# Optimal Placement of Multiple Feeder Terminal Units Using Intelligent Algorithms
## 3 Mathematical Model
### Objective Function
#### 3.2.3 Outage Loss  
The reliability of distribution network with FTUs is the key consideration of this optimization model. In distribution network planning, there is usually a contradiction between the economic objective and the reliability objective. The reliability objective is transformed into a part of the economic objective, to formulate the original multi-objective problem into a single-objective one, and the EENS is used as the reliability evaluation index reflecting the system or load points outage.  
Considering that the importance of load points varies in the distribution network due to users' preferences, which leads to different outage losses caused by unit power shortage at different load points. Therefore, a weight coefficient [15] is introduced to measure the differences among load points, as follows:  
\[SEENS=\sum_{i\in D}{(k\alpha_{i}+\beta_{i}+\gamma_{i})}ens_{i} \tag{10}\]  
where \(SEENS\) is the EENS of the system, \(D\) is the set of all load points, \(ens_{i}\) is the EENS of the load point \(i\), and \((k\alpha_{i}+\beta_{i}+\gamma_{i})\) is the weight coefficient.  
The parameters \(\alpha\), \(\beta\), and \(\gamma\), are used to express the differences of loads in three aspects respectively, namely: life safety, economy, and particularity. \(\alpha\) and \(\beta\) belong to {1, 2, 3, 4, 5}. The larger the value is, the greater the impact of losing the load on life safety or economy is. For example, hospital load has a great impact on life safety, so the parameter \(\alpha\) of hospital load is at the highest level of 5. Parameter \(\gamma\) indicates the particularity of load. For example, military load or government department load has little impact on life safety and economy, but this kind of load is also important. Their parameter \(\gamma\) can be set as the highest level 5, which makes up the defect that parameter \(\alpha\) and \(\beta\) cannot fully reflect the importance of load. Because the loss of life safety is the most serious compared to other losses, the parameter \(\alpha\) needs to be multiplied by the factor \(k\) to increase the proportion of life safety in these three aspects.  
The calculation formula for \(ens_{i}\) is as follows:  
\[ens_{i}=P_{i}U_{i} \tag{11}\]  
where \(P_{i}\) is the average load of the load point i, \(U_{i}\) is the annual average outage time of the load point i, which can be calculated by the reliability algorithm proposed in the Section 2 of this paper.  
In this optimization model, the outage loss of distribution network can be obtained by (12), which refers to the economic loss of the grid and users caused by the outage of distribution network:  
\[C_{ens}=SEENS\times\sigma \tag{12}\]  
where \(\sigma\) is the outage loss in per unit of power shortage. In order to ensure a high reliability of the distribution network with FTUs configuration, the outage loss of this model includes not only the direct loss caused by the outage, such as income loss of the utilities, production loss of the power consumption enterprises, but also the indirect loss caused by the outage on affecting the enterprise image of utilities and power consumption enterprises, that is, \(\sigma\) is the sum of direct loss and indirect loss of the whole society in unit power shortage.