# A Review of Power System Fault Diagnosis with Spiking Neural P Systems
## 2 Power System Fault Diagnosis with Spiking Neural P Systems
### Traction Power Supply Systems  
This section discusses the use of another variant of FRSNPS, i.e., weighted fuzzy reasoning spiking neural P systems (WFRSNPs) for performing the task of fault diagnosis in traction power supply systems of high-speed railways. A new method to perform the task of fault diagnosis in traction power supply system of high-speed railways (TPSSs) was introduced in 2015 [88]. Moreover, a new variant of FRSNPS, i.e., WFRSNPs (weighted fuzzy reasoning spiking neural P system) was used to perform this task. These models can efficiently express the status information of the protective relays and circuit breakers received from the SCADA system and then perform weighted matrix-based fuzzy reasoning algorithm to obtain fault confidence levels of the faulty sections. Problem description: Whenever any fault occurs in the power systems, at first the fault section is identified by the protective relays (PRs) and then the corresponding circuit breakers (CBs) are tripped in order to isolate the fault. It ensures that the other parts of the power system work normally. The main purpose of any fault diagnosis model is to identify the faults by analyzing the protective relay and circuit breaker information received from the SCADA system. In the proposed method in [88], a fault diagnosis unit is represented by a feeding section fed by a same traction substation. It is possible because the feeding sections work independently. Furthermore, after receiving the status information of PRs and CBs from SCADA, the faults on feeder lines, buses, traction transformers and auto-transformers in TSSs (traction substations), ATPs and section posts (SPs) are identified. Now we explain how the fault diagnosis for traction power supply system of high-speed railways (TPSSs) is performed using the framework of WFRSNPs. So, at first the structure and functioning of weighted fuzzy spiking neural P systems need to be discussed. **Definition 4**. : _A WFRSN P system (WFRSNPs) [88] of degree \(m\geq 1\) is a \((m+4)\)-tuple \(\Pi=(O,\sigma_{1},\ldots,\sigma_{m},syn,IN,OUT)\), where:_  
_(1) neurons \(\sigma_{1},\ldots,\sigma_{m}\) are of the form \(\sigma_{i}=(\theta_{i},c_{i},\overrightarrow{\omega_{i}},\lambda_{i},r_{i}),1 \leq i\leq m\) where:_  
_(a) \(\theta_{i}\in[0,1]\) is a real number which represents the potential value/electric impulses of spikes in neuron \(\sigma_{i}\);_  
_(b) \(c_{i}\in[0,1]\) is a real number which represents the truth value associated with neuron \(\sigma_{i}\);_  
_(c) \(\overrightarrow{\omega_{i}}=(\omega_{i1},\ldots,\omega_{iN_{i}})\) is a vector where each element of the tuple is a real number in \((0,1]\) and \(\omega_{ij}(1\leq j\leq N_{i})\) represents the weight which is present on the jth output synapse of neuron \(\sigma_{i}\). Moreover, \(N_{i}\in\mathbb{N}\) and it represents the number of synapses from neuron \(\sigma_{i}\). The vector \(\overrightarrow{\omega_{i}}\) represents the output weight vector of neuron \(\sigma_{i}\)._  
_(d) The firing threshold of neuron \(\sigma_{i}\) is denoted by the real number \(\lambda_{i}\in[0,1)\);_  
_(e) \(r_{i}\) represents a firing /spiking rule present in \(\sigma_{i}\). These rules are of the form \(E/a^{\theta}\to a^{\theta}\), where \(\theta\), \(\beta\in[0,1]\) are real numbers. The threshold/firing condition is different from the FRSNPS models [84] and it is a combination of two conditions, i.e., \(E=\{a^{n},\theta\geq\lambda_{i}\}\). So the rule is applicable if and only if neuron \(\sigma_{i}\) receives at least \(n\) spikes from the antecedent neurons and the potential value satisfies the condition \(\theta\geq\lambda_{i}\);_  
Similarly, as in [84; 89], the neurons in WFRSNPs are also composed of two types, i.e., proposition and rule neurons. The rule neurons consist of three types, i.e., _general_, _and_, and _or_. The proposition neurons work as input neurons. The working of the \(general,and\), and _or_ rule neurons is similar to working of the rules neurons in FDSNPS [89].