# A Review of Power System Fault Diagnosis with Spiking Neural P Systems
## 2 Power System Fault Diagnosis with Spiking Neural P Systems
### Transformers
Another fault diagnosis method of power transformer based on DGA and FRSNPS is introduced in [128]. The FRSNPS model and the reasoning algorithm used in [128] are same as [84]. In this model, the faults in transformers are identified using linguistic variables, membership functions with low, medium and high descriptions for each gas signature and the inference rule base. In fact, the linguistic terms in [128] are very low (VL), low (L), medium (M), high (H), very high (VH), very low (VL). Similarly, little high, low, rather high, too high, high, little low, rather low and too high are the linguistic terms in [84]. In [84], the faults are divided into mainly four types, i.e., General overheating fault occurs, Serious overheating fault occurs, The partial discharge occurs, The spark discharge occurs. Moreover, the faults are Low energy discharge, High energy discharge, Partial discharge, Thermal faults \(T<300\)\({}^{\circ}\)C, Thermal faults \(300\)\({}^{\circ}\)C \(<T<700\)\({}^{\circ}\)C, Thermal faults \(T>700\)\({}^{\circ}\)C. In order to identify these faults, at first the judgements are translated into numerical expression by fuzzy numbers with the help of membership functions. The fault types interpretation of DGA and linguistic terms (L.T) are different from the proposed model in [84]. Next, four gas ratio (IEC 60599) signature is given as input to the FRSNPS and performance of the method is analyzed based on this method. From the test case results, it is inferred that the proposed method in [128], significantly improves the diagnosis accuracy of the power transformer. A novel method of identifying faults for oil-immersed power transformers using the framework of SNPS is recently introduced in [91]. In this method, a new variant of SNPS, i.e., learning spiking neural P system (LSNPS) is introduced to perform this task. More specifically, the fault diagnosis method in [91] is based on LSNPs with belief AdaBoost and it is used for fault diagnosis in oil-immersed power transformer. Now in order to explain the diagnosis process, at first the structure and working of the LSNPs with AdaBoost model are explained. LSNPs models have a feedforward network structure and can be mathematically formulated in the following manner. Since the sets \(O,IN,OUT,syn\) represent the same as in [84]. So we will not explain them in detail. A LSN P system (LSNPS) [91] is a construct \(\Pi=(O,\{\sigma^{1}_{p1},\ldots,\sigma^{1}_{pk},\sigma^{3}_{p1},\sigma^{5}_{p1 }\},\)\(\{\sigma^{2}_{r1},\ldots,\sigma^{2}_{m},\sigma^{4}_{r1},\ldots,\sigma^{4}_{rn}\},\)\(syn,IN,OUT\}\) where  
(1) The proposition neurons have the form \(\sigma^{h}_{pi}=\{0,w^{h}_{ij},\lambda^{h}_{i},r^{h}_{i}\}\), where \(h\) and \(i\) denote the label of the layers in the network and the label of proposition neurons respectively. (a) 0 denotes that the potential value is zero in all proposition neurons. (b) The synapses connecting the proposition neurons and rule neurons are associated with weights \(w^{1}_{ij}=rand(0,1),i=1,\ldots,k,j=1,\ldots,n\) and \(w^{3}_{ij}=1,j=1,\ldots,n\). The learning strategy associated with this model is to find a set of weights with the highest accuracy rate. (c) \(r^{h}_{i}\) represents the fring/spiking rule and it is of the form \(r^{1}_{i}:E^{1}/a^{\alpha_{i}}\to a^{\alpha_{i}},i=1,\ldots,k\), where \(E^{1}=\{\alpha_{i}\geq\lambda^{1}_{i}\}\), and \(\lambda^{1}_{i}=0,i=1,\ldots,k\). The last neuron is called as bias neuron and \(\alpha_{k}=1\). The fring/spiking rule present in the third layer has the form \(r^{3}_{1}:E^{3}/a^{p}\to a^{p}\), where \(E^{3}=\{p\geq\lambda^{1}_{1}\},\lambda^{3}_{1}=0\) and \(p=\theta_{1}\vee\theta_{2}\vee\ldots\wedge\theta_{n}\). The firing rule present in the last layer is of the form \(r^{5}_{1}:a\to a\). (2) The rule neurons are of the form \(\sigma^{k}_{rj}=\{0,1,1,r^{k}_{j},r^{k}_{j}\}\), where \(k\) and \(j\) denote the label of the layers in the network and the label of rule neurons respectively. (a) The potential value of all rule neurons is \(0\).