# A Review of Power System Fault Diagnosis with Spiking Neural P Systems
## 2 Power System Fault Diagnosis with Spiking Neural P Systems
### Power Transmission Networks
Type 2: \(R_{i}(c_{i}):p_{1}(\theta_{1})\
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(ii) \(T\) represents the sequence time of spikes, and at each unit time the decision- making neuron \(DN\) produces a spike. In this manner, a pulse value sequence is formed and it is then recorded in the DN after \(T\) unit time. (iii) \(f_{i}\) represents a forgetting rule of the \(i\)-th DN and it is of the form \(E/\{a^{\theta_{di/T}}\rightarrow\lambda;g=0\}\). The \(g\) in the forgetting rule represents the reasoning step of the reasoning algorithm of the srSNPs, i.e., the self- updating matrix reasoning algorithm. After application of the rule \(f_{i}\), the spikes in the \(D_{i}\) are emptied and the calculation process will be reinitialized (i.e., \(g=0\)). The firing condition \(E=\{\theta^{\prime}_{di/T}\
eq\theta_{di/T}\}\) represents that the pulse value in \(D_{i}\) has changed. (b) \(C_{j}=(\theta_{cj/T},T,f_{j},A_{rj}),1\leq j\leq t\), represents the \(j\)-th condition neuron (CN) in \(M_{e}\). It also represents a protective relay or circuit breaker in the targeted power transmission network. (i) The value of \(\theta_{cj/T}\) in \(C_{j}\) is either equals to 0 or 1. It also represents the pulse value of the \(j\)-th CN at time \(T\). When the protection device corresponding to \(C_{j}\) acts, the value of \(\theta_{cj/T}\) is 1 and vice versa. (ii) \(T\) represents the sequence time of spikes, and a spike is produced by CN at each unit time. Next, a pulse value sequence is formed and after \(T\) unit time it is recorded in the CN. (iii) \(f_{j}\) represents the forgetting rule of the \(j\)-th CN and it is of the form \(E/\{a^{\theta_{cj/T}}\rightarrow\lambda;g=0\}\). After application of the rule \(f_{j}\), the spikes in \(C_{j}\) are emptied and the calculation process will be reinitialized (i.e., \(g=0\)). The firing condition \(E=\{\theta^{\prime}_{cj/T}\
eq\theta_{cj/T}\}\) represents that pulse value in \(C_{j}\) has changed. (c) \(A_{rj}\) represents an apoptosis rule in \(M_{e}\) and it is of the form \(E/\{C_{j}\}\rightarrow\{Algorithm1^{\{L\}}\}\). When \(A_{rj}\) is applied, then apoptosis rule in \(C_{j}\) is executed in order to determine whether it lives or dies. It means that CNs execute \"Apoptosis algorithm for condition neurons\" and as output the survival condition neuron (containing important information) set \(L\) is obtained. During this period, CNs and redundant information die and they do not participate in fault reasoning any further. Note that the firing condition \(E=\{g=0\cap sig_{j}=0\}\) indicates that the rule \(A_{rj}\) can be applied if and only if in the initial configuration (i.e., \(g=0\)) \(sig_{j}=0\). (3) \(\sigma_{i}=(\theta_{i},r_{i},e_{i}),1\leq i\leq p\), represents the \(i\)-th proposition neuron (PN) corresponding to a protection device or the equipment. Similarly, \(\sigma_{j}=(\delta_{j},r_{j}),1\leq j\leq q\), represents the \(j\)-th rule neuron (RN) corresponding to a fault production rule where \(p+q=m\). (a) \(\theta_{i}\) and \(\delta_{j}\) represent the pulse values (equal to 0 or 1) in proposition neuron \(\sigma_{i}\) and rule neuron \(\sigma_{j}\), respectively. (b) \(r_{i}\) represents a firing rule of \(\sigma_{i}\) with the form \(E/a^{\theta}\to a^{\theta}\), where \(E=\{a\}\) represents the firing condition. \(r_{i}\) is applicable when \(\sigma_{i}\) contains a spike. At this time, \(\sigma_{i}\) consumes a spike with pulse value \(\theta\), produce a new spike with the same pulse value, and transmits it to its postsynaptic neurons. \(r_{j}\) represents a firing rule of \(\sigma_{j}\) with the form \(E/a^{\delta}\to a^{\theta}\), where \(E=\{a\}\) is the firing condition. The firing condition represents that once \(\sigma_{j}\) contains a spike, \(r_{j}\) can be applied and \(\sigma_{j}\) consumes a spike with pulse value \(\delta\) and subsequently produces a spike with pulse value \(\beta\) (equals to 0 or 1). Next, the spike is transmitted to its postsynaptic neurons. (c) \(e_{i}\) represents a self-updating rule of the form \(E/a^{\theta}\to a^{\theta}\).