# Maintenance Management of a Transmission Substation with Optimization
## 2 Maintenance Model Based on the RCM Concept
### Definition of EPS Elements  
The subject of our analyses is the EPS. It comprises generation units, lines, and substations. In substations, there are disconnectors, circuit breakers, power transformers, and other elements. The elements of the EPS represent a set of elements \(S_{\text{el}}=[el_{k};\ 1\leq k\leq n_{\text{el}};\ k\in\mathbb{N}]\), where \(n_{\text{el}}\) is the number of elements in the entire EPS, \(el\) is the element in the EPS, and \(k\) is the counter of the EPS elements. All these elements form a database with characteristic variables, such as estimation of technical condition, economic indicators, reliability indicators, and indicator of importance. A set of elements \(S_{\text{kel}}=\{kel_{r};\ 1\leq r\leq n_{\text{kel}};\ r\in\mathbb{N}\}\) is created, where \(n_{\text{kel}}\) is the number of kinds of elements used in the EPS, \(kel\) is the kind of elements used in the EPS, and \(r\) is the counter of kinds of elements used in the EPS. Data on the entire EPS are needed for the computation of the reliability indicators of the EPS, technical condition of elements, and maintenance costs. From the set of elements \(S_{\text{el}}\), only those elements were observed that are a part of the TS.  
The model enables scheduling of maintenance tasks with regard to the state of the system, taking into consideration economic effects and reliability of operation of individual switching bays in the TS.  
The analysis includes only switching bays and transformers that are elements of the observed TS. A switching bay is a set of elements in the substation that belongs to the main element (transformer or transmission line). A switching bay is an assembly of switchgear elements (disconnectors, circuit breakers, etc.), and can be either line bay, transformer bay, or bus coupler bay [27]. Bays in the TS form a set of bays \(S_{\text{SB}}=\{S_{\text{SB}},l;\)\(S_{\text{SB}},l\subset S_{\text{el}};\)\(1\leq l\leq n_{\text{SB}};\)\(l\in\mathbb{N}\}\), where \(n_{\text{SB}}\) is the number of switching bays. The \(l\)th bay in the TS comprises a certain number of elements and forms the set of elements of the \(l\)th bay \(S_{\text{SB},l}=\{\)\(l_{\text{SB},l}\); \(1\leq m\leq n_{\text{SB},l}\); \(m\in\mathbb{N}\}\), being a subset of the set of elements \(S_{\text{el}}\), where \(n_{\text{SB},l}\) is the number of elements in the \(l\)th bay of the TS and \(m\) is the counter of elements in the TS bay. A switching bay can be considered as a new EPS element. The reason for this is that, during revision, the entire bay is always in a de-energized state and is maintained as a whole. The analysis of a TS also includes power transformers. The set of bags in the TS is, thus, case extended to the number of transformers \(n_{\text{T}}\). It is defined as \(S_{\text{T}}=\{TR_{l};\)\(1\leq l\leq n_{\text{T}};\)\(l\in\mathbb{N}\}\), where \(l\) is the counter of transformers in the TS. The set of TS elements, therefore, consists of switching bays and transformers, and is defined as \(S_{\text{SU}}=\{S_{\text{SU},l};\)\(S_{\text{SU}}=S_{\text{SB}}\cup S_{\text{T}};\)\(1\leq q\leq n_{\text{SU}};\)\(q\in\)N; \(n_{\text{SU}}=n_{\text{SB}}+n_{\text{T}}\}\), where \(q\) is the counter of switching bays and transformers and \(n_{\text{SU}}\) is the number of observed switching bays and transformers of the TS.