## 1 Introduction  
Wireless power transmission is a promising technology with great potential for the future due to its advantages of convenient charging and high safety performance, and it is currently widely used in various fields [1, 2, 3], including electronics (such as smartphones and smart homes), medical applications (such as miniaturized pacemakers and implantable health monitoring devices), and industry (such as electric vehicles and drones). In 2007, a team led by Professor [PERSON] at the Massachusetts Institute of Technology proposed wireless power transfer (WPT) technology based on magnetic-coupling resonance (MCR) [4]. In the MCR WPT system, the transmitting and receiving coils are designed to resonate at the operating frequency, establishing a stable and efficient energy transfer channel for power transmission. The limitations of copper coils in traditional WPT systems are mainly due to their limited current-carrying capacity and low-quality factor (Q). In recent years, research has been conducted to establish magnetic resonance radio energy transmission systems using high-quality factor superconducting coils as resonant coils, which improves the energy transmission performance of the systems. The research on high-temperature superconducting WPT systems has mainly focused on coil structure design and transmission efficiency [5, 6, 7, 8, 9, 10]. Ref. [5] presents the wireless power transfer via strongly coupled magnetic resonances utilizing a high-temperature superconducting (HTS) coil and a copper coil as intermediate resonators. Simulation and experimental results demonstrate that the use of HTS and copper repeating coils can significantly enhance the space magnetic induction intensity, resulting in improved transmission efficiency and extended transmission distance. In Ref. [6], the analysis indicates that wireless power transfer (WPT) systems using high-temperature superconducting (HTS) coils exhibit higher efficiency and longer operational times in the low frequency range of kHz compared to WPT systems using copper coils. In Ref. [7], the investigation of the effect of various HTS coil configurations on the transmission performance of WPT systems revealed that flat coil and spiral coil designs can be effectively applied to relatively low-frequency WPT systems. On the other hand, the solenoid coil design can achieve the lowest total loss in WPT system applications operating at higher frequencies. In Ref. [8], a model system was fabricated using high-temperature superconducting (HTS) double-pancake coils composed of REBCO tape, and the transmission efficiency characteristics were investigated to evaluate the possibility of using HTS coils for high-efficiency wireless power transmission systems operating in the low-frequency region of kilohertz. The results indicate that HTS coils can achieve high-efficiency wireless power transmission in the low-frequency region of kilohertz. In Ref. [9], an experimental investigation was conducted to analyze the effect of coil offset on the transmission efficiency and load-received power (LRP) in a HTS magnetically coupled resonant wireless power transfer system. The results demonstrated a monotonic decrease in transmission efficiency as the offset distance increased. Additionally, an optimal offset distance was identified, which maximized the LRP. In Ref. [10], a high-temperature superconducting (HTS) WPT system is proposed, and its transmission performance is experimentally tested over a range of operating frequencies (33 kHz to 342 kHz), enabling high-efficiency energy transmission at low operating frequencies. However, in certain practical applications, such as when an underwater autonomous vehicle (AUV) is docked at a subsea base station for wireless charging [11], perfect alignment between the transmitter and receiver coils is rarely achieved.