# Optimal Placement of Multiple Feeder Terminal Units Using Intelligent Algorithms
## 5 Case Study and Discussion
### Test System Structure and Parameters  
There are 26 load points in the system. The number of users in each load point is set as 50, and the coefficient of life safety parameter is set as 3. The type and average load of each load point are shown in Table 1. The values of parameters \(\alpha\), \(\beta\), and \(\gamma\) of various load points are listed in Table 2. The failure rate and average repair time of each element are provided in Table 3, and the unit of failure rate for the line is times/yr.km. The length of each branch can refer to [22]. According to the comprehensive cost table of distribution network engineering of Guangdong Power Grid provided by Guangdong Power Grid Planning and Research Centre and the internal report of CSG, the price of a \"one remote\" terminal unit is $706.95, a \"two remote\" terminal unit is $3534.77, a \"three remote\" terminal unit is $4241.72, and the social and economic loss caused by power shortage of distribution network is 3.25 $/kWh. The annual cost of maintaining the FTUs accounts for 10% of the initial investment, the discount rate is 10%, and the planning period is 5 years.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Load Point No.** & **Load Point Type** & **Average Load/kW** \\ \hline
1-2, 20, 21 & Resident load & 426.9 \\
4, 6, 15, 25 & Resident load & 417.1 \\
9-11, 13, 26 & Resident load & 321.3 \\
5, 8, 17, 23 & Industrial load & 624.7 \\
3 & Government load & 624.7 \\
7, 14, 18, 22, 24 & Commercial load & 408.9 \\
12, 16, 19 & Office load & 378.6 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The type and average load of each load point.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Load Point Type** & \(\alpha\) & \(\beta\) & \(\gamma\) \\ \hline Large hospital load & 5 & 2 & 1 \\ Business center load & 1 & 2 & 1 \\ Large factory load & 1 & 5 & 1 \\ Governmental agency load & 1 & 1 & 4 \\ Communication enterprise load & 1 & 4 & 2 \\ Railway system load & 2 & 2 & 2 \\ Scientific research institution load & 1 & 1 & 3 \\ Other loads & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The values of parameters \(\alpha\), \(\beta\) and \(\gamma\) of various load points.  
Figure 4: The Roy Billinton test system (RBTS) BUS 5 system.  
It can be found from Figure 5 that GA has the worst stability with the largest difference of 10 runs. So that multiple simulation is recommended if GA is used for FTUs placement optimization. Although the stability of ACO is better than that of GA, ACO is easy to fall into local optimal solution, which is a serious drawback especially in such problems. DPSO has the best performance, with the best stability, and the closest results to the global optimal solution.  
It can be seen more clearly from Table 6 that DPSO is the most stable algorithm, followed by ACO and GA. In terms of convergence speed, DPSO completes the convergence process in about 10 generations on average; ACO takes the most iterations while consumes the same solution time as DPSO, which is less than 0.1 seconds; by contrast, GA consumes the longest convergence time and has a moderate iteration number.  
To sum up, DPSO is the most suitable method for the proposed FTUs placement optimization.