High-Efficiency Sine-Wave Current Pulses Charging Method in Wireless Power-Transfer System Applications

Abstract

There has been extensive discourse surrounding energy storage equipment and technologies for sustainable energy solutions. To address the need for prolonging the operational lifespan of energy storage equipment, this research introduces a high-efficiency charging method that integrates wireless power-transfer (WPT) technology. In the proposed LLC-S charger, the diodes of the receiver side rectify the incoming power while generating interleaved sinusoidal wave current pulses for charging two lead-acid battery energy storage systems (BESSs). This approach offers the advantage of providing rest intervals for BESSs and mitigating the impact of electrochemical reactions, thus promoting their overall durability. To validate the proposed charger, two 60 V/14 Ah BESSs as storage equipment within the solar power system are utilized for the charging tests. The results revealed that the utilization of sine-wave current pulses for charging enabled soft switching at both the transmitter and receiver sides, resulting in an overall average efficiency exceeding 80%. Experimental data derived from a prototype with a maximum output power of 1391 W during charging demonstrated that BESSs could be fully charged in a mere 1.61 h, achieving an impressive efficiency of 98%. These findings substantiate the feasibility and effectiveness of utilizing sine-wave current pulses for charging.

1. Introduction

Wireless power transfer is a safe charging method that has been extensively used for charging electric vehicles, mobile phones, biomedical implants, and other devices. Wireless transmitters can transmit green energy through the air to receivers that are located at distances ranging between 0 and 100 cm. Although wireless power transfer was first demonstrated by Nikola Tesla through the invention of the Tesla coil [1], notable breakthroughs in WPT technology were not achieved until the early 21st century. In 2007, a research team at the Massachusetts Institute of Technology (MIT) proposed strongly coupled magnetic resonance for WPT [2] as a replacement for the traditional inductive power-transfer method, which has low efficiency and coupling. Magnetic resonance-based wireless charging technology [3] was first developed in 2008 when researchers at an MIT laboratory lit a 60 W light bulb using a wireless power-transfer system; the efficiency of their system was estimated to be 15%. To improve the conversion efficiency of wireless power systems, several experts have attempted to optimize the circuit structure, cost, and efficiency of such systems. For example, Noeren et al. [4] and Tran et al. [5] have developed wireless chargers with maximum conversion efficiencies of 92.0% and 97.08%, respectively. Although the charger developed by Tran et al. has a relatively high conversion efficiency, it is composed of four coils resulting in an excessively complex circuit structure and excessively high circuit cost. Ramezani et al. [6] developed a wireless charger with a conversion efficiency of 94.8%; nevertheless, this charger comprises an LCC-series compensation circuit, resulting in a complex and costly structure. Furthermore, Park et al. [7] presented a wireless charger with a maximum conversion efficiency of 92.7% in the WPC/PMA mode, and Yoo et al. [8] presented a half-bridge LLC resonant converter with a conversion efficiency of 93%. Corti et al. [9] also proposed a wireless charger with a conversion efficiency of 90.0%, and Nama et al. [10] designed a wireless charger with a conversion efficiency of 91.26%. Additionally, Li et al. [11] developed a double-sided LCC wireless charger with a maximum conversion efficiency of 96%.

On the basis of the preceding literature review, the present study developed a wireless charger with a low circuit cost, high circuit efficiency, and simple circuit structure for achieving high-efficiency wireless charging through the use of green energy; the charger applies an interleaved method to deliver power in the form of sine waves. Figure 1 illustrates the circuit diagram of the proposed wireless charger. This circuit contains an inverter, a resonance tank consisting of an LLC-S compensation network, and a rectifier circuit. This research employs magnetic resonance for the achievement of wireless power transmission. The technology can be described as follows: In Figure 1, the DC power input undergoes switching through four active switches in the full-bridge inverter, resulting in the generation of a high-frequency square-wave AC voltage. This AC voltage is then directed to the LLC compensation network. Utilizing the fundamental harmonic approximation (FHA), the square-wave AC voltage can be represented as an AC signal through the Fourier series equation. Subsequently, the signal is amplified by the LLC compensation network to produce the AC power supply for the transmitting coil. The relationship between the transmitting coil and the receiving coil is based on coupled inductance application, with the mutual inductance contingent upon factors such as air-gap distance, the number of coils, and the diameters encompassed by the coils. The amplified AC power effectively transfers power from the input to the receiver side across the air gap, with both the receiver and transmitting sides resonating at the same frequency; that is, the magnetic resonance method. On the receiver side, a coil and a capacitor combination form a series resonance circuit. The primary function of the receiver side is to receive the AC power transmitted from the transmitting coil and subsequently supply DC power to the load through output rectifier diodes. In general, a conventional LLC-S compensation resonant circuit contains a leakage inductor and a self-inductor. By contrast, the LLC-S resonance compensation circuit used in the proposed charger contains an additional winding of a small and independent air-core inductor ℓ_t instead of a leakage inductor to reduce system cost and weight and increase design freedom. For enhanced conversion efficiency, in a study referenced as [11], simulations were conducted for both the S–S (Series–Series) and LCC (LCC resonant) compensation systems with elevated mutual inductance values. The findings indicate that the SS compensation topology exhibits superior efficiency. Notably, the LLC structure, a variant of SS compensation, offers increased controllability. As a result, it has been chosen as the preferred configuration for the present research. In addition, because of the innate function of the LLC resonance compensation network, the four active switches on the transmitter side can achieve zero-voltage switching (ZVS), and the diode on the receiver side can approximately achieve ZVS and zero-current switching (ZCS), which improves the conversion efficiency during charging. This study conducted experiments to verify the performance of the proposed wireless charger. The proposed charger completed the charging of two lead-acid BESSs in 2.0 h, achieved a maximum output power of 1391 W, and exhibited a maximum efficiency of 98%.

The remarkable features of this research encompass its significant contributions to the following aspects:

• In contrast to the square-wave pulse-charging method, this research demonstrates that the electrochemical reaction rate of the battery can catch up with the charging current. This novel charging method serves as an indirect safeguard for the battery, effectively prolonging its cycle life;
• Introducing interleaved charging technology allows for the simultaneous charging of multiple batteries, addressing the limitations of traditional single-output charging methods;
• The charger incorporates a small independent air-core inductor, eliminating the issue of difficult-to-control leakage inductance. This enhancement enhances design flexibility and enables the realization of the LLC-S charger;
• Compared to conventional LLC converters, the receiver side of the circuit features a reduced number of components, while soft switching technology further enhances the overall circuit efficiency. This results in a simple, cost-effective, and easily maintainable circuit, well-suited for high-power battery-charging applications;
• This research offers a comprehensive design process along with equipment brands and models, simplifying the replication and implementation of the proposed wireless circuit.

The rest of this paper is organized as follows. Section 2 describes the operating principle of the charger’s circuit. Section 3 describes the characteristics of the proposed charger and its charging method considerations. Section 4 details the design procedure for the proposed charger. Section 5 presents the experimental results, including the measured waveforms, charging time, and efficiency of the prototype. Section 6 provides the study conclusion.

2. Operational Principle

Figure 1 displays the circuit structure of the proposed sine-wave current pulses wireless charger. This charger contains four power transistors (S₁–S₄) that form the inverter on the transmitter side, an LLC-S resonance compensation network, and interleaved output circuits composed of a half-bridge rectifier. Figure 2 illustrates the timing diagram of the proposed circuit. This circuit involves eight operating modes, as marked I~VIII at the bottom of Figure 2, the working interval is shown by the dotted line, and each of which is described as follows.

(1)

Mode I [Figure 3a, t₀ ≤ t < t₁]: At t₀, the resonant current i_t flows through the parasitic diodes of switches S₁ and S₂; therefore, the voltage of these switches can be reduced to 0 V to enable the switches to achieve ZVS in the next turn-on period. On the receiver side, the battery bank of b₂ is in the charging state. The equivalent circuit for mode I operation is displayed in Figure 3a;

(2)

Mode II [Figure 3b, t₁ ≤ t < t₂]: Between t₁ and t₂, the current i_dc flows forward to switches S₁ and S₂; thus, these switches are turned on under the ZVS manner. In the resonance compensation network, the resonant inductor ℓ_t, the transmitting coil L_t, and the capacitor C_t are in resonance. Moreover, the current i_Cr charges the battery bank of b₁. The equivalent circuit for mode II operation is in Figure 3b;

(3)

Mode III [Figure 3c, t₂ ≤ t < t₃]: Switches S₁ and S₂ remain turned on until t₃ is reached. The resonant current reaches its maximum value at t₂; therefore, the voltages of the inductor ℓ_t, L_t, and capacitor C_t begin to reverse in the resonance compensation network, and the voltage polarity across inductor L_r and capacitor C_r changes. The battery bank of b₁ is continuously charging during mode III, and the equivalent circuit for mode III operation is shown in Figure 3c;

(4)

Mode IV [Figure 3d, t₃ ≤ t < t₄]: Between t₃ and t₄, all switches(S₁–S₄) are in the off state because of the deadtime process. Because the resonant current i_t flows in a freewheeling state through switches S₃ and S₄, the voltages v_ds3 and v_ds4 can be quickly reduced to 0 V to enable ZVS operation. Moreover, the resonance-tank voltage v_t reverses polarity at t₃. On the receiver side, current i_Cr continues to charge the battery bank of b₁. The equivalent circuit for mode IV operation is shown in Figure 3d;

(5)

Mode V [Figure 3e, t₄ ≤ t < t₅]: Between t₄ and t₅, switches S₃ and S₄ are in a zero-voltage state because the resonant current i_t flows in a freewheeling state. The battery bank of b₁ is charged continuously during mode V operation, and the equivalent circuit of mode V operation is illustrated in Figure 3e;

(6)

Mode VI [Figure 3f, t₅ ≤ t < t₆]: At t₅, the current i_t begins to commutate, and switches S₃ and S₄ are turned on under ZVS. On the receiver side, currents i_Cr and i_Lr also begin to, and rectifier diode d₂ is turned on under ZVS; therefore, battery b₂ begins charging. The equivalent circuit of mode VI operation is shown in Figure 3f;

(7)

Mode VII [Figure 3g, t₆ ≤ t < t₇]: Switches S₃ and S₄ are continuously turned on. At t₆, multiple voltages, including the capacitor voltages v_Ct, and v_Cr, inductor voltage vℓ_t, and coil voltages v_Lt and v_Lr, are set to 0 V. Moreover, the currents, including the resonant current i_t, capacitor current i_Cr, and inductor current i_Lr, are in a peak value state. The battery bank of b₂ continues to be charged until t₇. The equivalent circuit of mode VII operation is displayed in Figure 3g;

(8)

Mode VIII [Figure 3h, t₇ ≤ t < t₀]: Between t₇ and t₀, switches S₁–S₄ are again switched off because of the deadtime process. The resonant current i_t flows through the parasitic diodes of switches S₁ and S₂, which forces the voltages v_ds1 and v_ds2 to decrease to 0 V; thus, a ZVS state is created in the next turn-on period. Furthermore, the polarity of the resonant tank voltage v_t changes again. The resonant current i_r on the receiver side still charges the battery bank of b₂ to complete a cycle of interleaved charging. The equivalent circuit for mode VIII is presented in Figure 3h.

3. Circuit Characteristics and Charging Method Considerations

3.1. LLC-Converter Characteristics

The LLC converter has been widely used because of its high power density and high efficiency; thus, it is adopted for the proposed charging method. The characteristics of an LLC circuit are illustrated in Figure 4. The figure shows six curves of quality factor Q from 0.2 to 8, in which the y-axis represents the normalized gain of the converter, the x-axis represents the normalized frequency, and the red dotted line represents the dividing line between ZCS and ZVS. Following the peak value of each curve, a zero-current switching zone and a zero-voltage switching zone can be constructed. The figure shows that the smaller the quality factor Q has, the higher the normalized gain, which shows that the larger the load R_L value (light load) under the constant characteristic impedance, the higher the voltage gain. That is, the smaller quality factor can occur; on the contrary, the higher quality factor can occur at heavy load conditions. In order to reduce the high circulating current on the transmitting side, the ratio of these two parameters, L_t and ℓ_t, can usually be adjusted. When the inductance L_t is larger, a relatively small circulating current can be obtained, which can effectively reduce the current loss and heating of the transmitting-side devices, thereby improving the overall efficiency. Based on the above description and corresponding to the curve in Figure 4, a larger inductance L_t can be mapped as a quality factor curve with a high Q value.

To further analyze the efficiency of the LLC converter under different loads, the simulation results are shown in Figure 5. The figure shows four curves from 1 to 100 Ω different loads, where the y-axis represents the conversion efficiency of the converter, the x-axis represents the operating frequency f_s, and the red dotted line represents the dividing line between ZCS and ZVS. From the curve of 1 Ω load, it can be seen that operating at the resonant frequency has a maximum conversion efficiency of 81%; it also shows that this curve has the smallest bandwidth, which is not conducive to the stability of the system. For the curve of 10 Ω load, both conversion efficiency and bandwidth are developing towards a better trend, and it has a maximum conversion efficiency of 97.87%. When the load is equal to 100 Ω, the maximum conversion efficiency can reach 100%. Moreover, it has the widest bandwidth among these curves.

In order to further understand the relationship between the transmitting coil inductance L_t and the air inductance ℓ_t (K = L_t/ℓ_t) in the LLC-S system, the simulation results of fixed quality factor Q and the inductance ratio K under normalized frequency are shown in Figure 6. It can be seen from the figure that a small K value has a high voltage gain, which means that the circulating current at the transmitter side is also larger. Conversely, a larger K value can obtain a smaller circulating current on the transmitter side. For general LLC converters, the K value ranges from about 5~10.

3.2. Equivalent AC Circuit Analysis

The conventional S–S resonant circuit is applied in the WPT system [12,13]. The compensation capacitor at the transmitter side is independent of the load, and it is suitable for charging the battery. In the meantime, its output provides a constant current characteristic, which is a natural advantage for battery charging. The S–S compensation system achieves high and stable transmission efficiency at low mutual inductance. Furthermore, it delivers the highest output power at a fixed input power compared to other systems. However, the disadvantage of this second-order series resonant circuit is that the DC gain is always less than one, which means that can only be limited to step-down operation. The LLC circuit structure belongs to the series resonant converter (SRC), which is realized by adding an additional inductor to the original second-order series resonant circuit. Relatively, the LLC converter can perform both step-up and step-down functions, which improves the disadvantage that the second-order series resonant circuit can only operate at step-down mode, simultaneously, the converter has a wide output power control range and can also realize zero voltage switching. Therefore, the LLC converter with high efficiency is applied to the transmitting side of the WPT system, and the LC converter with a step-down function is applied to the receiving side, which is to form the LLC-S wireless charger proposed in this study.

Figure 7 illustrates the equivalent AC circuit of the proposed LLC-S wireless charger, and the pink dotted line in the figure represents the mutual inductance coupling model. The resonant current i_t flows through the transmitting coil L_t and generates a time-variant magnetic field around the coil. Moreover, the receiving coil L_r cuts off the magnetic field to induce a voltage. The magnitude of the induced voltage depends on the air gap between the transmitting and receiving coils, the coil lengths, the number of coil turns, and the derivative of the magnetic field with respect to time. Because an air gap exists between the transmitting coil L_t and receiving coil L_r, the mutual inductance M generated by the two coils affects their voltages, in addition to affecting the power and conversion efficiency of the system.

On the basis of Kirchhoff’s voltage law (KVL), the following equations can be derived for the circuit presented in Figure 7.

$$\left\{\begin{array}{l}{Z}_1{i}_t-j\omega M{i}_r=v_t\\ -j\omega M{i}_t+Z_2{i}_r=0\end{array}\right.$$

(1)

where Z₁ is the equivalent impedance of the transmitter side, Z₂ is the equivalent impedance of the receiver side, and Z_r in Figure 7 is the same as Z₂, which is the equivalent impedance of the receiver side. The impedances Z₁ and Z₂ can be expressed as Equation (2).

$$\left\{\begin{array}{l}{Z}_1=R_{Lt}+j\omega \mathsf{\ell }t+R_{\mathsf{\ell }t}+\frac{1}{j\omega C_t}+j\omega L_t\\ Z_2=j\omega L_r+R_{Lr}+\frac{1}{j\omega C_r}+R_L\end{array}\right.$$

(2)

According to Equation (1), the resonant current i_t on the transmitter side and the resonant current i_r on the receiver side can be expressed as follows:

$$\left\{\begin{array}{l}{i}_t=\frac{Z_2\cdot v_t}{Z_1{Z}_2+{(\omega M)}^2}\\ i_r=\frac{j\omega M\cdot v_t}{Z_1{Z}_2+{(\omega M)}^2}\end{array}\right.$$

(3)

When the proposed wireless charger operates at resonance, the capacitive reactance and inductive reactance are identical in magnitude but opposite in polarity, as expressed in Equation (4):

$$\left\{\begin{array}{l}j\omega \mathsf{\ell }t+\frac{1}{j\omega C_t}+j\omega L_t=0\\ j\omega L_r+\frac{1}{j\omega C_r}=0\end{array}\right.$$

(4)

Equations (2) and (4) can be rearranged, as follows:

$$\left\{\begin{array}{l}{Z}_1=R_{Lt}+R_{\mathsf{\ell }t}\\ Z_2=R_{Lr}+R_L\end{array}\right.$$

(5)

According to the equivalent dependent power source (−j$\omega$Mi_r) of the transmitter, the equivalent impedance reflected from the receiver side to the transmitter side can be shown as follows:

$$Z_r^{\prime }=\frac{{(\omega M)}^2}{Z_r}$$

(6)

where the apostrophe ‘‘$\prime$’’ indicates the variables of the receiver side that correspond to those of the transmitter side.

The total impedance of the overall circuit can be derived as follows:

$$Z_t=(R_{Lt}+j\omega \mathsf{\ell }t+R_{\mathsf{\ell }t}+\frac{1}{j\omega C_t}+j\omega L_t)+\frac{{(\omega M)}^2}{(j\omega L_r+R_{Lr}+\frac{1}{j\omega C_r}+R_L)}$$

(7)

On the basis of the preceding equation, the input power P_i and the output power P_o can be expressed as follows:

$$\left\{\begin{array}{l}{P}_i=v_t\cdot i_t=\frac{v_t{}^2(R_{Lr}+R_L)}{(R_{Lt}+R_{\mathsf{\ell }t})(R_{Lr}+R_L)+{(\omega M)}^2}\\ P_o=i_r{}^2\cdot R_L=\frac{v_t{}^2{(\omega M)}^2{R}_L}{{[(R_{Lt}+R_{\mathsf{\ell }t})(R_{Lr}+R_L)+{(\omega M)}^2]}^2}\end{array}\right.$$

(8)

Therefore, the conversion efficiency of the proposed charger can be derived as follows:

$$\eta =\frac{{(\omega M)}^2{R}_L}{[(R_{Lt}+R_{\mathsf{\ell }t})(R_{Lr}+R_L)+{(\omega M)}^2](R_{Lr}+R_L)}\times 100\%$$

(9)

The sinusoidal current generated by the resonant circuit originates from the high-frequency square wave switched by switches S₁–S₄; however, the resonant circuit allows only the power of the fundamental component to pass through. According to FHA, the fundamental frequency of the Fourier series of voltage can be expressed as follows:

$$v_r\left(t\right)={{\displaystyle \sum }}_{n=1,3,5\dots }^{\infty }\frac{4v_{b1}}{n\pi }\sin (n\omega t)$$

(10)

The fundamental component of the voltage v_r1 can be derived as follows:

$$v_{r1}=\frac{4v_{b1}}{\pi }\sin (\omega t)$$

(11)

where v_r is the output voltage of the AC-equivalent model in Figure 7, v_b1 is the battery-bank voltage of b₁, n is the number of harmonics, and ω is the angular frequency.

The power of the receiving coil is rectified by a half-bridge circuit and converted into the charging battery voltage v_b1 and current i_b1. Thus, the average value of the charging current i_b1 can be derived as follows:

$$\begin{gathered} i_{b1,avg}=\frac{1}{2\pi }{{\displaystyle \int }}_0^{\pi }{i}_{b1m}\sin \omega td\left(\omega t\right) \\ =\frac{i_{b1m}}{\pi } \end{gathered}$$

(12)

The maximum value of the charging current i_b1 can be expressed as follows:

$$i_{b1m}=\pi \cdot i_{b1,avg}$$

(13)

The equivalent AC impedance R_e can be expressed as follows:

$$\begin{gathered} R_e=\frac{v_{r1m}}{i_{b1m}}=\frac{\frac{4v_{b1}}{\pi }}{\pi \cdot i_{b1,avg}} \\ =\frac{4}{{\pi }^2}\cdot \frac{v_{b1}}{i_{b1,avg}} \\ =\frac{4}{{\pi }^2} \cdot R_L \end{gathered}$$

(14)

where R_L is the impedance presented by the battery during charging, including ohmic internal resistance and polarization internal resistance. The impedance R_L will change with the charging time, and it is proportional to the equivalent AC impedance R_e.

3.3. Considerations Regarding the Charging Methods

In addition to the charging efficiency of the converter, another issue that needs attention is the battery-charging methods. Lead-acid batteries are widely used in the energy storage equipment [14,15,16,17,18] of renewable energy and microgrid systems because of their low cost and safety. In general, five charging methods exist for batteries: constant-voltage (CV) charging, constant-current (CC) charging, constant-current–constant-voltage (CC–CV) hybrid-charging, pulse-charging, and reflective-charging methods [19,20,21,22,23,24,25]. To achieve fast charging, the CC charging method is usually used; however, other charging methods are more suitable for certain types of batteries. For example, the CC–CV hybrid charging method is suitable for lithium batteries, whereas the pulse-charging or reflective-charging methods are suitable for lead-acid batteries. Additionally, it is crucial to closely monitor battery temperature fluctuations during the charging process, particularly in rapid charging scenarios. Stringent temperature-control standards apply when charging lead-acid batteries, with a recommended upper limit of 45 °C. This limitation is primarily attributed to the chemical reactions occurring within the battery. Specifically, during these reactions, the positive plate generates lead dioxide, while the negative plate produces velvety lead. Elevated temperatures can lead to the formation of coarse particles in these substances, resulting in reduced binding forces and an increased risk of active material detachment from the plates. Such detachment can potentially lead to a short circuit between the battery plates. In [26], at a pulse frequency of 1 Hz, the pulse-charging method was determined to be the most effective approach to battery charging; moreover, the current pulse was noted to increase the Faradaic efficiency of the battery. That is, it reduces the water decomposition rate, and the pulse current does not change the electrochemical steps in the oxygen evolution mechanism. An increase in the current-pulse amplitude can engender a considerable increase in the average double-layer current, which can result in rapid charging. However, in the pulse-charging method, a battery pack is charged using a rectangular current pulse, and a short rest time is provided to reduce the intensity of the electrochemical reaction of the battery. If a high rectangular current pulse is used to charge the battery pack in the aforementioned method, the charging time can be reduced, thus resulting in fast charging. However, in theory, the slope of such current can be expressed as follows:

$$di(t)/dt=\infty$$

(15)

In the conventional pulse-charging method, the current pulse varies infinitely with time; consequently, the electrochemical reaction of the battery may not be able to match the rapidly changing speed of the charging current. To address this limitation, this study developed a wireless charger that can generate interleaved high-frequency, sine-wave current pulses for enhancing lead-acid BESSs, and the schematic diagram of the waveform is shown in Figure 8. In this circuit, the receiving coil of the LLC-S resonance compensation network generates a high-frequency sinusoidal current i_r. This current flows through an interleaved rectifier, which can generate two interleaved high-frequency sinusoidal current pulses, namely i_b1 and i_b2, with a phase difference of $180°$. With the circuit diagram of Figure 1 and the operational diagram of Figure 8, when the current i_b1 charges the battery bank of b₁, the charging current of the battery bank of b₂ is 0 A; that is, the battery bank of b₂ is in a resting state. However, when the current i_b2 charges the battery bank of b₂, the charging current of the battery bank of b₁ is 0 A; that is, the battery bank of b₁ is in a resting state. Thus, the two BESSs, namely b₁ and b₂, operate in an interleaved charging mode. This mode allows the batteries to be charged with a high current to achieve fast charging. Moreover, the interleaved charging mode includes a half-cycle rest time, which enables the electrochemical reaction of the batteries to be slowed down, and their cycle life to be effectively extended. Therefore, the proposed high-efficiency wireless charger provides high-frequency sinusoidal current pulses, which can be expressed as follows:

$$d{i}_r(t)/dt=\omega I_{m}sin\omega t$$

(16)

Equation (16) indicates that the high-frequency sinusoidal current pulses of the proposed charger do not vary infinitely with time; instead, these pulses are a function of the circuit resonance frequency ω and peak current I_m. Therefore, if the circuit parameters of the proposed charger are appropriately designed, the proposed charger can effectively moderate the internal electrochemical reaction of the battery to extend its cycle life.

Table 1. Comparison of performance indexes between half-bridge and full-bridge rectifiers.

Circuit Structure Performance Index	Half-Bridge Rectifier	Full-Bridge Rectifier
Charging method	Sine-wave current pulses	DC charging
Number of charging	2	1
Diode	2	4
LC filter	None	Need
Rest time	50% period	None
Circuit structure	Double voltage	Rectifier
Cost	Low	High

compares the advantages and disadvantages of the half-bridge charging structure and conventional full-bridge rectifier. The table shows the number of components, battery rest time and cost, etc., indicating that the benefits of using the half-bridge charging structure are more than the full-bridge one.

4. Design Procedure

To ensure the appropriate operation of the proposed wireless charger, the parameters of its resonance compensation network must be suitably designed. However, the LLC resonance compensation network of the proposed charger is composed of three components, and the circuit design is more complicated than that of the second-order one. Hence, the parameters of the resonance compensation network must be designed through a comprehensive procedure, conducted in a strict sequence. The steps involved in the design of a novel high-efficiency sine-wave current pulses wireless charger system with a 20 cm air gap are detailed in the following sections.

4.1. Design of the Resonance Compensation Network

Figure 9 presents the design flow chart of the proposed charger. The design procedure involves determining the charging voltages v_b1 and v_b2 and the currents i_b1 and i_b2 according to the capacity and performance of the BESSs; selecting the resonance frequency f_m; and determining the capacitance of capacitor C_t, the inductance ratio K value, the number of transmitting coil turns N₁, the parameters of the resonant inductor ℓ_t of the compensation network of the transmitter side, the capacitance of capacitor C_r, and the number of receiving coil turns N₂.

The angular frequency ${\omega }_m$ at which the transmitter and receiver at resonance can be expressed as follows:

$${\omega }_m=\frac{1}{\sqrt{\left(L_t+{\mathsf{\ell }}_t\right)C_t}}=\frac{1}{\sqrt{L_r{C}_r}}$$

(17)

According to Equation (17), the capacitances of the compensation capacitors on the transmitter and receiver sides can be derived as follows:

$$C_t=\frac{1}{{(2\pi f_m)}^2(L_t+{\mathsf{\ell }}_t)}$$

(18)

And

$$C_r=\frac{1}{{(2\pi f_m)}^2{L}_r}$$

(19)

where f_m is the resonance frequency. It is worth noting that although the three components of LLC are connected in series, even if the capacitance C_t is increased, the same effect as that of increasing inductance ℓ_t can be achieved by Equation (17). However, inductors and capacitors produce different impedances under various frequencies, which will directly affect the characteristic impedance and quality factor of the WPT system and, ultimately, change the characteristics of the entire system. Therefore, increasing the capacitance C_t cannot achieve the same effect as increasing inductance ℓ_t.

In this study, planar circular coils were selected as the transmitter and receiver for power transfer. The power-transmission efficiency can be increased by appropriately setting the mutual inductance M between the coils, the self-inductance L of the coils, and the angular frequency of the coils ω. The WPT coil used in this study was equivalent to a coaxial parallel air-core coil, as shown in Figure 10. The mutual inductance M between the transmitting and receiving coils can be expressed as follows [27]:

$$M=\frac{{\mu }_0\times \pi \times N_1\times N_2\times r_1^2\times r_2^2}{2\times {\left(r_1^2+d^2\right)}^{\frac{3}{2}}}$$

(20)

where ${\mu }_0$ is the air permeability coefficient, L_t is the inductance of the transmitting coil, L_r is the inductance of the receiving coil, r₁ is the outer diameter of the transmitting coil, r₂ is the outer diameter of the receiving coil, d is the distance between the transmitting and receiving coils, and N₁ and N₂ are the numbers of transmitting and receiving coil turns, respectively.

The self-inductance of a coil can be expressed as follows:

$$L_t=\frac{N_1{\varphi }_1}{i_t}$$

(21)

For a uniform magnetic field, according to Equations (20) and (21), the self-inductance of the transmitting coil can be expressed as follows:

$$L_t=\frac{{\mu }_0\times \pi \times N_1^2\times r_1}{2}$$

(22)

The self-inductance of the receiving coil can be expressed as follows:

$$L_r=\frac{{\mu }_0\times \pi \times N_2^2\times r_2}{2}$$

(23)

In the design procedure of the transmitting coil, the main parameters to be maximized were the coil quality factor Q and coupling coefficient k. In conventional coil design, the value of k is set between 0.3 and 0.5 to fix the coil inductances L_t and L_r. In a wireless transformer, the maximum possible value of k is 0.5. When the coil inductances L_t, coil L_r, and the mutual inductance M are known, the coupling coefficient k can be determined as follows:

$$k=\frac{M}{\sqrt{L_t{L}_r}}$$

(24)

The quality factors Q can be expressed as follows:

$$Q=\frac{\sqrt{L_r/C_r}}{R_e}$$

(25)

According to the design flow chart displayed in Figure 9 and Equations (17)–(25), the voltage and current of the two BESSs must first be determined. Five 12 V lead-acid batteries were connected in series to form a battery group, and two battery groups were created. Considering that the 1 C charging current of the lead-acid battery used is 14 A, the charging current is set to be 8.5 A. Next, considering that an increase in the switching frequency increases the voltage induced in the receiving coil, the conduction loss, Joule loss in the coil, and core loss were increased. Therefore, the resonant frequency f_m is set to 34 kHz. The capacitance of capacitor C_t was set to 0.05 μF [27,28,29,30,31,32]. The inductance ratio K value is set to 10; but, for actual adjustment, the optimal parameter approximately equals 11. The air gap between the transmitter and receiver sides was determined to be 20 cm. The number of transmitting coil turns N₁ was set to 25, and the outer diameter r₁ of this coil was set to 0.31 m. The transmitter inductance calculated using Equation (22) was 382.44 μH; however, the measured transmitter inductance was 400.4 μH. In order to make the switches S₁–S₄ operate under ZVS condition, the operating frequency f_s must be higher than the resonant frequency. According to the literature [33,34,35], the optimal design frequency range is around 1.05~1.2 times the resonant frequency. In this study, the resonant frequency of 1.1 times is determined to be the operating frequency of the system, which is 37.4 kHz, which is actually 37.9 kHz after adjustment. Subsequently, on the basis of Equation (17), the inductance ℓ_t of the transmitter side was determined to be 37 μH. Similarly, at the same resonance frequency 34 kHz, the capacitance of capacitor C_r was set to 0.1 μF [27,28,29,30,31,32]. The number of receiving coil N₂ was set to 18, and the outer diameter r₂ of this coil was set to 0.28 m. The receiver inductance calculated using Equation (23) was 179.07 μH; however, the measured receiver inductance was 219.1 μH. Furthermore, the mutual inductance M between the coils was calculated to be 133.15 μH by using Equation (20), and the coupling coefficient k was determined to be 0.45 by using Equation (24).

4.2. Design of the Resonance Compensation Network

This study attempted to design a high-efficiency wireless charger with a rated power of 1500 W and a switching frequency of 37.9 kHz. The transmitting coil of the proposed charger transmits power mainly through the magnetic field generated by the current flowing through it. Power is transferred from the transmitting coil to the receiving coil over an air gap of 20 cm to supply the load. According to the characteristics of the full-bridge circuit, the sustained voltages of switches S₁–S₄ must be higher than the input voltage V_dc. The sustained current of each switch is expressed in Equation (26). Considering the conduction losses of the circuit components, the IXTK120N65X2 power semiconductor field-effect transistor model was adopted in this study. This model has an on resistance of R_DS(on) of ≤23 mΩ and enables the maximum sustained voltage and current to reach 650 V and 120 A, respectively.

$$i_{DS}>\frac{v_t}{Z_{tc}}$$

(26)

where v_t is the maximum resonant voltage of the transmitter side, and Z_tc is the characteristic impedance of the compensation network on the transmitter side.

4.3. Rectifier Diodes

To analyze the voltages across the rectifier diodes of the proposed circuit, the following assumptions can be made: the battery bank of b₁ can be assumed to have stopped charging, and the battery bank of b₂ can be assumed to be charging. If the forward conduction voltage V_F of the diode d₁ is ignored, the maximum voltage of the diode d₁ should be sustained as:

v_d1 = v_b1 + v_b2

(27)

According to Equation (27), d₁ must withstand the combined voltage of the battery banks of b₁ and b₂. However, when the battery bank of b₂ is charging, the sum of the voltages v_Lr and v_Cr must be higher than the battery voltage v_b2; thus, the voltage flowing across diode d₁ can be expressed as follows:

v_d1 = v_Cr + v_Lr + v_b1

(28)

Combining Equations (27) and (28) yields the following equation:

v_b2 < v_Lr + v_Cr

(29)

The peak diode current of the half-bridge rectifier can be shown in Equation (13). In this study, the breakdown voltage and peak current of the rectifier were determined, and the IQBD60E60A1 ultra-fast diode was selected to meet the requirements of the half-bridge rectifier. This diode can sustain a voltage and current of 600 V and 60 A, respectively, at a forward conduction voltage of 1.3 V. The reverse recovery time of the aforementioned diode ranges from 40 to 220 ns.

5. Experimental Results

On the basis of the aforementioned analysis, a wireless charging system with the sine-wave current pulses charging method was developed. The system will be employed in a standalone solar array power system, comprising five modules in series and two modules in parallel. Each module is specified at 30.6 V/8.17 A. During the experiment, a 3000 W power supply was utilized to simulate a solar array, with a power tolerance that can reach up to 3100 W (155 V/20 A).

Table 2. Specification of the proposed charger.

Symbol	Parameter	Value
Vdc	Nominal input voltage	155 V
fs	Switching frequency	37.9 kHz
fm	Resonance frequency	34 kHz
Hg	Air gap	20 cm
Po	Rated output power	1500 W
ib1	Charging current	5.4~12.6 A
ib2	Charging current	6.2~12.48 A
vb1	Battery voltage	59.45~77.53 V
vb2	Battery voltage	59.77~77.33 V

presents the specifications of the proposed charger,

Table 3. Various parameters of the resonance tank.

Symbol	Parameter	Model/Value
S1–S4	Active switch	IXTK120N65X2
D1–D2	Rectifier Diode	IQBD60E60A1
Lt	Transmitting coil inductance	400.4 $\mu$H
Lr	Receiving coil inductance	219.1 $\mu$H
lt	Air-core inductance	37 $\mu$H
K	Inductance ratio	10.82
k	Coupling coefficient	0.45
Ct	Transmitting-side compensation capacitance	0.05 $\mu \mathrm{F}$
Cr	Receiving-side compensation capacitance	0.1 $\mu \mathrm{F}$

presents the parameters of the resonance-tank components, and

Table 4. Experimental equipment and instruments.

Option Equipment	Brand	Model
Power supply	Gitek	GR-15H20H
Oscilloscope	Tektronix	TDS 2024B
Differential probe	Sanhua	LDP6110
Amplifier Current probe	Tektronix	TCPA300 TCP312A
LCR meter	Microtest	6376
Battery	Yuasa	REC14-12

provides an overview of the experimental equipment and instruments utilized in this study. Using the parameters, equipment, and instruments outlined above, we will proceed to measure the following waveforms and curves.

Measured waveforms of switches S₁ and S₃ under heavy load are shown in Figure 11, where the pink waveforms are the voltages, and the green ones are the currents. As indicated in Figure 11a,b, these switches performed ZVS operation to achieve soft switching. Figure 12 illustrates the measured waveforms of the components on the transmitter side, where the pink colors represent the voltage waveforms of different components on the transmitter side, and green ones represent the current on the transmitter side." Figure 12a shows the voltage v_t and current i_t of the resonance tank on the transmitter side. The waveforms of voltage v_t and current i_t reflect the switching statuses of the four active switches. Figure 12b presents the voltage and current of compensation capacitor C_t, indicating that the peak voltage reached nearly 2000 V. Figure 12c illustrates the measured voltage and current of the transmitting coil. The coil must withstand a voltage and current of approximately 4000 V_P-P and 40 A_P-P, respectively. Finally, Figure 12d displays the measured voltage and current waveforms of the air-core inductor ℓ_t. The reason for the peak voltage oscillation in the figure was that the leakage inductance of the air-core inductor and the stray capacitance in the circuit oscillated when the active switch of the inverter was turned on.

Measured waveforms for each component on the receiver side are shown in Figure 13, where the pink colors represent the voltage waveforms of different components on the receiver side, and green ones represent the current on the receiver side. Figure 13a shows the voltage v_r and current i_Cr of the resonant tank on the receiver side, and the peak value of the current i_Cr was approximately 32 A. The measured waveforms of the compensation capacitance C_r and the coil L_r are shown in Figure 13b,c, respectively. From Figure 13b, it can be seen that the peak voltage of the compensation capacitor C_r was approximately 1400 V, and the peak voltage of the coil L_r was approximately 1550 V. They illustrate that the second-order series resonant circuit was adopted for the proposed circuit, and the receiver side has a step-down characteristic. Thus, the large increase in charging current is beneficial for fast charging.

Figure 14 illustrates the measured waveforms of the rectifier diodes, where the pink color waveforms are the voltages, and the green ones are the currents. As indicated in Figure 14a, the voltage across the diode d₁ was approximately 140 V, which was equivalent to the voltage of the two BESSs. The waveform of v_d1 exhibited a slope, which was related to the voltage difference between the charge and discharge of the batteries; this can be explained using Equations (27)–(29). According to the measured waveforms displayed in Figure 14a,b, the rectifier diodes can achieve ZVS turn on and ZCS turn off, which are soft switching features.

The proposed high-efficiency sine-wave current pulses wireless charger was used to charge the two BESSs, and relevant charging data were recorded every 15 s. The recorded data included the charging voltages v_b1 and v_b2, charging currents i_bl and i_b2, and charging power and charging efficiency η. Figure 15 displays the charging voltages v_b1 and v_b2 of the BESSs, where the blue curves are the charging process voltage curve of BESSs, and the red circles are the initial voltage. The initial values of v_b1 and v_b2 were 59.45 V and 59.77 V, respectively. At the beginning of the charging process, the voltage difference between the charger and the batteries was large, resulting in an instantaneous increase in the current, and the voltages of the battery banks of b₁ and b₂ increased to 60.17 V and 60.50 V, respectively. Subsequently, the internal chemical reaction of the batteries became stable, and the voltages decreased and then increased. After the battery banks were charged for 1.61 h, the battery voltages approximated the rated value of 77.5 V, and charging was stopped. Specifically, the voltages of b₁ and b₂ after charging for 1.61 h were 77.53 V and 77.33 V respectively, which represented their full-charging voltages.

Figure 16 presents curves representing the charging currents of b₁ and b₂, where the black colors are the charging process current curve of BESSs, and the red circles are the initial current during charging. According to these curves, the currents at the beginning of the charging process were approximately 12 A. After approximately 3 min of charging, the charging currents were maintained at approximately 8–9 A. After approximately 1.1 h of charging, the charging currents of b₁ and b₂ decreased to approximately 8 A. Subsequently, the charging currents of the batteries gradually decreased until the charging time reached 1.61 h; at this time, the batteries were fully charged. The reason for the many current spikes in the figure was the active switch switches at a high frequency, which caused noise interference during signal sampling.

Figure 17 illustrates curves representing the charging power of the proposed charger, where the blue colors are the charging power curves, and the red circles are the initial charging power. According to these curves, the total charging power of the two BESSs under interleaved charging was up to 1391 W during the initial part of the charging process. This power then decreased to 835 W after 1.61 h of charging; at this time, the batteries were fully charged.

Figure 18 displays the charging efficiency of the proposed charger, where the blue color is the efficiency during charging, and the two red circles are the lowest and highest efficiency points respectively. As indicated in this figure, during the initial part of the charging process, the BESSs exhibited their lowest impedance, voltage, and capacity. Therefore, the voltage difference between the charger and batteries differed considerably, which resulted in the generation of a high charging current; thus, the initial charging efficiency was 78%, which was the lowest throughout the charging process. The voltages of the BESSs gradually increased with the charging current; consequently, the difference between the voltages of the charger and batteries gradually decreased, which resulted in a decrease in the charging current. The power provided by the charger gradually decreased as a result, and the charging efficiency increased. The highest charging efficiency was 98% and was achieved just before the end of the charging process. In addition, the charging current is relatively high when the battery is just being charged, which conforms to the characteristics of the high quality factor of the LLC converter. The conversion efficiency is poor when working under a heavy load condition. When the battery is close to being fully charged, the required charging current is small, which also complies with the low quality factor characteristic of the LLC converter, and has higher efficiency when operating under a light load condition.

During the charging period of the two BESSs, Figure 19 displays the temperature-measured curves of the batteries, where the blue colors represent the temperature curves of the upper and lower of the batteries, and the orange colors represent the ambient temperature. In Figure 19a, it illustrates the temperature curves of the BESS b1, including battery-surface temperature and ambient temperature. Initially, the temperature curve experiences a rapid ascent, primarily attributed to a substantial charging current of 12 A. At the 13.44 min mark, the peak temperature of 42.12 °C is reached. Subsequently, the curve exhibits a gradual decline, stabilizing within the range of 37 to 38 °C. As the BESS approaches full charge, the charging current diminishes progressively, resulting in a decreasing trend in the temperature curve. Correspondingly, Figure 19b displays the temperature curves of the BESS b2, encompassing battery-surface temperature and ambient temperature. The highest temperature, 41.93 °C, is recorded at the 14.1 min mark. Given that both BESSs utilized new batteries for the testing, the temperature curves exhibit similar patterns.

The transmitting and receiving coils of the proposed charger are, respectively, presented in Figure 20a–c, showing the 20 cm air gap between these coils. In Figure 20a,b, the red double arrows represent the inner diameter of the coils, and the orange double arrows represent the outer diameter of the coils. In Figure 20c, the red arrows point to the transmitting and the receiving coils respectively, and the red double arrows represent the coil distance. To fabricate the high-voltage compensation capacitors C_t and C_r, multiple metalized polypropylene film capacitors were connected in series and parallel, as shown in Figure 21a,b. Figure 21c depicts the air-core inductor ℓ_t, which was wound with multistrand wires by using a plastic sleeve. The inductance of this inductor was measured to be 37 μH at a frequency of 50 kHz, and its quality factor Q was 78.

6. Conclusions

The paper comprehensively examines the operational principle, design process, and experimental waveform measurements related to the proposed charger. The experimental findings clearly illustrate that the LLC resonant tank efficiently converts input power, enabling the transmitter coil to achieve a substantial step-up in voltage. By adjusting the inductance ratio (K value), it is possible to restrict the circulating current at the transmitter side within a safe operational range. Furthermore, under a switching frequency of 37.9 kHz, the four active switches and two rectifier diodes exhibit soft switching characteristics. The receiving coil received a magnetic field from the transmitting coil over an air gap of 20 cm; the induced voltage has been significantly stepped down. Conversely, the current is augmented to facilitate the wireless charging of two BESSs with storage capacities of 60 V and 14 Ah, respectively. The recorded data reveals a maximum output power of 1391 W and an impressive charging efficiency of 98%. These results underscore the effectiveness of the circuit topology and charging method in optimizing green energy storage with minimal energy loss. This outcome presents a compelling solution to address the growing energy scarcity on Earth.

In contrast to conventional wireless chargers that typically employ LCC circuit topologies, combined with DC charging for fast charging, this study’s proposed charging strategy not only enhances charging efficiency but also prolongs the battery’s cycle life. This high-efficiency wireless charger has the potential to revolutionize the use of green energy sources, reducing our reliance on traditional power grids, curbing carbon emissions, and minimizing environmental impacts. Its applicability in electric vehicles, industrial automation, and smart homes stands to reduce energy wastage and offer greater convenience and scalability. In conclusion, efficient wireless chargers hold significant promise for improving energy efficiency and environmental protection. This, in turn, contributes to the sustainability of our energy resources, aligning with our broader goals of promoting a greener and more sustainable future.