## 4 Results and Discussion  
The efficiency of the proposed method is assessed by simulation in MATLAB \(\copyright\)version R2015 on the networks of variable sizes and complexities, i.e., IEEE 34 (\(N_{1}\)) and 85 (\(N_{2}\)) nodes RDNs. The computer system used for simulation of the proposed method has Intel(c)CoreTM 3-2350M CPU with frequency of 2.30 GHz and the RAM of 4 GB. System  
Figure 3: Flow chart for the proposed method. data are taken from [32]. The minimization problem given in (1) is solved through the step given in Section 3.3. To test the accuracy and efficiency of the proposed method, static and seasonal load profiles (where load varies in different seasons) are considered, termed as case study 1 (\(CS_{1}\)) and case study 2 (\(CS_{2}\)), respectively. In \(CS_{1}\), total active and reactive loads for \(N_{1}\) is 4636 kW and 2873 kvar, while for \(N_{2}\), 2514.3 kW and 2564.6 kvar, respectively throughout the year. The load data for both RDNs, according to \(CS_{2}\), is given in Table 1. Other parameters used are: \(C_{p}=168\$/\)kWyear, \(C_{q}=25\$/\)kvaryear, \(C_{c}=5\$/\)kvar, and capacitor life expectancy = 10 years. Figures 4 and 5 explain the load demand for \(N_{1}\) and \(N_{2}\) for \(CS_{2}\), respectively. Furthermore, two use cases are considered according to the selection of capacitor values. In use case 1, the capacitor sizes are taken as continuous variables, as calculated by the algorithm, irrespective of the market availability. In use case 2, the capacitor sizes are taken as discrete values in near proximity of the calculated values by the algorithm. This is done in order to select the capacitors available in the market. For both use cases, the capacitor values correspond to the reactive power supply range from 150 kvar to 1200 kvar. However, in use case 2, the capacitor values are incremented in steps of 150 kvar in order to get market available sizes. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Months** & \multicolumn{2}{c}{**Active Load (kW)**} & \multicolumn{2}{c}{**Reactive Load (kvar)**} \\ \hline
**Network** & \(\mathbf{N_{1}}\) & \(\mathbf{N_{2}}\) & \(\mathbf{N_{1}}\) & \(\mathbf{N_{2}}\) \\ \hline January–March & 4636 & 2514 & 2873 & 2564 \\ April–June & 8345 & 4525 & 5172 & 4616 \\ July–September & 6491 & 3520 & 4022 & 3590 \\ October–December & 6027 & 3268 & 2061 & 3333 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Seasonal load profile for both networks. Figure 4: Seasonal load profile for \(N_{1}\). Figure 5: Seasonal load profile for \(N_{2}\). optimization algorithm is only allowed to select specified (commercially available) values of capacitors. It is obvious from Table 2 that the proposed method provided better results than PGSA [33], BFA [36], and GA [35]. The results of \(N_{2}\) are presented in Table 3 for \(CS_{1}\), which are compared with other algorithms. As shown in Table 3, for use case 1, optimal placement of the capacitor is done at locations 27, 29, 30, 64, 51, 50, 67, 19, 46, and 80, with a 2134.5 kvar injection in the system. Similarly, for use case 2, capacitors are placed at locations 25, 48, 51, 64, 18, 68, 12, 61, and 44, with a 2250 kvar injection. The placement of these capacitors in \(N_{2}\) minimized the active power loss from 319 to 140.8943 kW, which is a 55.85% reduction for use case 1, and to 145.20 kW for use case 2, which is a 54.504% reduction. Likewise, for both use cases of capacitors, reactive power losses reduced from 182 to 80.7297 kvar (55.68% reduction) for use case 1 and to 82.65 kvar (54.625% reduction) for use case 2, respectively. Comparative to other algorithms considered, the proposed method provides better results. After optimizing the system with PSO, the total annual cost of the system is reduced to USD 23,670/year from USD 53,619/year in use case 1 with net savings of USD 29,950/year. For use case 2, the total annual cost of system is reduced to USD 24,394/year with savings of USD 29,224/year.