## 3 Data Derivation System of Electric Field Modeling  
The MMC valve is a core component in the actual operation of the MMC-HVDC power transmission system. As a high-voltage, high-capacity power electronic device, the structure of the MMC valve is determined by the system parameters [23; 24]. The design parameters of the MMC valve were derived based on the system parameters. The potential that determines the distribution of the electric field originates from the voltage parameters during system operation.  
By conducting a theoretical analysis of the process of establishing the electric field model of the MMC valve and combining it with the relationship analysis of the MMC valve and the main circuit parameters.  
The data derivation system for the electric field modeling parameters of the MMC valve is defined as follows:  
\[\left\{\begin{array}{l}\mathbf{X}_{\text{in}}\rightarrow\mathbf{\Phi(x) }\rightarrow\mathbf{Y}_{\text{out}}\\ \\ \mathbf{X}_{\text{in}}=\left[\begin{array}{c}U_{\text{dc}}\\ P_{\text{dc}}\\ Q\end{array}\right]\end{array}\right. \tag{1}\]  
Figure 4: Electric field equivalence between discrete conductors and a continuous conductor.  
In Equation (1), \(\mathbf{X}_{\text{in}}\) and \(\mathbf{Y}_{\text{out}}\) are the input and output matrix, \(\mathbf{\Phi}\)(x) are data derivation system, \(U_{\text{dc}}\) is the DC voltage of the MMC, \(P_{\text{dc}}\) and \(Q\) are the active power and reactive power of MMC. The data derivation system matrix \(\mathbf{\Phi}\)(x) and output \(\mathbf{Y}_{\text{out}}\) are defined as follows:  
\[\mathbf{\Phi}(x)=\left[\begin{array}{c}\mathbf{F}_{\text{sm}}(\text{x})\\ \mathbf{F}_{\text{shield}}(\text{x})\\ \mathbf{F}_{\text{insulator}}(\text{x})\\ \mathbf{F}_{\text{beam}}(\text{x})\\ \mathbf{F}_{\text{ring}}(\text{x})\end{array}\right]\text{ and }\mathbf{Y}_{\text{out}}=\left[\begin{array}{c}\mathbf{Y}_{\text{sm}}\\ \mathbf{Y}_{\text{shield}}\\ \mathbf{Y}_{\text{insulator}}\\ \mathbf{Y}_{\text{beam}}\\ \mathbf{Y}_{\text{ring}}\end{array}\right] \tag{2}\]  
In Equation (2), \(\mathbf{F}_{\text{sm}}\)(x) is the submodule parameters calculation matrix, \(\mathbf{F}_{\text{shield}}\)(x) is the shielding cover parameters calculation matrix, \(\mathbf{F}_{\text{insulator}}\)(x) is the insulator parameters calculation matrix, \(\mathbf{F}_{\text{beam}}\)(x) is the support frame parameters calculation matrix, \(\mathbf{F}_{\text{ring}}\)(x) is the grading ring parameters calculation matrix, \(\mathbf{Y}_{\text{sm}}\) is the modeling parameters of submodules, \(\mathbf{Y}_{\text{shield}}\) is the modeling parameters of shielding covers, \(\mathbf{Y}_{\text{insulator}}\) is the modeling parameters of insulators, \(\mathbf{Y}_{\text{beam}}\) is the modeling parameters matrix of support frames, \(\mathbf{Y}_{\text{ring}}\) is the modeling parameters of grading rings.  
According to the principles of electric field calculation for the MMC valve and the analysis of key factors, the electric field modeling parameters for the MMC valve are categorized into five distinct categories. The data derivation system \(\mathbf{\Phi}\)(x) and the modeling parameters data \(\mathbf{Y}_{\text{out}}\) are structured accordingly. The following sections provide a detailed analysis of each of these five categories.