## 5 Electric Field Calculation Results  
Based on the aforementioned discussion, an electric field calculation model has been established using the high-speed modeling method proposed in this paper. To verify the effectiveness of the high-speed modeling method described in this paper, a \(\pm\)320 kV 1000 MW MMC-HVDC system that has been in operation for more than five years was selected as the research object. In the engineering design and operation process, there have been extensive studies and verifications on the electrostatic field of the converter valve. The main parameters of \(\pm\)320 kV, 1000 MW MMC-HVDC transmission system are shown in Table 1.  
In accordance with data derivation system described previously, the system parameters in Table 1 are calculated and derived. The resulting parameters for the MMC valve are presented in Table 2.  
According to the method described in Equation (6), the dimensions of the capacitor can be determined from its capacitance and rated voltage, allowing for the rapid construction of the electric field analysis model for the submodule. The valve tower features a three-tier structure, with each valve component comprising six sub-modules. The dimensions and structure of the MMC valve support frame can be readily determined based on Equations (15) and (16). For components such as the shielding cover and grading ring, the limited available forms facilitate easy determination of their dimensions. The component models of the submodule, support frame, grading ring, and shielding cover are illustrated in Figure 5.  
The modeling parameters for interlayer insulators can be derived from Equation (18) based on the number of sub-modules per layer. The insulation level of the MMC valve to ground is determined by the DC voltage of the MMC-HVDC system, and the modeling parameters of the ground insulators can be obtained from Equation (19). By leveraging the position parameters of all components, which are calculated using the data derivation system, the electric field model of the MMC valve can be rapidly established. The process of establishing the electric field model for the MMC valve is illustrated in Figure 6. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters of System** & **Value** \\ \hline DC voltage \(U_{\text{dc}}\) & \(\pm\)320 kV \\ DC transmission power Pdc & 1000 MW \\ Connection configuration & symmetrical bipolar \\ Sub-module topological & half-bridge \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of onshore MMC-HVDC system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters of MMC Valve** & **Value** \\ \hline DC voltage \(U_{\text{dc}}\) & 1.5625 kV \\ Rated voltage of the IGBT & 3.3 kV \\ Rated voltage of sub-module & 1.6 kV \\ Rated voltage of capacitor & 2.1 kV \\ Capacitance of sub-module & 10 mF \\ Rated number of sub-modules per arm & 200 \\ Number of sub-modules per valve & 72 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters calculated by the data-derived system. The maximum electric field on the outer surface of the MMC valve is located at the surface of the shielding cover. To achieve faster and more accurate calculation of the electric field strength, the shielding cover is discretized for modeling parameter calculation in accordance with Equation (22). The values of \(N_{\text{m}}\) and \(N_{\text{h}}\) m are both initially set to 1, discretization modeling and mesh are shown in Figure 7.  
To compare the advantages of the method proposed in this paper, electric field modeling and calculation of the MMC valve are investigated using conventional analysis methods. The initial meshing diagrams for conventional modeling and distributed modeling are shown in Figure 8.  
Figure 5: Model of the submodule, support frame, grading ring, and shielding cover. Figure 6: The process of establishing the electric field model for the MMC valve. Figure 7: Discretization modeling and mesh of shielding cover.