## 4 Case Analysis
### Cases with Complete Fault Feature Information  
Taking \(f_{4}\)-\"I/O module fault of merging unit (Bus merging unit \(\rightarrow\) Line merging unit)\" as an example, when the fault occurs, the fault feature information is shown in Table 9:  
Establish the integrated alarm information set \(A\) as shown in (14):  
\[A=\{a_{1},a_{2},a_{3},\ldots,a_{16}\}=\{1,1,1,0,1,\ldots,0\} \tag{14}\]  
Establish the link information of GOOSE and SV set \(I\) as shown in (15):  
\[I=\{I_{1},I_{2},I_{3},\ldots,I_{9}\}=\{1,0,0,1,1,\ldots,0\} \tag{15}\]  
Establish device self-checking information set \(I\) as shown in (16):  
\[\left\{\begin{aligned} & C=\{C_{\text{{CML}}},C_{P},C_{TT}\}\\ & C_{M\sqcup T_{2T}}=\{0,0,\ldots,0\}\\ & C_{P_{2T}}=\{0,0,\ldots,0\}\\ & C_{1T_{2T}}=\{0,0,\ldots,0\}\\ \end{aligned}\right. \tag{16}\]  
The voltage and current sampling values are shown in (17):  
\[\left\{\begin{aligned} & S=\{M_{1},M_{2}\}\\ & M_{1}=\{I_{A1},I_{B1},I_{C1},U_{A1},U_{B1},U_{C1}\}\\ & M_{2}=\{I_{A2},I_{B2},I_{C2},U_{A2},I_{B2},U_{C2}\}\\ \end{aligned}\right.=\left\{\begin{aligned} & S=\{M_{1},M_{2}\}\\ & M_{1}=\left\{\begin{aligned} & 3.023,3.028,3.016,\\ & 57.488,57.558,57.549\end{aligned}\right\}\\ & M_{2}=\left\{\begin{aligned} & 2.969,2.958,2.894,\\ & 57.402,58.218,56.473\end{aligned}\right\}\\ \end{aligned}\right. \tag{17}\]  
After preprocessing by the Min-Max method, the sampling data are transformed into (18):  
\[\left\{\begin{aligned} & S^{\prime}=\left\{{M_{1}}^{\prime},{M_{2}}^{ \prime}\right\}\\ &{M_{1}}^{\prime}=\left\{\begin{aligned} & 0.9781,0.9768,0.9729,\\ & 0.9810,0.9822,0.9821\\ & M_{2}}^{\prime}=\left\{\begin{aligned} & 0.9577,0.9542,0.9335,\\ & 0.9796,0.9935,0.9637\end{aligned}\right\}\\ \end{aligned}\right. \tag{18}\]  
After the fault occurs, a total of 9 alarm messages are received within 30 s after receiving the alarm message of \"abnormal alarm of the merging unit \", which is greater than 3, so the fault diagnosis of the protection system of the intelligent substation is triggered. The fault feature set \(X\)= \(\{A\,.\,I,C,S^{\prime}\}\) is constructed by calling fault feature information and processing data, as shown in Formulas (14)-(18). Input into the GBDT  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Fault Type** & **Fault Feature Information** \\ \hline \hline  & Abnormal alarm of merging unit \\  & SV total alarm \\  & GOOSE total alarm \\  & SV interruption of merging unit \\  & GOOSE interruption of merging unit \\  & SV interruption of protection device \\  & SOOSE alarm of intelligent terminal \\  & Protection locking \\ \hline \hline \end{tabular}
\end{table}
Table 9: Fault feature information of \(f_{4}\).  
based fault diagnosis system for diagnosis, input \(X\) into the 12 binary classifiers in the GBDT algorithm, respectively, and calculate the probability P as shown in Table 10.  
It can be seen that this fault is most likely to be \(f_{4}\), and the output diagnostic result set \(\mathrm{R}=\{f_{1},f_{2},f_{3},f_{4},\ldots\}=\{0,0,0,1,\ldots\}\), then it is considered that this fault belongs to the \"I/O module fault of merging unit (Bus merging unit \(\rightarrow\) Line merging unit)\", so the diagnosis is correct.  
To verify whether the method in this paper has a generally high accuracy under the condition of complete fault feature information, 1125 groups of samples that have not been used were selected from historical fault samples. The fault diagnosis is carried out by this method. The steps are shown in the above, and the distribution of fault samples and diagnosis results are shown in Table 11.  
The final accuracy rate is 99.29%, which has high accuracy under the condition of complete fault feature information.