## 4 Overcurrent Protection Coordination Results, Analysis and Discussion
### Protection Coordination Results in Scenario 1  
Optimal protection coordination results of the OCRs in Scenario 1 which are calculated by the GA, GSA and hybrid PSO-GSA are indicated in Table 4. In this table, \(I_{f}\) is the \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Faults at Bus 7** & **Faults at Bus 13** & **Faults at Bus 5** \\ \hline _Primary protection_: the REC Can-Thanh 36 OCR & _Primary protection_: the REC Can-Thanh 36 & _Primary protection_: the REC Can-Thanh 163 OCR \\ \hline _Backup protection_: the 471 Hao-Vo OCR & _Primary protection_: the REC Hao Vo OCR & _Backup protection_: the REC Hao-Vo OCR \\ \hline _Backup protection_: None & _Backup protection_: the 471 Hao-Vo OCR & _Backup protection_: the REC Hao-Vo OCR \\ \hline Maximum fault currents at Bus 2 are detected by the 471 Hao-Vo OCR: [25.8; 24.3; 22.3; 20.4] kA & Maximum fault currents at Bus 13 are detected by the REC Can-Thanh 163 OCR: 10.7; 10.3; 6.5] kA & Maximum fault currents at Bus 5 are detected by the REC Can-Thanh 163 OCR: [4.9; 4.4; 4.2; 2.3] kA \\ \hline \end{tabular}
\end{table} 
Table 3: Numerical fault-current calculation results are detected by the OCRs corresponding to four different operation scenarios of the real 22 kV distribution network. tripping-current threshold selected for the 50P and 50G functions of the OCRs, as referred to Section 2.3.5. \(t_{trip}^{defined}\) is the pre-defined tripping time of the 50P and 50G functions of the OCRs. Moreover, the TDS multiplier and \(A\), \(B\), and \(C\) coefficients of the 51P and 51G OC functions of the OCRs are shown in the table. It is noted that the CTI is selected to 0.30\(-\)0.35 s. For example, when a 3 ph-G fault is at Bus 2, the 471 Hao-Vo relay is the primary relay while there is not any backup relay. The tripping time of the 471 Hao-Vo relay is 0.01 s to clear the fault at Bus 2. On the other hand, when a typical 3 ph-G fault is given at the end point of the feeder (at Bus 5) as referred to a dashed line (a) in Figure 10, the REC Can-Thanh 163 OCR is the primary relay while the REC Hao-Vo relay and the 471 Hao-Vo relay are the backup relays. Based on the optimal setting parameters obtained by the ASPC system for these OCRs, their tripping time \(t_{trip}\) to clear the fault at Bus 5 are also indicated in Table 4. The results have demonstrated that the CTI constraints from Equations (3)-(5) are completely satisfied. Figure 11 shows the optimal protection characteristic curves of the OC relays in Scenario 1 of the DN. Regarding the obtained coordination results of 51P/G and 50P/G functions, Relay 1 represents the OC protection function embedded into the REC Can-Thanh 163 recloser; Relay 2 represents the OC protection function integrated into the REC Hao-Vo recloser; and Relay 3 indicates the OC protection function used to control the 471 Hao-Vo circuit breaker. When the 3 ph-G fault occurs at Bus 2, the maximum 3 ph-G fault current is 25.8 kA as shown in Table 3, so the 471 Hao-Vo OCR only takes 0.01 s to send a tripping signal to the 471 Hao-Vo CB. When the 3 ph-G fault occurs at Bus 5, the maximum 3 ph-G fault current is 4.9 kA as indicated in Table 3, so the primary operation time of the REC Can-Thanh 163 OCR is 0.01 s, the backup operation times of the REC Hao-Vo OCR and the 471 Hao-Vo OCR are 0.31 s\(-\)0.32 s and 0.61 s\(-\)0.62 s, respectively, according to results of three different algorithms as seen at the table and the left-side of Figure 11. Additionally, \(I_{trip}\) represents the tripping-current threshold of 50P/G functions of the REC Can-Thanh 163 OCR. It can be observed that the characteristic curves of 51P/G functions in the OCR are certainly followed by the exponential function. However, there is a proposed protection combination of 51P/G and 50P/G functions, the inverse-time characteristic curves of 51P/G functions are terminated at the tripping-current threshold of