# Maintenance Management of a Transmission Substation with Optimization
## 3 Data for the Maintenance Model of an Existing 400/110-220/110 kV Transmission Substation
### Data on Technical Condition c and Importance i  
Table 2 shows the calculated data on the importance of individual significant states of the RCM model of the TS \(i_{\text{J}}\), average importance of bays by various significant states \(i_{q}\), technical condition (technical indicator) \(c_{q}\), and average deviation \(d_{q}\) for all bays, calculated using (5). The average importance of TS bays by each SS is determined in a similar way with (4). \[i_{\text{avg}}=I\cdot w_{\text{SS}}^{\text{T}} \tag{4}\]  
The common index \(d\) is defined on the basis of the index of technical condition \(c\) and index of importance \(i_{\text{avg}}\). It represents the uniform participation of technical condition and importance of \(c\) and \(i_{\text{avg}}\) of the device. The index \(d\) encompasses the bays and power transformers of the TS and is defined by (5). \[d=\frac{c+i_{\text{avg}}}{\sqrt{2}} \tag{5}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**q**} & \multirow{2}{*}{**Code**} & \multicolumn{2}{c}{**Voltage**} & \multicolumn{5}{c}{**Importance i\({}_{\text{j}}\)**} & \multicolumn{5}{c}{**Average Importance**} & **Condition** & **Distance** \\  & & **Level (kV)** & **SS\({}_{1}\)** & **SS\({}_{2}\)** & **SS\({}_{3}\)** & **SS\({}_{4}\)** & **SS\({}_{5}\)** & **SS\({}_{6}\)** & **SS\({}_{7}\)** & **SS\({}_{8}\)** & **SS\({}_  
The average value of costs of expected outages by each SS for all TS bays is calculated using (6) as the vector of costs of expected outages \(\mathbf{C}_{\text{in,avg}}\). \[C_{\text{in,avg}}=C_{\text{in}}\cdot\mathbf{w}_{SS}^{T} \tag{6}\]  
All these values from Table 2 are input data of the optimization process, and the basis for the \(c-i_{\text{avg}}\) diagram for all 31 bays (Figure 2b). In the \(c-i_{\text{avg}}\) diagram, the \(x\)-axis represents the index of importance \(i\), and the \(y\)-axis the index of technical condition \(c\). For both indexes \(c\) and \(i\) to be considered equally, the line \(x\) needs to be rotated by the angle \(\beta=45^{\circ}\). The point on the \(c-i_{\text{avg}}\) diagram represents a couple \(c\) and \(i_{\text{avg}}\) for the switching bay \(q_{\text{s}}\). The RCM diagram in Figure 2 represents a graphical representation of the main data, which are the importance and technical conditions of elements from Table 2. The importance of elements was averaged, due to the need for a better visualization and request for a uniform solution for the determination of maintenance frequency of elements. The bay code in Table 2 consists of one letter and three digits. The letter represents the type of bay: line bay (L), transformer bay (T), or bus coupler bay (C). The first digit indicates the voltage level of the bay (1-110 kV, 2-220 kV, and 4-400 kV). The last two digits represent the sequence number of the bay. The code for power transformers consists of two letters (Tr) and three digits. The first digit indicates the voltage level of the primary winding, the second is the secondary winding, and the third is the sequence number of the transformer. Figure 2a shows the \(c-i\) diagram with the condition of all elements in all significant states of the index \(i_{\text{j}\prime}\), while Figure 2b shows the \(c-i_{\text{avg}}\) diagram with the average index of the element \(i_{\text{j}\prime}\). In comparison to the diagram in Figure 2a, the diagram in Figure 2b shows only one point on the \(c-i\) diagram for the TS elements. \(d_{1}\) and \(d_{2}\) are bounds between the areas of action and are defined by the TSO. These areas represent risk of failures on devices. The colors in the \(c-i\) diagram describe the kind of maintenance tasks. In the green area, there are prescribed regular inspections of HV devices; in the yellow area, there are maintenance interventions that require equipment revision; and in the red area, there are the cases where the equipment needs to be replaced. The deviation \(d_{q}\) defines as to which area an individual TS element belongs [1,26].