## 3 Results
### Reliability  
Since a typical distribution system accounts for 40% of the cost to deliver power and 80% of customer reliability problems, the designing and operating of distribution systems are critical for financial success of a utility company and customer satisfaction. The reliability improvement can be obtained in term of the reduction of outage duration. Figure 8 shows the cost versus system reliability [41].  
Interruptions and outages can be studied using predictive reliability assessment tools that can predict customer reliability characteristics based on system topology and component reliability data. In order to achieve this, distribution reliability indices are calculated. Such reliability indices should be concerned with both duration and frequency of outage [42].  
The reliability of the case study is calculated by the FMEA (Failure mode and effect analysis) method. The recloser reduces the outages and improves the reliability.  
The method FMEA is based on the maintenance philosophy aimed at failure-free operation and reliability-centered maintenance (RCM). The task of RCM is to perform the analysis in such a way as to minimize the negative effects, and to help solving problems effectively or to prevent them [43].  
Table 5 shows the outage rate of the case study feeder in 2018. The total outage of the main feeder is 27.03 h that includes 15.4 h of preventive maintenance (PM) over the year.  
The recloser location is suggested to be at the half-way point of the radial feeder, assuming a uniformly distributed load. This would yield a 50% reliability improvement to customers upstream from the recloser. Similarly, locations at 1/3 and 2/3 of the feeder length should be considered if two reclosers are placed [19]. Figure 9 shows two sections with recloser relay. In case of a fault on the feeder in section B, the recloser relay operates and disconnects the faulty section from the healthy part. Therefore, the customers in section B and DG will remain in the power system. However, without the recloser relay, a fault on the feeder will disconnect the customers and DG from rest of the power system.  
Figure 8: Cost versus system reliability [42].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Cause**} & \multicolumn{3}{c}{**Number**} & \multirow{2}{*}{**FOR hrs/yr**} \\ \cline{3-4}  & & **Total** & & **Outages** \\ \hline \multirow{3}{*}{2018} & PM & 2 & 2 & 15.4 \\  & Relay Operation & 22 & 2 & 0.31 \\ \cline{1-1}  & Other Outages & 4 & 4 & 11.32 \\ \cline{1-1}  & & **Total Outages (hours)** & & 27.03 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Outage rate of the case study feeder in 2018. PM: preventive maintenance.  
The failure parameters of the case study are as follows:  
\[\lambda_{A}=2.8 r_{A}=3\] \[\lambda_{B}=1.7 r_{B}=2\]  
where \(\lambda\) is the failure rate on the feeder, and \(r\) is the failure duration of the feeder.  
Considering outage times except for PM times, the average duration of outages of the feeder is obtained:  
\[r_{A}=\frac{\sum\limits_{m=1}^{n}\left(\lambda_{m}\times r_{m}\right)}{\sum \limits_{m=1}^{n}\lambda_{m}}=\frac{2.8\times 3+1.7\times 2}{4.5}=2.62=r_{B}\]  
For the whole feeder, the result is the same.  
After installing the relay within 0.4 h, the operation averages of outages in A and B paths are presented as follows:  
\[r_{A}=\frac{\sum\limits_{m=1}^{n}\left(\lambda_{m}\times r_{m}\right)}{\sum \limits_{m=1}^{n}\lambda_{m}}=\frac{2.8\times 0.4+2.2\times 3}{4.5}=1.71\]  
\[r_{B}=\frac{\sum\limits_{m=1}^{n}\left(\lambda_{m}\times r_{m}\right)}{\sum \limits_{m=1}^{n}\lambda_{m}}=\frac{2.8\times 3+1.7\times 2}{4.5}=2.62 \tag{8}\]  
The average duration of power outages (hours) in section A decreases from 2.62 to 1.71 h.  
Figure 9: Reliability sections of the case study.