## 2 Electrothermal Model of Spiral Structure GISA
### Parameters of \(\pm\)550 kV DC GISA  
The structural design of the \(\pm\)550 kV DC GISA and ZnO varistors requires reference parameters. The calculation method of the varistors is related to these parameters [19]. Table 1 describes the main reference parameters. The arrester's DC reference voltage and continuous operating voltage determine the number of single-column ZnO varistors. The total number is related to the rated absorbed energy of the arrester and ZnO varistor. The number of ZnO varistors is obtained in Equations (1)-(3). The number of ZnO varistors for a single column can be calculated in Equation (1); the number of ZnO varistors for the whole \(\pm 550\) kV DC GISA can be calculated in Equation (2); and the number of columns of the \(\pm 550\) kV DC GISA can be calculated in Equation (3). \[N_{0}=\frac{k\times U_{MOA}}{U_{R}} \tag{1}\]  
\[N=\frac{S\times W_{MOA}}{W_{R}} \tag{2}\]  
\[M=\left\lceil\frac{N}{N_{0}}\times\beta\right\rceil \tag{3}\]  
where \(N_{0}\) is the number of single-column ZnO varistors, \(k\) and \(S\) are the safety margin factors, \(U_{MOA}\) is the reference voltage of the arrester, \(W_{MOA}\) is the rated absorbed energy of the arrester, \(U_{R}\) is the reference voltage of the ZnO varistor, \(W_{R}\) is the rated absorbed energy of the ZnO varistor, \(M\) is the column number, and \(\beta\) is the current distribution coefficient. The \(\pm 550\) kV DC GISA is applied to the offshore wind power converter platform. The environmental conditions of the offshore platform are harsh, and the space layout is limited. The operating conditions of the equipment are more complex, and the surge arrester needs to withstand more severe conditions [24]. Under harsh conditions, vibration poses a more significant threat to the ZnO varistor stacking of surge arresters [25]. The spiral structure reduces the overall length of the ZnO varistors, making them more compact and miniaturized. As shown in Figures 1 and 2, the spiral structure looks like a solenoid, and the length of the ZnO varistors is reduced by screwing the ZnO varistors to the spacers. This structure relies on spacers to connect the ZnO varistors. The varying current flows through the ZnO varistors and spacers, creating a magnetic field. Due to the superposition and cancellation of the magnetic induction lines, the magnetic field strength is most significant in the triangular region encased by the spacers. This structure acts as an inductor and resists changes in current. If the arrester is used in an AC scenario, the rate of current change is considerable. The self-generated inductors can generate undesirable overvoltage that affects the transmission of electrical energy to the circuit. In Figure 1, the structure can superpose the self-generated inductor. In Figure 2, the structure can offset the self-generated inductor. The DC GISA of the offshore wind power flexible DC converter system is used in a DC environment, and the multi-column arresters are in parallel. By utilizing the characteristics of the self-generated inductor to resist current changes, this unique structure of Figure 1 can make the current distribution among ZnO varistor columns more uniform. In Figure 3, insulating rods and insulating boards are arranged around the ZnO varistors, which can not only support but also endure vibration. The length is reduced by 56.25% from a 3.2 m linear structure to a 1.40 m spiral structure. Connecting three single columns, as in Figure 3, in parallel, the core of the \(\pm\)550 kV DC GIS arrester can be obtained. The \(\pm\)550 kV DC GIS arrester is a tank arrester mainly composed of a basin insulator, a conductive rod, a tank, a shield cover, and a core as Figure 4. The basin insulator is fixed on the top of the tank, with a conductive rod connected underneath the basin insulator, and the conductive rod is connected to the ZnO varistor core through the shield cover, and the tank is filled with SF\({}_{6}\) gas. The accumulation of higher voltages can induce tip discharges.