Design and Implementation of an IPT Charger with Minimum Number of Elements for Battery Charging Applications

Abstract

Inductive power transfer (IPT) systems have been extensively studied and incorporated into various industrial applications. An IPT system with the capability to provide constant current output (CCO) and constant voltage output (CVO) is necessary to ensure optimal battery performance. However, the resistance of the battery will continue to increase during the charging process, making it difficult for the system to realize load-independent CCO and CVO with zero phase angle (ZPA) operation. Therefore, this paper proposes an LC/S compensated IPT system, which can provide CCO and CVO at fixed frequencies. ZPA operation can be maintained in both CC and CV modes for low reactive power loss. Moreover, the total number of compensation elements of the system is minimized, with only one compensation capacitor on the receiving side, which ensures not only the low cost of the system but also a compact receiver. Finally, the correctness and feasibility of the proposed system are verified with simulations and experiments.

1. Introduction

Since traditional wired power supply methods limit the flexibility of electrical equipment and have potential safety hazards, inductive power transfer (IPT) is proposed to provide flexible and reliable power transmission. Inductive power transfer is a technology using electromagnetic fields or electromagnetic waves to transmit electrical energy contactlessly. Due to the inherent advantages of IPT, it has significant research value and broad application prospects. At present, IPT has been applied in various industrial applications, such as portable electronic devices [1,2], light-emitting diode (LED) lighting applications [3,4], biomedical implants [5,6], electric vehicles [7,8], unmanned aerial vehicles [9,10], underwater applications [11], etc.

Lithium-ion batteries are widely used as energy storage devices due to their safety, good high-temperature performance, extended service life, and high energy density [12]. It is well known that the load of the battery continues to increase during battery charging. To ensure battery performance and prolong battery life, an IPT system with stable constant current output (CCO) and constant voltage output (CVO) should be designed according to the battery charging law. Figure 1 shows a typical battery charging curve. Generally, the battery is first charged in CC mode. As the battery load continues to increase, the battery charging voltage increases. Once the charging voltage reaches a preset value, the system switches to CV mode. The charging current of the battery then gradually decreases until charging is completed.

In recent years, scholars have made many innovative attempts to design an IPT system with CCO and CVO functions. In general, IPT systems have four basic topologies, namely, series-series (SS), series-parallel (SP), parallel-series (PS), and parallel-parallel (PP) [13]. It has been proven that under specific parameters, SS and PS can provide load-independent CCO characteristics, while SP and PP can provide load-independent CVO characteristics [14,15]. To realize reliable CCO and CVO functions, in [13], the aforementioned four basic topologies are combined, and hybrid topologies combining SS and PS, and SP and PP, respectively, are proposed. In addition, refs. [16,17,18,19] all achieved CCO and CVO characteristics with ZPA operation by designing different hybrid topologies. However, the proposed structures in [13,16,17,18,19] must introduce additional AC switches and compensation elements, which increases the cost and size of the systems. Therefore, the hybrid topology switching method is not the optimal solution for achieving CCO and CVO characteristics. In view of this, the authors in [20] proposed a method to achieve CCO and CVO characteristics by changing the operating frequency. Although complex topology switching is not required, SS topology can only achieve purely resistive input impedance in CC mode. In CV mode, ZPA operation cannot be satisfied, which will inevitably lead to massive power loss. In [21], the authors proposed an S/S/P topology that can provide CCO and CVO characteristics at two frequencies. Unfortunately, the volume, weight, and cost of the receiver are increased due to a bulky filter inductor behind the rectifier in this system. In [22], Vu et al. deduced and verified that a dual LCC topology could realize CCO and CVO characteristics at two frequency points. However, due to the large number of compensation components derived from this topology, this solution suffers from the same structural drawbacks as [21]. In [23], the authors presented a new three-coil parameter design approach to achieve CCO and CVO by modifying the frequency. In addition, Tran et al. [24] comprehensively analyzed a four-coil IPT system and realized CCO and CVO functions at two distinct frequency points. However, the three-coil IPT system in [23] and the four-coil IPT system in [24] both have a rigorous mutual inductance relationship, which increases the design difficulty and instability of the system. Given this, this article proposes an LC/S compensated IPT system that can realize stable CCO and CVO characteristics under two fixed ZPA operating frequencies through reasonable parameter design. Notably, the total number of compensation elements of the system is minimized, with only one compensation capacitor on the receiving side, which ensures not only the low cost of the system, but also a compact receiver. The CLC/N compensated IPT system proposed in [25] has no compensation components on the receiving side, which further optimizes the receiving side of the system from the perspective of compactness. However, the research in [25] achieved only CCO characteristics with ZPA operation through reasonable parameter design. Therefore, the research in [25] is only suitable for CC charging applications, such as LED driving. It is worth noting that the LC/S compensated IPT system proposed in this paper is suitable for charging with fixed coupling or low fluctuation, which is the same as the hybrid topologies of [16,17,18,19] and the dual-frequency topologies of [20,21,22,23,24].

Section 2 of this article describes a basic analysis of the proposed LC/S compensated IPT system. This section provides an overall analysis of the circuit topology and the principles for realizing CCO/CVO characteristics and ZPA operation. In Section 3, the system parameter tuning scheme is given. Firstly, a simulation analysis of the loosely coupled transformer (LCT) is carried out using the electromagnetic simulation software Maxwell. Then, the design steps of the system parameters are given. Next, an equivalent model is established in MATLAB to conduct preliminary verification of the proposed IPT system. Section 4 describes the design of the system switching strategy. Section 5 describes experiments for verifying the above theoretical analysis, and the advantages of the LC/S compensated IPT system proposed in this paper are summarized. Finally, Section 6 concludes the article.

2. Circuit Model and Theoretical Analysis

2.1. Circuit Model

Figure 2 shows the circuit structure diagram of the proposed LC/S compensated IPT system. L_p and L_s represent the self-inductance of the transmitting and receiving coils, and L₁ is the compensation inductance. R₁, R_p, and R_s represent the parasitic resistance of the compensation inductance and coils. Since the values of R₁, R_p, and R_s are very small, they can be ignored in the analysis in the interest of simplification. M represents the mutual inductance between the transmitting and receiving coils. The transmitting side of the system includes a constant DC power supply U_d, a high-frequency inverter (HFI) consisting of four MOSFETs (Q₁–Q₄), a series compensation inductor L₁, a parallel compensation capacitor C₁, and a transmission coil L_p; the receiving side includes a receiving coil L_s, a series compensation capacitor C₂, and a rectifier connected in parallel with a filter capacitor C_F. The full-bridge rectifier provides DC power for the battery load R_L. Figure 3 shows a simplified circuit diagram of the topology, in which the square wave voltage U_in driven by the HFI and the value of the equivalent load R_ac can be expressed as:

Figure 2. Circuit diagram of the LC/S compensated IPT system.

Figure 2. Circuit diagram of the LC/S compensated IPT system.

Figure 3. Simplified circuit diagram of the LC/S compensated IPT system.

Figure 3. Simplified circuit diagram of the LC/S compensated IPT system.

$$R_{\mathrm{ac}}=\frac{8R_{\mathrm{L}}}{{\pi }^2}, U_{\mathrm{in}}=\frac{2\sqrt{2}{U}_{\mathrm{d}}}{\pi }$$

(1)

According to Figure 3, the loop equation of the topology should satisfy the following:

$$\left[\begin{array}{c}{U}_{\mathbf{in}}\\ 0\\ 0\end{array}\right]=\left[\begin{array}{ccc}{Z}_1+Z_{\mathrm{m}}& -Z_{\mathrm{m}}& 0\\ 0& j\omega M& Z_{\mathrm{s}}+R_{ac}\\ -Z_{\mathrm{m}}& Z_{\mathrm{p}}+Z_{\mathrm{m}}& j\omega M\end{array}\right]\left[\begin{array}{c}{I}_{\mathbf{1}}\\ I_{\mathbf{p}}\\ I_{\mathbf{s}}\end{array}\right]$$

(2)

where Z₁, Z_m, Z_p, and Z_s are equivalent impedances expressed as

$$\{\begin{array}{l}{Z}_1=j\omega L_1\\ Z_{\mathrm{m}}=\frac{1}{j\omega C_1}\\ Z_{\mathrm{p}}=j\omega L_{\mathrm{p}}\\ Z_{\mathrm{s}}=j\omega L_{\mathrm{s}}+\frac{1}{j\omega C_2}\end{array}$$

(3)

I₁ is the input current phasor of the topology. I_p and I_s represent the current phasors of the transmitting and receiving loops, respectively. According to Formula (2), the expression of the current phasors can be calculated as

$$\{\begin{array}{l}{I}_{\mathbf{1}}=\frac{({\omega }^2{M}^2+R_{\mathrm{ac}}{Z}_{\mathrm{m}}+R_{\mathrm{ac}}{Z}_{\mathrm{p}}+Z_{\mathrm{s}}{Z}_{\mathrm{m}}+Z_{\mathrm{p}}{Z}_{\mathrm{s}})U_{\mathbf{in}}}{A{R}_{\mathrm{ac}}+B}\\ I_{\mathbf{p}}=\frac{Z_{\mathrm{m}}(R_{\mathrm{ac}}+Z_{\mathrm{s}})U_{\mathbf{in}}}{A{R}_{\mathrm{ac}}+B}\\ I_{\mathbf{s}}=-\frac{j\omega M{Z}_{\mathrm{m}}{U}_{\mathbf{in}}}{A{R}_{\mathrm{ac}}+B}\end{array}$$

(4)

where A and B in the denominator can be expressed as

$$\{\begin{array}{l}A=Z_1{Z}_{\mathrm{m}}+Z_1{Z}_{\mathrm{p}}+Z_{\mathrm{p}}{Z}_{\mathrm{m}}\\ B=Z_1{Z}_{\mathrm{m}}{Z}_{\mathrm{s}}+Z_1{Z}_{\mathrm{p}}{Z}_{\mathrm{s}}+Z_{\mathrm{m}}{Z}_{\mathrm{p}}{Z}_{\mathrm{s}}+{\omega }^2{M}^2{Z}_1+{\omega }^2{M}^2{Z}_{\mathrm{m}}\end{array}$$

(5)

2.2. Analysis of CCO Characteristics and ZPA Operation

Based on the above analysis, when R_ac is not included in the expression of I_s, CCO characteristics can be realized. It is clear from Formula (4) that if A = 0 holds, I_s is independent of R_ac, namely

$$Z_1{Z}_{\mathrm{m}}+Z_1{Z}_{\mathrm{p}}+Z_{\mathrm{m}}{Z}_{\mathrm{p}}=0$$

(6)

When Equation (6) holds, the input impedance Z_in of the proposed system can be expressed as

$$Z_{\mathrm{in}}=\frac{U_{\mathbf{in}}}{{{\rm I}}_{\mathbf{1}}}=\frac{{\omega }^2{M}^2(Z_1+Z_{\mathrm{m}})}{{\omega }^2{M}^2+Z_{\mathrm{m}}{R}_{\mathrm{ac}}+Z_{\mathrm{p}}{R}_{\mathrm{ac}}+Z_{\mathrm{m}}{Z}_{\mathrm{s}}+Z_{\mathrm{p}}{Z}_{\mathrm{s}}}$$

(7)

According to Formula (7), if the following Formula (8) is established, the input impedance Z_in is pure resistance, and the ZPA input of the system is realized.

$${\omega }^2{M}^2+Z_{\mathrm{m}}{Z}_{\mathrm{s}}+Z_{\mathrm{p}}{Z}_{\mathrm{s}}=0$$

(8)

The conditions for satisfying CCO and ZPA input can then be summed up as

$$\{\begin{array}{l}{Z}_1{Z}_{\mathrm{m}}+Z_1{Z}_{\mathrm{p}}+Z_{\mathrm{m}}{Z}_{\mathrm{p}}=0\\ {\omega }^2{M}^2+Z_{\mathrm{m}}{Z}_{\mathrm{s}}+Z_{\mathrm{p}}{Z}_{\mathrm{s}}=0\end{array}$$

(9)

When Formula (9) is established, the current expressions can be simplified as

$$\{\begin{array}{l}{{\rm I}}_{\mathbf{1}}=\frac{(R_{\mathrm{ac}}{Z}_{\mathrm{m}}+R_{\mathrm{ac}}{Z}_{\mathrm{p}})U_{\mathbf{in}}}{{\omega }^2{M}^2(Z_1+Z_m)}\\ {{\rm I}}_{\mathbf{p}}=\frac{Z_{\mathrm{m}}(R_{\mathrm{ac}}+Z_{\mathrm{s}})U_{\mathbf{in}}}{{\omega }^2{M}^2(Z_1+Z_m)}\\ {{\rm I}}_{\mathbf{s}}=-j\frac{Z_{\mathrm{m}}{U}_{\mathbf{in}}}{\omega M(Z_1+Z_m)}\end{array}$$

(10)

The input impedance Z_in and the transconductance gain G can be simplified as

$$Z_{\mathrm{in}}=\frac{{\omega }^2{M}^2(Z_1+Z_{\mathrm{m}})}{(Z_{\mathrm{m}}+Z_{\mathrm{p}})R_{\mathrm{ac}}}$$

(11)

$$G=\frac{{{\rm I}}_{\mathbf{s}}}{U_{\mathbf{in}}}=\left|j\frac{Z_{\mathrm{m}}}{\omega M(Z_1+Z_{\mathrm{m}})}\right|$$

(12)

Obviously, according to Formula (11), the input impedance Z_in is related only to R_ac, so the system input impedance is purely resistive, and ZPA input can be achieved under different loads. According to Formula (12), the transconductance gain G is independent of R_ac. Therefore, the proposed system can achieve CCO functions.

2.3. Analysis of CVO Characteristics and ZPA Operation

As in the analysis in the previous section, the output voltage U_s can be obtained as

$$U_{\mathbf{s}}=-\frac{j\omega M{Z}_{\mathrm{m}}{R}_{\mathrm{ac}}}{A{R}_{\mathrm{ac}}+B}=-\frac{j\omega M{Z}_{\mathrm{m}}{U}_{\mathbf{in}}}{A+\frac{B}{R_{\mathrm{ac}}}}$$

(13)

According to Formula (13), when the condition B = 0 is established, the output voltage U_s is independent of R_ac, and CVO characteristics can be realized, namely

$$Z_1{Z}_{\mathrm{m}}{Z}_{\mathrm{s}}+Z_1{Z}_{\mathrm{p}}{Z}_{\mathrm{s}}+Z_{\mathrm{m}}{Z}_{\mathrm{p}}{Z}_{\mathrm{s}}+{\omega }^2{M}^2{Z}_1+{\omega }^2{M}^2{Z}_{\mathrm{m}}=0$$

(14)

Furthermore, the input impedance Z_in of the proposed system can be expressed as

$$Z_{\mathrm{in}}=\frac{U_{\mathbf{in}}}{{{\rm I}}_{\mathbf{1}}}=\frac{(Z_1{Z}_{\mathrm{m}}+Z_1{Z}_{\mathrm{p}}+Z_{\mathrm{p}}{Z}_{\mathrm{m}})R_{\mathrm{ac}}}{{\omega }^2{M}^2+Z_{\mathrm{m}}{R}_{\mathrm{ac}}+Z_{\mathrm{p}}{R}_{\mathrm{ac}}+Z_{\mathrm{m}}{Z}_{\mathrm{s}}+Z_{\mathrm{p}}{Z}_{\mathrm{s}}}$$

(15)

According to Formula (15), if Formula (16) holds, it can be guaranteed that the input impedance Z_in has no imaginary part and is related only to R_ac, namely, the realization of the ZPA operation.

$$Z_{\mathrm{m}}+Z_{\mathrm{p}}=0$$

(16)

The conditions for satisfying CVO and ZPA input can then be summed up as

$$\{\begin{array}{l}{Z}_1{Z}_{\mathrm{m}}{Z}_{\mathrm{s}}+Z_1{Z}_{\mathrm{p}}{Z}_{\mathrm{s}}+Z_{\mathrm{m}}{Z}_{\mathrm{p}}{Z}_{\mathrm{s}}+{\omega }^2{M}^2{Z}_1+{\omega }^2{M}^2{Z}_{\mathrm{m}}=0\\ Z_{\mathrm{m}}+Z_{\mathrm{p}}=0\end{array}$$

(17)

According to the above conditional equations, the input impedance Z_in and the voltage gain E can be simplified as

$$Z_{\mathrm{in}}=\frac{Z_{\mathrm{p}}{Z}_{\mathrm{m}}{R}_{\mathrm{ac}}}{{\omega }^2{M}^2}$$

(18)

$$E=\frac{U_{\mathbf{s}}}{U_{\mathbf{in}}}=\left|j\frac{\omega M}{Z_{\mathrm{p}}}\right|$$

(19)

Obviously, according to Formula (18), the input impedance Z_in is related only to the equivalent load resistance R_ac, so the system can achieve ZPA input under different loads. According to Formula (19), the voltage gain E is not affected by the equivalent load resistance R_ac, and therefore the system can realize CVO at the full load.

2.4. Determination of Compensation Capacitor Value

Based on the above analysis, to realize the CCO and CVO characteristics and ZPA operation meeting battery charging requirements, the compensation capacitors C₁ and C₂ must simultaneously satisfy Equations (9) and (17). Therefore, the expressions of compensation capacitors C₁ and C₂ can be obtained by associating Equations (3), (9) and (17).

$$\{\begin{array}{l}{C}_1=\frac{1}{({\omega }_{\mathrm{cc}}^2-{\omega }_{\mathrm{cv}}^2)L_1}\\ C_2=\frac{{({\omega }_{\mathrm{cc}}^2-{\omega }_{\mathrm{cv}}^2)}^3{L}_1}{2{\omega }_{\mathrm{cc}}^2{\omega }_{\mathrm{cv}}^6{M}^2}\end{array}$$

(20)

3. Design and Preliminary Verification

The theoretical analysis in Section 2 shows that the proposed LC/S compensated IPT system can realize CCO and CVO characteristics with ZPA operation at fixed operating frequencies. This section describes the structural design of the LCT, providing a strict system parameter design process. In addition, by building an equivalent model, the above theoretical analysis is preliminarily verified.

3.1. LCT Structure Design

LCTs are generally designed with circular, square or rectangular structures. According to [26], square coils have higher mutual and self-inductance than circular coils of the same diameter. Moreover, the mutual inductance of square coils is more stable under horizontal offset, but the current at the corners of the square coils is typically uneven due to collector and proximity effects. To avoid the impact of the corners on the current and reduce loss, a rounded corner design can be selected. Therefore, both the transmitting coil L_p and the receiving coil L_s of the proposed LC/S compensated IPT system adopt a square coil structure with rounded corners. The specific parameters of the coils L_p and L_s are shown in

Table 1. Dimensional parameters of the designed LCT.

Parameters	Transmitting Coil Lp	Receiving Coil Ls
Outer diameter	210 mm	280 mm
Internal diameter	156 mm	196 mm
Turns of coils (n)	9	14
Specifications of Litz wire	400 strands	400 strands

.

Since there is compensation inductance L₁ on the transmitter side, it will generate unnecessary coupling interference with L_p and L_s, which complicates the design and affects the efficiency of system energy transmission. Therefore, this article considers the decoupling design of the series compensation inductor L₁ and LCT. According to [27], unipolar coils and bipolar coils placed in parallel have no coupled mutual inductance in case of alignment. Figure 4 shows the magnetic field distribution diagrams generated by unipolar and bipolar coils. B and I in the figure represent the magnetic field and current of the coils respectively. Generally, unipolar coils generate a magnetic field away from the center of the magnetic field, while bipolar coils produce a magnetic field distributed along the axis (long axis or width axis). When the unipolar coil and the bipolar coil are coaxially placed in parallel, since the magnetic flux generated by the bipolar coil is symmetrical along the space, the magnetic flux flowing into the unipolar coil is equal to the magnetic flux flowing out of the bipolar coil. Therefore, the unipolar coil and the bipolar coil are decoupled from each other, i.e., there is no coupled mutual inductance between them. This decoupling design can maximize the space utilization of the magnetic coupling coil, reduce the size of the IPT system, and ensure that the transmitting coil L_p transmits power only to the receiving coil L_s, improving the transmission efficiency and stability of the system.

To verify the correctness of the decoupling design according to the structural parameters in Table 1, a model of the compensation inductance L₁ and LCT was created using the electromagnetic simulation software Maxwell, as shown in Figure 5. The compensation inductor L₁ uses a bipolar (DD) coil, whereas the coils L_p and L_s employ square unipolar coil structures with rounded corners. Wherein L_p is placed immediately on L₁, L_s is positioned directly above L_p, and the three coils are placed coaxially and parallel. The ferrite is placed outside the coil to reduce series impedance and enhance electromagnetic performance. Finally, a simulation analysis is carried out using the electromagnetic field analysis software Maxwell to estimate the self-inductance values of L₁, L_p and L_s, as well as the values of M_p1 (mutual inductance between L₁ and L_p), M_s1 (mutual inductance between L₁ and L_s) and M_ps (mutual inductance between L_p and L_s). The simulation results are listed in

Table 2. Simulation values for compensation inductance and LCT.

Parameters	Value	Parameters	Value
L1	80 $\mathsf{\mu }\mathrm{H}$	Mp1	1.21 $\mathsf{\mu }\mathrm{H}$
Lp	45 $\mathsf{\mu }\mathrm{H}$	Ms1	0.26 $\mathsf{\mu }\mathrm{H}$
Ls	136.68 $\mathsf{\mu }\mathrm{H}$	Mps	26 $\mathsf{\mu }\mathrm{H}$

. It can be seen from Table 2 that the values of M_p1 and M_s1 are nearly 0, which is an intuitive proof for the design of the above-mentioned decoupling characteristics.

3.2. Parameter Design

This section presents the parameter design steps of the proposed system. A flow chart of the parameter design is depicted in Figure 6.

Step 1:

The operating angular frequencies ω_cc and ω_cv of the proposed system in CC and CV modes are determined in accordance with the specific applications.

Step 2:

Determine the appropriate transconductance gain G and voltage gain E.

Step 3:

Set the size and turns of L₁, L_p and L_s.

Step 4:

The self-inductances of L₁, L_p and L_s and mutual inductance M are estimated by Maxwell.

Step 5:

The compensation capacitances C₁ and C₂ can be calculated by using Equation (20).

Step 6:

Judge whether Equations (9) and (17) are satisfied. If Equations (9) and (17) hold, system parameters are successfully designed. If Equations (9) and (17) are not satisfied, the design parameters are unreasonable. Repeat step 3 until Equations (9) and (17) are hold.

Finally, the theoretical system parameters are summarized in

Table 3. Design values of crucial parameters in the proposed LC/S compensated IPT system.

Parameters	Value	Parameters	Value
fcc	90 kHz	C1	108.58 nF
fcv	72 kHz	C2	32.93 nF

.

3.3. Preliminary Verification

In this section, the equivalent models of the LC/S compensation IPT system under CC and CV modes are established in MATLAB, and the functions of the system are initially verified. According to the data in Table 2 and Table 3 and the established equivalent model, the relation curve of the system input impedance angle and the transconductance/voltage gains changing with frequency under different loads can be generated. Through the simulation analysis of the equivalent model, Figure 7 and Figure 8 verify that load-independent CCO and CVO can be achieved at two distinct ZPA operating frequency points.

4. Design of Switching Strategy

As was confirmed in the previous section, the proposed LC/S compensated IPT system can achieve CCO and CVO characteristics at two distinct ZPA operating frequencies through appropriate parameter design, without the need for redundant AC switches (ACS). Figure 9 shows the switching strategy for the system charging mode. Figure 10 depicts the mode-switching part in the green box in Figure 9. More specifically, when the IPT system starts to work, the charging voltage U_bat and current I_bat of the battery are synchronously measured by the voltage and current sensors, and the values are sent to the controller. U_set is the charging voltage specified in CV mode, namely, the critical voltage at the transition point (U_set = 45 V) between CC mode and CV mode. When U_bat < U_set, the controller charges in CC mode at the CC frequency f_cc. As the voltage continues to rise until U_bat ≥ U_set, the controller charges in CV mode at the CV frequency f_cv. As the charging current decreases, the IPT system stops working when the charging current I_bat < I_min is detected. I_min is the specified minimum charging current (I_min = 0.25 A).

5. Experimental

To verify the above theory, a confirmatory experimental prototype of the proposed system was constructed. The hardware of the prototype is shown in Figure 11. It consists of a DC voltage source, a compensation inductor L₁, compensation capacitors C₁ and C₂, an LCT, an HFI, a rectifier, a resistive load, and an oscilloscope. Referring to the LCT structural parameters in Table 2, the coil used for the experiment is wound, as illustrated in Figure 12. As shown in Figure 12, the transmitting coil L_p is placed just above the series compensation inductor L₁, ensuring the compactness of the whole IPT system. In addition, the coupling mutual inductances between L_p and L₁ and between L_s and L₁ are both zero as measured by the LCR meter, which verifies the theoretical analysis of the decoupling coil in Section 3. The measured values for each piece of hardware are shown in

Table 4. Measured values of specific parameters in the proposed LC/S compensated IPT system.

Parameters	Value	Parameters	Value
fcc	90 kHz	C1	107.73 nF
fcv	72 kHz	C2	32.61 nF
L1	$80.63 \mathsf{\mu }\mathrm{H}$	Rp	0.12 Ω
Lp	$45.35 \mathsf{\mu }\mathrm{H}$	Rs	0.08 Ω
Ls	$138.03 \mathsf{\mu }\mathrm{H}$	Rm	0.16 Ω
M	$26.23 \mathsf{\mu }\mathrm{H}$	Iout	2.5 A
Ud	82 V	Uout	45 V

.

Figure 13 displays the waveforms of U_in, I₁, I_out and U_out at an operating frequency of 90 kHz when the loads are 10 Ω and 15 Ω, respectively. According to Figure 13, U_in and I₁ are always in phase under different loads. In addition, I_out remains at 2.5 A, which means that ZPA operation and CCO are realized. Figure 14 displays the experimental waveforms of U_in, I₁, I_out and U_out at an operating frequency of 72 kHz when the loads are 25 Ω and 50 Ω, respectively. Consistent with the above analysis, according to Figure 14, when the operating frequency is 72 kHz, the system can achieve CVO with ZPA operation. In summary, it is verified by experiments that the LC/S compensated IPT system proposed in this study can realize CCO and CVO characteristics at fixed ZPA operating frequency points. Therefore, the charging requirements of the battery are satisfied.

The energy transmission efficiency curve of the system during the whole charging process is displayed in Figure 15. In CC charging mode, the energy transfer efficiency of the system increases rapidly from 89.2% to 92.8%. When the equivalent load rises to 18 Ω, the operating frequency of the system is switched from ω_cc to ω_cv for CV charging mode. In CV charging mode, the peak energy transfer efficiency of the system is 94.4%. In addition, the power transfer efficiency of the system stays at a relatively high level throughout the charging process, which ensures high efficiency of the proposed LC/S compensated IPT system.

To illustrate the advantages of the proposed LC/S compensated IPT system, a summary is given below:

(i)

The proposed LC/S compensated IPT system does not require redundant AC switches and complex control algorithms, and shifts between two fixed operating frequencies to realize CCO and CVO with ZPA operation, which not only makes the system simpler in structure, but also makes control of the system more convenient. In addition, the total number of compensation elements of the system is minimized, with only one compensation capacitor on the receiving side, ensuring a compact and low-cost receiver.

(ii)

The proposed LC/S compensated IPT system adopts a coil decoupling design, which eliminates the coupling mutual inductance between the compensation inductor L₁ and the LCT, maximizing space utilization.

6. Conclusions

To satisfy the charging requirements of the battery first in the CC stage and later in the CV stage, this article proposed an IPT system based on LC/S compensation. The system enables full-load-range ZPA operation as well as load-independent CCO and CVO at distinct operating frequencies. The detailed circuit analysis and parameter design process of the proposed system are provided in this article, and experiments verify its output characteristics. Notably, the series compensation inductor is designed as a DD structure to eliminate coupling interference between the inductor and the LCT, which not only reduces the complexity of system parameter design, but also reduces the space used by the magnetic coupling coil. Moreover, the total number of compensation elements of the system is minimized, with only one compensation capacitor on the receiving side, which not only ensures the low cost of the system but also makes the receiver more compact.