# A Review of Power System Fault Diagnosis with Spiking Neural P Systems
## 2 Power System Fault Diagnosis with Spiking Neural P Systems
### Fault Lines Detection  
In [85], a fault diagnosis method based on FRSNPS model was introduced to solve the problem of detecting fault lines in a small current grounding systems. The authors analyzed six features of current/voltage signals in a small current grounding system. Furthermore, the analysis was done by considering transient and steady components. Moreover, a fault measure is considered and it is further used to quantify that a line has faults. Next, the idea of information gain degree was introduced in order to understand the importance of six features of current/voltage signals. Then in order to reduce the features, the concept of rough set theory was applied and it was followed by construction of fault line detection models based on the framework of FRSNPS.  
Problem description: The fault diagnosis approach in [85] is considered for a 110 kV/35 kV distribution network with 6 feeders. At any time a single-phase-to-ground fault can occur in the distribution network and during this time the fault can occur in any of the 6 lines, i.e., lines 1-6 or in the bus. This fault affects the safe and stable operation of the distribution network. Moreover, the faults compromise the security of the system. So it is necessary to identify the faults in the distribution networks as soon as possible.  
The fault line detection method proposed in [85] for a small current grounding system are divided into four processes, i.e., (1) feature analysis, (2) fault measure calculation, (3) feature information fusion and (4) fault line detection model construction. The framework of this method consists of zero sequence current/voltage signals, transient and steady component signal features, fault measures, information gain degree, rough set theory and fault line detection model with rFRSN P systems. Furthermore, the fault line detection method is based on fuzzy reasoning spiking neural P systems with real numbers (rFRSNPs).  
Now we discuss the fault diagnosis process in detail. We start with discussing the structure and functioning of rFRSNPs. rFRSNPs models have similar structure as FRSNPS models and can be represented mathematically in the following manner.  
**Definition 9**.: _An rFRSN P system [87; 90] of degree \(m\geq 1\) is a \((m+4)\)-tuple \(\Pi=(O,\sigma_{1},\ldots,\sigma_{m},\)\(syn,\)\(IN,OUT)\), where:_  
_(2) The neurons \(\sigma_{1},\ldots,\sigma_{m}\) are of the form \(\sigma_{i}=(\theta_{i},c_{i},r_{i}),1\leq i\leq m\), where:_  
_(a) \(\theta_{i}\in[0,1]\) is a real number and it represents the potential value of spikes (i.e., value of electrical impulses) contained in neuron \(\sigma_{i}\);_  
_(b) \(c_{i}\in[0,1]\) is a real number and it represents the fuzzy truth value corresponding to neuron \(\sigma_{i}\);_  
_and_  
_(c) \(r_{i}\) represents the firing /spiking rule in neuron \(\sigma_{i}\) and it is of the form \(E/a^{\theta}\to a^{\theta}\)where \(E\) is the firing condition and \(\theta,\beta\in[0,1]\) are real numbers;_The working of the rFRSNPS and FRSNPS [84] is similar. So in this section we do not explain it in detail. Moreover, like the FRSNPS models [84], rFRSNPS models contain two types of neurons, i.e., proposition neurons and rule neurons. The fuzzy production rules in the framework of rFRSNPS can be expressed in the similar manner as shown in Section 2.1. Since we have already described the construction of these rules in detail, we skip their explanation in this section.