# A Review of Power System Fault Diagnosis with Spiking Neural P Systems
## 2 Power System Fault Diagnosis with Spiking Neural P Systems
### Fault Section Estimation of Power Systems  
This section discusses the use of a novel model in SNPS, i.e., optimization spiking neural P systems (OSNPS) [130], for fault section estimation of power systems. OSNPS was introduced in 2014 with the purpose of solving optimization problems using the framework of spiking neural P system. In [52; 126], a framework based on OSNPS was introduced to solve the power system fault section estimation (FSE) problem. FSE can be formulated as an optimization problem. OSNPS models are very efficient and after receiving the PRs and CBs information from SCADA system, these models are capable of searching and output fault sections automatically. Furthermore, these models are very efficient while identifying single as well as multiple faults even with incomplete and uncertain messages received from the SCADA system. Problem Description: The fundamental purpose of FSE problem in power system is to obtain a fault hypothesis which is capable of explaining warning signals with maximum degree of confidence and it is based on optimization methods. It is also possible to formulate the FSE problem as \(0-1\) programming problem with an objective function as in the Equation (5). This equation is derived from the causality between a fault and the statuses of PRs and CBs received from the SCADA system. The fault hypothesis is obtained by using the optimization method. More specifically, by finding the minimum value of  
\[E(S)=\sum_{j=1}^{n_{c}}|c_{j}-c_{j}^{*}(S,R)|+\sum_{k=1}^{n_{r}}|r_{k}-r_{k}^{* }(S)| \tag{5}\]  
where:  
(1) \(n_{c}\) represents the numbers of circuit breakers (CBs) and \(n_{r}\) represents the number of protective relays;  
(2) \(E(S)\) is status function of all the sections in a power system;  
(3) The status of sections in a power system is represented by an \(n\)-vector \(S\). The number \(n\) represents the number of sections: when section \(i\) is faulty, then \(s_{i}=1\); otherwise, \(s_{i}=0,i=1,...,n\);  
(4) In a protection system, the real status of the \(j\)th circuit breaker is denoted by \(c_{j}(1\leq j\leq n_{c})\) and it also can be expressed as the \(j\)th element of an \(n_{c}\)-vector. When \(CB_{j}\) trips, then \(c_{j}=1\); otherwise, \(c_{j}=0\);  
(5) In a protection system, expected status of the \(j\)th circuit breaker is represented by \(c_{j}^{*}(S,R)(1\leq j\leq n_{c})\) and it is also expressed as the \(j\)th element of an \(n_{c}\)-vector. When \(CB_{j}\) trips, then \(c_{j}^{*}=1\); otherwise, \(c_{j}^{*}=0\);  
(6) In a protection system, the real status of the \(k\)th protective relay is denoted by \(r_{k}(1\leq k\leq n_{r})\) and it is also expressed as the \(k\)th element of an \(n_{r}\)-vector. When the \(k\)th protective relay is operated, then \(r_{k}=1\); otherwise, \(r_{k}=0\);  
(7) In a protection system, the expected status of the \(k\)th protective relay is denoted by \(r_{k}^{*}(S)(1\leq k\leq n_{r})\) and it also can be expressed as \(k\)th element of an \(n_{r}\)-vector. When the \(k\)th protective relay operates, \(r_{k}^{*}=1\); otherwise, \(r_{k}^{*}=0\). In [126], the OSNPS model has been used to minimize \(E(S)\) in Equation (5) and it also helps in fulfilling the task of fault section estimation in power systems. From SCADA system the real status of protective relays and CBs can be obtained. However, from the operational principles and protection structures of power systems, the expected status of PRs and CBs can be achieved. Then the OSNPS is used to obtain the minimum value of \(E(S)\) and it is done only when all the expected status and real status of PRs and CBs are obtained. Furthermore, the vector elements of \(S\) are obtained according to the minimum value of \(E(S)\) in Equation (5). Now we explain the fault diagnosis method and in order to do so at first the structure and working of the OSNPS model are described. **Definition 6**.