# Optimal Placement of Multiple Feeder Terminal Units Using Intelligent Algorithms
## 2 The Reliability Algorithm
### Failure Mode and Effect Analysis  
In this Section, the main difference between the proposed reliability algorithm and the traditional reliability algorithm is the criterion of outage time at each load point. For description convenience, the main feeder point (MFP) of an element \(j\) is defined as: the intersection point of the main feeder and branch feeder on the minimum path between element \(j\) and power point. If element \(j\) is a component of the main feeder, then the MFP of element \(j\) is the first node of element \(j\). The MFP definition of a load point \(i\) is similar to that of element \(j\). Then the associated path (AP) between element \(j\) and load point \(i\) is defined as: the feeder segment between the MFP of element \(j\) and the MFP of load point \(i\).  
The outage time \(T_{ij}\) of a load point \(i\) caused by the failure of an element \(j\) is related to the type of the FTUs installed on the switching elements in the AP between faulty element \(j\) and load point \(i\). In the following, the outage time \(T_{ij}\) of a load point \(i\) will be discussed by classification.  
Figure 3 is a classification diagram for the outage time \(T_{ij}\) analysis.  
**Circumstance A:** Faulty element \(j\) is on the branch line, and fuse or CB is installed at the outlet of the branch line.  
**A1.**: Element \(j\) and load point \(i\) are on the same branch line. Load point \(i\) cannot be isolated from element \(j\) and be restored, so the outage time of load point \(i\) is \(T_{ij}=t_{1}+t_{2}+t_{3}\).
**A2.**: Element \(j\) and load point \(i\) are not on the same branch line. Element \(j\)'s failure can be quickly isolated by the fuse or the CB and will not result in outage at load point \(i\), so \(T_{ij}=0\).
**Circumstance B:** Faulty element \(j\) is on the main feeder, or on the branch line without fuse or CB at the outlet of the branch line.  
In this circumstance, the fault impact of element \(j\) depends on the switch types on the AP between element \(j\) and load point \(i\).  
**B1.**: There is one or more type C switch on the AP.  
**B11.**: The MFP of load point \(i\) is upstream to that of element \(j\), or there is a tie switch at the end of the feeder which enables the load points to be transferred to another feeder. Then \(T_{ij}\)=\(t_{1}\) because load point \(i\) can be restored by controlling the adjacent upstream and downstream type C switches and the tie switch remotely. As the example shows in Figure 3, switches S2, S7, and S8 are operated remotely when a fault occurs in segment EF, and the outage time of load points LD1 and LD7 is \(t_{1}\).
**B12.**: The MFP of load point \(i\) is downstream to that of element \(j\), and there is not any tie switch at the end of the feeder. The load point \(i\) cannot be remotely isolated from the fault or be restored before the fault repair, \(T_{ij}=t_{1}+t_{2}+t_{3}\).
**B2.**: There is no type C switch on the AP, but there are type A or type B or type D switches.
**B21.**: The MFP of load point \(i\) is upstream to that of element \(j\), or there is a tie switch at the end of the feeder. \(T_{ij}\)= \(t_{1}+t_{2}\) because load point \(i\) can be restored after manual fault location and isolation. In Figure 3, after isolating LD1 and LD7 from the fault remotely, fault location for segment CG is carried out, and finally switches S5 and S6 are operated. Then, load points LD2-LD4 and LD6 regains electricity services. Therefore, their outage time is \(t_{1}\) + \(t_{2}\).
**B22.**: The MFP of load point \(i\) is downstream to that of element \(j\) without any tie switch at the end of the feeder, \(T_{ij}=t_{1}+t_{2}+t_{3}\).
**B3.**: There is no switch on the AP. It means that element \(j\) and load point \(i\) both belong to the MFS, and element \(j\) cannot be restored until element \(j\) is repaired, \(T_{ij}\)= \(t_{1}+t_{2}+t_{3}\). LD5 in the case of Figure 3 is an example of such sub scenario.