## 3 Electric Field Detection Method of Degraded Insulators Based on Sensitive Insulators
### Criterion for Sensitive Insulators  
Assuming the insulator string is dry and free from pollution, with good insulation performance, infinite resistance, and no leakage conductivity considered, the insulator string is equivalent to the pure capacitor chain, and the equivalent circuit diagram of insulators is as follows Figure 11.  
Figure 10: The electric field curve of the insulator under the effect of sag.  
The capacitance of insulators in the figure is \(C_{s1}=C_{s2}=\ldots=C_{sn}=\ldots=C_{s0}\); the ground capacitance is \(C_{g1}\), \(C_{g2}\),..., \(C_{gn}\)...; the capacitance to the transmission line is \(C_{11}\), \(C_{12}\)..., \(C_{ln}\)...; and the voltage at the high end of the insulator string is set to \(U\). If the voltage borne by \(m\) insulator(s) is \(V\), [PERSON]'s law is used for any insulator \(C_{sn}\) as follows:  
\[C_{s0}(e_{n+1}-e_{n})-(C_{gn}+C_{ln})V_{n}+C_{ln}V=0 \tag{6}\]  
where \(V_{n}\) and \(e_{n}\) represent the potential and voltage borne of the \(n\)th insulator.  
Suppose the sum of \(C_{gn}\) and \(C_{ln}\) is independent of \(n\). In case of an assumption of Equation (7), Equation (6) is solved [28]:  
\[\left\{\begin{array}{l}\frac{C_{gn}}{C_{0}}=\alpha\\ \frac{C_{11}}{C_{0}}=\beta\\ \alpha+\beta=\gamma^{2}\end{array}\right. \tag{7}\]  
so the potential distribution of insulator string can be obtained, as shown in Equation (8):  
\[V_{n}=V\frac{\sinh n\gamma}{\sinh n\gamma}+\frac{V\beta}{\gamma^{2}}\bigg{[}1 -\frac{\sinh n\gamma+\sinh(m-n)\gamma}{\sinh n\gamma}\bigg{]} \tag{8}\]  
According to Equation (8), if one of the insulator strings is a degraded insulator, its capacitance \(C_{0}\) decreases, resulting in a significant decrease in its voltage, which is bound to redistribute the voltage in the whole insulator string, thus causing a difference between the voltage borne by all insulators and the voltage with no degradation and an increase in the space electric field strength of other insulators. At the same time, if degraded insulators appear at different positions in the insulator string, the difference between voltages is also varying.  
Therefore, in the case of degradation in the insulator string, regardless of the number of degraded insulators, the electric field around some insulators always changes greatly due to degradation, which is the most sensitive from the whole insulator string, so these insulators are called sensitive insulators. If the space electric field of a sensitive insulator is measured and compared with the space electric field at the position without degradation, the insulation performance of the insulator string can be judged. According to Equation (8), when the sensitive insulator itself is deteriorated, the voltage borne by it decreases, resulting  
Figure 11: Equivalent circuit diagram of an insulator.  
in the decrease of the space electric field; if the degraded insulator is located in other positions, the voltage distributed by the sensitive insulator will increase to a certain extent; therefore, the location of the degraded insulator can be accurately determined whether or not it is in the sensitive insulator group.