## 1 Introduction  
The modular multilevel converter-based high-voltage direct current (MMC-HVDC) transmission system is a primary solution for large-scale renewable energy integration. With the continuous maturation of MMC-HVDC technology, an increasing number of offshore wind farms, both domestically and internationally, are expected to be connected to the grid via this system, particularly those located in deep-sea areas [1]. However, the high maintenance costs, long maintenance cycles, and significant challenges associated with offshore converter stations pose numerous unresolved issues [2]. Among these, the safety and stability of the MMC valves are particularly prominent. The core equipment of MMC consists of sub-modules based on semiconductor devices, such as half-bridge sub-modules with two power devices (e.g., IGBTs) and full-bridge sub-modules with four power devices (e.g., IGBTs). These power devices in the converter valves serve dual functions: circuit switching and power transmission. Unlike conductors, semiconductors have both free electrons and holes as charge carriers, and factors such as carrier concentration, diffusion current, and mobility can all affect the current-carrying characteristics of the semiconductor. Therefore, the overcurrent capability of MMC converter valves is very limited, and improper handling can lead to severe consequences [3]. Overcurrent in valves is generally caused by system faults or equipment failures. The control and protection strategies, protection settings, the timing of fault occurrence, and the circuit characteristics after a fault can all influence the fault current. After a fault occurs, the operating states of nonlinear components in the circuit change, altering the characteristics of the fault current. Furthermore, under high-frequency excitation, the impact of distributed parameters in the MMC valves becomes more pronounced, making the analysis of overcurrent more complex and challenging [4]. Therefore, research on the overcurrent characteristics of valves is of great importance, and the study of the development process and influencing factors of overcurrent is both complex and challenging. The low safety margin due to overcurrent in MMC is a major concern for the safe operation of offshore wind power MMC-HVDC transmission systems. Currently, research on the fault characteristics of offshore MMC valve continues to be a hot topic in the industry [5; 6; 7]. To address the issue of overcurrent, reference [8] proposes a DC fault protection scheme consisting of main protection, directional pilot protection, and faulty pole identification. In 2021, a current-limiting requirement of the MMC-HVDC system and the performance of three types of superconducting fault current limiter (SFCL) were proposed by [PERSON] [9]. In 2022, [PERSON] analyzed the discharge current of the capacitor and the current limiting characteristics of the superconducting fault current limiter (SFCL) when a fault occurred in the MMC system [10]. While these studies have analyzed the phenomenon and development process of overcurrent, they have not investigated the influencing factors of overcurrent, especially the insulation faults of equipment and the potential overcurrent anomalies caused by arresters in the system. To investigate the development of overcurrent under fault conditions, [PERSON] analyzed a dynamic reactive current optimization strategy that combines MMC energy control capability with transient overload capability to achieve onshore AC fault ride-through in 2024 [11]. The influence of new energy of an AC system on DC fault current characteristics in the MMC-HVDC system was studied by [PERSON] in 2023 [12]. However, in the analysis of the overcurrent fault loop in these articles, the impact of stray capacitances and the nonlinear characteristics of surge arresters in the MMC-HVDC system during transient processes were not considered.