# A Review of Power System Fault Diagnosis with Spiking Neural P Systems
## 2 Power System Fault Diagnosis with Spiking Neural P Systems
### Metro Traction Power Systems  
The framework for solving fault diagnosis of metro traction power systems was introduced in [82]. This task of fault diagnosis was performed by a modified variant of FRSNPS, i.e., MFRSNPs. In [82], the proposition and rule neurons are introduced to represent the information about the protective relays and circuit breakers from SCADA. Then the fuzzy reasoning algorithm based on the MFRSNPs is performed to identify the fault section in the metro traction power supply systems. Problem description: Metros are one of the most important mode of urban transport in 21 st century. Metro traction power supply systems (MTPSSs) are considered as a special variant of distribution networks with direct current (DC) power supply. Traction power supply systems are also known as the energy systems of rail transportation systems. It also ensures the safe and reliable operations in trains. The operations of MTPSSs can be impacted by failure of equipments, interruption of power services etc. So in order to keep the working of MTPSSs smooth, it is necessary to design fault diagnosis methods where the fault sections can be identified by the dispatchers efficiently and the power supply to the system is restored as soon as possible. The fault diagnosis of MTPSS is considered very challenging because of mainly two reasons, i.e., (1) two-way feeding power supply approach; (2) complex protection system caused by the DC power supply mode. In [82], a fault diagnosis approach for MTPSS was introduced based on modified FRSNPS. However, the framework of the fault diagnosis method is similar to the framework as mentioned in [89]. MFRSNPS is another variant of FRSNPS and the structure of this model is similar to FRSNPS with some exceptions. The structure and working of the MFRSNPS model is as follows. **Definition 5**. : _A MFRSN P system (MFRSNPS) [82] of degree \(m\geq 1\) is a \((m+4)\)-tuple \(\Pi=(\mathcal{O},\sigma_{1},\ldots,\sigma_{m},\textit{sym},\textit{IN}, \textit{OUT})\), where:_  
_(1) The neurons \(\sigma_{1},\ldots,\sigma_{m}\) are of the form \(\sigma_{i}=(\theta_{i},c_{i},r_{i},\lambda_{i}),1\leq i\leq m\), and_  
_(a) \(\theta_{i}\in[0,1]\) is a real number which represents the potential value of spikes in neuron \(\sigma_{i}\);_  
_(b) \(c_{i}\in[0,1]\) is a real number which represents the truth value of neuron \(\sigma_{i}\);_  
_(c) \(r_{i}\) represents a firing/ spiking rule in neuron \(\sigma_{i}\) and it is of the form \(E/a^{\theta}\to a^{\beta}\), where \(\theta,\beta\in[0,1]\) are real numbers. The firing condition is \(E=\{a^{\theta},\theta>\lambda_{i}\}\) and it means that the rule is applicable if and only if neuron \(\sigma_{i}\) receives at least \(n\) spikes as input or from the antecedent neurons and \(\theta>\lambda_{i}\) (\(\lambda_{i}\in[0,1]\) is a real number which represents the firing threshold of neuron \(\sigma_{i}\)). Otherwise, it is not applicable. Furthermore, after application of this rule in neuron \(\sigma_{i}\), a spike with potential value \(\theta\) is consumed and a spike with potential value \(\beta\) is produced._  
_(d) \(\lambda_{i}\) is a real number in [0,1) representing the firing threshold of neuron \(\sigma_{i}\);_  
The fault diagnosis rules considered for MTPSSs are different from the rules in [84; 88; 89; 129] and they are of three types:  
(1) _General Rule \(R_{i}\):_ If \(p_{j}(\theta_{j})\) THEN \(p_{k}(\theta_{k})(CF=c_{i})\), where \(p_{j}\) and \(p_{k}\) are propositions, \(c_{i}\in[0,1]\) is a real number (certainty factor of such rule \(R_{i}\)); \(\theta_{j},\theta_{k}\in[0,1]\) are real numbers (truth values of \(p_{j}\) and \(p_{k}\)); \(\theta_{k}=\theta_{j}*c_{i}\) (truth value of \(p_{k}\)).