## 1 Introduction  
Due to the manufacturing or complex operating conditions, there might be insulation failures or defects in the insulation of the MMC valve. The analysis of the electric field in the MMC valve has become extremely important. In particular, the MMC-HVDC system has been widely used in recent years. With the continuous increase in voltage and capacity, the MMC valve, as a core component of the MMC-HVDC transmission system, is facing increasing challenges [1, 2, 3, 4]. The MMC valve is subjected to highly complex and demanding current and voltage conditions during operation. Consequently, the electric field characteristics of the MMC valve have a significant impact on the safety and stability of the MMC-HVDC transmission systems. In particular, under fault conditions with impulse excitation, the distributed parameters of the MMC valves, especially the stray capacitance, can have a severe impact on the system [5; 6; 7]. The method of electric field analysis is commonly employed to calculate the stray parameters of converter valves. Research on electric field analysis of high-voltage equipment is relatively mature, with a wide variety of calculation theories and commercial software available. However, the electric field analysis of complex equipment and environments, such as converter valves, remains a research hotspot in the industry. With the increasing demand for high power density in electrical equipment, the accurate and efficient calculation of the electric field for complex equipment continues to be a challenging issue. To investigate the accurate electric field characteristics of the converter valve, the 3D model of \(\pm\)420 kV flexible converter valve tower by Creo software and the electric field distribution for the valve tower are calculated by ANSOFT software in reference [8]. In reference [9], through simplification FEM model of the valve tower in ANSYS Q3D Extractor, the capacitances are calculated. However, the modeling process of the aforementioned methods for electric field calculation is relatively complex, and the amount of work involved in the computation is considerably large. To enhance the efficiency of electric field calculation for HVDC equipment, reference [10] adopted the method of the equivalent gas conductivity to achieve calculation of electric field distribution quickly. To address the problem of large calculation amount of transient field in the valve hall model, reference [11] proposes an instantaneous potential load method to study the electric field characteristics of UHV-VSC valve hall. To reduce the computational load in the process of electric field calculation, reference [12] proposes a simplified calculation model of the radiative near field of the electric field in the circuit breaker valve hall. Similarly, reference [13] presents a simplified approach for the MMC valve, employing the finite element method to compute the stray capacitances. In summary, the modeling process and methods for the electric field analysis of converter valves are of great significance. The electric field accurate analysis of the MMC valve is significant for the design of the MMC valve and the MMC-HVDC system. In the aforementioned studies, the modeling process of the converter valve has not been analyzed. However, previous studies have focused on theoretical calculations and model simplification, neglecting a systematic and detailed process. In some of the analyses of electric field modeling method in these articles, both the insulators and the shape of the outer conductors are ignored, which will significantly reduce the accuracy of the electric field calculation. How to improve the accuracy and efficiency of electric field calculation during the modeling process has not been addressed. Meanwhile, in the model process of the converter valve, the conventional import method or the re-establishment of the electric field model based on the mechanical model is adopted. This will result in a very long time required for the establishment of the converter valve electric field model.