Design and Implementation of a Wireless Power Transfer System Using LCL Coupling Network with Inherent Constant-Current and Constant-Voltage Output for Battery Charging

Abstract

The constant current followed by constant voltage (CC-CV) charging method is commonly employed for battery charging, effectively extending battery life and reducing charging time. However, as charging progresses, the battery’s internal resistance increases, complicating the charging circuit. This paper designs a wireless power transfer system utilizing an LCL coupling network for battery charging. The system employs frequency modulation (FM) to manage its CC and CV output characteristics at two fixed frequency points. The influence of the LCL coupling network parameters on system output characteristics was investigated using MATLAB. A simulation model was developed in the PSIM environment to validate the CC and CV output characteristics. The simulation results show that the system has load-independent constant-current and constant-voltage characteristics at two different frequency points. In order to verify the theoretical analysis, an experimental platform was also established. Experimental results demonstrate that the proposed system operates effectively in CC mode, maintaining constant output current across various loads, while in CV mode, it effectively regulates output voltage for different loads. The designed frequency modulation controller ensures a rapid response to sudden changes in load resistance, regardless of operating in CC or CV modes.

1. Introduction

With the rapid development of renewable energy and the increasing popularity of electric vehicles, batteries have become widely used as efficient energy storage devices across various fields [1,2,3], due to their advantages of high energy density and good cycle stability. The constant current followed by constant voltage (CC-CV) charging method has been widely adopted in battery-charging processes [4,5], as shown in Figure 1.

It can be seen that the battery-charging process can be divided into two stages. Stage 1: CC charging mode: the battery voltage increases rapidly while the charging current remains constant. Stage 2: CV charging mode: the battery current declines rapidly while the voltage remains stable. Additionally, the equivalent internal resistance of the battery increases during the whole charging process, which brings huge challenges to the constant-current or constant-voltage charging of batteries. Various control strategies have been investigated to provide the required output current or output voltage for time-variable loads against different charging stages. One common approach involves using a DC-DC converter on either the primary or secondary side to regulate the output voltage or current, which has been widely adopted in battery-charging processes [6,7]. In reference [6], a buck converter was adopted on the secondary side to regulate the system’s output voltage and current, enabling constant-voltage or constant-current charging of the battery. In order to track the optimal load and improve the system’s efficiency, a DC-DC converter was used in a wireless power transfer system that utilized an S-S-type resonant network to transfer energy in [7]. However, this method leads to additional power losses and high system costs, and necessitates extra space for the installation of the DC-DC converter [8].

Magnetic coupling wireless power transfer (MCWPT) systems enable efficient, convenient, and safe energy transfer through electromagnetic fields, making them particularly suitable for applications such as smartphones, electric vehicles, and medical devices [9,10,11]. One of the most important parts of these MCWPT systems is the resonant compensation network, which significantly enhances system efficiency and minimizes reactive power [12,13,14]. This resonant compensation network demonstrates excellent output characteristics, providing either constant voltage or constant current [15]. Specifically, the series–series (S-S)-type compensation network delivers a load-independent constant-current output in [16], whereas the LCL-S-type compensation network ensures a load-independent constant-voltage output in [17].

Therefore, some researchers have proposed using a hybrid topology design to adjust the connected resonant compensation network through switch switching, thereby achieving constant-current or constant-voltage mode control. In [18], a dual-topology WPT system was proposed, which achieves both CC and CV outputs by switching between S-S and series–parallel (S-P) topologies with different compensation parameters. However, the proposed circuit is quite complex, incorporating a center-tapped loosely coupled transformer and four switches. Reference [19] presents a novel topology that combines LLC and LCL-T resonant tanks to facilitate the CC and CV charging of lithium batteries, significantly reducing the operational switching frequency range compared to traditional LLC converters. This system utilizes switching to adjust the resonant compensation network connected to the secondary side, enabling control in either constant-current or -voltage mode. In [20], series and parallel compensation circuits are thoroughly discussed, leading to the development of a hybrid topology that delivers both load-independent output current and load-independent output voltage. A hybrid topology-based charging strategy for electric bicycles (EBs) using a single high-frequency inverter (HFI) to provide configurable constant-current (CC) and constant-voltage (CV) outputs was proposed in [21]. The system utilizes two AC switches to achieve CC and CV outputs without the need for complex control schemes or wireless communication. The above structures employ additional switches to facilitate the transition between constant-current and constant-voltage modes, resulting in higher system costs and increased control complexity. Reference [22] introduced a primary-side control technique employing phase-shift modulation for series–series (SS) and series–parallel (SP) compensated wireless power transfer (WPT) systems, enabling CV and CV charging. However, phase-shift control exhibits limitations such as sensitivity to parameter variations affecting regulation and stability, and heightened design complexity under varying load conditions, which collectively reduce efficiency and scalability in WPT systems.

To reduce system costs, eliminate additional switches for mode switching, and further enhance system compactness, some researchers have explored higher-order resonant compensation networks, which enable the system to achieve CC or CV charging at different operating frequencies. Reference [23] proposed a WPT system to achieve CC and CV output characteristics by utilizing two additional intermediate coils with resonant capacitors to achieve CC and CV output at two fixed frequencies. A novel three-coil WPT system was proposed to achieve CC and CV charging. A novel three-coil WPT system to address the limitations of achieving CC and CV charging modes was introduced in [24]. The addition of extra coils to achieve CC or CV output results in increased system complexity, higher costs, and larger system volume. Additionally, the mutual coupling between the coils complicates the theoretical modeling of the system and introduces greater challenges in system control. Reference [25] presents a design method for achieving CC and CV charging in an inductive power transfer (IPT) system with minimal frequency variation using a double-sided LCC compensation network at two resonant frequencies. The use of three resonant compensation components on both the primary and secondary sides provides the system with greater design flexibility, but also increases its cost and size.

This paper presents a wireless charging system based on an LCL coupling network, designed for battery-charging applications. By carefully optimizing the parameters of the LCL resonant network, the system inherently provides load-independent constant-current and constant-voltage output without any additional switches, which simplifies the system structure and reduces system costs. The system can achieve load-independent constant-current or constant-voltage output characteristics at two different operating frequencies. Thus, by implementing FM around these two resonant frequency points, only slight frequency adjustments are needed to maintain the desired constant-voltage or constant-current output characteristics.

The remainder of the manuscript is arranged as follows: The LCL equivalent coupling model is built and the control system is designed in Section 2. Section 3 analyzes the influence of LCL resonant network parameters on system output characteristics in detail and verifies the load-independent CC and CV characteristics of the system. The system characteristic scanning and dynamic response test experiments are conducted in Section 4. Finally, a brief conclusion is given in Section 5.

2. System Analysis and Control System Design

2.1. Topology of the Designed System Using LCL Resonant Network

The topology of the proposed system is shown in Figure 2, where an input voltage source and a battery are integrated. The double-sided LCL resonant network, comprising a pair of coupled coils $L_p$, $L_s$ and their corresponding resonant compensation components ($C_p$, $C_s$, $L_1$, $L_2$), serves to transfer energy from the primary side to the secondary side while also being used as an isolation device. $U_{in}$ and $U_b$ are the input voltage and battery voltage, respectively. The high-frequency full-bridge inverter, comprising four switches $Q_1$∼$Q_4$, converts DC power into high-frequency AC power $U_{AB}$, which serves as the input of the LCL resonant coupling network. Furthermore, the full-bridge rectifier composed of four diodes $D_1$∼$D_4$ rectifies the received AC power from the LCL resonant network into DC power for the battery. In addition, M is the mutual inductance between the primary resonant coil $L_p$ and the secondary resonant coil $L_s$. Additionally, the input voltage source and battery port are equipped with voltage-stabilizing capacitors $C_{in}$ and $C_o$ to maintain the stability of their respective port voltages.

2.2. Analysis of LCL Coupling Equivalent Model

Figure 3 shows the simplified LCL coupling model, ignoring the internal resistance of the coils where the primary LCL resonant network’s input and output currents are denoted as $I_1$ and $I_P$, respectively. $I_S$ and $I_2$ are the secondary LCL resonant network’s input and output currents. $Z_1$ and $Z_2$ represent the total system impedance and the secondary LCL resonant network impedance, respectively.

$U_{AB}$ stands for the inverter output voltage, which also serves as the input for the LCL network and can be expressed as follows.

$$U_{AB}={\displaystyle \frac{2\sqrt{2}}{\pi }}{U}_{in}$$

(1)

The rectifier and its subsequent resistance can be equivalent to $R_{ac}$ shown in Equation (2), while the battery’s equivalent internal resistance is R.

$$R_{ac}={\displaystyle \frac{8}{{\pi }^2}}R$$

(2)

Thus, a two-port network of the primary-side LCL resonant network can be established as follows.

$$\left[\begin{array}{cccc}1& 0& 0& 0\\ 1& 0& -Z_{11}& -Z_{12}\\ 0& 1& -Z_{21}& -Z_{22}\\ 0& 1& 0& Z_{\mathrm{eq}}\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{in}}\\ U_{\mathrm{p}}\\ I_1\\ I_{\mathrm{p}}\end{array}\right]=\left[\begin{array}{c}{U}_{\mathrm{in}}\\ 0\\ 0\\ 0\end{array}\right]$$

(3)

where $Z_{11}$, $Z_{12}$, $Z_{21}$, and $Z_{22}$ are the Z-parameters of the two-port network of the primary side; $Z_{eq}$ is the equivalent impedance of the secondary LCL resonant to the primary LCL resonant network. Additionally, $\omega$ is the switching angular frequency.

$$Z_{eq}={\displaystyle \frac{{M\omega }^2}{Z_2}}$$

(4)

From the two-port network model, it can be deduced that the primary LCL coupling network’s input current $I_1$, output voltage $U_p$, and system impedance $Z_1$ are as follows. Here, $A=1-{\omega }^2{C}_{\mathrm{p}}{L}_{\mathrm{p}},B=\omega C_{\mathrm{p}}{Z}_{\mathrm{eq}}$.

$$I_{\mathrm{p}}={\displaystyle \frac{U_{\mathrm{in}}}{Z_{\mathrm{eq}}(1-C_{\mathrm{p}}{L}_1{\omega }^2)-\mathrm{j}(C_{\mathrm{p}}{L}_{\mathrm{p}}{L}_1{\omega }^3-L_1\omega -L_{\mathrm{p}}\omega )}}$$

(5)

$$U_{\mathrm{p}}={\displaystyle \frac{\mathrm{j}{Z}_{\mathrm{eq}}{U}_{\mathrm{in}}}{\mathrm{j}{Z}_{\mathrm{eq}}(1-C_{\mathrm{p}}{L}_1{\omega }^2)+(C_{\mathrm{p}}{L}_{\mathrm{p}}{L}_1{\omega }^3-L_1\omega -L_{\mathrm{p}}\omega )}}$$

(6)

$$Z_1={\displaystyle \frac{Z_{\mathrm{eq}}+\mathrm{j}\omega (L_{\mathrm{p}}A-C_{\mathrm{p}}{Z}_{\mathrm{eq}}^2+L_1{A}^2+L_1{B}^2)}{A^2+B^2}}$$

(7)

Similarly, the two-port network of the secondary LCL resonant network can be established as shown below, where $Z_{11}^{\prime }$, $Z_{12}^{\prime }$, $Z_{21}^{\prime }$ are the secondary LCL two-port Z parameters.

$$\left[\begin{array}{cccc}1& 0& 0& 0\\ 1& 0& -Z_{11}^{\prime }& -Z_{12}^{\prime }\\ 0& 1& -Z_{21}^{\prime }& -Z_{22}^{\prime }\\ 0& 1& 0& R_{\mathrm{ac}}\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{s}}\\ U_{\mathrm{out}}\\ -I_{\mathrm{s}}\\ I_{\mathrm{out}}\end{array}\right]=\left[\begin{array}{c}{U}_{\mathrm{s}}\\ 0\\ 0\\ 0\end{array}\right]$$

(8)

According to coupling theory, $U_s$ is affected by $I_p$ and the mutual inductance M between coils $L_p$ and $L_s$, which can be expressed as follows.

$$U_s=j\omega M{I}_p$$

(9)

According to Equation (8), the output current $I_o$, the output voltage $U_o$, and the secondary LCL resonant impedance $Z_1$ can be obtained, where $C=1-{\omega }^2{C}_{\mathrm{s}}{L}_2$, $D=\omega C_{\mathrm{s}}{R}_{\mathrm{ac}}$.

$$I_{\mathrm{o}}={\displaystyle \frac{U_{\mathrm{s}}}{R_{\mathrm{ac}}(1-C_{\mathrm{s}}{L}_{\mathrm{s}}{\omega }^2)-\mathrm{j}(C_{\mathrm{s}}{L}_2{L}_{\mathrm{s}}{\omega }^3-L_{\mathrm{s}}\omega -L_2\omega )}}$$

(10)

$$U_{\mathrm{out}}={\displaystyle \frac{R_{\mathrm{ac}}{U}_{\mathrm{s}}}{R_{\mathrm{ac}}(1-C_{\mathrm{s}}{L}_{\mathrm{s}}{\omega }^2)-\mathrm{j}(C_{\mathrm{s}}{L}_2{L}_{\mathrm{s}}{\omega }^3-L_{\mathrm{s}}\omega -L_2\omega )}}$$

(11)

$$Z_2={\displaystyle \frac{R_{\mathrm{ac}}+\mathrm{j}\omega (L_{2}C-C_{\mathrm{s}}{R}_{\mathrm{ac}}^2+L_{\mathrm{s}}{C}^2+L_{\mathrm{s}}{D}^2)}{C^2+D^2}}$$

(12)

It is evident that the imaginary part of Equation (10) must be set to zero to realize the secondary LCL resonant network constant-current characteristic. Then, the derivation of the resonance condition and the output current of the secondary LCL resonant network are illustrated in Equations (13) and (14), respectively.

$${\omega }_s={\displaystyle \frac{1}{\sqrt{C_s{L}_s}}}$$

(13)

$$I_o={\displaystyle \frac{U_s}{j\omega L_s}}$$

(14)

It can be derived from Equations (9) and (14) that $I_o$ is relevant to $I_p$. To ensure the stability of the output current, the primary side current must be subjected to further control measures. Specifically, by setting the real part in Equation (3) to zero, the resonance condition of the primary side LCL coupling network can be obtained.

$${\omega }_c={\omega }_p={\displaystyle \frac{1}{\sqrt{C_p{L}_1}}}$$

(15)

Given that $L_1$ = $n_1$$L_p$, $L_2$ = $n_2$$L_s$, $I_o$ can finally be expressed as

$$I_o={\displaystyle \frac{k{U}_{in}}{j{\omega }_c\sqrt{L_p{L}_s}{n}_1}}$$

(16)

where both the primary and secondary LCL resonant networks are in resonance, satisfying ${\omega }_c$ = ${\omega }_p$ = ${\omega }_s$. It can be seen from Equation (16) that $I_o$ is affected by the coupling coefficient k, input voltage $U_{in}$, coil size, and coefficient $n_1$, but has a constant-current output characteristic under different loads.

Similarly, in order to achieve a constant-voltage output from the secondary LCL coupling network, it is evident from Equation (11) that the secondary resonant network must fulfill the following equation:

$${\omega }_v={\displaystyle \frac{\sqrt{1+\frac{1}{n_2}}}{\sqrt{C_s{L}_s}}}$$

(17)

Thus, the following equations can be obtained:

$$Z_2={\displaystyle \frac{R_{\mathrm{ac}}+\mathrm{j}{\omega }_v\frac{1}{n_2}{C}_{\mathrm{s}}{R}_{\mathrm{ac}}^2}{n_2^2+(1+\frac{1}{n_2})\frac{C_{\mathrm{s}}}{L_{\mathrm{s}}}{R}_{\mathrm{ac}}^2}}$$

(18)

$$Z_{\mathrm{eq}}={\displaystyle \frac{{\left({\omega }_{v}M{n}_2\right)}^2}{R_{\mathrm{ac}}}}-\mathrm{j}{n}_2{\omega }_v^3{M}^2{C}_{\mathrm{s}}$$

(19)

$$U_{out}={\displaystyle \frac{j{\omega }_{v}M{U}_{in}}{j\frac{1}{n_2^2}\left[(n_1-\frac{1}{n_2})L_p+\frac{k^2{L}_s(1+1/n_2)}{n_1{C}_p}\right]-\frac{k^2{L}_s(1+1/n_2)}{n_1{C}_p{R}_{ac}}}}$$

(20)

It can be seen from Equation (20) that the secondary LCL resonant network can achieve a constant-voltage output approximately when $R_{ac}$ is far larger than $n_1$. From the above analysis, it can be concluded that by properly configuring the parameters of the LCL resonant network, a constant-current output can be achieved under light load conditions, and a constant-voltage output can be achieved under heavy load conditions, which allows the LCL resonant network to be utilized in battery-charging applications.

2.3. Parameter Design of the Proposed System

Based on the above analysis, the system achieves load-independent CC and CV outputs at two resonant frequency points by appropriately configuring the parameters of the LCL coupling network. The flowchart for the system parameter design process is shown in Figure 4. The design process begins with determining the operating frequency for the constant-current output mode, along with the desired output current and other system parameters. In this design, the input power supply is set to 30 V, and the output current is specified as 1.5 A. Subsequently, the size and turns of the coils can be determined. And the inductance of the primary and secondary coils, as well as the mutual inductance between the coils, are measured. Using these values, the related resonant compensation network parameters are calculated to ensure the desired performance of the system.

2.4. Control System Design

From the above analysis, it can be seen that by properly configuring the LCL coupling network parameters, the system’s load-independent constant-current and constant-voltage output can be achieved at two different frequency points, which can be used for battery charging. Thus, the control system can be designed as shown in Figure 5. The designed system operates in two modes: constant-current mode and constant-voltage mode, which can be switched by mode selection. The battery-charging current $I_o$ and voltage $V_o$ are measured using current and voltage sensors, which are then compared to the reference charging values $I_{oref}$ and $V_{oref}$, respectively. The errors between the measured and reference currents, as well as the differences between the measured and reference voltages, serve as inputs for FM controllers. The output of the FM controller, after being processed through a limiter, determines the operating frequency f of the system.

3. The LCL Resonant Network Parameter Design and Simulation Verification

To verify the correctness of the theoretical analysis, the appropriate LCL coupling network is designed to provide constant-current output under light-load conditions and constant-voltage output under heavy-load conditions.

3.1. Parameter Scanning Simulation

The parameter scanning simulation was carried out in MATLAB2023 to explore the influence of $\omega$, coefficients $n_1$ and $n_2$, and the coupling coils’ inductance $L_p$ and $L_s$ on the LCL resonant network output. And part of the simulation parameters are listed in

Table 1. Part of the scanning simulation parameters in MATLAB.

Parameter	Values
Input voltage $U_{in}$	24 V
Normalized switching angular frequency ${\omega }_n$	0.5~2
Equivalent load $R_{ac}$	10~90 ohms
Primary resonant inductance $L_p$	8.5 u
Primary resonant capacitor $C_p$	0.4 u
Secondary resonant inductance $L_s$	17.5 u
Secondary resonant capacitor $C_s$	0.2 u
coefficient $n_1$, $n_2$	0.5~2
Coupling coefficient k	0.3

.

Figure 6 shows the variation curve of $I_{out}$ with normalized angular frequency ${\omega }_n$ under different loads, where $n_1$ = $n_2$ = 1, ${\omega }_n$ = $\omega$/${\omega }_c$. Under different loads, the output current increases first and then decreases as ${\omega }_n$ increases. In addition, when ${\omega }_n$ = 1, the LCL coupling network has a load-independent constant-current characteristic output.

Figure 7 shows that the LCL resonant network output voltage varies with the normalized angular frequency under different loads, where $n_1$ = $n_2$ = 1, and ${\omega }_n$ = $\omega$/${\omega }_v$. It can be seen that $U_{out}$ initially rises before gradually decreasing when ${\omega }_n$ increases from 0.5 to 2. Notably, within a wide frequency range of ${\omega }_n$ from 0.9 to 2, $U_{out}$ almost remains unaffected by the changes in $R_{ac}$, which demonstrates that the LCL resonant network has a constant output voltage under the condition that ${\omega }_n$ > 0.9.

In order to investigate the influence of different coefficients on the system output current, the output current of the LCL resonant network was obtained under a load of 20 ohms for various combinations of coefficients $n_1$ and $n_2$, as shown in Figure 8. It can be observed that as ${\omega }_n$ increases, $I_{out}$ initially rises and then decreases. Furthermore, when $n_1$ is fixed, the system has a constant-current output characteristic at ${\omega }_n$ = 1 under different values of $n_2$. Notably, as $n_2$ increases, $I_{out}$ varies with ${\omega }_n$ quickly. Additionally, the output of the LCL resonant network approximates a constant voltage, displaying load-independent characteristics for different combinations of $n_1$ and $n_2$ when ${\omega }_n$ > 1.3.

Figure 9 presents a 3D plot illustrating the output current and voltage of the LCL resonant network as functions of $L_p$ and $L_s$ when the system operates at frequencies ${\omega }_c$ and ${\omega }_v$, respectively, with a load of 20 ohms and $n_1$ = $n_2$ = 1. It can be seen that both the maximum output current and maximum output voltage decrease as $L_p$ and $L_s$ increase. Therefore, smaller values of $L_p$ and $L_s$ are preferable to achieve higher current and voltage gains.

The parameter scanning simulation results show the influence of coefficients $n_1$, $n_2$, $\omega$, $L_p$, and $L_s$ on the input characteristics of the LCL resonant network. It can be seen that by appropriately configuring the LCL resonant network parameters, the constant-current or constant-voltage output of the system can be achieved, independent of the load conditions.

3.2. Simulation Verification in PSIM

As illustrated in Figure 5, two PI controllers are employed to regulate the system in either constant-current (CC) or constant-voltage (CV) operation modes. Each controller introduces small perturbations around the fixed frequency corresponding to the selected operation mode, enabling the system to maintain stable output in either constant-current or constant-voltage conditions. To validate the effectiveness of the designed controllers, the AC sweep function in PSIM was utilized to analyze the system’s frequency response.

Figure 10 and Figure 11 show the Bode diagrams of the system under different loads in constant-current mode and constant-voltage mode, respectively. As illustrated in Figure 10, the system operates in constant-voltage mode with a crossover frequency of 10.2 kHz and a phase margin of 52.3°. In contrast, as depicted in Figure 11, the system operates in constant-current mode with a crossover frequency of 5.76 kHz and a significantly higher phase margin of 122.2°. These results confirm that the system remains stable under both CC and CV modes.

4. Experimental Platform Verification

An experimental platform has been built to verify system efficiency as displayed in Figure 12, where the electronic load is used to simulate the resistance of the battery during charging. The detailed experiment parameters are depicted in

Table 2. The system parameters.

Parameter	Values
Primary inductance $L_1$	8.5 u
Secondary inductance $L_s$	17.5 u
Primary resonant inductance $L_p$	8.5 u
Primary resonant capacitor $C_p$	0.4 u
Secondary resonant inductance $L_s$	17.5 u
Secondary resonant capacitor $C_s$	0.2 u
DSP controller	dsPIC33FJ64GS606
Voltage sensor	HVS-AS3.3
Current sensor	CHCS-PS3.3-15A

. In addition, the two switches on each half-bridge inverter are in a complementary state with a duty cycle of 0.5.

4.1. System Characteristic Scanning

The system characteristic scanning experiment aims to verify the relationship between system output and switching frequency across various load conditions, where a 12 V voltage source is used as the system input. Figure 13 and Figure 14 present the curves illustrating the variations in system output current and voltage as the switching frequency changes from 80 kHz to 130 kHz under different loads. In addition, ${\omega }_c$ and ${\omega }_v$ can be calculated as 85 K and 120.2 K, respectively, by Equations (15) and (17).

Figure 13 shows that the load current varies with switching frequency under different loads (R = 4 Ω, 8 Ω, 12 Ω). It can be seen that the load current shows a trend of first increasing and then decreasing with an increase in switching frequency. So, FM can be used to adjust the load current. Moreover, the load-independent constant-voltage characteristic of the system can be obtained approximately when the switching frequency is near ${\omega }_c$.

Figure 14 shows the load voltage curve with the switching frequency under different loads (R = 30 Ω, 50 Ω, 70 Ω). As the switching frequency f increases from 80 K to 130 K, the load voltage shows a trend of first increasing and then decreasing, so the load voltage can be adjusted by the PF control. In addition, the system has a constant-voltage characteristic independent of the load when the switching frequency is near ${\omega }_v$.

4.2. System Dynamic Response Test

The system dynamic response experiment aims to verify the effectiveness of the designed controller, which can be divided into two phases: phase 1: the system’s dynamic response to sudden load changes in CC mode; phase 2: the system’s response to sudden load changes in CV mode. In addition, a 30 V voltage source is used as the system input and an electronic load is used to simulate the change in load resistance during battery charging. Moreover, when the system operates in CC mode, the load current is set to 1.5 A, while in CV mode, the load voltage is set to 33 V.

Figure 15 illustrates the dynamic response of the system when the load suddenly changes from 5 ohms to 20 ohms in CC mode, with the system output current set to 1.5 A. It can be seen that Figure 15a illustrates the system’s operation in CC mode under a load resistance of 5 ohms, achieving a load current of 1.55 A with an efficiency of 80.6%. Figure 15b demonstrates the system operating in CC mode with a load resistance of 20 ohms, delivering a load current of 1.47 A and achieving an efficiency of 83.9%. It is evident from these figures that the output current is effectively maintained at the desired value. Figure 15c depicts the dynamic response characteristics of the system during the sudden load change from 5 ohms to 20 ohms. The results show that after the load change, the load current quickly stabilizes at the set value within 8 ms, indicating that the designed controller effectively manages sudden load changes while operating in CC mode.

In order to show the advantages of the proposed system compared to related works, a detailed comparison is presented in

Table 3. Comparison results between proposed system and previous related work.

Proposed in	Ref. [21]	Ref. [22]	Ref. [23]	Ref. [25]	This Work
Modulation	Switches	PSM	FM	FM	FM
Additional switches	YES	NO	NO	NO	NO
Additional coils	NO	NO	YES	NO	NO
Compensation components	7	2	6	6	4

. As shown in Table 3, the proposed system requires fewer resonance compensation components and eliminates the need for additional switches. These features significantly contribute to reducing system cost and simplifying the control strategy, demonstrating the system’s practicality.

Figure 16 shows the system dynamic response waveform and the system steady-state waveform when the system is in CC mode and the load resistance suddenly changes from 25 to 50 ohms, where the system output voltage is set as 33V. Figure 16a,b are the steady-state waveforms of the system when the load resistance is 25 ohms and 50 ohms, respectively, showing that the designed controller can control the system output voltage to the designed value under different loads. As shown in Figure 16a, the system achieves a load current of 1.33 A, a load voltage of 33.2 V, and an efficiency of 82.1%. Similarly, Figure 16b illustrates the system operating with a load voltage of 33.3 V, a load current of 0.713 A, and an efficiency of 79.5%. Figure 16c is the dynamic response of the system to load changes. It can be seen that after the load change, the load current reaches a new steady state after a short drop of 10 ms. During this process, the load voltage remains stable at 33 V, indicating that the designed controller can cope with the change in load resistance in CV mode and maintain the stability of the system output voltage.

5. Conclusions

This paper proposes a novel wireless power transfer system based on an LCL coupling network with a load-independent CC or CV output for battery charging. FM control has been applied to adjust the CC or CV output characteristic of the system, providing flexibility and reliability during the charging process. The impact of LCL coupling network parameters on system output characteristics was assessed in a MATLAB environment. A PSIM simulation model was built to verify the correctness of the theoretical analysis. The simulation results show that the system can achieve load-independent constant-current or -voltage output characteristics at two different frequency points. Finally, an experimental platform based on the dsPIC33FJ64GS606 digital controller was built to verify the system’s robustness during sudden load resistance changes when the system operates in CC or CV mode. The experimental results show that when the load resistance experiences a significant change from 5 ohms to 20 ohms, representing a 300% increase in load, the system has an excellent dynamic performance by quickly responding and stabilizing within 8 ms with the desired load current of 1.5 A. The system also has an excellent dynamic response during sudden load changes from 25 ohms to 50 ohms with a desired voltage of 33 V. Thus, the designed controller can respond quickly to sudden load changes and maintain the output current or voltage at the desired value regardless of whether the system is in CC or CV mode.