An Integrated Double-Sided LCC Compensation Based Dual-Frequency Compatible WPT System with Constant-Current Output and ZVS Operation

Abstract

This article presents an integrated double-sided inductance and double capacitances (DS-LCC) compensation based dual-frequency compatible wireless power transfer (WPT) system. A cascaded single-phase multi-frequency inverter (CSMI) is constructed to generate the independent dual-frequency power transfer signals. In order to achieve the load-independent constant-current output (CCO) at two frequencies, an integrated DS-LCC compensated topology is reconstructed. By configuring the frequency-selective resonating compensation (FSRC) network in the primary side, the power transfer signals at two frequencies can be superimposed into a single transmitting coil, reducing the cost and volume of the system. Furthermore, to implement zero-voltage switching (ZVS) of the CSMI throughout the entire power range, a general parameter design method of the proposed system is also introduced. A 1.5-kW experimental prototype is built to validate the practicability of the presented dual-frequency compatible WPT System. The system can supply power to different loads at two frequencies simultaneously with CCO and ZVS properties. The peak efficiency reaches 91.75% at a 1.2-kW output power.

1. Introduction

Wireless power transfer (WPT) technology is a promising power supply technology developed in recent years. Compared with the traditional wired energy transfer, it can effectively avoid the problems of spark and electric shock, and has advantages in improving the reliability, safety, convenience, and extending the service life of the equipment [1,2,3,4]. As a result, this novel alternative technology has been applied in many applications requiring electrical power transfer from a supply to a load without the need for physical contacts, including electric vehicles, unmanned aerial vehicles, underwater vehicles, automated guided vehicles, consumer electronics and biomedical implants [5,6,7,8].

At present, most of the power supply targets of WPT systems are single loads. Power is supplied to a single load through a single transmitting coil or multiple transmitting coils at a specific frequency. The efficiency of a single-frequency system is higher and easier to align, but it is more difficult to design a single-frequency system for a wide range of loads. Therefore, a multi-frequency system can overcome this issue. In addition, the single-load WPT system with single-frequency operation has some limitations, such as weak power transfer capacity, poor frequency compatibility and low spatial freedom [9,10,11]. With the application demand and the continuous development of technology, the research on WPT has gradually developed from single-load WPT system to “one-to-two” or even “one-to-many” multi-frequency and multi-load WPT. When a plurality of secondary side receivers with the same natural frequency as the primary side transmitter are in the magnetic field formed by the transmitting coil, wireless power transfer from one transmitter to multiple electrical devices at different operating frequencies can be achieved simultaneously [12,13].

In the multi-frequency and multi-load WPT system, because the power is transferred to the load end corresponding to different frequencies only through a common transmitting coil, it is necessary to carry out multi-frequency superposition modulation on the inverter, so as to generate power superposition signals of different frequencies [14,15]. In [16,17], a cascade structure of multiple inverters was proposed, in which multiple square wave voltages of different frequencies were generated by the cascade of multiple inverters on the primary side, and the multi-frequency power signals were coupled and superimposed on the transmitting coil by the same number of transformers. However, the use of a large number of inverters and transformers greatly increases the volume and cost of the system. Refs. [18,19,20] utilized the multi-frequency superposition modulation method based on sinusoidal pulse width modulation (SPWM), by superimposing sinusoidal modulated waves of different frequencies to form hybrid modulated waves, and modulating them with high-frequency carrier, the inverter can generate multi-frequency superimposed power signal. This structure only uses one inverter, which has the advantages of simple structure and easy implementation. However, under SPWM modulation, all four switches of the single-phase inverter operate in a hard switching state, and the excessively high switching frequency leads to a sharp increase in switching losses. In [21,22], A multi-frequency superposition modulation method based on neutral point clamped-multilevel inverters (NPC-ML) was proposed, this method uses NPC-ML to generate multilevel square wave signals, which contain multiple power signals of different frequencies, Therefore, the superposition transfer of multi-frequency signals can be realized only by a single inverter. However, in this way, some switches of the inverter still cannot achieve soft switching operation, and the switching loss is still very large.

In the multi-frequency multi-load WPT system, it is crucial to ensure independent transmission of power signals at different frequencies [23]. Since the receiving circuit has a high impedance at a non-resonant frequency, the crosstalk between signals of different frequencies can be locally suppressed. Therefore, it is necessary to construct additional wave traps in the transmitter circuit to demodulate the multi-frequency superposition modulation signal to further suppress the multi-frequency crosstalk problem and ensure the independence of the multi-frequency signals [24,25]. Ref. [26] proposed a method of multi-frequency demodulation using tunable capacitor array, in which the natural resonant frequency of the primary circuit can be changed by switching the compensation capacitor, so as to realize frequency tracking. However, this scheme requires a large capacitor array, reducing the practicality and applicability of the system. Ref. [27] proposed a continuously adjustable capacitor scheme that simulates the real capacitance characteristics by controlling the input voltage of the resonant network port, which can realize the continuous tracking of the resonant frequency. However, this method is based on the idea of time-sharing multiplexing to realize the demodulation of multi-frequency signals, and can only realize the power transfer at a single frequency at each moment, which violates the principle of multi-frequency and multi-load transfer in essence, and the power transfer capacity is limited. In addition, the multi frequency resonant compensation topology was also studied in [28,29,30], However, the above research schemes generally have a common issue, that is, the design of resonant compensation network only considers the frequency selection characteristics of the target frequency, ignoring the frequency blocking characteristics of other transmission frequencies. Thus, these schemes cannot completely eliminate crosstalk between signals of different frequencies.

In order to address the above issues, this article presents an integrated double-sided inductance and double capacitances (DS-LCC) compensation based dual-frequency compatible WPT system. First, a cascaded single-phase multi-frequency inverter (CSMI) is constructed to generate the dual-frequency power transmission signals. Next, in order to implement the load-independent constant-current output (CCO) and zero-voltage switching (ZVS) at two specified frequencies, the DS-LCC compensated topology is reconstructed based on the frequency-selective resonating compensation (FSRC) network, and a general design procedure of the resonant parameters is introduced for general applications. Ultimately, the practicability and effectiveness of the presented dual-frequency compatible WPT system are verified by a 1.5-kW experimental prototype.

2. Theoretical Analysis of the Proposed Dual-Frequency Compatible WPT System

The schematic diagram of the proposed integrated DS-LCC compensation based dual-frequency compatible WPT system is shown in Figure 1. The entire system constitutes a CSMI, a reconstructed primary LCC compensation network, and two receivers. Among these, the cascaded multi-frequency inverter is composed of two half-bridge inverters, and it is utilized to convert the common dc-link voltage U_dc to the ac voltages u_ini (i = 1, 2) at two specified resonant frequency ω₁ and ω₂. It should be noted that the subscript “i” represents the number of channels corresponding to the two resonant frequencies, which will not be repeated in subsequent sections. In practical, two full-bridge inverter also can be used to construct the system. Compared with full-bridge inverters, the use of half-bridge inverters can reduce the utilization rate of dc bus voltage, but it allows two transmission channels to share a dc power supply and a common ground wire and can reduce the number of power switch, which reduces the volume and cost of the system and improve the integration, this is the main reason why we use cascaded half-bridge structure. Generally, u_ini is a half-square wave with a fixed duty cycle of 0.5, and the fundamental harmonic analysis (FHA) method is used for qualitative analysis. In this case, only the fundamental harmonic of u_ini is considered, and its root mean square (RMS) value is denoted as U_ini, and can be derived as:

$$U_{ini}=\left|\stackrel{·}{U_{ini}}\right|={\displaystyle \frac{\sqrt{2}}{\pi }}{U}_{\mathrm{dc}}, \left(\mathrm{i}=1,2\right)$$

(1)

In the primary side, two LCC compensation networks are cascaded and reconstructed based on the FSRC network, so as to provide independent dual-frequency power transmission channels. Each reconstructed primary LCC compensation network comprises a resonant inductor L_i1, two resonant capacitors C_pi1 and C_fi1, and a FSRC network. In order to suppress the crosstalk between the two power transmission channels and ensure the independence of the dual-frequency signals, the FSRC network is utilized to provide a path for the power signal transmission at the target resonant frequency and block the power signal transmission at another resonant frequency. The specific working principle and parameter design criteria of the FSRC network will be discussed in subsequent sections. By reconstructing the primary LCC compensation network, the loop currents of the two power transmission channels i_p1 and i_p2 can be superimposed into a single transmitting coil to reduce the cost and volume of the system.

In the secondary side, the two receivers are composed of two receiving coils, two normal LCC compensation networks, two single-phase bridge rectifiers (SBR), and two dc loads. Among these, the SBR is used to convert the ac voltage u_oi to the charging voltage U_bi, and a dc capacitor C_oi is used to stabilize U_bi. Under this scenario, the inputs and outputs of the SBR have the following relationships:

$$\left\{\begin{array}{l}{U}_{\mathrm{b}\mathrm{i}}={\displaystyle \frac{\pi \sqrt{2}}{4}}{U}_{\mathrm{o}\mathrm{i}}\\ I_{\mathrm{b}\mathrm{i}}={\displaystyle \frac{2\sqrt{2}}{\pi }}{I}_{\mathrm{o}\mathrm{i}}\end{array}\right., \left(\mathrm{i}=1,2\right)$$

(2)

where U_oi and I_oi are the RMS values of the AC inputs of each SBR. Based on (2), an ac equivalent resistance R_oi can be deduced as:

$$R_{\mathrm{o}\mathrm{i}}={\displaystyle \frac{8}{{\pi }^2}}{R}_{\mathrm{L}\mathrm{i}}, \left(\mathrm{i}=1,2\right)$$

(3)

For the loosely coupled transformer (LCT), a transmitting coil and two receiving coils form a three-coil structure. L_p is the self-inductance of the single transmitting coil, L_s1 and L_s2 are the self-inductance of the two receiving coils. M₁ and M₂ are the mutual inductance between the single transmitting coil and two receiving coils, M₁₂ is the mutual inductance between the two receivers. The coupling coefficient of the LCT is defined as

$$k_1={\displaystyle \frac{M_1}{\sqrt{L_{\mathrm{p}}{L}_{\mathrm{s}1}}}}, k_2={\displaystyle \frac{M_2}{\sqrt{L_{\mathrm{p}}{L}_{\mathrm{s}2}}}}, k_{12}={\displaystyle \frac{M_{12}}{\sqrt{L_{\mathrm{s}1}{L}_{\mathrm{s}2}}}}$$

(4)

According to some previous literatures [17,27], it can be known that when two receiving coils are overlapped slightly or separated from each other by a distance, the cross-coupling effect can be ignorable, namely, k₁₂ << 1. Therefore, only the cross-coupling between the single transmitting coil and two receiving coils is considered in this paper. Under this condition, and according to Equations (1) and (2), the CSMI and SBR in Figure 1 can be replaced by two sinusoidal voltage sources and an AC equivalent load, respectively. Meanwhile, the LCT is considered equivalent to a mutual-inductance model based on the transformer theory. As a result, the proposed DS-LCC dual-frequency compatible WPT system in Figure 1 can be simplified as a mutual-inductance model-based equivalent circuit to simplify the analyses and calculations, as shown in Figure 2.

In Figure 2, it should be noted that although both receivers and the common transmitter are coupled, because the receiving circuit has a high impedance at a non-resonant frequency and the FSRC network can suppress the crosstalk between the dual-frequency power transmission channels, the equivalent circuit operating at two different frequencies can be analyzed and calculated independently. In the primary side, according to the analysis of LCC resonant network in previous literatures, when the inductor L_i1 and capacitor C_pi1 are resonant, i.e., ω_i ² = 1/(L_i1C_pi1), the load-independent primary side loop current in each power transmission channels can be deduced as:

$$\stackrel{·}{I_{\mathrm{pi}}}={\displaystyle \frac{\stackrel{·}{U_{\mathrm{ini}}}}{j{\omega }_{\mathrm{i}}{L}_{\mathrm{i}1}}}={\displaystyle \frac{U_{\mathrm{ini}}}{{\omega }_{\mathrm{i}}{L}_{\mathrm{i}1}}}\angle -{90}^{\circ },\left(\mathrm{i}=1,2\right)$$

(5)

According to the Kirchhoff’s current law (KCL), the dual-frequency superposition current passing through the primary side coil is

$$\stackrel{·}{I_{\mathrm{p}}}=\stackrel{·}{I_{\mathrm{p}1}}+\stackrel{·}{I_{\mathrm{p}2}}$$

(6)

On the basis of satisfying Equation (5), if the resonant condition ω_i² = 1/(L_seiC_pi2) is also satisfied in each secondary side, where L_sei is the equivalent inductance that includes the series connection of L_si and C_fi2, and L_sei = L_si − 1/(ω_i²C_fi2), the load-independent ac output current in each receiver can be deduced as:

$$\stackrel{·}{I_{\mathrm{o}\mathrm{i}}}={\displaystyle \frac{M_{\mathrm{i}}\stackrel{·}{U_{\mathrm{ini}}}}{j{\omega }_{\mathrm{i}}{L}_{\mathrm{i}1}{L}_{\mathrm{sei}1}}}={\displaystyle \frac{M_{\mathrm{i}}{U}_{\mathrm{ini}}}{j{\omega }_{\mathrm{i}}{L}_{\mathrm{i}1}{L}_{\mathrm{sei}1}}}\angle -{90}^{°},\left(\mathrm{i}=1,2\right)$$

(7)

3. Working Principle and Parameter Design Criteria of the FSRC Network

According to the above analysis, in order to implement the load-independent CCO of the dual-frequency power transmission channels in the proposed system, it is not only necessary to satisfy the resonant conditions associated with CCO characteristics, but more importantly, to suppress the crosstalk between the dual-frequency channels by utilizing the FSRC networks. Thus, in this section, the construction method of the FSRC network for dual-frequency power transfer is considered in detail.

As shown in Figure 2, the equivalent impedance of the FSRC network can be derived as:

$$\begin{array}{ll}\hfill Z_{\mathrm{FSRC}\_\mathrm{i}}& ={\displaystyle \frac{1}{1/j\omega L_{\mathrm{x}\mathrm{i}}+j\omega C_{\mathrm{x}\mathrm{i}}}}+Z_{\mathrm{ai}}\hfill \\ & ={\displaystyle \frac{j\omega L_{\mathrm{x}\mathrm{i}}}{1-{\omega }^2{L}_{\mathrm{x}\mathrm{i}}{C}_{\mathrm{x}\mathrm{i}}}}+Z_{\mathrm{ai}}\hfill \end{array}$$

(8)

For each power transmission channel, the basic working principle of the FSRC network is to provide a power transmission path at the target resonant frequency and block the power signal transmission at another resonant frequency, i.e.,

$$\left\{\begin{array}{l}\underset{\omega \to {\omega }_{\mathrm{on}}}{\lim }\left|Z_{\mathrm{FSRC}\_\mathrm{i}}\right|=0 \\ \underset{\omega \to {\omega }_{\mathrm{off}}}{\lim }\left|Z_{\mathrm{FSRC}\_\mathrm{i}}\right|=\infty \end{array}\right.$$

(9)

where ω_on is the natural resonant frequency of one power transmission channel, and ω_off is the natural resonant frequency of another power transmission channel. By combining Equations (8) and (9), the following relational expressions are obtained:

$$\left\{\begin{array}{l}1={\omega }_{\mathrm{off}}^2{L}_{\mathrm{x}\mathrm{i}}{C}_{\mathrm{x}\mathrm{i}} \\ Z_{\mathrm{ai}}={\displaystyle \frac{-j{\omega }_{\mathrm{on}}{L}_{\mathrm{x}\mathrm{i}}}{1-({\omega }_{\mathrm{on}}/{\omega }_{\mathrm{off}}{)}^2}}\end{array}\right.$$

(10)

From Equation (10), it can be seen that if ω_on >ω_off, Z_ai is a positive complex number, i.e., Z_ai consists of an inductor L_ai (Z_ai = jω_onL_ai), and L_ai can be calculated as

$$L_{\mathrm{ai}}={\displaystyle \frac{{\omega }_{\mathrm{off}}^2{L}_{\mathrm{x}\mathrm{i}}}{{\omega }_{\mathrm{on}}^2-{\omega }_{\mathrm{off}}^2}}$$

(11)

If ω_on < ω_off, Z_ai is a negative complex number, i.e., Z_ai consists of a capacitor C_ai (Z_ai = 1/jω_onC_ai), and C_ai can be calculated as

$$C_{\mathrm{ai}}={\displaystyle \frac{{\omega }_{\mathrm{off}}^2-{\omega }_{\mathrm{on}}^2}{L_{\mathrm{x}\mathrm{i}}{\omega }_{\mathrm{on}}^2{\omega }_{\mathrm{off}}^2}}$$

(12)

For a multi-frequency WPT system, when the resonant frequencies of different power transmission channels are relatively close, there will be obvious crosstalk issue, resulting in the analysis and design of the system are not accurate. In order to avoid this issue, under the premise of meeting application requirements and constraints, the difference between each operating frequency should be improved as much as possible in the design. In this paper, the two resonant frequencies are specified as ω₁ = 125,664 rad/s (f₁ = 20 kHz), and ω₂ = 534,071 rad/s (f₂ = 85 kHz). According to the above analysis, the structures of the two FSRC networks in Figure 2 can be determined, as shown in Figure 3.

The function of FSRC 1 is to provide a power transmission path at ω₁ and block the power signal transmission at ω₂, and the function of FSRC 2 is just the opposite. In order to realize the above functions, the parameters of the two FSRC networks need to be designed. First, in the two FSRC networks, the parallel resonant inductor L_xi has no parameter constraint and has high parameter design freedom. Considering that a too large inductance value of L_xi will increase the cost and volume, while a too small value of L_xi will introduce large parameter errors. On balance, the inductance of L_x1 and L_x2 in Figure 3 are designed to be 50 μH. Next, according to the two resonant frequencies ω₁ and ω₂, and by using Equations (10)–(12), the values of the remaining resonant parameters in the two FSRC networks can be obtained separately. The designed resonant parameters are listed in

Table 1. Designed parameters of the two FSRC networks.

Note	Symbol	Value
Resonance frequency of FSRC 1	f1	20 kHz
Resonance frequency of FSRC 2	f2	85 kHz
Parallel resonant inductance of FSRC 1	Lx1	50 µH
Parallel resonant inductance of FSRC 2	Lx2	50 µH
Parallel resonant capacitance of FSRC 1	Cx1	70.12 nF
Parallel resonant capacitance of FSRC 2	Cx2	1266.51 nF
Series resonant capacitance of FSRC 1	Ca1	1196.40 nF
Series resonant inductance of FSRC 2	La2	2.93 µH

.

Using the parameters listed in Table 1, the impedance magnitude of Z_{FSRC_i} versus frequency is calculated by using MATLAB 2021a tool, as shown in Figure 4. The red and blue curves represent the variation of the impedance of Z_{FSRC_1} and Z_{FSRC_2} with frequency, respectively. It should be noted that in order to make the curve easier to navigate, the logarithmic representation is used to normalize the magnitude of Z_{FSRC_i}. When f = 20 kHz, the impedance magnitude of Z_{FSRC_1} is close to zero, while the impedance magnitude of Z_{FSRC_2} is close to infinity, while when f = 85 kHz, the impedance magnitude of Z_{FSRC_2} is close to zero, while the impedance magnitude of Z_{FSRC_1} is close to infinity. Figure 4 show that the FSRC 1 network has a conduction effect on the 20 kHz power signal, and a blocking effect on the 85 kHz power signal, while the FSRC 2 network has a conduction effect on the 85 kHz power signal, and a blocking effect on the 20 kHz power signal. The above analysis results show that the structure and parameter design of FSRC networks meet the requirements of dual-frequency power transmission.

4. Parameter Design Method of the Proposed Dual-Frequency WPT System

For the DS-LCC compensated WPT system, CCO and zero phase angle (ZPA) are two major considerations for parameter tuning. Since the implementation of CCO for the DS-LCC compensation based dual-frequency WPT system has been given in Section 2, the implementation of ZPA should be discussed here.

In Figure 2, the total equivalent impedances of the secondary and primary sides in two power transmission channels are defined as Z_si and Z_ini, respectively, and they can be calculated as

$$\left\{\begin{array}{l}{Z}_{\mathrm{s}\mathrm{i}}= j\omega L_{\mathrm{si}}+R_{\mathrm{si}}+1/j\omega C_{\mathrm{fi}2}+{\displaystyle \frac{1/j\omega C_{\mathrm{pi}2} (j\omega L_{\mathrm{i}2} + R_{\mathrm{oi}})}{1/j\omega C_{\mathrm{pi}2} + j\omega L_{\mathrm{i}2} + R_{\mathrm{oi}}}}\\ Z_{\mathrm{ini}}= j\omega L_{\mathrm{i}1}+{\displaystyle \frac{1/j\omega C_{\mathrm{pi}1} (j\omega L_{\mathrm{p}} + 1/j\omega C_{\mathrm{fi}1}+R_{\mathrm{p}}+Z_{\mathrm{ri}}+Z_{\mathrm{FSRC}\_\mathrm{i}})}{1/j\omega C_{\mathrm{pi}1} +j\omega L_{\mathrm{p}} + 1/j\omega C_{\mathrm{fi}1}+R_{\mathrm{p}}+Z_{\mathrm{ri}}+Z_{\mathrm{FSRC}\_\mathrm{i}}}}\end{array}\right.$$

(13)

where Z_ri is the reflected impedance. Z_ri is converted from the secondary side to the primary side, and is deduced as: Z_ri = ω²M_i²/Z_si. The phase angles of the Z_si and Z_ini are defined as:

$$\left\{\begin{array}{l}{\theta }_{\mathrm{s}\mathrm{i}}={\displaystyle \frac{180^{°}}{\pi }}{\tan }^{-1}{\displaystyle \frac{\mathrm{Im}\left({\mathrm{Z}}_{\mathrm{s}\mathrm{i}}\right)}{\mathrm{Re}\left({\mathrm{Z}}_{\mathrm{s}\mathrm{i}}\right)}}\\ {\theta }_{\mathrm{ini}}={\displaystyle \frac{180^{°}}{\pi }}{\tan }^{-1}{\displaystyle \frac{\mathrm{Im}\left({\mathrm{Z}}_{\mathrm{ini}}\right)}{\mathrm{Re}\left({\mathrm{Z}}_{\mathrm{ini}}\right)}}\end{array}\right.$$

(14)

In the DS-LCC compensation based dual-frequency WPT system, θ_si and θ_ini should generally be tuned to zero to minimize VA rating of the system. For an LCC compensation network, as shown in Figure 2, the decisive condition for ZPA is that the equivalent inductance of both arms is equal, and both resonate with the parallel compensation capacitance. In each secondary side, when the resonant condition ω_i² = 1/(L_seiC_pi2) is satisfied, the condition for θ_si to be zero is L_sei = L_i2. Based on this, by combining Equations (2) and (7), the constant charging currents of both receivers can be deduced as:

$$I_{\mathrm{b}\mathrm{i}}={\displaystyle \frac{2\sqrt{2}{M}_{\mathrm{i}}{U}_{\mathrm{ini}}}{\pi {\omega }_{\mathrm{i}}{L}_{\mathrm{i}1}{L}_{\mathrm{i}2}}}$$

(15)

In this paper, based on existing experimental conditions and application requirements, a set of system-level parameters are specified, as listed in

Table 2. Specified system-level parameters of the dual-frequency WPT system.

Note	Symbol	Value
DC-link input voltage	Udc	150 V
Resonance frequency of channel 1	f1	20 kHz
Resonance frequency of channel 2	f2	85 kHz
Charging current of channel 1	Ib1	6 A
Charging current of channel 2	Ib2	6 A
Primary coil inductance	Lp	364.3 µH
Secondary coil inductance of channel 1	Ls1	227.1 µH
Secondary coil inductance of channel 2	Ls2	227.1 µH
Mutual inductance of channel 1	M1	41.42 µH
Mutual inductance of channel 2	M2	41.42 µH

.

During the parameter design process of a DS-LCC compensated WPT system, firstly, it is necessary to calculate the double-side compensation inductances according to the specified constant charging current value. In this paper, in order to simplify the design process, we consider the design of the double-side compensation inductances as symmetric. Thus, by using the parameters listed in Table 2 and Equation (15), the double-side compensation inductances in dual-frequency channels can be calculated as: L₁₁ = L₁₂ = 57.79 µH, and L₂₁ = L₂₂ = 28.03 µH.

After determining the double-side compensation inductances, all remaining capacitances in the system can be calculated based on the aforementioned CCO and ZPA conditions. In the primary side, because both the impedance magnitude of Z_{FSRC_1} and Z_{FSRC_2} are close to zero, the condition for θ_ini to be zero is L_i1 = L_p − 1/(ω_i²C_fi1). Thus, the normalized capacitances of C_f11 and C_f21 can be calculated as 206.6 nF and 10.43 nF, respectively. However, in practical WPT applications, it is necessary to fine-tune the normalized resonant parameters to achieve the ZVS of the inverter. For a normal DS-LCC compensated WPT system, introducing 5~10% reduction in the normalized C_fi1 is a common way to implement ZVS without sacrificing the CCO characteristics of the system. As a result, the practical capacitances of C_f11 and C_f21 in this paper are ultimately designed to be 190 nF and 9.5 nF, respectively. The designed resonant parameters of the dual-frequency WPT system are listed in

Table 3. Designed resonant parameters of the dual-frequency WPT system.

Note	Symbol	Value
Dual-side resonant inductances of channel 1	L11 & L12	57.79 µH
Dual-side resonant inductances of channel 2	L21 & L22	28.03 µH
Dual-side parallel resonant capacitances of channel 1	Cp11 & Cp12	1095.8 nF
Dual-side parallel resonant capacitances of channel 1	Cp21 & Cp22	125.1 nF
Primary series resonant capacitances of channel 1	Cf11	190.0 nF
Primary series resonant capacitances of channel 2	Cf21	9.5 nF
Secondary series resonant capacitances of channel 1	Cf12	374.0 nF
Secondary series resonant capacitances of channel 2	Cf22	17.6 nF

.

In addition, Z_ai and C_fi1 in Figure 2 can be equivalent to a total impedance, so that the redundancy of the compensation topology is reduced without affecting the frequency-selection characteristic of the FSRC networks. As shown in Figure 5, according to the parameters listed in Table 1 and Table 3, the series impedances in the red and blue dashed boxes can be equivalent to the capacitors C_e1 and C_e2, which can be calculated as:

$$\left\{\begin{array}{l}{C}_{\mathrm{e}1}={\displaystyle \frac{C_{\mathrm{a}1}{C}_{\mathrm{f}11}}{C_{\mathrm{a}1}+C_{\mathrm{f}11}}} \\ C_{\mathrm{e}2}={\displaystyle \frac{C_{\mathrm{f}21}}{1-{\omega }_2^2{L}_{\mathrm{a}2}{C}_{\mathrm{f}21}}}\end{array}\right.$$

(16)

By substituting the relevant parameters in Table 1 and Table 3 into Equation (16), the capacitances of C_e1 and C_e2 are calculated as: 164 nF and 9.6 nF, respectively.

5. Experimental Verification

In order to verify the practicability and effectiveness of the presented dual-frequency compatible WPT system, a 1.5-kW experimental prototype of the DS-LCC compensation based dual-frequency WPT system is configured, as shown in Figure 6. For this study, our major considerations in the design of magnetic couplers are twofold. First, the relative distance between the two receiving coils should be as far away as possible to eliminate the coupling between the two receiving coils. Second, the position of the two receiving coils relative to the common transmitting coil should be as symmetrical as possible to ensure that the two power transmission channels have the same magnetic coupling parameters. Under these two design guidelines, we designed a set of three-coil magnetic coupler, Figure 6b and

Table 4. Measured dimensional and magnetic parameters of the LCT.

Parameter	Value
Air gap distance Turns per coil	100 mm Np: 21; Ns1: 30; Ns2: 30
Primary coil dimensions	790 mm × 240 mm (Outer size) 660 mm × 110 mm (Inner size)
Secondary coil dimensions	230 mm (Outer size); 70 mm (Inner size)
Litz wire dimensions	AWG 9 (2.91 mm)
Secondary coil center distance Primary coil inductance Lp Secondary coil inductance of channel 1 Ls1 Secondary coil inductance of channel 2 Ls2 Coupling coefficient between transmitter and receiver 1 k1 Coupling coefficient between transmitter and receiver 1 k2 Coupling coefficient between receiver 1 and 2 k12	600 mm 362.9 µH 228.3 µH 228.3 µH 0.145 0.143 0.003

show the practical structure and parameters of the magnetic coupler designed. It can be seen that the practical parameters of the designed magnetic coupler meet the pre-designed requirements. The practical resonant parameters are measured with an LCR meter, and the maximum deviation between the designed parameters and practical parameters is found to be less than 2%.

Based on the aforementioned experimental constructions, the experimental test of the constructed system is carried out under varying load conditions. The transient waveforms with load fluctuations are shown in Figure 7. It should be noted that in the practical charging process, the equivalent internal resistance of the battery varies continuously within a certain range, and in this study, we adopted electronic load for experimental verification. Due to the limitations of time and equipment, it is difficult to simulate the continuous change of load. Therefore, 4 load points (5 Ω, 10 Ω, 15 Ω, and 20 Ω) are uniformly selected as test samples in the whole power range. It can be seen that although the R_L1 and R_L2 both vary from 5 Ω to 20 Ω, the charging currents I_b1 and I_b2 are both approximately equal to 6A and remain almost constant. In addition, the CSMI can achieve ZVS operation under different load conditions. The above experimental analysis indicates that the proposed dual-frequency WPT system can implement the dual-frequency power transfer with load-independent CCO and ZPA operation.

In order to verify the dual-frequency superposition and frequency selection characteristics of the proposed system, the FFT analyses of transmission currents i_p, i_o1, and i_o2 are carried out under 5 Ω and 10 Ω load conditions, respectively. As shown in Figure 8a,b, when R_L1 = R_L2 = 5 Ω, the magnitudes of i_p1 and i_p2 components are 13.09 A and 6.35 A, while when R_L1 = R_L2 = 10 Ω, the magnitudes of i_p1 and i_p2 components are 13.15 A and 6.35 A. Figure 8a,b indicate that the current of the transmitting coil i_p consists of only 20 kHz and 85 kHz frequency components, and the magnitude of the two frequency components is almost constant under different load conditions. Figure 8a,b not only confirms the derivation and analysis of Equations (5) and (6), but also proves that the designed FSRC networks can superimpose the dual-frequency current components i_p1 and i_p2 to the transmitting coil, and the current of the transmitting coil i_p has load-independent constant current characteristics. As shown in Figure 8c,d, under varying load conditions, the ac output currents i_o1 and i_o2 only contain their corresponding resonant frequency components, and there is almost no interference from another channel. In addition, both i_o1 and i_o2 present load-independent CCO characteristics, which confirms the derivation and analysis of Equation (7). The above experimental results prove that the proposed system can implement the load-independent dual-frequency power transfer.

To investigate and compare the system efficiency for different cases, the DC-DC efficiencies of the dual-frequency system are measured. First, the efficiency of the system under the independent operation of a single frequency channel is measured. As shown in Figure 9, in the power range of 150–750 W, the efficiency of both 20 kHz and 85 kHz frequency channels increases first and then decreases. Under the same power conditions, the efficiency of the 85 kHz channel is slightly higher than that of the 20 kHz channel, and we believe that the reason is that the transmission current of the 85 kHz channel is lower than that of the 20 kHz channel. In addition, the overall efficiency of the system when dual-frequency channel operate simultaneously is also measured. The variation trend of the overall efficiency of the dual-frequency WPT system is similar to that of the single-frequency channel operation, and the peak efficiency reaches 91.75% at a 1.2-kW output power.

6. Comparison and Discussion

Recently, a variety of dual-frequency WPT system have been presented to implement the independent dual-frequency power transfer. To clarify the unique contributions of the proposed dual-frequency WPT system in this article, a comprehensive performance comparison with the existing methods is presented in

Table 5. Summary and comparison of the existing dual-frequency WPT system.

Reference	Multi-Frequency Superposition Method	Maximum Efficiency	ZVS Operation	Operating Frequency	CV/CC	Topology Structure	Design Complexity	Rating POWER
[16]	Integration of multiple inverters via transformers	80%	Yes	176.7 kHz & 206.3 kHz	No	LCL-S	High	65 W
[17]		86.7%	Yes	190 kHz & 210 kHz	No	S-S	High	100 W
[18]	Hybrid modulation waves sinusoidal pulse width modulation	70%	No	20 kHz & 80 kHz	CC	S-S	Medium	40 W
[19]		85%	No	100 kHz & 200 kHz	No	S-S	Medium	120 W
[20]		88%	No	20 kHz & 85 kHz	CV	LCC-S	Medium	100 W
[21]	Neutral point clamped-multilevel inverters	78.9%	No	100 kHz & 300 kHz	CV	LCC-S	Medium	125 W
[22]		89.3%	No	100 kHz & 200 kHz	CV	LCC-S	Medium	1000 W
This article	Cascaded single-phase multi-frequency inverter	91.75%	Yes	20 kHz & 85 kHz	CC	DS-LCC	Low	1500 W

.

Refs. [16,17] indicate that the methods based on integration of multiple inverters via transformers can implement the ZVS operation of the multiple inverters, but cannot achieve load-independent constant output property, and the use of a large number of inverters and transformers greatly increases the design complexity and lower the system efficiency. In [18,19,20,21,22], although the methods based on SPWM and NPC-ML can reduce the design complexity, the system efficiency is still relative low because the ZVS operation cannot be satisfied. In addition, due to the limitation of system efficiency, the existing methods are difficult to apply in large power applications.

The main contributions and improvements of the proposed method over existing methods are summarized as follows:

(1)

This article reconstructed the conventional DS-LCC compensated WPT system by using CSMI and FSRC, the load-independent CCO property and ZVS operation at two specified frequencies can be implemented simultaneously.

(2)

The proposed method has low design complexity and can significantly improve the system efficiency, and can be applied to multi-frequency and multi-load wireless charging with higher power level.

7. Conclusions

In order to address the issue of hard-switching operation and power crosstalk of different frequency channels in conventional dual-frequency dual-load WPT system. This article proposes an integrated DS-LCC compensation based dual-frequency compatible WPT system to implement dual-frequency power transfer. On the basis of conventional DS-LCC compensated WPT system, the load-independent CCO and ZVS under dual-frequency power transmission condition are achieved by constructing CSMI and FSRC. The working principle of the proposed system is analyzed in detail, and the general parameter design procedure are introduced. A 1.5-kW experimental prototype is constructed to verify the rationality and feasibility of the proposed system.