## 3 Results and Analysis of Ultraviolet Photon Counting
### Variation Characteristics of Photon Count Based on Discharge Intensity
The positive correlation between the photon count and the corona current indicates that the variation in the photon count accurately reflects the intensity of the discharge on the conductor. This suggests that changes in the photon count can provide a reliable indication of the discharge intensity of the conductor. From the above research, it can be observed that there was a positive correlation between the ultraviolet photon counts and the corona discharge current. Therefore, the discharge conditions of the conductor can be monitored using ultraviolet photon counts. In the laboratory, discharge experiments were conducted using a mini corona cage to perform corona discharge detection on three different specifications of smooth conductors under positive-polarity DC voltage. To observe weak corona discharge signals, the gain of the ultraviolet imaging camera was set to 100%, and the observation distance was set to 2 m. The relationships among the ultraviolet photon count, corona current, and voltage are studied, and the results are shown in Figure 5. From the figure, it can be observed that both the photon count and corona current increased with the increase in voltage. Additionally, the growth patterns of both variables appear to be similar or approximate. In the early stage of discharge, the photon count and corona current exhibited a slower increase with the voltage. As the voltage increased, the photon count and corona current showed a close-to-linear increase. However, once the voltage reached a certain level, the photon count and the corona current increased in an approximately exponential manner with the voltage. The corona inception voltage of the conductor was determined using the inflection point method. The theoretical corona inception voltage calculated based on empirical equations and the corona inception voltage obtained through experimental measurements are presented in Table 2.  
For the smooth conductor, the corona inception voltage obtained through measurements based on different corona discharge effects was generally consistent. From Table 2, it can be observed that the corona inception voltages obtained using three different methods for the smooth conductor had minimal differences. The maximum difference between the corona inception voltage obtained through the ultraviolet photon method and the empirical formula method was approximately 5%, while the maximum difference between the corona inception voltage obtained through the corona current method and the empirical formula method was approximately 7.5%. This indicates that the corona inception voltage obtained through the ultraviolet photon method was closer to the theoretical value. By using the  
Figure 4: The relationship between photon count and corona current at different voltages. least squares fitting algorithm, the different conductor voltages and their corresponding ultraviolet photon counts can be fitted, resulting in a functional relationship, as shown in Table 3. In the table, \(U\) represents the voltage on the conductor, the unit is V, and \(n\) represents the ultraviolet photon count. The calculation of the fitting coefficients shows that the fitted function has a coefficient of determination (R-squared) value greater than 0.99, which is close to 1. This indicates that the least squares fitting method provides a good fit for the relationship between the voltage and the ultraviolet photon count in relation to the three different specifications of conductors. From the fitting results, it can be observed that the relationship between the