Design of Inductive Power Transfer Charging System with Weak Coupling Coefficient

Abstract

Inductive power transfer (IPT) technology is used in various applications owing to its safety features, robust environmental adaptability, and convenience. In some special applications, the charging pads are required to be as compact as possible to accommodate practical spatial requirements, and even size requirements dictate that the diameter of the charging pad matches the air gap. However, such requirements bring about a decrease in the transmission efficiency, power, and tolerance to misalignment of the system. In this paper, by comparing a double-sided inductor–capacitor–capacitor (LCC), double-sided inductor–capacitor–inductor (LCL), series–series (SS), and inductor–capacitor–capacitor–series (LCC-S) compensation topologies in IPT systems, we identified a double-sided LCC compensation topology that is suitable for weak coupling coefficients. Furthermore, this study modeled and simulated the typical parameters of coreless coils in circular power pads, such as the number of coil layers, turns, wire diameter, and wire spacing, to enhance the mutual inductance of the magnetic coupler during misalignment and long-distance transmission. A wireless charging system with 640 W output power was built, and the experimental results show that a maximum dc-dc efficiency of over 86% is achieved across a 200 mm air gap when the circular power pad with a diameter of 200 mm is well aligned. The experimental results show that using a suitable compensation topology and optimizing the charging pad parameters enables efficient IPT system operation when the coupling coefficient is 0.02.

1. Introduction

IPT technology has gained widespread adoption due to its advantages of high power and efficiency in near-field wireless power transfer, making it suitable for various applications such as electric vehicles [1,2,3,4,5], medical implant devices [6,7], and underwater vehicles [8,9,10]. However, in several narrow applications, such as inter-satellite modules, internal machinery with rotating components, or high-voltage transmission line monitoring equipment [11], the need arises for smaller charging pads to conserve space and reduce weight. As the size of coils decreases and the air gap increases, the coupling coefficient between the coils typically falls within the range of 0.015–0.03, which makes the transmission efficiency and stability of the system decrease. There is no doubt that optimizing coil design to enhance the coupling coefficient under large air gaps is crucial [12].

Many different compensation topologies have been proposed for tuning two coils at resonant frequency in order to work in a range of misalignment types or air gaps; these include four basic compensation topologies [13,14,15,16], LCC-LCC [1,2,3,4,17,18,19], LCL-LCL [20,21], and LCC-Series [9,22,23]. Usually, the constant-current output topologies suitable for wireless charging are the SS, LCL-LCL, and LCC-LCC compensation topologies. The resonant frequency of the SS compensation topology can be independent of the coupling coefficient and load [13,15], but the input impedance of the compensation topology is dependent on the coupling coefficient and load, which can be dangerous if misaligned or the load changes [16,24,25]. The design of an LCL compensation topology usually requires the compensation inductance value to be equal to the coil inductance value [20]. The LCC-LCC compensation topology has constant-current output, achieves a fixed operation frequency within a range of loads and air gaps, and is less sensitive to the variations of mutual inductance [4,18,19,26,27].

In an IPT system, the magnetic coupler plays an important role, and well-designed coupling coils and magnetic material core are essential. Many types of coil topologies have been proposed to enhance the coupling coefficient and tolerance to misalignment. Circular coils and rectangular coils are commonly used configurations in IPT systems. Several studies have focused on improving the performance of circular coils [28,29,30,31,32,33,34], while a method to enhance the quality factor (Q) of rectangular coils is reported in [35]. Additionally, Double D (DD) coils have been presented in [36], and they have been widely used in electric vehicle IPT systems due to their lower leakage flux from the outside of the coil and higher average flux path compared with other coil topologies [5,36,37,38,39]. In addition, there are also some methods available to increase the transmission distance by adding more coils [40,41] or designing new charging pads [11,42].

However, the conditions for these techniques are difficult to achieve efficient transmission in narrow engineering applications. Compared to previous literature, the primary contribution of this paper is the design methodology of a long-distance and efficient two-coil IPT system, which can be divided into two main aspects. First, it uses the typical parameters of the coreless coil such as the number of coil layers, turns, wire diameter, and wire spacing to establish a mathematic model in order to optimize the design of the multi-layer charging pads to save space and increase mutual inductance. Second, by comparing the outputs of commonly used compensation topologies under varying coupling coefficients, a double-sided LCC compensation topology suitable for weak couplings is selected.

This paper is structured as follows: Initially, the coupling coefficient of a charging pad composed of a single-layer circular coil and ferrite is simulated. Subsequently, double-sided LCC, double-sided LCL, SS, and LCC-S compensation topology wireless charging systems using the same charging pad diameter of 200 mm are designed to simulate changes in efficiency under different coupling coefficients or load, thereby identifying the compensation topology suitable for weak coupling IPT charging. Furthermore, this study proceeds to model and analyze the number of layers, turns, wire diameter, and wire spacing in coreless coils to optimize the charging pad design. Finally, a prototype circular charging pad with a diameter of 200 mm and a double-sided LCC compensation topology is built. It is verified that when the air gap is 200 mm and well aligned, the wireless charging system achieved an output power of 640 W with an efficiency exceeding 86%.

2. Comparison of Different Compensation Topologies

2.1. Magnetic Field Simulation of Charging Pad in Weak Coupling IPT System

An efficient IPT system necessitates the employment of suitably designed charging pads, as the coupling coefficient diminishes rapidly when the air gap is comparable to the diameter of the charging pad. While commonly used DD coils offer a higher average flux path compared to circular coils, circular coils are more suitable for weak coupling IPT systems due to their higher central magnetic flux density. The circular coils considered in this work for the charging pad of the primary transmitter and secondary receiver rely on magnetic field simulations of single-layer circular coils with ferrite cores to ascertain the mutual inductance and coupling coefficient between the coils across different air gaps. This preliminary analysis serves as foundational guidance for the development of the prototype charging pad discussed in Section 3.

The circular coils employed for Ansys Maxwell magnetic field simulations consist of a single layer, comprising 17 turns, with a diameter of 200 mm. The Litz wire utilized has a diameter of 3 mm, and the wire spacing is set at 3.2 mm. Four pieces of ferrite were used, each with a size of 100 mm × 100 mm × 5 mm. The root mean square (RMS) value of the excitation current was 3 A. The operation frequency was 83 kHz, selected based on the frequency range specified in the ISO 19363:2020 standard [43] for wireless charging of electric vehicles.

Figure 1a illustrates a coreless circular coil with a self-inductance of 48 $\mathsf{\mu }\mathrm{H}$. The charging pad, when equipped with ferrite, has a self-inductance of 85 $\mathsf{\mu }\mathrm{H}$. Figure 1b shows that the mutual inductance of charging pads decreases rapidly as the air gap increases. When the air gap is 200 mm, the mutual inductance is 2.359 $\mathsf{\mu }\mathrm{H}$ and the self-inductance is 85 $\mathsf{\mu }\mathrm{H}$, resulting in a coupling coefficient of less than 0.03 for air gaps greater than 200 mm. The simulation results suggest that a single-layer circular charging pad is suitable when the air gap is less than the radius of the circular coil. However, the coupling coefficient drops below 0.03 when the air gap equals the diameter of the charging pad, necessitating the use of multi-layered circular coils to maintain efficient IPT as the air gap increases.

2.2. Basic Characteristics of Different Compensation Topologies

The S and LCC compensation topologies are commonly used to realize IPT. With an increase in the air gap and misalignment, the coupling coefficient of the system is less than 0.03 and the dc-dc efficiency decreases rapidly. In this section, the model of compensation topology is established, and the output power and efficiency of different topologies under different coupling coefficients are analyzed.

Figure 2 shows the different compensation topologies used to transfer power from the inverter to load resistance, R_L. C₁ and C₂ are parallel compensation capacitors of the transmitter and receiver side, respectively. L₁ and L₂ represent the compensation inductance. L_p and Ls represent self-inductance, and associated transmitting and receiving coil resistances are represented by R_p and R_s. C_p and C_s are series compensation capacitors of L_p and Ls, respectively. Z_s represents the equivalent impedance of the secondary circuit; Z_r represents the impedance reflected by the secondary circuit to the primary circuit; Z_p represents the overall impedance of the entire system after inversion. M represents mutual inductance between coils. ω₀ represents the resonant angular frequency, ω₀ = 2πf, and f represents the operation frequency of the system.

k represents the coupling coefficient between the transmitting and receiving coils, and it is given by Equation (1):

$$k={\displaystyle \frac{M}{\sqrt{L_p{L}_s}}}$$

(1)

In this paper, L_p and L_s have a larger self-inductance than the transmitting coil in Annex A of ISO 19363:2020, L_p = L_s = 285 $\mathsf{\mu }\mathrm{H}$. The capacitance and inductance values of the compensation topology are calculated according to Equation (2).

$$\left\{\begin{array}{l}{\omega }_{0\_LCC-LCC}^2={\displaystyle \frac{1}{L_1{C}_1}}={\displaystyle \frac{1}{\left(L_p-L_1\right)C_p}}={\displaystyle \frac{1}{L_2{C}_2}}={\displaystyle \frac{1}{\left(L_s-L_2\right)C_s}}\\ \begin{array}{l}{\omega }_{0\_LCL-LCL}^2={\displaystyle \frac{1}{L_1{C}_1}}={\displaystyle \frac{1}{L_p{C}_1}}={\displaystyle \frac{1}{L_2{C}_2}}={\displaystyle \frac{1}{L_s{C}_2}}\\ {\omega }_{0\_SS}^2={\displaystyle \frac{1}{L_p{C}_p}}={\displaystyle \frac{1}{L_s{C}_s}}\end{array}\\ {\omega }_{0\_LCC-S}^2={\displaystyle \frac{1}{L_1{C}_1}}={\displaystyle \frac{1}{\left(L_p-L_1\right)C_p}}={\displaystyle \frac{1}{L_s{C}_s}}\end{array}\right.$$

(2)

Drawing upon the previous literature and assuming coil self-inductance, we determined the parameters necessary for comparing these topologies at an equivalent output power. These parameters are summarized in

Table 1. Parameters of the double-sided LCC, SS, and LCC-S compensation topologies.

Symbol	Parameter	LCC-LCC	LCL-LCL	SS	LCC-S
UAB	First-order rms value of input voltage	≤250 V
f	Resonance frequency	83 kHz
P	Designed power	~640 W
Lp	Self-inductance of the transmitting coil	$285 \mathsf{\mu }\mathrm{H}$
Ls	Self-inductance of the receiving coil	$285 \mathsf{\mu }\mathrm{H}$
Rp	AC resistance of the transmitting coil	$0.25 \mathsf{\Omega }$
Rs	AC resistance of the receiving coil	$0.25 \mathsf{\Omega }$
Cp	Primary-side series compensation capacitor	14.1 nF	/	12.9 nF	14.1 nF
Cs	Secondary-side series compensation capacitor	14.1 nF	/	12.9 nF	12.9 nF
L1	Primary-side compensation inductance	$25 \mathsf{\mu }\mathrm{H}$	$285 \mathsf{\mu }\mathrm{H}$	/	$25 \mathsf{\mu }\mathrm{H}$
L2	Secondary-side compensation inductance	$25 \mathsf{\mu }\mathrm{H}$	$285 \mathsf{\mu }\mathrm{H}$	/	/
R1	AC resistance of L1	$0.15 \mathsf{\Omega }$	$0.25 \mathsf{\Omega }$	/	$0.15 \mathsf{\Omega }$
R2	AC resistance of L2	$0.15 \mathsf{\Omega }$	$0.25 \mathsf{\Omega }$	/	/
C1	Primary-side parallel compensation capacitor	147 nF	12.9 nF	/	147 nF
C2	Secondary-side parallel compensation capacitor	147 nF	12.9 nF	/	/

.

For ideal double-sided LCC, double-sided LCL, SS, and LCC-S compensated wireless charging systems operating at f₀, the output power is calculated by:

$$\left\{\begin{array}{l}{P}_{out\_LCC-LCC}={\displaystyle \frac{M^2{U}_{AB}^2{R}_L}{{\omega }_o^2{C}_2^2{\left(L_1+R_1{C}_1\left(R_p+Z_{r\_LCC}\right)\right)}^2(R_s\left(R_L+R_2\right)+{\omega }_0^2{L}_2^2{)}^2}}\\ \begin{array}{l}{P}_{out\_LCL-LCL}={\displaystyle \frac{{\omega }_o^2{M}^2{U}_{AB}^2{R}_L}{{\left(j{\omega }_0{L}_2+R_L+R_2+j{\omega }_0{C}_2\left(j{\omega }_0{L}_s+R_s\right)\left(R_L+R_2\right)\right)}^2{\left(Z_{r\_LCL}+R_p+j{\omega }_0{L}_p+j{\omega }_0{L}_1\left(j{\omega }_0{L}_1+R_1\right)\left(Z_{r\_LCL}+R_p\right)\right)}^2}}\\ P_{out\_SS}={\displaystyle \frac{{\omega }_o^2{M}^2{U}_{AB}^2{R}_L}{{\left(R_p(R_s+R_L)+{\left({\omega }_{o}M\right)}^2\right)}^2}}\end{array}\\ P_{out\_LCC-S}={\displaystyle \frac{M^2{U}_{AB}^2{R}_L}{L_1^2{\left(R_L+R_s+R_1{\omega }_o^2{C}_1^2\left(R_p(R_s+R_L)+{\left({\omega }_{o}M\right)}^2\right)\right)}^2}}\end{array}\right.$$

(3)

$Z_{r\_LCC}$ and $Z_{r\_LCL}$ are the reflection impedance from the secondary side to the primary side of the double-sided LCC and double-sided LCL compensation topology, respectively.

$$\left\{\begin{array}{l}{Z}_{r\_LCC}={\displaystyle \frac{{\omega }_o^2{M}^2\left(R_L+R_2\right)}{{\omega }_o^2{L}_2^2+R_s\left(R_L+R_2\right)}}\\ Z_{r\_LCL}={\displaystyle \frac{{\omega }_o^2{M}^{2}j{\omega }_0{C}_2\left(R_L+R_2\right)}{j{\omega }_0{L}_2+R_L+R_2+j{\omega }_0{C}_2\left(j{\omega }_0{L}_s+R_s\right)\left(R_L+R_2\right)}}\end{array}\right.$$

(4)

The transmission efficiency can be calculated by Equation (5):

$$\left\{\begin{array}{l}{\eta }_{LCC-LCC}={\displaystyle \frac{M^2{R}_L}{{{\omega }_o^{2}C}_2^2{C}_1\left(R_p+Z_{r\_LCC}\right)\left(L_1+R_1{C}_1\left(R_p+Z_{r\_LCC}\right)\right){\left(R_s\left(R_L+R_2\right)+{\omega }_0^2{L}_2^2\right)}^2}}\\ \begin{array}{l}{\eta }_{LCL-LCL}={\displaystyle \frac{\omega M^2{R}_L}{C_1\left(R_p+Z_{r\_LCL}\right){\left(j{\omega }_0{L}_2+R_L+R_2+j{\omega }_0{C}_2\left(j{\omega }_0{L}_s+R_s\right)\left(R_L+R_2\right)\right)}^2\left(Z_{r\_LCL}+R_p+j{\omega }_0{L}_p+j{\omega }_0{L}_1\left(j{\omega }_0{L}_1+R_1\right)\left(Z_{r\_LCL}+R_p\right)\right)}}\\ {\eta }_{SS}={\displaystyle \frac{{\omega }_o^2{M}^2{R}_L}{(R_s+R_L)\left(R_p(R_s+R_L)+({\omega }_{o}M{)}^2\right)}}\end{array}\\ {\eta }_{LCC-S}={\displaystyle \frac{{{{\omega }_0^{2}M}^{2}R}_L}{\left(R_s+R_L+R_1{\omega }_o^2{C}_1^2\left(R_p(R_s+R_L)+{\left({\omega }_{o}M\right)}^2\right)\right)\left(R_p\right(R_s+R_L)+{\omega }_0^2{M}^2)}}\end{array}\right.$$

(5)

Figure 3 compares the efficiency of the double-sided LCC, double-sided LCL, SS, and LCC-S compensation topologies when only considering the equivalent resistance of the inductance.

Figure 3a shows that the double-sided LCC compensation topology exhibits higher efficiency compared to the LCL-LCL, LCC-S, and SS compensation topologies. Figure 3b shows that the double-sided LCC compensation topology achieves a higher average efficiency in comparison to the LCL-LCL, LCC-S, and SS compensation topologies under weak coupling conditions. Owing to the increase in I_p for the SS compensation and higher average transmission efficiency of double-sided LCC compensation under weak coupling coefficient, this paper selects the double-sided LCC compensation topology for the IPT system under weak coupling.

3. Modeling of Coupling Coils

3.1. Modeling of Coreless Coils

The k of charging pads is a significant parameter which is determined by the coils’ self-inductance and mutual inductance. Keeping k within a reasonable range is a significant condition of ensuring stable IPT. The self-inductance of the coil mainly depends on the outer diameter d_out of the coil, the inner diameter d_in of the coil, the number of single-layer coil turns N, the number of coil layers m, the wire spacing S_w, and wire diameter D_w. The mutual inductance of the coils depends on the coil shape and relative position of the coil.

The self-inductance L of a regular polygon hollow coil can be calculated by the following Neumann formula [44]. L can be calculated by Equation (6):

$$\left\{\begin{array}{l}L={\displaystyle \frac{{\mu }_0{N}^2{d}_{a\nu g}{c}_1}{2}}(\mathrm{l}\mathrm{n}{\displaystyle \frac{c_2}{\rho }}+c_3+c_4{\rho }^2)\\ d_{a\nu g}={\displaystyle \frac{d_{out}+d_{in}}{2}}\\ \rho ={\displaystyle \frac{d_{out}-d_{in}}{d_{out}+d_{in}}}\end{array}\right.$$

(6)

where ${\mu }_0$ is the permeability of vacuum. The specific parameters are shown in

Table 2. Self-inductance parameters of different coreless coils.

Coil Shape	c1	c2	c3	c4
Circular coil	1.00	2.46	0.00	0.20
Rectangular coil	1.27	2.07	0.18	0.13

.

The error of this method increases with the increase in the ratio between S_w and D_w of the coil. The fitting effect is more accurate when S_w is less than or equal to D_w. The error is 8% when S_w is three times D_w.

According to Maxwell’s theory, the M of the coupling coils is related to the coil current in a single period. Take an asymmetric, single-layer coupling coreless circular coil without misalignment as an example, as shown in Figure 4.

The M of the axisymmetric coupling coreless circular coil can be expressed as Equation (7) [45].

$$M={\mu }_0{N}_1{N}_2{\displaystyle \frac{\sqrt{r_1{r}_2}}{a}}[(2-a^2)K-2E]$$

(7)

In Equation (7), the average radii of the two coils are r₁ and r₂, respectively, N₁ and N₂ are the turns of the two coils, and h is the air gap, where:

$$\left\{\begin{array}{l}a=\sqrt{{\displaystyle \frac{4r_1{r}_2}{h^2+{\left(r_1+r_2\right)}^2}}}\\ K={\int }_0^{{\displaystyle \frac{\pi }{2}}}{\displaystyle \frac{1}{\sqrt{1-a^2{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta }}}d\theta \\ E={\int }_0^{{\displaystyle \frac{\pi }{2}}}\sqrt{1-a^2{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta }d\theta \end{array}\right.$$

(8)

N₁ and N₂ are limited when the coil size is limited, so the number of coil layers m needs to be increased to improve L and M, and multiple single-layer coupling coils can simulate the multi-layer coil. According to Equation (6), the self-inductance of a coil with turn number N and layer number m can be expressed as Equation (9):

$$L^{\ast }={\displaystyle \frac{{\mu }_0{\left(mN\right)}^2{d}_{a\nu g}{c}_1}{2}}\left(\mathrm{l}\mathrm{n}{\displaystyle \frac{c_2}{\rho }}+c_3\rho +c_4{\rho }^2\right)\approx m^{2}L$$

(9)

Equation (9) suggests that the self-inductance of a multi-layer coil is approximately equal to the self-inductance of a single-layer coil multiplied by the square of the coil layers. Nonetheless, the self-inductance of coils does not consistently rise with the coil layers due to wire spacing. Specifically, as the number of layers increases, the effective air gap between coupled coils expands, which in turn diminishes both coil self-inductance and mutual inductance. The self-inductance of multi-layer coupling coils with larger intervals can also be understood as the superposition of the self-inductance of each layer of coils and the internal mutual inductance, which can be expressed as Equation (10):

$$L^{\ast }=\sum _{i=1}^m{L}_i+2\sum _{i=1}^{m-1}\sum _{j=i+1}^m{M}_{ij}$$

(10)

The M between multi-layer coupling coils can be understood as the mutual inductance superposition of multiple single-layer transmitting coils and multiple single-layer receiving coils. For coils with few layers, the mutual inductance formula of single-layer coupling coils can be directly calculated.

When the IPT system works at high-frequency alternating current, the relationship between the AC resistance of Litz wire and the operation frequency can be described by Equation (11) [46]:

$$R_{AC}=K_c{\displaystyle \frac{4\rho L_{coil}}{\pi N_S{D}_S}}[H+2({\displaystyle \frac{N_S{D}_S}{D_w}}{)}^2({\displaystyle \frac{D_S\sqrt{f}}{265}}{)}^4]$$

(11)

where K_c is the length correction coefficient, usually 1.04~1.056; L_coil is the length of the coil wire; N_s is the number of Litz wire strands; D_s is the single strand diameter of the Litz wire; H is the ratio of AC resistance to DC resistance of single strand wire; and $\rho$ is the conductivity of the Litz wire.

Equation (11) shows that the L_coil of circular coil is smaller than that of rectangular coil for the same outer diameter and number of turns, so a circular coil is more suitable for weak coupling IPT. The output power of the double-sided LCC compensation topology can be obtained as:

$$P_{out}=P_{out\_LCC-LCC}-I_{p\_rms}^2\ast R_{AC}-P_{loss-diode}-P_{loss-MOSFET}$$

(12)

The mutual inductance, self-inductance, and AC resistance of the coupling coils can be calculated using parameters such as the number of coil layers, turns, and wire spacing, etc.

3.2. Designing Coreless Coupling Coils to Optimize Mutual Inductance

The coupling coefficient is less than 0.03 when the coil diameter and air gap are equal, so M should be increased as much as possible to make the double-sided LCC compensation topology work efficiently under a weak coupling coefficient. In this work, the coil diameter and the air gap have been determined, so the coupling coefficient can only be improved by designing the number of coil layers, turns, wire diameter, and wire spacing. By using Equations (6) to (12), the coreless circular coil parameters of a weak coupling IPT system are calculated and designed. The detailed design process is shown in Figure 5.

M must be at least 7.7 $\mathsf{\mu }\mathrm{H}$ to achieve k = 0.027 when L_p = L_s = 285 $\mathsf{\mu }\mathrm{H}$. Therefore, the mutual inductance of IPT should be improved by optimizing the S_w, D_w, m, and N of coupling coils, while keeping the coil self-inductance and air gap fixed.

The maximum number of coil turns is limited because the coil diameter and wire diameter are limited. Figure 6 shows the influence of different D_w, S_w, and m values on the mutual inductance of the coreless circular coupling coils when N = 17. When the circular coil diameter and the air gap are 200 mm, the simulation results show that, when D_w = 2 mm, S_w = 0 mm, m = 2, and N = 17, the mutual induction reaches the target value in the case of positive alignment and changes slightly in the case of a small lateral misalignment, which is suitable for weak coupling coefficient IPT. The modeling of coreless circular coils helps determine the number of layers, turns, wire diameter, and wire spacing for the charging pad.

4. Experiment

Using the parameters in

Table 3. Parameter values of IPT prototype.

Parameter	f0	Lp/Ls	Rp/Rs	Cp,s	L1,2	C1,2	m	N	Dw	Sw
Value	83 kHz	$285 \mathsf{\mu }\mathrm{H}$	$0.21 \mathsf{\Omega }$	14.1 nF	$25.1 \mathsf{\mu }\mathrm{H}$	147 nF	2	17	2 mm	2 mm

, a 640 W experimental platform for an IPT system was built.

The charging pad is shown in Figure 7a. In Figure 7b, the capacitors C₁ and C_s are shown mounted on a circuit board. L1, as shown in Figure 7c, is fabricated by winding Litz wire on ferrite. The experimental platform is shown in Figure 7d. The IPT characteristics of the double-sided LCC compensation topology under conditions of weak coupling coefficient are examined, with the air gap set at 200 mm for the test.

The efficiency from the DC voltage source to the DC electronic load, also known as dc-dc efficiency, of the IPT prototype with no misalignment, an air gap of 200 mm, and a coil diameter of 200 mm is shown in Figure 8 as a function of the output power. The experimental results show that the double-sided LCC IPT system can achieve stable power transmission under a weak coupling coefficient with the same coil diameter and air gap.

The maximum dc-dc efficiency of the simulated system is 87.7%, whereas the maximum measured efficiency is 86.6%, owing to the presence of a rectifier, inverter, and non-ideal components within the circuit. However, the IPT prototype has the capability to demonstrate a dc-dc efficiency consistently exceeding 79% when the coupling coefficient is 0.02.

5. Discussion

This paper proposes a method utilizing multi-layer circular coils in conjunction with a double-sided LCC compensation topology to achieve efficient IPT under weak coupling conditions. The charging pads discussed in the literature usually employ single-layer coils [8,19]; however, the weak coupling occurring when the air gap equals the diameter of the single-layer coil leads to detuning and reduced efficiency. The modeling of coreless circular coils helps to optimize the number of layers, turns, wire diameters, and wire spacing of the charging pad to increase mutual inductance during misalignment and long-distance transmission.

Table 4. Comparison of IPT systems.

Reference	Year	Compensation Topology	Frequency	Air Gap or k	Efficiency (%)	Power
[11]	2019	LCL-S	547.7 kHz	700~1600 mm	15~32.5	16.7 W (1500 mm)
[42]	2019	SS	450 kHz	1175 mm	37	60 W
[47]	2019	S-S-S-S	4.02 MHz	900~1100 mm	22~46	30.5 W (900 mm)
[22]	2020	LCC-S	60 kHz	0.293~0.5	73~86	100 W
[3]	2022	LCC-LCC	85 kHz	0.08~0.18	83~87.55	3.3 kW
[23]	2023	LCC-S	200 kHz	34 mm	83.4	160 W
[19]	2024	LCC-LCC	100 kHz	100 mm	93.4~91	100 W
This paper	2024	LCC-S	83 kHz	200 mm	79~86.6	640 W

provides a comparison of the performance of IPT prototypes.

This paper elucidates through simulations that single-layer coils are better suited when the air gap is less than the coil radius. Furthermore, a charging pad with enhanced mutual inductance via multi-layer coreless circular coils is employed and, in conjunction with double-sided LCC compensation topology, constitutes an IPT prototype capable of delivering 640 W output power. The experimental results show that this prototype achieves a maximum dc-dc efficiency of 86.6%, with the dc-dc efficiency consistently exceeding 79% when the coupling coefficient is 0.02.