Method for Multi-Target Wireless Charging for Oil Field Inspection Drones

Abstract

Wireless power transfer (WPT) systems are critical for enabling safe and efficient charging of inspection drones in flammable oilfield environments, yet existing solutions struggle with multi-target compatibility and reactive power losses. This study proposes a novel frequency-regulated LCC-S topology that achieves both constant current (CC) and constant voltage (CV) charging modes for heterogeneous drones using a single hardware configuration. By dynamically adjusting the operating frequency, the system minimizes the input impedance angle (θ < 10°) while maintaining load-independent CC and CV outputs, thereby reducing reactive power by 92% and ensuring spark-free operation in explosive atmospheres. Experimental validation with two distinct oilfield inspection drones demonstrates seamless mode transitions, zero-phase-angle (ZPA) resonance, and peak efficiencies of 92.57% and 91.12%, respectively. The universal design eliminates the need for complex alignment mechanisms, offering a scalable solution for multi-drone fleets in energy, agriculture, and disaster response applications.

1. Introduction

In oilfield inspection, the traditional manual method is high-risk and costly. Uncrewed inspection offers a safer, more efficient alternative. However, among the different methods used to charge oilfield inspection drones, traditional wired power poses fire and explosion risks in flammable, explosive environments. At the same time, providing power to inspection drones is challenging due to fixed charging positions and the complex oilfield environment, which has become a major obstacle to the industry’s development. Wireless power transfer (WPT) technology, a spark-free, flexible technology [1,2], has become the first choice for improving the safety and efficiency of inspection [3,4,5,6].

In contrast to traditional inspection scenarios, such as factories and power grids, oilfields present challenges, such as complex terrain, fluctuating environmental conditions, and diverse operational drones. Such conditions necessitate uncrewed inspections with multi-device collaboration and multi-angle coverage. However, WPT technology faces challenges in multi-target charging due to variations among different inspection drones. The term multi-target charging in this work refers to the capability of a single transmitter coil to adaptively charge different drones with varying receiver parameters (coil inductance L_s, mutual inductance M, and battery specifications) through frequency regulation without requiring simultaneous charging of multiple devices. Multi-device inspection cannot be charged effectively due to excess reactive power. Recent advancements in drone WPT systems prioritize lightweight designs and compatibility with heterogeneous battery chemistries. For explosive oilfield environments, LiFePO₄ batteries (5200 mAh, 23–36 V) are preferred due to their low thermal runaway risk, which mandates WPT systems that operate with the smallest possible reactive power and a near-zero input impedance phase angle (θ < 10°) to prevent spark generation [4]. Furthermore, constant current (CC) and constant voltage (CV) charging are indispensable to optimize charging efficiency and ensure safety in challenging environments. Therefore, investigating WPT systems that can realize CC and CV charging and achieve multi-target charging is imperative [7,8,9].

Different methods can be used to improve efficiency and active power to achieve multi-target charging, as shown in Figure 1 [10,11]. The magnetic coupler’s ability to support multi-target charging depends on the relative coil position, transmission distance, and coupling structure transmission distance, as well as the magnetic coupling structure [12,13]. The topology is designed to match the impedance and provide reactive power compensation. Even with excellent coil multi-target charging ability, an inappropriate topology can still lead to impedance mismatch, resulting in incomplete energy absorption by the load and a decrease in the received active power [14]. Therefore, when evaluating the ability of multi-target charging, it is crucial to optimize the parameters of the topology. Therefore, both the coupler design and the compensation topology parameters must be optimized to ensure good multi-target charging performance in a WPT system.

Recent advancements in wireless power transfer (WPT) technologies have significantly contributed to the development of drone charging systems. Various compensation topologies, such as LCC-S, LCC-LCC, and S-SP, have been explored to optimize power transfer efficiency and system stability under different operational conditions. For instance, Mou et al. [15] provided a comprehensive review of near-field WPT technologies for drone charging, highlighting the design challenges and potential solutions associated with inductive and capacitive power transfer methods. Similarly, Chittoor et al. discussed the fundamentals and applications of drone wireless charging, emphasizing the need for efficient multi-drone charging systems [16]. These studies underscore the importance of developing robust WPT systems capable of accommodating multiple drones with varying power requirements.

However, existing research primarily focuses on single-drone charging scenarios, with limited exploration of multi-target charging systems that can simultaneously accommodate drones with heterogeneous power requirements. For example, studies have examined the multi-target charging capabilities of various topologies, including LCC–S, LCC–P, and S–LCC, demonstrating that these configurations can achieve similar power outputs with equal coil parameters [17]. Nonetheless, these investigations primarily compare different topologies without delving into parameter adjustments to enhance multi-target charging performance. Additionally, compensation requirements have been proposed to achieve maximum efficiency in different WPT applications, specifically addressing the impact of offset and load variations on resonance for S–S and LCC–LCC topologies [18,19]. While optimizing system parameters has been a popular research topic, many studies assume identical load batteries, which does not align with practical scenarios requiring constant current (CC) and constant voltage (CV) charging for varied loads. Moreover, although duty cycle adjustment can address some challenges, it introduces high-frequency harmonics that amplify conducted and radiated electromagnetic interference (EMI), thereby compromising nearby communication devices [20]. Thus, it remains a suboptimal solution. To address this challenge, our study proposes a novel frequency-regulated LCC-S compensation topology designed to facilitate adaptive charging for multiple drones with varying power demands. By employing frequency modulation techniques, the system can dynamically adjust its output to provide constant current (CC) or constant voltage (CV) charging modes required by each drone. This approach aims to enhance the flexibility and efficiency of multi-drone charging systems, contributing to the broader adoption of autonomous drone operations.

To address the above challenges, this study proposes a frequency-regulated LCC–S resonant topology that enables adaptive CC and CV charging for different drones via frequency control only, without the need for any hardware reconfiguration. By designing a unified transmitter-side compensation network and adjusting the excitation frequency, the system can provide either load-independent constant current (CC) or constant voltage (CV) charging to different drones with varying coil parameters and battery profiles. This frequency-selective mode switching ensures that the system always operates near the ZPA condition, thus minimizing reactive power and maximizing safety and efficiency.

Compared to existing approaches that rely on duty cycle modulation, secondary-side switching, or hybrid topologies with additional control circuits, our method achieves dual-mode charging and multi-target adaptability in a single, fixed-circuit structure. This greatly reduces control complexity and hardware overhead. Experimental validation with two distinct oilfield inspection drones demonstrates seamless mode transitions, efficient operation (peak transfer efficiency up to 92.3%), and robust performance across different load and coupling conditions. Prior studies, such as those using LCCL-S or hybrid reconfigurable topologies, still require active switching to achieve CC/CV transition, whereas our approach accomplishes this purely through frequency tuning. Therefore, the proposed method offers a scalable, low-complexity solution for multi-drone wireless charging in harsh environments, such as oilfields, agriculture, and disaster response.

Specifically, Section 2 derives the CC and CV charging of the LCC–S topology by regulating the frequency and determines the relationship between the input impedance angle and the frequency. Therefore, a method for achieving multi-target charging by adjusting frequency is proposed. Then, the parameter design method is described. In Section 3, the proposed charging topology and method are verified. Finally, conclusions are drawn in Section 4.

2. Materials and Methods

2.1. Theoretical Analysis

The equivalent topology of the WPT system based on the LCC–S loose-coupling transformer model is shown in Figure 2. The topology model of the WPT system can be substituted by the decoupling equivalent topology model in Figure 3.

Based on the multi-target charging requirements, L_s1 represents the receiving coil of inspection drone A, and C_ss1 corresponds to its complementary secondary series compensation capacitor. (C_X represents the Capacitance of the compensation capacitor C_X in the LCC-S topology, and L_X represents the inductance of the compensation inductor L_X in the LCC-S topology.) The control circuit’s power consumption during charging is integrated into the load model by combining the internal circuit resistance [9]. The mutual inductance naturally forms a gyrator [21]. To meet the load-independent constant voltage output, the model needs to be simplified into two gyrators. Because the topology has fewer secondary components and more primary components, the receiving coil L_s1 and the complementary secondary series compensation capacitor C_ss1 can be transformed into the primary according to the characteristics of gyrator impedance conversion [22], as shown in Figure 4.

The modified reactance Z_Ls and Z_Css (Z_X represents the equivalent impedance of X in the LCC-S topology) can be represented as

$$\left\{\begin{array}{l}{Z}_{Ls}=-{\displaystyle \frac{1}{G^2(j\omega L_s)}}={\displaystyle \frac{{\omega }^2{M}^2}{j\omega L_s}}\hfill \\ Z_{Css}=-{\displaystyle \frac{1}{G^2(1/j\omega C_{ss})}}={\omega }^2{M}^2(j\omega C_{ss}).\hfill \end{array}\right.$$

(1)

According to (1), the transformed capacitance of Z_Ls is capacitive, and the transformed inductance of Z_Css is inductive.

After the equivalent transformation of the above capacitors, the LCC–S topology at the operating frequency of the system in the CV stage f_cv has a gyrator model, as shown in Figure 4. To construct a cascade of the two gyrators, the capacitors Z_Ls and Z_Css form a parallel resonant circuit. The resonant components L_p, C_ps, C_pp, and L_ps in front of the capacitor constitute a T-type gyrator.

The fundamental harmonic approximation method [23] is used to analyze topology characteristics [24]. The corresponding resonant conditions are shown as

$$\left\{\begin{array}{l}1-{{\omega }_{cv}}^2{C}_{ss}{L}_s=0\hfill \\ {\displaystyle \frac{1}{C_{ps}}}+{\displaystyle \frac{1}{C_{pp}}}={{\omega }_{cv}}^2{L}_p\hfill \\ 1-{{\omega }_{cv}}^2{L}_{ps}{C}_{pp}=0.\hfill \end{array}\right.$$

(2)

The voltage gain at f_cv is

$$G_{CV}={\displaystyle \frac{U_L}{U_{in}}}={\displaystyle \frac{j}{{\omega }_{cv}M}}{\displaystyle \frac{{\omega }_{cv}{L}_{ps}}{j}}={\displaystyle \frac{L_{ps}}{M}}.$$

(3)

Therefore, the output characteristic of the topology is a load-independent constant voltage source.

If the charging drone changes, the self-inductance of the receiving coil changes from L_s1 to L_s2, and the mutual inductance changes from M₁ to M₂. It is sufficient to calculate C_ss2, satisfying (4) based on L_s2 without changing f_cv, achieving a constant voltage output independent of the load.

$$1-{{\omega }_{cv}}^2{C}_{ss2}{L}_{s2}=0.$$

(4)

To achieve constant current output, the topology illustrated in Figure 4 should be simplified into a cascaded three-gyrator form. According to the distribution of topology components, the topology can be appropriately split such that the resonant compensation inductor L_ps is split into two reactances in series (Z_p1 and Z_p2), the inductance of the coil L_p and the compensation capacitor C_ps are split into two reactances in series, and the resonant compensation capacitor C_ps is split into two inductances in series. That is,

$$\left\{\begin{array}{l}j{\omega }_{cc1}{L}_{ps}=Z_{p1}+Z_{p2}\hfill \\ j{\omega }_{cc1}{L}_p+{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{ps}}}=Z_{p3}+Z_{p4}.\hfill \end{array}\right.$$

(5)

The second split creates a T-type gyrator device composed of electrical resistors Z_p2 and Z_p3 and a compensation capacitor C_pp. According to the characteristics of the T-type gyrator, both Z_p2 and Z_p3 are inductive, as shown in Figure 5.

Using the equivalent transformation of the electrical resistance of the gyrator, Z_p1 is transformed into Z_p5 after the T-type gyrator. Z_p4, Z_Ls, and Z_Css form a π-type gyrator.

The transformed Z_p5 can be expressed as

$$Z_{p5}={\displaystyle \frac{1}{{{\omega }_{cc1}}^2{C_{pp}}^2{Z}_{p1}}}.$$

(6)

Upon the equivalent transformation of electrical resistance, the LCC–S topology with f_cc1 is shown in Figure 6.

To construct the cascade of three gyrators, the resonance conditions that T-type and π-type gyrators should satisfy are

$$\left\{\begin{array}{l}{\displaystyle \frac{Z_{Css}{Z}_{Ls}}{Z_{Css}+Z_{Ls}}}=Z_{p5}\hfill \\ Z_{p2}=Z_{p3}=-{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{pp}}}\hfill \\ Z_{p4}+{\displaystyle \frac{Z_{Css}{Z}_{Ls}}{Z_{Css}+Z_{Ls}}}=0.\hfill \end{array}\right.$$

(7)

The current gain at f_cc1 is

$$G_{CC}={\displaystyle \frac{I_L}{U_{in}}}={\displaystyle \frac{Z_{p5}}{Z_M{Z}_{Cpp}}}.$$

(8)

At this point, the structure operates as an independent constant current source. If the receiving coil changes, G_CV will change with Z_M, but it will still be constant. Therefore, the output characteristic remains a load-independent constant current source.

The LCC–S topology achieves constant voltage and constant current output at f_cv and f_cc1, respectively. By regulating the frequency, the structure can achieve CC and CV charging without changing its topology. If the charging drone changes, the structure can be adapted by changing only C_ss according to (2). The output characteristics of CV and CC are then realized again at f_cv and f_cc1, respectively. Thus, the topology eliminates the need for a post-rectifier DC–DC converter by achieving load-independent CC and CV characteristics through frequency regulation. This design choice reduces system complexity and avoids efficiency penalties [8].

From (1), (2), (5), (6), and (7), the following can be obtained.

$$\left\{\begin{array}{l}{Z}_{p1}=j{\omega }_{cc1}{L}_{ps}+{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{pp}}}\hfill \\ Z_{p2}=Z_{p3}=-{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{pp}}}\hfill \\ Z_{p4}=j{\omega }_{cc1}{L}_s+{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{ps}}}+{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{pp}}}\hfill \\ Z_{p5}={\displaystyle \frac{Z_{Css}{Z}_{Ls}}{Z_{Css}+Z_{Ls}}}={\displaystyle \frac{({\omega }^2{M}^2)j\omega C_{ss}}{1-{\omega }^2{L}_s{C}_{ss}}}.\hfill \end{array}\right.$$

(9)

Using the elimination method, the resonant capacitor is eliminated to obtain the following.

$$\left\{\begin{array}{l}1-{{\omega }_{cv}}^2{C}_{ss}{L}_s=0\hfill \\ 1-{{\omega }_{cv}}^2{C}_{pp}{L}_{ps}=0\hfill \\ \begin{array}{l}{Z}_{p4}+Z_{p5}=j{\omega }_{cc1}{L}_s+{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{ps}}}+\\ {\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{pp}}}+{\displaystyle \frac{({\omega }^2{M}^2)j\omega C_{ss}}{1-{\omega }^2{L}_s{C}_{ss}}}=0\end{array}\hfill \\ {\displaystyle \frac{1}{C_{ps}}}+{\displaystyle \frac{1}{C_{pp}}}={{\omega }_{cv}}^2{L}_p.\hfill \end{array}\right.$$

(10)

From (9), two sets of relationships between ω_cc1 and ω_cv can be deduced.

$${\omega }_{cc1}={\displaystyle \frac{{\omega }_{cv}}{\sqrt{1\pm k}}}\Rightarrow {\displaystyle \frac{L_p}{L_{ps}}}={({\displaystyle \frac{1\pm k}{k}})}^2.$$

(11)

“k”, the coupling coefficient between coils, is expressed as

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

(12)

If parameters L_p, L_s1, and M₁ are known, the remaining parameters, f_cc1, k₁, L_ps, C_pp, C_ps, and C_ss1, can be determined by setting f_cv. Finally, the f_cc1 frequency of the CC stage was chosen by verifying the emission and receiving coil inductances.

The issue requires that once the primary topology is set, changing the charging object to inspection drone B must maintain high active power and high-efficiency charging. Although the structure can still achieve constant current output, it no longer resonates, and the input impedance is no longer purely resistive. This precludes achieving the zero-phase angle (ZPA) and results in high reactive power, so multi-target charging cannot be achieved.

The input impedance can be represented as (13), and the resistance angle can be represented as (14), while

$$\begin{gathered} \begin{array}{l}a=L_{p}R{\omega }_{cc1}\\ b=M^2{{\omega }_{cc1}}^4-L_{\mathrm{p}}{L}_{\mathrm{s}}{{\omega }_{cc1}}^4+2L_{\mathrm{p}}{L}_s{{\omega }_{cc1}}^2{{\omega }_{cv}}^2-L_p{L}_s{{\omega }_{cv}}^4\\ \mathrm{c}={{\omega }_{cc1}}^4-{{\omega }_{cv}}^2\end{array} \\ {Z}_{in}=Z_{Lps}+Z_{Cpp}-{\displaystyle \frac{{Z_{Cpp}}^2(Z_{Ls}+Z_{Css}+R)}{(Z_{Cpp}+Z_{Cps}+Z_{Lp})(Z_{Ls}+Z_{Css}+R)-{Z_M}^2}}={\displaystyle \frac{j{L}_p{\omega }_{cc1}{k}^2}{{(k-1)}^2}}-{\displaystyle \frac{j{L}_p{{\omega }_{cv}}^2{k}^2}{\omega {(k-1)}^2}}+{\displaystyle \frac{{L_p}^2{{\omega }_{cv}}^4{k}^4(j{L}_s{{\omega }_{cc1}}^2+R{\omega }_{cc1}-j{L}_s{{\omega }_{cv}}^2)}{{\omega }_{cc1}{(k-1)}^4(b+j{L}_{p}R{{\omega }_{cc1}}^3-j{L}_{p}R{\omega }_{cc1}{{\omega }_{cv}}^2)}}. \end{gathered}$$

(13)

$$\tan \theta ={\displaystyle \frac{\mathrm{Re}(Z_{in})}{\mathrm{Im}(Z_{in})}}={\displaystyle \frac{(a^2{c}^2+b^2)c{L}_{\mathrm{p}}{k}^2-(a^{2}c{L}_p{{\omega }_{\mathrm{c}\mathrm{v}}}^4{k}^4-bc{L_p}^2{L}_s{\omega }_{cc1}{{\omega }_{cv}}^4{k}^4){\left(k-1\right)}^2}{(b{L_{\mathrm{p}}}^{2}R{{\omega }_{\mathrm{c}\mathrm{v}}}^4{k}^4+c^2{L_p}^3{L}_{s}R{{\omega }_{cv}}^4{k}^4){\left(k-1\right)}^2}}.$$

(14)

When parameters L_p, L_s, M, ω_cv, and R_L are set, the input impedance angle θ and the output current are functions of ω_cc1. Therefore, in the CC stage, without influencing the basic CC characteristics, the output current can be allowed to vary within an acceptable range, and θ can be reduced by adjusting the system frequency f again to reduce the reactive power and achieve multi-target charging.

2.2. Parameter Design

According to the characteristics of the inverter and the rectifier, the voltage gain G_VV and current gain G_VI of the entire structure can be calculated as

$$\left\{\begin{array}{c}{G}_{VV}={\displaystyle \frac{U_{CD}}{U_{\mathrm{in}}}}={\displaystyle \frac{U_L}{E}}\\ G_{VI}={\displaystyle \frac{I_{CD}}{U_{\mathrm{in}}}}={\displaystyle \frac{{\pi }^2{I}_L}{8E}}.\end{array}\right.$$

(15)

To accurately calculate the inductance and mutual inductance of the compensator coils in the LCC-S topology, we adopted a hybrid approach combining electromagnetic simulation and experimental validation. Specifically, the transmitter and receiver coils were modeled in COMSOL Multiphysics 6.2 using a 3D finite-element method to extract key parameters, such as the self-inductances (L_p, L_s1, L_s2) and mutual inductances (M₁, M₂). This modeling method is well-established in high-power WPT systems. For example, SKorvaga and PaveleK compared circular and square coupling coils using 3D simulation for a 44 kW system, demonstrating geometry-dependent effects on mutual inductance and magnetic field uniformity [25]. Similarly, Luo and Wei analyzed planar spiral coil configurations and derived analytical expressions validated through simulation and measurement, which guide inductance prediction in tightly or loosely coupled WPT coils [26].

To ensure the simulation’s accuracy, the calculated values were validated using an LCR meter, measuring coil inductance and quality factor under the actual winding and fixture conditions. This dual verification approach ensures the reliability of parameters used in the compensator design.

Based on the application requirements, the self-inductance L_p of the transmitting coil, the self-inductance L_s1 of the receiving coil in inspection drone A, and the corresponding mutual inductance M₁ are all known. Similarly, the self-inductance L_s2 of the receiving coil in inspection drone B and the corresponding mutual inductance M₂ are also known.

To achieve CV, the compensation capacitor in the secondary circuit can be calculated through (2)

$$\left\{\begin{array}{c}{C}_{ss1}={\displaystyle \frac{1}{{{\omega }_{cv}}^2{L}_{s1}}}\\ C_{ss2}={\displaystyle \frac{1}{{{\omega }_{cv}}^2{L}_{s2}}}.\end{array}\right.$$

(16)

The coupling coefficients k₁ and k₂ between the transmitting coil and the receiving coil of inspection drones A and B can be represented as

$$\left\{\begin{array}{l}{k}_1={\displaystyle \frac{M_1}{\sqrt{L_p{L}_{s1}}}}\\ k_2={\displaystyle \frac{M_2}{\sqrt{L_p{L}_{s2}}}}.\end{array}\right.$$

(17)

Thus, the primary compensation circuit can be initially designed based on the parameters of inspection drone A. From (4), (11), and (12), it follows that

$$\left\{\begin{array}{l}{L}_{ps}={({\displaystyle \frac{k_1}{1\pm k_1}})}^2{L}_P\\ C_{pp}={\displaystyle \frac{1}{{{\omega }_{cv}}^2{L}_{ps}}}\\ C_{ps}={\displaystyle \frac{1}{{{\omega }_{cv}}^2(L_p-L_{ps})}}.\end{array}\right.$$

(18)

For CC and CV charging requirements, the structure should comprise three gyrators in the CC stage. At f_cc1, the inductive reactance can be expressed as

$$\left\{\begin{array}{l}{Z}_{p1}=j{\omega }_{cc1}{L}_{ps}+{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{pp}}}={\displaystyle \frac{j{L}_p({{\omega }_{cc1}}^2-{{\omega }_{\mathrm{cv}}}^2){k_1}^2}{{\left(k_1-1\right)}^2}}\hfill \\ Z_{p2}=Z_{p3}=-{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{pp}}}={\displaystyle \frac{j{L}_p{{\omega }_{cv}}^2{k_1}^2}{{\omega }_{cc1}{\left(k_1-1\right)}^2}}\hfill \\ Z_{p4}=j{\omega }_{cc1}{L}_p+{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{ps}}}+{\displaystyle \frac{1}{j{\omega }_{cc1}{C}_{pp}}}={\displaystyle \frac{j{L}_p\left({{\omega }_{cc1}}^2-{{\omega }_{cv}}^2\right)}{{\omega }_{cc1}}}\hfill \\ Z_{p5}={\displaystyle \frac{Z_{Css2}{Z}_{Ls2}}{Z_{Css2}+Z_{Ls2}}}=-{\displaystyle \frac{{j{M}_2}^2{{\omega }_{cc1}}^3}{L_{s2}\left({{\omega }_{cc1}}^2-{{\omega }_{cv}}^2\right)}}.\hfill \end{array}\right.$$

(19)

If the charging object is changed to inspection drone B at this time and the frequency is still the CC stage frequency f_cc1 of inspection drone A, the output characteristics still meet the CC output requirements, and the output current can be expressed as

$$I_L=-{\displaystyle \frac{j{M}_2{\mathrm{U}}_{in}{{\omega }_{cc1}}^3{\left(k_1-1\right)}^2}{L_p{L}_{s2}{{\omega }_{cv}}^2{k_1}^2\left({{\omega }_{cc1}}^2-{{\omega }_{cv}}^2\right)}}.$$

(20)

However, at this time, the π-type gyrator composed of Z_p5, Z_p4, Z_Ls, and Z_Css is no longer resonant, and the input impedance is no longer purely resistive.

In this case, the relationship between the tangent of the impedance angle θ and the angular frequency ω can be expressed as

$$\tan \theta ={\displaystyle \frac{\mathrm{Re}(Z_{in})}{\mathrm{Im}(Z_{in})}}={\displaystyle \frac{(a^2{c}^2+b^2)c{L}_{\mathrm{p}}{k_1}^2-(a^{2}c{L}_p{{\omega }_{\mathrm{cv}}}^4{k_1}^4-bc{L_p}^2{L}_{s2}\omega {{\omega }_{cv}}^4{k_1}^4){\left(k_1-1\right)}^2}{(b{L_{\mathrm{p}}}^{2}R{{\omega }_{\mathrm{cv}}}^4{k_1}^4+c^2{L_p}^3{L}_{s2}R{{\omega }_{cv}}^4{k_1}^4){\left(k_1-1\right)}^2}}.$$

(21)

The output current I_L can be expressed as

$$I_L={\displaystyle \frac{{\mathrm{U}}_{in}{\mathrm{Z}}_{\mathrm{Cpp}}{\mathrm{Z}}_{\mathrm{M}}}{\left({\mathrm{Z}}_{\mathrm{Cpp}}{\mathrm{Z}}_{\mathrm{Cps}}+{\mathrm{Z}}_{\mathrm{Cpp}}{\mathrm{Z}}_{\mathrm{Lp}}+{\mathrm{Z}}_{\mathrm{Cpp}}{\mathrm{Z}}_{\mathrm{Lps}}+{\mathrm{Z}}_{\mathrm{Cps}}{\mathrm{Z}}_{\mathrm{Lps}}+{\mathrm{Z}}_{\mathrm{Lp}}{\mathrm{Z}}_{\mathrm{Lps}}\right)\left(R_L+{\mathrm{Z}}_{\mathrm{Css}}+{\mathrm{Z}}_{\mathrm{Ls}}\right)-({\mathrm{Z}}_{\mathrm{Cpp}}+{\mathrm{Z}}_{\mathrm{Lps}}){{\mathrm{Z}}_{\mathrm{M}}}^2}}.$$

(22)

The output current expression depends on the frequency f and R_L, and its magnitude is inversely related to the battery’s internal resistance R_L. During actual charging, the internal resistance of the battery changes within the range [R_Lmin, R_Lmax], corresponding to an output current variation range of [I_Lmin, I_Lmax]. Therefore, the output current change rate μ can be expressed as

$$\mu ={\displaystyle \frac{\mathrm{\Delta }{I}_L}{I_{L\max }}}={\displaystyle \frac{I_{L\max }-I_{L\min }}{I_{L\max }}}.$$

(23)

After L_p, L_s, k, ω_cv, and R_L are known, the current change rate μ in the CC stage can be less than α%, and, by adjusting system frequency f again, θ is reduced to [−β, β]. Thus, the reactive power can be reduced. This method not only realizes CC and CV charging but can also achieve multi-target charging. The equivalent resistance base point r is determined according to the variation range of the load equivalent resistance value of the charging drone in the CC stage.

Finally, we can calculate the new frequency f_cc2 of the CC stage when R_L = r and θ = 0. At the same time, at this new frequency f_cc2 of the CC stage, with the change in the load equivalent resistance value, whether θ is within the range of [−β, β] and whether the rate of change in the current, μ, is less than α% are determined. If it is established, f_cc2 is the new frequency of the CC stage. Similarly, the other new frequencies of the CC stage of more inspection drones can be found according to this method.

3. Results

This study employs a combination of simulation and experimental approaches to analyze the performance of the proposed LCC-S compensated WPT system for multi-drone charging applications. Initially, the system’s electrical parameters were modeled and simulated using COMSOL Multiphysics 6.2 to evaluate the magnetic field distribution and coupling efficiency under various alignment conditions. Subsequently, prototype coils were fabricated, and their inductance and quality factors were measured using an LCR meter to validate the simulation results. The experimental setup was designed to test the system’s ability to maintain constant current (CC) and constant voltage (CV) outputs across different load conditions, thereby demonstrating its suitability for charging multiple drones with diverse power requirements.

Based on the system parameter design method shown in Figure 7, a set of theoretical parameters for WPT systems is listed in

Table 1. Parameters of the wireless charging system.

Parameter	Value	Parameter	Value
Lp	281.12 μH	fcv	100 kHz
Ls1	163.774 μH	fcc1	118.9 kHz
Ls2	242.044 μH	fcc2	121.323 kHz
M1	62.79 μH	Lps	48.116 μH
M2 k	80.939 μH 0.2926	Css1 Css2	15.467 nF 10.465 nF
Cpp d1	52.644 nF 5 cm	Cps d2	10.871 nF 8 cm

. Two commercial oilfield inspection drones (A and B) were prototyped.

Drone A: Equipped with a LiFePO4 battery (23–36 V, 5200 mAh) and a compact receiver coil (L_s1 = 163.774 μH), operating at a 5 cm air gap (d₁). This mimics short-range inspections in confined wellhead areas [2].

Drone B: Features an extended-range LiFePO4 pack (27–47 V, 6500 mAh) and a larger coil (L_s2 = 242.044 μH) with an 8 cm gap (d₂), suitable for long-duration pipeline monitoring [21]. The transmitting coil (L_p = 281.12 μH) uses 0.1 mm/1050-strand Litz wire optimized for 100–120 kHz operation to balance skin effect losses and weight constraints [23].

Meanwhile, the mechanical guide ensured coil alignment. The mechanical alignment approach is consistent with established practices in industrial drone charging, where mechanical guides are commonly used to ensure precise coil positioning. For example, a recent review in Sensors by Galimov [27] classifies mechanical positioning mechanisms in landing stations, including active systems that use linear drives or push plates to center misaligned drones on charging pads. Such designs, as demonstrated in their analysis, achieve millimeter-level alignment accuracy without relying on complex sensor feedback, making them ideal for harsh environments like oilfields, where GPS signals may be unreliable. Because the charging drone has been adjusted using a mechanical device, this paper is developed in the case of coil alignment. To validate the rationality of the analysis presented, according to the parameters in Table 1, a set of experimental equipment that meets the requirements was built. The experimental device is shown in Figure 8. On the primary side, the full-bridge inverter is composed of four silicon carbide MOSFETs (IMZ120R045M1) that convert the DC voltage into AC voltage. On the secondary side, the diodes for the full-bridge rectifier are IDW40G120C5B diodes. All four coils use 0.1 mm/1050-strand Litz wire, and the controller chip model is MPC5674F.

3.1. Inspection Drone A

Figure 9 shows the variations in output current I_L, output voltage U_L, and input impedance phase angle θ as functions of operating frequency under different load resistances, with the receiver parameters set as L_s1 = 163.774 μH and M₁ = 62.79 μH. It can be observed that across multiple load conditions, the output voltage curves intersect around 100 kHz, indicating that the voltage remains nearly constant at this frequency, signifying the constant voltage (CV) operation point. Similarly, the current curves intersect at approximately 118.9 kHz, where the output current remains stable regardless of load, confirming the constant current (CC) point. In both cases, the input impedance phase angle θ approaches zero, meaning the system operates at resonance or near-ZPA conditions. This ensures minimal reactive power and enhanced power transfer efficiency, fulfilling the core charging requirements of lithium-based drone batteries. Notably, the ZPA condition is achieved not only at full load but across a wide resistance range from 19 Ω to 39 Ω, verifying the robustness of the system.

To simulate the actual charging process of the battery, an electronic load is used to simulate the equivalent resistance of the battery, and the actual charging curve of a set of lithium-ion phosphate batteries is used for comparison [28]. Based on the battery requirements of drone A, the system input DC voltage E is 30 V. As shown in Figure 10, during the CC stage, the output current I_L stabilizes at approximately 1.23 A. The output voltage U_L gradually increases from 23 V to 36 V, and the battery equivalent resistance R_L varies from 19 Ω to 29 Ω. During the CV stage, the output voltage U_L remains at 36 V, and the output current I_L gradually decreases from its maximum value of 1.233 A to a minimum of approximately 0.922 A. The battery equivalent resistance R_L varies from 29 Ω to 39 Ω. The load charging voltage is 35.9 V and 36.1 V before and after charging mode switching. The rate of change in the charging voltage of the load before and after switching is only 0.56%. In addition, the efficiency before and after switching is higher than 91%. When the system switches from CC to CV modes, the load voltage does not dramatically jump, which ensures safe charging of the battery system.

Figure 11 provides experimental waveforms of inverter voltage U_in, inverter current I_in, and rectifier-side voltage U_L for both CC and CV stages. In Figure 11a, under CC operation with R_L = 25 Ω and f = 118.9 kHz, the U_L waveform shows a linear rise, and I_in remains nearly constant in amplitude. More importantly, U_in and Iin are in phase, indicating that the inverter sees a purely resistive load (θ = 0°), which confirms resonant operation. In Figure 11b, during CV operation with R_L = 30 Ω and f = 100 kHz, U_L is held constant at 36 V, while I_in gradually declines, matching the expected behavior of battery charging in CV mode. Again, U_in and I_in remain phase-aligned, reaffirming that the system operates under ZPA in both modes. The waveforms also show that there is no overshoot or oscillation during mode switching, which is critical for battery safety. These waveform results validate both the theoretical design and the practical feasibility of the frequency-controlled dual-mode charging system.

3.2. Inspection Drone B

Based on the parameters in Table 1 and considering the requirements, the charging drone is changed to inspection drone B (with self-capacitance L_s2 and mutual inductance M₂). The variations in I_L, U_L, and θ at different frequencies and load resistances are shown in Figure 12. The output voltage U_L of the WPT system remains constant at 100 kHz, achieving ZPA operation. However, at f_cc1 for inspection drone A (118.9 kHz), although the output current I_L is constant, the input impedance angle θ is very large, and the input impedance is no longer purely resistive, rendering ZPA impossible. As a result, excessive reactive power is generated, and the multi-target charging ability of the WPT system is poor.

Moreover, as shown in Figure 12, the current image at a f_cc1 of 118.9 kHz is relatively smooth, and the frequency variation is relatively small, which is consistent with the prediction in the preceding text. Therefore, it is possible to reduce the input impedance angle θ to [−β, β] by adjusting the frequency again while maintaining a current change rate within [0, a%], basically achieving the output characteristics of a constant.

Based on practical requirements, β = 10° and a = 5. As shown in Figure 13, by adjusting the frequency of the CC stage, the input impedance angle θ can be significantly reduced under various load resistance conditions, thereby reducing its reactive power.

In order to accurately replicate the charging dynamics of the battery, an electronic load is employed to emulate the equivalent internal resistance of the battery. This setup allows for a precise comparison with the empirical charging profile of a lithium-ion phosphate battery pack. Based on the battery requirements of drone B, the system input DC voltage E is 30 V. In the CC stage, the battery equivalent resistance R_L varies between 20 Ω and 43 Ω. According to the method described above, 26 Ω is selected as the reference point r of the load equivalent resistance. So, f_cc2 = 121.323 kHz is calculated. As shown in Figure 14, after setting the new CC frequency f_cc2 in the CC stage, the output current I_L varies between 1.086 and 1.071, and the current change rate μ is only 1.38% (<5%), which satisfies the basic characteristics of the CC stage. At the same time, the output voltage U_in gradually increases from 27.21 V to 46.83 V. Therefore, the frequency regulation method has little effect on the current in the CC stage, which verifies its feasibility. During the charging CV stage, the output voltage U_L is kept at approximately 47 V, and the output current I_L gradually decreases from 1.071 A to the minimum current, which is approximately 0.7724 A. The battery equivalent resistance R_L ranges from 43 Ω to 61 Ω. The load charging voltage is 46.83 V and 47.1 V before and after charging mode switching. The rate of change in the charging voltage of the load before and after switching is only 0.58%. In addition, the efficiency before and after switching is higher than 91%. When the system switches from CC to CV modes, the load voltage does not dramatically jump, which ensures safe charging of the battery system.

The change in the impedance angle θ at different equivalent resistances for the inspection drone at f_cc1 and f_cc2 is shown in Figure 15. Applying the new CC frequency f_cc2 effectively reduces the input impedance angle within the prescribed range, decreasing the reactive power and achieving multi-target charging.

Figure 16a shows the waveforms of the inverter output voltage U_in, the output current I_in, and the load charging voltage U_L at the new CC frequency f_cc2 and an equivalent resistance value of 43 Ω. The rectifier output current I_L is almost constant, verifying that this method does not significantly affect the constant current characteristics in the CC stage. Additionally, Figure 15 shows that θ and the equivalent resistance are positively correlated. Therefore, the impedance angle θ reaches its maximum value when the equivalent resistance is 43 Ω. At this point, the phase difference between the inverter output current I_in and the inverter output voltage U_in is less than 10°, indicating that using the new CC frequency f_cc2 can effectively reduce θ to the required range, thereby meeting the inverter output current I_in. Figure 16b presents the waveforms of the inverter output voltage U_in, the output current I_in, and the load charging voltage U_L in the CV stage. The load charging voltage U_L remains constant, and the output current and output voltage are in phase, indicating that the WPT system is in the ZPA state.

These results demonstrate that the proposed frequency-regulated LCC–S system can reliably achieve both constant current and constant voltage charging across different drone configurations using frequency control alone. The experimental validation covered two distinct inspection drones with significantly different receiver coil parameters and battery characteristics. In both cases, seamless CC and CV transitions were observed without hardware reconfiguration, and near-zero phase angle operation was maintained, confirming theoretical predictions.

Table 2. Comparative summary of representative WPT systems for drone applications in terms of regulation strategy, efficiency, adaptability, and support for multi-target charging.

Ref (Year)	Nominal Gap	Output Voltage	CC/CV Reg.	Peak Eff.	CC/CV Method	Freq. (kHz)	Supports Multi-Target?
Vu et al. (2018) [9]	~15 cm	~400 V (EV battery)	CC and CV	~92% (coils)	Double-sided LCC topology	85 (fixed)	✖ No (single fixed load)
Ramezani et al. (2020) [6]	15 cm	~400 V (CV only)	CV only	~90%	Passive LCC tuning	85 (fixed)	✖ No
Hu et al. (2021) [5]	10–25 cm	N/A	Adaptive only	~88%	Harmonic-based duty control	85 (fixed)	✖ No
Galimov et al. (2020) [27]	~15 cm	~400 V	CC and CV	97.3%	Frequency switching (LCC-S)	85/105	✖ No
Ji et al. (2023) [28]	~8 cm	~30 V	CC and CV	~90%	Hybrid switching (relay)	100 (fixed)	✔ Yes (hardware switch)
Li et al. (2024) [3]	~10 cm	~5 V	CV	~94%	Dual-LCC network	85 (fixed)	✖ No
Luo et al. (2018) [26]	5–15 cm	(CC only)	CC only	~90%	Cap tuning only	85 (fixed)	✖ No
This work	5–8 cm	23–47 V	CC and CV	92.3%	Frequency regulation only	100–121.3	✔ Yes (multi-drone adaptive)

compares our proposed system with representative wireless power transfer (WPT) methods cited in this study. Key metrics, such as the nominal coil gap, the output regulation type, efficiency, adaptability, and support for multi-target operation, are presented. Compared to other methods, our approach achieves constant current and constant voltage charging without switching hardware, maintains high efficiency, and is fully adaptable to varying drone configurations.

Although only two drone types were tested, they represent a wide range of practical drone charging scenarios in terms of inductance, mutual coupling, and battery voltage. This selection was intentional, aiming to verify the system’s adaptability without excessive experimental redundancy. The success of this approach in both cases, supported by consistent efficiency above 91%, validates the generalizability of the method. These results confirm that the proposed solution is robust, scalable, and applicable to broader drone fleets in oilfields and other high-risk environments.

4. Conclusions

This study presents a pioneering wireless charging framework tailored for oilfield inspection drones, addressing the critical challenges of multi-target charging in hazardous environments. The paper proposes a universal method in which, by regulating the frequency, the WPT system achieves CC and CV charging for two different inspection drones, and the reactive power is greatly reduced to achieve multi-target charging. First, we analyzed the LCC–S topology under constant voltage (CV) and constant current (CC) modes by constructing a frequency-dependent gyrator model. The system forms a two-gyrator cascade at the CV frequency and a three-gyrator configuration at the CC frequency, enabling load-independent voltage and current outputs, respectively. Second, to support multi-target charging, we designed a frequency adjustment strategy based on the relationship between the input impedance angle and operating frequency. By selecting a base resistance within the drone battery’s equivalent range, the optimal CC frequency can be determined to ensure ZPA operation, minimize reactive power, and maintain high efficiency. This method is scalable to drones with diverse coupling and load characteristics. Finally, a set of experimental equipment based on the LCC–S topology was built according to the battery of actual inspection drones. The system can achieve CC and CV charging when charging inspection drone A, with the system operating in the ZPA state. Similarly, when charging inspection drone B, it can achieve CV and CC charging. In the CV stage, the system operates in the ZPA state; in the CC stage, the frequency is regulated at f_cc2. With a current change rate of only 1.36%, the input impedance angle θ range is [−3°,8°], which basically satisfies the ZPA. In both constant current and constant voltage charging modes, the system consistently maintained high efficiency, achieving 92.57% for drone A and 91.12% for drone B, thereby validating the energy performance of the proposed approach. The proposed method was validated on two kinds of drones with distinct coupling and battery parameters, demonstrating stable CC/CV transitions and consistent ZPA operation across load variations. Although the experiments focused on two representative cases, the theoretical framework and observed performance confirm the generalizability of the approach to a wider range of drone configurations.

In future work, we plan to further optimize the coil design for drone-specific applications. We recognize that lightweight construction and frequency-appropriate wire selection are critical factors in airborne WPT systems. Specifically, we will explore the use of finer Litz wire gauges for improved high-frequency performance and reduced AC resistance. We also intend to investigate alternative coil structures, such as planar windings and air-core geometries, to reduce system weight without compromising charging efficiency. These improvements will help tailor the system more precisely to the unique constraints of drones and support more scalable deployment in drone-based inspection tasks.