# Optimal Placement of Multiple Feeder Terminal Units Using Intelligent Algorithms
## 2 The Reliability Algorithm  
There are several reliability indices which are widely used by utilities, such as system average interruption frequency index (SAIFI), system average interruption duration index (SAIDI), customer average interruption duration index (CAIDI), average service unavailability index (ASAI), expected unsupplied energy (EENS), and so on. These indices assess the impact of outages on the system or customers from different perspectives, such as frequency and duration. To calculate these indices as the evaluation of the solution, the reliability of each load point is needed to be calculated first. In order to establish the mathematical model of reliability calculation, it is necessary to clarify the relationship between the fault management procedure and the FTUs. There are several details about the reliability algorithm which need to be shown. In this paper, it is considered that seven kinds of elements of distribution network are likely to fail, which are lines, transformers, fuses, SSs, tie switches, and loads. For each element, only permanent faults (which lead to sustained interruptions) are considered, while instantaneous faults are not considered. For the reasons of user outages, this paper only considers the element failures of the distribution network, and does not consider the scheduled outages. Besides, the \"three remote\" terminal units are assumed to be installed on the circuit breaker (CB) at the head of the feeder and the tie switch at the end of the feeder because these positions are very important for reliability. The Steps will be performed after the fault as follows. * The normally closed CB which is an adjacent upstream will operates because of the relay protection, and then all of the downstream load points will be de-energized. This process takes a very short time which can be ignored. * The area where exits any type C switching will be isolated preliminarily, and the power supply for some customers here can be resumed immediately instead of waiting until the fault being located accurately. Preliminary fault location can be done based on the information sent from the FTUs installed on the type B and type C switches, and then the adjacent upstream and downstream type C switches can be opened. This process takes a few minutes. * Maintenance operators will be arranged to patrol the feeder, check the display of the FTUs installed on the type A switches, and find out which feeder segment the fault exists in. The time spent on this process needs further calculation. * Maintenance operators will disconnect the adjacent upstream and downstream SSes and tie switches so that all load points outside the faulty feeder segment can be recovered. * The maintenance operators repair the faulty feeder segment, and then restore the load points connected to the faulty feeder segment after the repair. Normally, this step takes the longest time in the process of fault management. The procedure of the reliability algorithm for the distribution network with three kinds of FTUs is similar to the procedure of the traditional reliability algorithm, as shown in Figure 1. This procedure is based on failure mode and effect analysis (FMEA). However, the reliability algorithm considering three kinds of FTUs is fundamentally different from FMEA in the analysis and calculation of Steps 3 and 4. It should be noted that the reliability algorithm of this paper belongs to the analytic method. The characteristic of the analytic method is to traverse every possible fault element in the distribution network and assume that it has a fault (Steps 3 and 4). After the Step 3 and 4 of reliability algorithm are completed, the outage time and outage times of each load point caused by this fault are multiplied by the probability of this fault, which is the first sub step of Step 5. Therefore, it can be considered that the number of faults for each network element is the failure rate of this element.