# Improved Temporal Fuzzy Reasoning Spiking Neural P Systems for Power System Fault Diagnosis
## 2 ITFRSNP System
### Fault Case Analysis  
#### 4.1.1 Case 1 (Bus Fault)  
Considering Figure 5 as an example, a fault occurs at B18. Bp18 operates, and then CB1817 and CB1803 trip. The alarm messages are briefly described as Bp18(0), CB1817(35), and CB1803(40), where the brackets are the operation times, the first alarm message is the zero moment, and the unit is ms. The fault diagnosis process is as follows:  
1. \(CBS=\{\)CB1817, CB1803\(\}\) can be obtained from the alarm message. Traverse \(CBS\) and search for suspected faulty components. There are a subset \(COM_{1817}=\{\)B18, L1817, B17, L1727, L1617\(\}\), a subset \(COM_{1803}=\{\)B18, L0318, B03, L0203, L0304\(\}\), and a total set \(COMS=\{\)B18\(\}\).
2. B18 is selected for fault diagnosis. CB1803 connected to B18 is selected for the search, and its corresponding bus PR is Bp18, respectively. According to the alarm messages, the spike values of \(\sigma_{p1}\), \(\sigma_{p2}\), \(\sigma_{p4}\), and \(\sigma_{p5}\) are 0.9833, 0.85, 0.8564, and 0, respectively, and their time-point constraints are [40, 40], [40, 40], [0, 0], and \(\varnothing\), respectively.
3. The adjacent line corresponding to CB0318 is L0318, the CB at the far end is CB0318, and the remote backup PR is Lp0318s. Because the alarm information is not received from the above PRs and CBs, \(n_{\text{CEBPR},\text{c}}=0\), \(n_{\text{CEBPR},\text{c}}=1\), \(T_{\text{CEBPR}}=\varnothing\), \(n_{\text{rPR},\text{c}}=0\), \(n_{\text{rPR},\text{c}}=1\), and \(T_{\text{rPR}}=\varnothing\). Substituting them into (21) to obtain the spike values and time-point constraints for \(\sigma_{p3}\) and \(\sigma_{p6}\) are 0.2 and \(\varnothing\), respectively.
4. \(\alpha_{p(11)}^{0}\) and \(T_{p(11)}^{0}\) of the fault diagnosis model for the CB1803 subnet are as follows: \[\left\{\begin{array}{l}\mathbf{\alpha}_{p(11)}^{0}=[0.9833,0.85,0.2,0.8564,0,0.2,0,0,0]^{\text{T}}\\ \mathbf{T}_{p(11)}^{0}=[[40,40],[40,40],\varnothing,[0,0],\varnothing,\varnothing, \varnothing,\varnothing,\varnothing]^{\text{T}}\end{array}\right.\] (30)
5. \(\mathbf{\alpha}_{p(11)}^{0}\), \(\mathbf{T}_{p(11)}^{0}\) and model parameters are imported into the reasoning algorithm, the diagnosis results of the CB1803 subnet are \(\alpha_{p10(11)}=0.9199\), \(T_{p10(11)}=[-40,-10]\).
6. Similarly, \(\mathbf{\alpha}_{p(12)}^{0}\) and \(\mathbf{T}_{p(11)}^{0}\) of the fault diagnosis model for the CB1817 subnet are as follows: \[\left\{\begin{array}{l}\mathbf{\alpha}_{p(12)}^{0}=[0.9833,0.85,0.2,0.8564,0,0.2,0,0,0]^{\text{T}}\\ \mathbf{T}_{p(12)}^{0}=[[35,35],[35,35],\varnothing,[0,0],\varnothing,\varnothing, \varnothing,\varnothing,\varnothing]^{\text{T}}\end{array}\right.\] (31)
7. Similarly, the diagnosis results for the CB1817 subnet are \(\alpha_{p10(12)}=0.9199\) and \(T_{p10(12)}=[-40,-10]\).
8. \(\alpha_{p10(11)}\), \(T_{p10(11)}\), \(\alpha_{p10(12)}\) and \(T_{p10(12)}\) are substituted into (28), and the diagnosis results \(\alpha_{(1)}=0.9199\) and \(T_{(1)}=[-40,-10]\) for B18. \(\alpha_{(1)}\) and \(T_{(1)}\) are substituted into (29), and the measured value of B18 is \(\eta_{(1)}=0.9439\), which is greater than 0.6. Therefore, B18 is a faulty component.  
This case demonstrates that the proposed method can diagnose bus faults and their corresponding time-point constraints.