## 3 State Evaluation and Fault Prediction of Protection System Based on Digital Twin Technology
### State Evaluation of Protection System Based on Matter-Element Extension
#### 3.2.2 State Evaluation Joint Domain and Classical Domain  
The joint domain is the total range of values of each characteristic quantity of the system to be evaluated, and the expression of the joint domain elements is  
\[R_{p}=\left(N,C_{i},V_{pi}\right)= \begin{bmatrix}N&C_{1}&\left\langle a_{p1},b_ {p1}\right\rangle\\ &C_{2}&\left\langle a_{p2},b_{p2}\right\rangle\\ &\vdots&\vdots\\ &C_{i}&\left\langle a_{pi},b_{pi}\right\rangle\\ &\vdots&\vdots\\ &C_{n}&\left\langle a_{pn},b_{pn}\right\rangle\end{bmatrix} ,\;(i=1,2,\cdots,n) \tag{2}\]  
where \(N\) is the protection system, \(V_{pi}\) is the range of values of the \(i\)-th characteristic quantity \(C_{i}\), and \(a_{pi}\) and \(b_{pi}\) represent the upper and lower limits specified by the characteristic quantity \(C_{i}\). This paper collects and analyzes the field export data of a 220 KV smart station in China Southern Power Grid in 2019, including SV/GOOSE state information, sampling \begin{table}
\begin{tabular}{c c} \hline
**Number** & **Characteristic Quantities** \\ \hline \(c_{1}\) & GOOSE general alarm \\ \(c_{2}\) & SV link general alarm \\ \(c_{3}\) & SV/GOOSE plug-in optical port \\ & receive/transmit power out of limits \\ \(c_{4}\) & Protection DSP sampling errors \\ \(c_{5}\) & Pilot protection channel anomaly alarm \\ \(c_{6}\) & SV sampling invalid \\ \(c_{7}\) & SV sampling out of step \\ \(c_{8}\) & MU data abnormalities \\ \(c_{9}\) & Merge unit sampling exception \\ \hline \end{tabular}
\end{table} 
Table 2: Main characteristic quantities of protection system. value information, communication channel information, etc., and sorts the upper and lower limits of the frequency of each characteristic in 24 h as shown in (3). \[R_{p}= \begin{bmatrix}N&c_{1}&[0,3]\\ &c_{2}&[0,3]\\ &c_{3}&[0,20]\\ &c_{4}&[0,3]\\ &c_{5}&[0,10]\\ &c_{6}&[0,3]\\ &c_{7}&[0,3]\\ &c_{8}&[0,3]\\ &c_{9}&[0,6]\end{bmatrix}  \tag{3}\]  
The classical domain is the numerical range of the characteristics of the system to be evaluated in this state level. The expression of classical domain matter-element is  
\[R_{j}= \begin{pmatrix}N_{j}&C_{1}&\langle a_{j1},b_{j1}\rangle\\ &C_{2}&\langle a_{j2},b_{j2}\rangle\\ &\vdots&\vdots\\ &C_{i}&\langle a_{ji},b_{ji}\rangle\\ &\vdots&\vdots\\ &C_{n}&\langle a_{jn},b_{jn}\rangle\end{pmatrix} ,(i=1,2,\cdots,n) \tag{4}\]  
Among them, \(R_{j}\) is the \(j\)-th state level divided, \(N_{j}\) is the protection system under the \(j\)-th state level, \(V_{ji}\) is the \(j\)-th state level, the value range specified in the \(i\)-th characteristic quantity \(C_{i}\), \(\langle a_{ji},b_{ji}\rangle\) is the upper and lower limits of the value range. By reviewing the relay protection status evaluation guidelines issued by the State Grid Corporation and related literature, the protection system equipment status levels are generally classified as normal, attention, abnormal, and serious abnormal. However, in the actual operation of the protection system equipment, the time required for the equipment to deteriorate to failure due to abnormal operating conditions is generally short, so this paper combines \"abnormal\" and \"serious abnormal\" into a \"severe\" state. The classical domain is set as \(R=\{R_{1},\ R_{2},R_{3}\}\), where \(R_{1-3}\) correspond to \"normal\", \"attention\" and \"severe\" levels, respectively. \"Normal\" means the equipment is in good operation. \"Attention\" indicates that the equipment is operating normally but some indicators have deteriorated and may fail if no intervention is made. \"Severe\" means that the equipment may fail soon or is already in a state of failure, and the equipment will be subject to fault prediction and diagnosis, and targeted, preventive maintenance. Based on the relay protection state evaluation guidelines, and combined with expert experience, manufacturer's instructions and actual research, the classical domain of the matter-element was set. The network channel operation is used as an example to illustrate the classical domain determination method for the characteristic quantity \(c_{1}\).