# Fault Diagnosis System of Power Grid Based on Multi-Data Sources
## 3 Realization of Fault Diagnosis Real-Time Processing System
### Fault Diagnosis and Information Missing Analysis  
3.1 Fault Diagnosis Confirmation and Operation Status Analysis of Related Circuit Breakers and Protections  
In this section, all the elements in \(V\_e3\) are investigated one by one to judge whether a fault occurs and whether relevant protections and circuit breakers operate normally. In order to simplify the model, the state space of a single relay protection device (or a circuit breaker) is divided into two categories: device fault and device normal. The state transition diagram is shown in Figure 7.  
According to [PERSON]'s state-space theory, the state transition matrix \(A\) is:  
\[A\ =\ \left[ \begin{array}{cc}1-\mu&\mu\\ \lambda&1-\lambda\end{array} \right] \tag{1}\]  
It is assumed that the fault probability of a device is \(p_{0}\) and the normal probability of the device is \(p_{1}\). The sojourn probability matrix \(T=[p_{0}\ p_{1}]\), and \(T\cdot A=T\), \(p_{0}+p_{1}=1\). The normal probability of a device defined as the correctness of the device, as Equation (2):  
\[p_{1}\ =\ \frac{\mu}{\lambda+\mu} \tag{2}\]  
Referring to the statistics of the China Electric Power Research Institute on the operation of Chinese grid relay protection devices and circuit breakers, the correctness of each protection and circuit breaker in this article is calculated by corresponding numerical values in references [15,16]. Taking the bus protection as an example. \(\Lambda=0.556\) (unit: times/(100 sets per year)), \(\mu=0.25\) (unit: times/h). According to Equation (2), the correctness of bus protection, namely BP. \(P=0.975\). MP. \(P=0.98\), NBP. \(P=0.96\), RBP. \(P=0.96\), TP. \(P=0.98\), and CB. \(P=0.97\) can be calculated similarly. What needs to be noted is that in actual engineering applications, accurate data statistics should be determined according to product, manufacturer, year of production, and other details. The correctnesses of protections and circuit breakers currently used have reached a high level (at least higher than 95%). Thus, the error between the general statistical value used in this paper and the actual statistical value is extremely small. In the subsequent calculation process, the calculation error caused by such a small error is also extremely small, and it will not change the final judgment on whether circuit breakers and protections are operating correctly. This is the conclusion that has been gotten after comparing the calculation process between extreme data (95%) and general statistical values. Therefore, in order to simplify the description and calculation, this article adopts the statistical values of the general meaning. Many types of protection only relate to one circuit breaker. Thus, these protections are only involved with one branch of the protection connection tree of a \(V\_e\) class element. It is assumed that when \(Vy\) (a \(V\_e\) class element) fails, according to the principle of relay protection stage coordination, the circuit breaker should trip arranged at the \(z\)-th position in a branch of \(Vy\) protection information connection tree is \(CBy\_z\). In \(CBy\_z\_PBF\), the protection, which should act arranged at the \(x\)-th position according to action time is \(Py\_z\_x\), and its protection correctness is denoted as \(py_{y\_z\_x}\). Figure 7: The state transition diagram. It is assumed that circuit breakers that should trip arranged before \(CBy\_z\) do not trip, and \(CBy\_z\) operates normally. The probability of \(Py\_z\_x\) action to remove the fault is:  
\[p(y\_z\_x)\ =\ \prod\
olimits_{i=1}^{x-1}\big{(}1-p_{Py\_z\_j}\big{)}p_{Py\_z\_x} \tag{3}\]  
Thus, the probability of \(CBy\_z\) tripping to remove the fault is:  
\[p(y\_z)\ =\ \sum\
olimits_{x=1}^{z=m}p(y\_z\_x) \tag{4}\]  
In Equation (4), \(zm\) denotes the number of protections that can be used to remove the \(Vy\) fault in \(CBy\_z\_PBF\). Remove the original assumptions. The new assumption is that \(CBy\_z\) operates normally.