## 3 Simulation Results and Experimental Validation
### Simulation Results of \(\pm\)550 kV DC GISA  
Energy is injected at the arrester's terminal to raise the temperature of the arrester ZnO varistor to about 80 \({}^{\circ}\)C. The simulation settings are consistent with those in Section 3.1. The three-dimensional model of the \(\pm\)550 kV DC GISA is appropriately simplified for the multi-physics simulation. After the simulation analysis, the electric field distribution, magnetic field distribution, and temperature distribution are obtained. The insulating parts and the arrester tank do not affect the results of the core, and the electromagnetic field and temperature changes in these parts are not significant. Only the core part is displayed when analyzing the results. The three-dimensional electric field distribution of the arrester core is shown in Figure 12.  
The maximum field strength is 4.85 kV/cm at the ZnO varistors. The ZnO varistors are surrounded by insulating boards and rods acting as supports. Due to this spiral structure, the electric field on the upper and lower surfaces of the insulating board is very different. It is necessary to pay attention to the dielectric strength in these parts.  
In Figure 13, the magnetic flux is mainly distributed around the spacers connected to the ZnO varistors, and there is relatively little around the ZnO varistors. The value goes from small to large as the color changes from gray to red. The red arrows on the section indicate the direction of the magnetic field. As can be seen from the distribution of the magnetic field in the cross-section, the magnetic field is mainly distributed inside the spiral structure. The simulation results show that the self-generated inductor of the \(\pm\)550 kV DC GISA single-column spiral core is 6.4 \(\mu\)H. The calculation of the self-generated inductor satisfies  
\[L=\frac{W}{I^{2}} \tag{17}\]  
where \(W\) is the total magnetic energy in the entire space and \(I\) is the value of the current passing through the conductor.  
The ZnO varistors have the most significant temperature rise of the arrester. When the temperature of the ZnO varistors rises from 20 \({}^{\circ}\)C to 85 \({}^{\circ}\)C, the maximum temperature of the spacers is 45 \({}^{\circ}\)C in Figure 14. Most of the injected overvoltage energy is absorbed by the ZnO varistors. The thermal conduction of the spacers and the ZnO varistors increases the temperature of the spacers. The temperature of the ZnO varistors near the spacers is relatively low. Heat is transferred from the ZnO varistors to o  
Figure 12: Three-dimensional electric field distribution of \(\pm\)550 kV DC GISA core.  
Figure 13: The magnetic induction intensity distribution of the core section of the arrester.  
heat conduction and convection. Heat conduction occurs in solid parts with temperature differences, and thermal convection occurs between solids and gases. The difference in V-I characteristics of each column ZnO varistors leads to uneven current distribution between columns. This leads to uneven temperature distribution of each column ZnO varistor. The temperature of the ZnO varistors near the spacers is lower, and the temperature of the ZnO varistors away from the spacers is higher. The temperatures of the ZnO varistors in the three columns away from the spacers are selected for a comparison. The highest temperature among the three ZnO varistors are 78 \({}^{\circ}\)C, 81 \({}^{\circ}\)C, and 85 \({}^{\circ}\)C. The temperature difference of the ZnO varistors under the same conditions is 7 \({}^{\circ}\)C. More critically, the higher the temperature, the greater the conductivity of the ZnO varistors. It is positive feedback, resulting in a higher temperature difference. This situation is detrimental to the continuous and reliable operation of the arrester.