## 4 Characterization of the Discharge of Insulation Defects in Switchgear
### Characterization of Characteristic Gases Generated by Metal Particle Discharge  
During the manufacturing, transportation, operation, and maintenance of switchgear cabinets, complex industrial control factors cause tiny metal particles to appear in the cavities. During normal operation of the air switchgear, tiny metal particles jump, and this movement changes with the continuous alteration of the working voltage phase. This variation results in a highly unstable partial discharge, thereby augmenting the complexity of  
Figure 15: Variation curves of gas volume fractions of CO, NO\({}_{2}\), and O\({}_{3}\) with partial discharge volume caused by the gap. (**a**) Variation curve of CO volume fraction with partial discharge volume. (**b**) Variation curve of NO\({}_{2}\) volume fraction with partial discharge volume. (**c**) Variation curve of O\({}_{3}\) volume fraction with partial discharge volume.  
research. The size, shape, material, and quantity of metal particles inside the switchgear can affect the generation of partial discharge. However, the number of metal particles inside the switchgear has the greatest impact on partial discharge. At the same time, for the convenience of experiments, this paper uses the number of free metal particles as the test variable to study the effect of the number of metal particles on partial discharge. The volume fraction data of the characteristic gases under different discharge durations with the number of free metal particles as a test variable are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Discharge Time (min)** & **Q (nC)** & **CO (uL/L)** & **NO2 (uL/L)** & **O3 (uL/L)** \\ \hline \multicolumn{5}{c}{50 Particles} \\ \hline
40 & 3 & 6 & 58 & 98 \\
80 & 4.1 & 7.5 & 70 & 110 \\
120 & 4.8 & 8 & 98 & 121 \\ \multicolumn{5}{c}{100 particles} \\
40 & 4 & 7 & 60 & 105 \\
80 & 4.9 & 10 & 75 & 120 \\
120 & 5 & 13.5 & 101 & 128 \\ \multicolumn{5}{c}{150 particles} \\
40 & 5 & 13 & 80 & 115 \\
80 & 5.8 & 14 & 105 & 128 \\
120 & 6.1 & 18 & 131 & 135 \\ \multicolumn{5}{c}{200 particles} \\
40 & 5.5 & 13.4 & 106 & 120 \\
80 & 6.4 & 24 & 143 & 140 \\
120 & 7 & 26 & 180 & 145 \\ \hline \end{tabular}
\end{table}
Table 1: Data table of volume fractions of gases characterized by metal particle defects.  
Figure 16: Fitted curves of CO, NO2, and O3 volume fractions versus partial discharge volume in Gap Discharge. (**a**) CO gas volume fraction fitting curve. (**b**) NO2 gas volume fraction fitting curve. (**c**) O3 gas volume fraction fitting curve.  
In the four experiments of 50, 100, 150, and 200 metal particles, the volume fractions of CO, NO\({}_{2}\), and O\({}_{3}\) were not high due to the discontinuous discharge process of metal particle defects. Due to its strong oxidizing properties, O\({}_{3}\) is prone to undergo redox reactions with other components in the air and easily oxidized substances in the insulation layer, thus reducing its impact on CO and NO\({}_{2}\). This results in a higher volume fraction of NO\({}_{2}\) gas. Mathematical fitting was performed on the data in Table 1, and the fitting curve is shown in Figure 17. The regression equation is shown in the following equation.  
\[y=-0.00648x_{CO}^{2}+0.36345x_{CO}+1.68393 \tag{12}\]  
\[y=-1.58597e^{-4}x_{NO_{2}}^{2}+0.06479x_{NO_{2}}+0.41323 \tag{13}\]  
\[y=0.07653x_{O_{3}}-4.20924 \tag{14}\]  
where \(x_{CO}\), \(x_{NO_{2}}\), \(x_{O_{3}}\) represent the volume fractions of CO, NO\({}_{2}\), and O\({}_{3}\) when the partial discharge is y.