# A Review of Power System Fault Diagnosis with Spiking Neural P Systems
## 2 Power System Fault Diagnosis with Spiking Neural P Systems
### Transformers
When FRSNP is used for fault diagnosis, fuzzy production rules and reasoning algorithms are the most important components. Fuzzy production rules help us to express the diagnosis knowledge which is extracted from real-world data while addressing the problem of fault diagnosis. Fuzzy production rules are generally of two types, i.e., simple and composite [84]. Simple fuzzy productions have the following form  
\[R_{i}\textbf{: IF }p_{j}\textbf{ THEN }p_{k}(CF=\tau_{j}) \tag{1}\]  
where \(\tau_{i}\in[0,1]\) represents CF and \(R_{i}\) is the \(i\)th fuzzy production rule, \(p_{j}\) and \(p_{k}\) are propositions with real truth values in \([0,1]\). The composite fuzzy production rules are generally divided into three types, i.e., type-1, type-2 and type-3. **Type 1**\(R_{i}\) **: IF \(p_{1}\) and \(p_{2}\) and...and \(p_{k-1}\) THEN \(p_{k}(CF=\tau_{i})\). ** (2)  
In this rule \(p_{1},p_{2},\ldots,p_{k}\) are propositions which are present in the antecedent part where the truth value of the propositions are \(\alpha_{1},\alpha_{2},\ldots,\alpha_{k-1}\). The confidence factor of the rule is represented by \(\tau_{i}\in[0,1]\). So correspondingly \(\alpha_{k}=min(\alpha_{1},\alpha_{2},\ldots,\alpha_{k-1})*\tau_{i}\) represents the truth value of the proposition \(p_{k}\). **Type 2**\(R_{i}\) **: IF \(p_{1}\) THEN \(p_{2}\) and \(p_{3}\) and...and \(p_{k}(CF=\tau_{i})\). ** (3)  
In this rule \(p_{1}\) is only one proposition present in the antecedent part of the rule with truth value \(\alpha_{1}\) and \(\tau_{i}\in[0,1]\) is the confidence factor. So correspondingly \(\alpha_{2}=\alpha_{1}*\tau_{i},\alpha_{3}=\alpha_{1}*\tau_{i},\ldots,\alpha_{k }=\alpha_{1}*\tau_{i}\) are the truth values of \(p_{2},p_{3},\ldots,p_{k}\) respectively. **Type 3**\(R_{i}\) **: IF \(p_{1}\) or \(p_{2}\) or...or \(p_{k-1}\) THEN \(p_{k}(CF=\tau_{i})\). ** (4)  
In this rule \(p_{1},\ldots,p_{k-1}\) are the propositions present in the antecedent part of the rule and they have truth values \(\alpha_{1},\alpha_{2},\ldots,\alpha_{k-1}\), respectively. \(\tau_{i}\in[0,1]\) represents the confidence factor of the rule. So, \(\alpha_{k}=max(\alpha_{1},\alpha_{2},\ldots,\alpha_{k-1})*\tau_{i}\) represents the truth value of the proposition \(p_{k}\). One of the most important aspect of the fault diagnosis models based on SNPS models is to reconstruct the fuzzy production rules using the framework of SNPS. In this case, the fuzzy production rules are reconstructed using the framework of FRSNPs. In order to perform this task, different types of neurons are required and the neurons in the FRSNPs model are divided into two types, i.e., proposition neuron and rule neuron. Moreover, not all the neurons are associated with truth values and these values are generally real numbers. Again, the truth values are associated with some of the proposition neurons before the reasoning algorithm is performed. The corresponding proposition neurons work as input neurons of the FRSNPs model where IEC ratios of gases are given as input. Moreover, the truth values of the neurons which do not have any value associated with them are derived using the known truth values and reasoning algorithm. The concepts of the firing mechanisms of the neurons and matrix operations are used in the reasoning algorithm introduced in [84]. Moreover, the proposed fault diagnosis model can efficiently model fuzzy production rules in a fuzzy diagnosis knowledge base and their reasoning process. It is also feasible and effective in identifying the faults in transformers. It can also handle incomplete and uncertain information received from the SCADA and efficiently process it in order to find faults. One of the major advantage of the proposed method is the graphical representation of the reasoning process which makes the reasoning process easily comprehensible. Finally, the reasoning process is parallel. So it can obtain results in much lesser time in comparison with tradition fault diagnosis models.