# Optimal Placement of Multiple Feeder Terminal Units Using Intelligent Algorithms
## 5 Case Study and Discussion
### Comparative Analysis of Configuration Schemes  
In this Section, the following two points need to be verified:  
Point 1: the configuration scheme by the proposed model with the reliability constraints is better than the current planning guideline configuration scheme of \"three remote\" terminal units for all Sses. Point 2: The LCC-based model for FTUs configuration optimization problem is more superior than the models built from other perspectives. Therefore, four schemes are compared in this section, including:  
Scheme 1: The proposed optimal placement scheme and multiple evaluation indexes. Scheme 2: The suboptimal solution of the model and method proposed in this paper. Scheme 3: The scheme that all SSs are equipped with \"three remote\" terminal units. The reliability indices are calculated by the reliability algorithm under the condition of DA, which is elaborated in Section 2. Scheme 4: The model with the minimum initial investment cost as the objective function and the reliability constraints consistent with scheme 1. Scheme 5: The model with the minimum sum of initial investment cost, maintenance cost and outage loss as the objective function, which also needs to meet the reliability constraints as same as scheme 1. According to the algorithm performance in Section 5.2, the DPSO is used to solve the optimization models of scheme 1, 2, 4, and 5. After running the DPSO 10 times, the FTUs configuration corresponding to the minimum value of its objective function is taken as the final solution of each scheme. In addition, the number of particles is 50, the number of iterations is 50, the inertia weight is 2, the cognitive acceleration constant and cooperative acceleration constant are both 2. The placement of FTUs in scheme 1, 2, 4, 5 is illustrated in Figure 6. The evaluation indexes of each scheme's final calculation result are summarized in Table 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Intelligent Algorithm** & \(t_{\text{com}}\)/s & \(n_{\text{com}}\) & **D** & **SD** & **RSD** \\ \hline ACO & 0.0726 & 24.2 & 0.5691 & 0.7544 & 0.1812 \\ GA & 0.9761 & 18.1 & 1.2324 & 1.1101 & 0.2682 \\ DPSO & 0.0378 & 10.7 & 0.2628 & 0.5126 & 0.1240 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimization performance results of three algorithms. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Intelligent Algorithm** & \(LCC\)/ & \(C_{\text{im}}\)/ & \(C_{\text{m}}\)/ & \(C_{\text{c}ns}\)/ & **SAIDI/** & **SAIFI/** & **CAIDI/** & **ASAI/** \\
**GA** & **k\$** & **k\$** & **k\$** & **k\$** & **(hr/yr.cust)** & **(times/yr.cust)** & **(hr/yr.cust)** & **(hr/yr.cust)** & **\%** \\ \hline ACO & 588.5416 & 32.31 & 3.231 & 108.1784 & 0.4740 & 0.1462 & 3.2432 & 99.9946 \\ GA & 585.1960 & 28.42 & 2.842 & 108.6759 & 0.4761 & 0.1462 & 3.2574 & 99.9946 \\ DPSO & 584.4979 & 29.27 & 2.927 & 108.2814 & 0.4747 & 0.1462 & 3.2483 & 99.9946 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation results of three algorithms. Figure 6: The placement of multiple FTUs in scheme 1, 2, 4, 5: (**a**) The placement of multiple FTUs in scheme 1; (**b**) The placement of multiple FTUs in scheme 2; (**c**) The placement of multiple FTUs in scheme 4; (**d**) The placement of multiple FTUs in scheme 5. The most satisfactory FTUs configuration in scheme 1 shown in Figure 6 is only equipped with \"three remote\" terminal units, without \"one remote\" terminal units and \"two remote\" terminal units. However, it cannot be explained that it is meaningless to model and solve the placement problem of multiple FTUs. Because this result is closely related to the values of original parameters taken in the test case (such as the purchase prices of the FTUs, the outage loss per unit electricity shortage, several troubleshooting times related to the management level of the utilities, failure rate and repair time of all elements in the distribution network, etc.).