows a strong magnetic field distribution to RX and TX. However, the H-field strength along line "I" (4 cm away from the TX edge) is always below the reference level, which reflects the fact that the WPT system does no harm to people nearby, even in a worst-case scenario. Therefore, the WPT system exhibits a good performance in an electromagnetic environment.

Experimental Verification
As shown in Figure 12, an experimental prototype was established, according to the parameters in Table 1, to verify the feasibility of the proposed structure and the correctness of the power equalization condition. The TX side was connected to a high-frequency AC power supply by a phase-shifted, full-bridge inverter; the working frequency was 200 The H-field strength along line "II" clearly shows a strong magnetic field distribution to RX and TX. However, the H-field strength along line "I" (4 cm away from the TX edge) is always below the reference level, which reflects the fact that the WPT system does no harm to people nearby, even in a worst-case scenario. Therefore, the WPT system exhibits a good performance in an electromagnetic environment.

Experimental Verification
As shown in Figure 12, an experimental prototype was established, according to the parameters in Table 1, to verify the feasibility of the proposed structure and the correctness of the power equalization condition. The TX side was connected to a high-frequency AC power supply by a phase-shifted, full-bridge inverter; the working frequency was 200 kHz and the actual input voltage of U S was 50 V. The compensation capacitor value was calculated according to the resonance conditions and operating frequency, and, at the same time, a parallel connection method was used to reduce voltage on the capacitor. The RX side was connected to a lamp, so it was not rectified, but directly output a high-frequency alternating current. For convenience, TX1 and TX2 were completely the same, as well as RX1 and RX2. Two oscilloscopes were used to measure and display the voltage and current parameters of the system. One was used to measure the drive voltage and input voltage, whereas the other was used to measure the current of TX1 and TX2. kHz and the actual input voltage of US was 50 V. The compensation capac calculated according to the resonance conditions and operating frequenc same time, a parallel connection method was used to reduce voltage on the RX side was connected to a lamp, so it was not rectified, but directly out quency alternating current. For convenience, TX1 and TX2 were complete well as RX1 and RX2. Two oscilloscopes were used to measure and displ and current parameters of the system. One was used to measure the driv input voltage, whereas the other was used to measure the current of TX1 a Figure 12. Experimental prototype, including high frequency power supply, TX an When h = 37 cm and m = n = 3, the currents in the TX1, TX2, RX1 and RX theoretically be 0.415 A, 0.415 A, 1.632 A and 1.632 A, respectively. When h m = n = 4, the currents in TX1, TX2, RX1 and RX2 loops were anticipated 0.317 A, 1.247 A and 1.247 A, respectively. Due to the harsher conditions con simulation (US increased to 100 V), the system electromagnetic environme improved in the experiment.

A. Experiment with the Known h and the Unknown m, n
When the transmission distance between TX1 and TX2 is h = 37 cm, RX on the first layer m and the second layer n should be 3, and the currents equal 0.415 A, according to the analysis in Section 3.1. Figure 13a shows the as Us = 49.2 V, and Figure 13b shows the currents in the transmitter coil loo A and the relay transmitter coil loop as ITX2 = 0.445 A. When h = 37 cm and m = n = 3, the currents in the TX1, TX2, RX1 and RX2 loops would theoretically be 0.415 A, 0.415 A, 1.632 A and 1.632 A, respectively. When h = 32.2 cm and m = n = 4, the currents in TX1, TX2, RX1 and RX2 loops were anticipated to be 0.317 A, 0.317 A, 1.247 A and 1.247 A, respectively. Due to the harsher conditions considered in the simulation (U S increased to 100 V), the system electromagnetic environment was further improved in the experiment.

A. Experiment with the Known h and the Unknown m, n
When the transmission distance between TX1 and TX2 is h = 37 cm, the number of RX on the first layer m and the second layer n should be 3, and the currents I TX1 , I TX2 should equal 0.415 A, according to the analysis in Section 3.1. Figure 13a  Both ITX1 and ITX2 increased slightly when compared with the theoretical values, which may be due to the nonlinear resistance of incandescent lamps connected to each receiver coil. The internal resistance of the incandescent lamp increased with the rising temperature, so the actual value of RR was larger than the simulation result, which would cause ITX1 and ITX2 to increase. As we can observe in Figure 13b, there was also a difference between ITX1 and ITX2. In fact, ITX1 equals ITX2 to a certain extent; that is, IRX1 was approximately equal to IRX2, which could prove the validity of the proposed structure and the correctness of the power equalization condition.
We also kept h = 37 cm and added the number of the RX m and n to 4. Figure 14a shows the input voltage as Us = 50.4 V, and Figure 14b shows ITX1 = 0.693 A and ITX2 = 0.466 A. The difference between ITX1 and ITX2 will grow larger as m and n increase further, which means the power received in each load starts to become unequal.

B. Experiment with the Known m, n and the Unknown h
When the number of RX on the first and second layers m = n = 4 kept the transmission distance as h = 32.2 cm, the current received in each load was 0.317 A, according to the analysis in Section 3.2. Figure 15a shows the input voltage as Us = 49.8 V, and Figure 15b shows the currents in the transmitter coil loop as ITX1 = 0.498 A and the relay transmitter coil loop as ITX2 = 0.42 A. When comparing the measured root mean square (RMS) values with the calculated values of ITX1 = ITX2 = 0.317 A, there is a difference between these two sets of data due to the existence of incandescent lamps. ITX1 equals ITX2, to a certain extent, so IRX1 is approximately equal to IRX2. Both I TX1 and I TX2 increased slightly when compared with the theoretical values, which may be due to the nonlinear resistance of incandescent lamps connected to each receiver coil. The internal resistance of the incandescent lamp increased with the rising temperature, so the actual value of R R was larger than the simulation result, which would cause I TX1 and I TX2 to increase. As we can observe in Figure 13b, there was also a difference between I TX1 and I TX2 . In fact, I TX1 equals I TX2 to a certain extent; that is, I RX1 was approximately equal to I RX2 , which could prove the validity of the proposed structure and the correctness of the power equalization condition.
We also kept h = 37 cm and added the number of the RX m and n to 4. Figure 14a shows the input voltage as U s = 50.4 V, and Figure 14b shows I TX1 = 0.693 A and I TX2 = 0.466 A. The difference between I TX1 and I TX2 will grow larger as m and n increase further, which means the power received in each load starts to become unequal. Both ITX1 and ITX2 increased slightly when compared with the theoretical values, which may be due to the nonlinear resistance of incandescent lamps connected to each receiver coil. The internal resistance of the incandescent lamp increased with the rising temperature, so the actual value of RR was larger than the simulation result, which would cause ITX1 and ITX2 to increase. As we can observe in Figure 13b, there was also a difference between ITX1 and ITX2. In fact, ITX1 equals ITX2 to a certain extent; that is, IRX1 was approximately equal to IRX2, which could prove the validity of the proposed structure and the correctness of the power equalization condition.
We also kept h = 37 cm and added the number of the RX m and n to 4. Figure 14a shows the input voltage as Us = 50.4 V, and Figure 14b shows ITX1 = 0.693 A and ITX2 = 0.466 A. The difference between ITX1 and ITX2 will grow larger as m and n increase further, which means the power received in each load starts to become unequal.

B. Experiment with the Known m, n and the Unknown h
When the number of RX on the first and second layers m = n = 4 kept the transmission distance as h = 32.2 cm, the current received in each load was 0.317 A, according to the analysis in Section 3.2. Figure 15a shows the input voltage as Us = 49.8 V, and Figure 15b shows the currents in the transmitter coil loop as ITX1 = 0.498 A and the relay transmitter coil loop as ITX2 = 0.42 A. When comparing the measured root mean square (RMS) values with the calculated values of ITX1 = ITX2 = 0.317 A, there is a difference between these two sets of data due to the existence of incandescent lamps. ITX1 equals ITX2, to a certain extent, so IRX1 is approximately equal to IRX2.

B. Experiment with the Known m, n and the Unknown h
When the number of RX on the first and second layers m = n = 4 kept the transmission distance as h = 32.2 cm, the current received in each load was 0.317 A, according to the analysis in Section 3.2. Figure 15a shows the input voltage as U s = 49.8 V, and Figure 15b shows the currents in the transmitter coil loop as I TX1 = 0.498 A and the relay transmitter coil loop as I TX2 = 0.42 A. When comparing the measured root mean square (RMS) values with the calculated values of I TX1 = I TX2 = 0.317 A, there is a difference between these two sets of data due to the existence of incandescent lamps. I TX1 equals I TX2, to a certain extent, so I RX1 is approximately equal to I RX2 . We also kept m = n = 4 and increased H to 37 cm. The input voltage Us, the currents in the transmitter coil loop ITX1, and the relay transmitter coil loop ITX2 are shown in Figure  14 above. The difference between ITX1 and ITX2 in Figure 15 is much less than that in Figure  14, which could also demonstrate the power equalization phenomenon.   The experimental and theoretical results are different, but the error is within the allowable range. On the one hand, the measured value of the coil's internal resistance is not accurate. On the other hand, it is caused by the winding error of the coil. The experimental results show that the power difference rate under the power equalization condition is smaller, which verifies the effectiveness of power equalization.

Conclusions
In this paper, a new type of WPT system, with multiple receivers in different layers, was proposed for application scenarios, such as electric vehicles in multistorey garages, which can balance the received power by adjusting the circuit resistance of the transmitter. The major contributions of this paper are as follows.
(1) A new stereo multireceiver WPT system is proposed, and the power equalization condition is derived. (2) A method for adjusting the resistance of transmitter loops is proposed, which can satisfy the power equalization condition under different transmission distances or We also kept m = n = 4 and increased H to 37 cm. The input voltage U s , the currents in the transmitter coil loop I TX1 , and the relay transmitter coil loop I TX2 are shown in Figure 14 above. The difference between I TX1 and I TX2 in Figure 15 is much less than that in Figure 14, which could also demonstrate the power equalization phenomenon. Table 2 shows the comparison of the theoretical and experimental values of TX current at different transmission distances and RX numbers. The power difference rate can be defined as follows: D P = P max − P min P max = I max − I min I max (12) The experimental and theoretical results are different, but the error is within the allowable range. On the one hand, the measured value of the coil's internal resistance is not accurate. On the other hand, it is caused by the winding error of the coil. The experimental results show that the power difference rate under the power equalization condition is smaller, which verifies the effectiveness of power equalization.

Conclusions
In this paper, a new type of WPT system, with multiple receivers in different layers, was proposed for application scenarios, such as electric vehicles in multistorey garages, which can balance the received power by adjusting the circuit resistance of the transmitter. The major contributions of this paper are as follows.
(1) A new stereo multireceiver WPT system is proposed, and the power equalization condition is derived.
(2) A method for adjusting the resistance of transmitter loops is proposed, which can satisfy the power equalization condition under different transmission distances or load numbers, without the need for redesigning coils or adding additional control circuits.
Experimental results show that, under the condition of satisfying power equalization, the power differential rate of the system is lower, which verifies the feasibility of the method. At the same time, the simulation results show that the H-field intensity around the working system is within the limit level of the ICNIRP-2018 standard, which proves that the proposed structure can also exhibit good performance in an electromagnetic environment. This study is of great value to the application of wireless charging systems with multiple identical loads.