# Maintenance Management of a Transmission Substation with Optimization
## 5 Results of Optimal RCM Maintenance
### Optimal Maintenance for the Observed TS  
The optimization was performed to obtain optimal parameters representing the frequency of maintenance activities \(\mathbf{p}_{\text{r,OPT}}\) and the optimal SS \(\mathbf{p}_{\text{SS,OPT}}\), in which the maintenance should be carried out. The maintenance of each TS bay is, therefore, conditioned by two optimization parameters. Figure 6 shows the results of optimal maintenance for the observed TS, where Figure 6a shows the optimization parameters from the vector \(\mathbf{p}_{\text{r,OPT}}\) (in years) for the revision performed in each individual switching bay or power transformers (the existing TBM maintenance methodology--red line, proposed optimal methodology--blue histogram). Figure 6b shows the optimal data of the second set of optimization parameters \(\mathbf{p}_{\text{SS,OPT}}\), which represents the proposal for maintenance. It provides the information about the selected SS of the EPS (possible future combination of generation, consumption, and power flows in the TS) when it would be most suitable to de-energize the TS elements and perform revision. Figure 5: Progress of the optimization process of common objective function and partial objective functions. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **No.** & **Without SA** & \
\begin{tabular}{c} _F and CR for the_ \\ **Whole Population** \\ \end{tabular} &
\begin{tabular}{c} _F and CR for Each Individual_ \\ **in the Population** \\ \end{tabular} \\ \hline \multirow{7}{*}{Value of objective function} & 1 & 0.410812 & 0.400430 & 0.400430 \\  & 2 & 0.409546 & 0.400430 & 0.400430 \\  & 3 & 0.407953 & 0.400430 & 0.400430 \\  & 4 & 0.409546 & 0.400430 & 0.400430 \\  & 5 & 0.407953 & 0.400430 & 0.400430 \\  & 6 & 0.409546 & 0.400430 & 0.400430 \\  & 7 & 0.407953 & 0.400430 & 0.400430 \\  & 8 & 0.409546 & 0.400430 & 0.400430 \\  & 9 & 0.407953 & 0.400430 & 0.400430 \\  & 10 & 0.409179 & 0.400430 & 0.400430 \\ \hline \multicolumn{2}{c}{Mean value of objective function} & 0.408999 & 0.400430 & 0.400430 \\ \hline \multicolumn{2}{c}{StD of objective function} & 0.000573 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean values and standard deviation of objective function for variants of SA. The summaries of optimal parameters are in the form of histograms, shown in Figure 7. They show that it would be most suitable to perform revision on 10 elements every year, on 13 every two years, and on 8 every three years. With the proposed maintenance methodology, only approximately one-third of switchyard elements kept yearly frequency of maintenance activities. For the existing TBM concept, all 31 elements were found to have the frequency of maintenance activities every year. Despite the optimally selected maintenance periods, it would be necessary to perform revision on 10 elements every year. A comparison of the selected significant states in Table 1 and the histogram of the most suitable significant states led to the conclusion that the most suitable significant states for de-energizing state are the TS elements. The optimization results of RCM maintenance methodology are presented in the \(c\)\(-\)\(i_{\text{avg}}\) diagrams in Figure 8. The \(c\)\(-\)\(i_{\text{avg}}\) diagram after the optimization (Figure 8a) was compared with the \(c\)\(-\)\(i_{\text{avg}}\) diagram before optimization (Figure 2b). The comparison of  
Figure 6: Results of optimization. (**a**) Period of maintenance works (the existing TBM concept—red line, proposed optimal methodology—blue histogram); (**b**) proposal of maintenance in possible significant states. Figure 7: Histogram of existing TBM concept and proposed optimal maintenance methodology. both \(c-i_{\text{avg}}\) diagrams showed that the points only moved vertically. Differences between the values of technical condition index \(c\) before and after the optimization for individual switching bays ranged between 0 and 18.