## 3 Data Derivation System of Electric Field Modeling
### Multidimensional Array Modeling of Shielding Cover  
The shielding cover significantly influences the electric field distribution of the MMC valve. The shielding covers of the MMC valve generally consist of two types, one with curved shapes located at the four corners, and the other with flat-plate shapes positioned at other locations. The electric field calculation parameters matrix of the MMC valve shielding covers are defined as follows:  
\[\mathbf{Y}_{\text{shieldC}}=\left[ \begin{array}{cccc}\mathbf{Y}_{\text{shieldC11}}& \mathbf{Y}_{\text{shieldC12}}&\cdots&\mathbf{Y}_{\text{shieldC1 NSC}}\\ \mathbf{Y}_{\text{shieldC21}}&\mathbf{Y}_{\text{shieldC22}}&\cdots&\mathbf{Y}_ {\text{shieldC2 NSC}}\\ \vdots&\vdots&\ddots&\vdots\\ \mathbf{Y}_{\text{shieldCLT1}}&\mathbf{Y}_{\text{shieldCLT2}}&\cdots&\mathbf{Y}_ {\text{shieldCLTNSC}}\end{array} \right] \tag{8}\]  
\[\mathbf{Y}_{\text{shieldP}}=\left[ \begin{array}{cccc}\mathbf{Y}_{\text{shieldP1 }}&\mathbf{Y}_{\text{shieldP12}}&\mathbf{Y}_{\text{shieldP13}}&\mathbf{Y}_{ \text{shieldP14}}\\ \mathbf{Y}_{\text{shieldP21}}&\mathbf{Y}_{\text{shieldP22}}&\mathbf{Y}_{ \text{shieldP23}}&\mathbf{Y}_{\text{shieldP24}}\\ \vdots&\vdots&\vdots&\vdots\\ \mathbf{Y}_{\text{shieldPLT1}}&\mathbf{Y}_{\text{shieldPLT2}}&\mathbf{Y}_{ \text{shieldPLT3}}&\mathbf{Y}_{\text{shieldPLT4}}\end{array} \right]\]  
In Equation (8), \(\mathbf{Y}_{\text{shieldC}}\) denotes the arc-shaped shielding covers at the four corners of each layer, \(\mathbf{Y}_{\text{shieldP}}\) denotes the flat-plate shielding covers, LT is the number of layers in the MMC valve, and NSC is the number of shielding covers in one layer of the MMC valve. The electric field modeling parameters of each shielding cover consist of three distinct sets of parameters. The modeling parameters matrix of each shield are defined as follows:  
\[\left\{ \begin{array}{c}\mathbf{Y}_{\text{shieldCj}}=\left[\begin{array}{c} \mathbf{E}(\text{shieldC})_{ij}\\ \mathbf{G}(\text{shieldC})_{ij}\\ \mathbf{SP}(\text{shieldC})_{ij}\end{array}\right]\\ \mathbf{Y}_{\text{shieldPij}}=\left[\begin{array}{c}\mathbf{E}(\text{shieldP})_ {ij}\\ \mathbf{G}(\text{shieldP})_{ij}\\ \mathbf{SP}(\text{shieldP})_{ij}\end{array}\right]\\ \end{array} \right. \tag{9}\]  
In Equation (9), \(\mathbf{Y}_{\text{shieldCj}}\) denotes the modeling parameters of the corner shielding cover \(j\) in the layer \(i\) of the MMC valve, \(\mathbf{Y}_{\text{shieldPij}}\) is the modeling parameters of flat plate shielding cover \(j\) in the layer \(i\) of the MMC valve. Shielding covers are arranged externally on the MMC valve and serves the functions of electromagnetic shielding and protection. The shielding covers are connected to the nearby submodules, forming an equipotential connection. The electrical parameter matrix \(\mathbf{E}(\text{shield})\) of the shield covers is defined as follows:  
\[\left\{ \begin{array}{c}\mathbf{E}(\text{shieldC})_{ij}=\left[\begin{array}[ ]{c}GV_{\text{shieldCj}}\\ MC_{\text{shield}}\end{array}\right]\\ GV_{\text{shieldCjj}}=GV_{\text{shieldC11}}+DS\cdot\mathbf{u}_{\text{smd}}=GV_{ \text{T}}+DS\cdot\mathbf{u}_{\text{smd}}\end{array} \right. \tag{10}\]  
In Equation (10), \(GV_{\text{smij}}\) is electric potential of the shield cover \(ij\) in the valve, \(DS\) is voltage coefficient, \(MC_{\text{shield}}\) is material properties of the shield covers. During the operation of the MMC valve, the shielding cover neither carries current nor performs power transmission. It protects the MMC valve by optimizing the electric field distribution, which is the primary objective of its design. The geometric parameter matrix of the shield is defined as follows:  
\[\mathbf{G}(\text{shieldC})_{ij}=EC(\text{shieldC})=\left[ \begin{array}{c} Form\\ X_{\text{50}}\\ Y_{\text{50}}\\ Z_{\text{50}}\\ ALR\end{array} \right] \tag{11}\]In Equation (11), _EC_(shield C) is a computational matrix for the geometric dimensions of the corner shielding cover, Form is the shape structure of the shield cover.