## 3 Simulation Results and Experimental Validation  
### Simulation Parameters  
Miniature prototype experiments can simplify complex research objects and physical problems. It can achieve the same goal with less effort and gain experience applying the original prototype. For the miniature prototype to be equivalent to the original prototype, the miniature prototype must be strictly proportional to the original prototype. Miniature prototype experiments can verify the accuracy of the prototype and simulation research methods. Then, the same process is used to research higher-voltage arresters. Figure 5 presents the model of the \(\pm 66\) kV DC GIS arrester. It is a miniature model of a \(\pm 550\) kV DC GIS arrester. The \(\pm 66\) kV DC GIS arrester core is a three-column parallel spiral stacked structure. Each column is equipped with 13 ZnO varistors in spiral stacking. The miniature prototype structure is like the \(\pm 550\) kV DC GIS arrester model. Under the premise of not affecting the calculation accuracy, the structure of the arrester is simplified. The excitation applied by the simulation is a standard 8/20 us lightning impulse current waveform [32; 33]. The current density of a single column is 42 A\(\cdot\)cm\({}^{-2}\). The material settings for each part of the arrester during simulation are shown in the Table 2.  
The operating voltage of the ZnO varistor is the 1 mA DC reference voltage [34]. When the voltage is higher than the operating voltage, the resistance of the ZnO varistor drops rapidly, and the corresponding current through the arrester rises rapidly. For the HVDC GISA, the application area is the lower side of the breakdown zone and the high current zone, where tiny voltage changes across the ZnO varistor can result in significant changes in the current through the ZnO varistor [34]. The current density through the ZnO varistor element is determined by [29]  
\[J(E)= \begin{cases}\frac{A_{1}}{P_{\text{gb}}}\exp\left(-\frac{E_{\text{g}}-\beta \sqrt{E}}{k_{\text{b}}T}\right)+A_{2}(\frac{E}{E_{\text{b}}})^{\alpha},J(E)<J_{ \text{U}}\\ D(T,J)\cdot\frac{A_{2}}{P_{\text{g}}}(E-E_{\text{U}})+J_{\text{U}},J(E)>J_{ \text{U}}\end{cases}  \tag{15}\]  
where \(J\) is the current density; \(E\) is the voltage gradient; \(A_{1}\), \(A_{2}\), and \(A_{3}\) are constant; \(\rho_{\text{gb}}\) is the pre-breakdown resistivity; \(E_{\text{g}}\) is the height of double Schottky barriers; \(\rho_{\text{g}}\) is the breakdown resistivity; \(\beta\) is a constant related to the electrical properties and geometrical structure of the ZnO varistors; and \(D(T,J)\) is a function of temperature and current density, which can be found in Figure 6.  
Due to the dispersive nature of the V-I characteristics of the ZnO varistor, the multi-column arrester has different currents between columns. It also makes the energy absorbed \begin{table}
\begin{tabular}{c c} \hline \hline
**Position** & **Material** \\ \hline ZnO varistor & ZnO \\ Conductor rod & Aluminum \\ Space & Aluminum \\ Tank & Aluminum \\ Insulating Board & Epoxy Resin \\ Insulating Rod & Epoxy Resin \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model material parameters. Figure 5: Prototype of the \(\pm\)66 kV DC GIS arrester. (**a**) is the internal composition of the \(\pm\)66 kV DC GIS arrester. (**b**) is the prototype of the \(\pm\)66 kV DC GIS arrester. Figure 6: The voltage–current curve of the ZnO varistor in a \(\pm\)550 kV DC GIS surge arrester. imbalanced between columns. The conductivity of the ZnO varistor is related to the input current and the temperature [35]. As the temperature increases, the conductivity of the ZnO varistor of the high-temperature column increases, resulting in greater current flow into the high-temperature column, which leads to a more significant temperature rise. The positive feedback makes the temperature distribution across the columns increasingly uneven.