## 5 Electric Field Calculation Results
As shown in Figure 8, the electric field model established using the conventional method has poor initial meshing quality, which fails to meet the required accuracy for field computation. When using the conventional method for electric field calculation, it is necessary to perform mesh refinement and optimization specifically tailored to the layout positions. This process typically requires multiple iterations of computation. The maximum electric field strength is used as a reference value. The relationship between calculation error rate, mesh density, and calculation time is shown in Figure 9.  
As shown in Figure 9, in the conventional calculation process, multiple mesh refinements are required to obtain a relatively accurate electric field strength, and the calculation time is relatively long. The electric field distribution obtained using the conventional method after multiple iterations and the electric field distribution obtained using the method proposed in this paper (with \(N_{\rm m}=1\) and \(N_{\rm h}=1\)) in a single calculation are shown in Figure 10.  
Figure 8: Initial meshing of conventional modeling (**a**) and initial meshing of distributed modeling (**b**). Figure 9: Curve between error rate, mesh, and calculation time. As shown in Figure 10, electric field strength of the MMC is calculated rapidly and accurately using the high-speed modeling method proposed in this paper. Methods such as the boundary element method, the method of the equivalent gas conductivity, and the instantaneous potential load method are not applicable for the external electric field analysis and stray capacitance calculation of the MMC valve, and the modeling process is still too complex. The traditional finite element electric field modeling and calculation method proposed in this paper has been applied in practical engineering and has been verified for its correctness through insulation design and fault analysis in practical engineering. The traditional method, which has been proven effective in practice, was selected in this paper to be compared with the high-speed modeling method. The analysis in this paper focuses on the electric field distribution of the MMC valve under the normal operating conditions of MMC-HVDC system. The comparison of the electric field calculation process using the high-speed modeling method presented in this paper and the conventional method is shown in Figure 7.0  
As shown in Table 3, the high-speed electric field modeling method proposed in this paper, based on the characteristics of electric field and its main influencing factors, directly derives modeling parameters from system parameters through data derivation. By omitting the process of simplifying mechanical models to electric field models, the modeling time is significantly reduced. Additionally, for regions of interest in the electric field, a distributed modeling approach is adopted, integrating the meshing process with model construction, thereby substantially enhancing the accuracy and speed of electrostatic field calculations. The establishment of the modeling parameter matrix requires a high level of professional knowledge from researchers and technicians. They need to be familiar with both the MMC-HVDC system and the MMC valve equipment and possess both theoretical and practical knowledge simultaneously. Figure 7.1 Electrical field distribution of the MMC valve with convention model (**a**) and discretization model (**b**).