# Maintenance Management of a Transmission Substation with Optimization
## 2 Maintenance Model Based on the RCM Concept
### Index of Importance i  
To calculate the importance of the EPS elements, the reliability indicators need to be calculated first. The first step in this calculation is a detailed analysis of the EPS as a whole. For the calculation of reliability indicators, we used a powerful program tool for steady-state calculations in the EPS, Neplan [26]. The Neplan program tool for calculation of reliability indicators requires data on outages of all EPS elements, as well as hourly data on generation and consumption for all EPS nodes. The analysis begins with a statistical survey of hourly data on generation and consumption in all EPS nodes, as well as an analysis of power flows in certain parts of the EPS in a certain period (one year or more). A clustering approach is used on the basis of historical data. Average values of power (\(\mu_{\text{P}}\)) and deviations from the average value (\(\sigma_{\text{P}}\)) are calculated for generation, consumption, and power flows. Combinations of strings of hourly data for the total power \(P_{\text{SYS}}\) are selected,which is defined as the total power of generation, consumption, and power flows for the entire EPS. The \(n_{\text{SS}}\) sets of significant states (SS) are selected for generation, consumption, and power flows for the combinations that appear most often. SS are states in the EPS with a certain quantity of generation, load flows, and consumption. Significant states are each a static snapshot that combines generation, consumption, and transmission. SS can be a variable (\(SS\)). \(S_{\text{SS}}=\{h_{\text{SS},j};1\leq j\leq n_{\text{SS}};j\in\text{N}\}\), where \(h_{\text{SS},j}\) is the characteristic hour from the selected \(j\)th set of states. Table 1 presents 9 selected SS for generation, consumption, and power flows that, to a certain extent, reflect the state of the EPS in the observed period. This is important in deciding when to implement maintenance of the TS elements. It is also possible to calculate the shares of frequency of occurrence of SS that are characterized by generation and consumption in the selected hours of the observed period. Thus, the vector of shares of selected states in the EPS \(w_{\text{SS}}=[w_{\text{SS},j}]\); \(0<w_{\text{SS},j}<1\) is calculated (Table 1). The weight \(w_{\text{SS},j}\) depends on the share of hours in an individual set \(S_{\text{SS},j}\) of the whole set of hours. For a certain past period, the data on outages of EPS elements are collected and modified in the reliability model of the Neplan program tool. In the model, it is also necessary to make possible changes of the EPS configuration. For each chosen \(j\)th SS reliability indicators are calculated in Neplan using the failure effect analysis (FEA) [28]. For the subsequent calculations, the costs are used of expected long duration outages of the EPS elements. The data on energy not supplied to the consumers \(W_{\text{ins},jk}\) in the case of an outage of a certain EPS element are included in the matrix \(w_{\text{ins}}=[w_{\text{ins},jk}]\), while the matrix \(w_{\text{ing}}=[w_{\text{ing},jk}]\) contains data on energy not produced in the generation units \(W_{\text{ing},jk}\). \(W_{\text{ins},jk}\) and \(W_{\text{ing},jk}\) for every significant state and every certain element of EPS are calculated with FEA in the program tool Neplan. They are reliability indicators. For each element \(r\) from the set of elements \(S_{\text{el}}\), the subset \(S_{\text{el},jr\upsilon}\) is created for each significant state \(j\), kind of elements \(r\), and a certain voltage level \(v\)\(S_{\text{el},jr\upsilon}=\{W_{\text{ins},jkr\upsilon},W_{\text{ing},jkr \upsilon};\)\(1\leq k\leq n_{\text{ke}};1\leq v\leq 3;k,v\in\text{N}\}\). For each significant state \(j\) and kind of elements \(r\), \(W_{\text{i}mmax,r\upsilon}\) is determined, which is the maximum value from the set \(S_{\text{el},jr\upsilon}\), and for a certain voltage level \(v\) from the set \(S_{\text{VL}}\); \(S_{\text{VL}}=\{110\text{ kV, 220 kV, 400 kV}\}\).