## 4 Results and Discussion
### 34 and 85 Node RDNs - \(Cs_{2}\)  
For this case study, two scenarios are considered. **Scenario 1 (\(S_{1}\)):** optimization is conducted for the period of January to March. Capacitor locations and sizes are determined. After an increase in load, no variations in capacitor size and location are made. Based on these sizes and locations, the results are analyzed for coming seasons. **Scenario 2 (\(S_{2}\)):** optimization is conducted for the same duration of January to March. Capacitor locations and sizes are determined. After variations in loads in coming seasons, optimal sizes of capacitors are determined, and results are compared with those of \(S_{1}\). Tables 4 and 5 contain the data for uncompensated \(N_{1}\) and \(N_{2}\) for \(CS_{2}\), respectively. For \(N_{1}\), results of seasonal load are displayed in Table 6 according to \(S_{1}\). For the January to March season, optimal capacitor placement is performed and kept for other forthcoming seasons. For use case 1, capacitors of sizes 150, 481, 836, and 539 are placed at locations 19, 21, 24, and 8. The active power loss is reduced to 158 from 221 kW--a 28.52% reduction. Similarly, reactive power loss has been reduced to 43 from 65.1007 kvar, i.e., a 33% reduction. Capacitor sizes for use case 2 are 300, 300, 600, and 600, placed at locations 17, 20, 23, and 8. The active power losses are reduced to 160 from 221 kW, i.e., a 27.88% reduction. Similarly, reactive power loss was reduced to 43 from 65.23 kvar, i.e., 30.52% reduction. For April-June, the load is increased to 1.8 times of the January-March load. With an increase in load, the losses also increased as shown in Table 4. Keeping sizes and locations of capacitors fixed at the January-March season results, it is observed that the active power loss reduction is 8% for use case 1 and 7.7% for use case 2. Similarly, reactive power loss reduction is 9.7% for use case 1 and 8.7% for use case 2. Consequently, the annual cost reduction is USD 120,883/year in use case 1. These results highlight the need for optimal capacitor placement in each season according to the respective load. Based on this observation, the results are improved in \(S_{2}\). The outcomes of the seasonal load profile for \(N_{1}\) are detailed in the Table 7 for \(S_{2}\). The increasing load alternatively increased system power losses, requiring optimization at each season. After the load change, according to the season, the results improved significantly if the capacitor placement was re-analyzed for updated network conditions. For example, when the load increased to 1.8 times of January-March in the second quarter, the losses increased to 782.1081 from 221.67 kW and to 229.309 kvar from 65.1007 kvar. To achieve better loss reduction and, hence, better annual savings, the sizes of the capacitors need to be updated only while installing them at similar locations, as in \(S_{1}\). The updated sizes are now 160, 1134, 1200, and 853, injecting the total of 3347 kvar. It can be seen in Table 7 that the active power loss is reduced to 28.99%, which is only 8% in \(S_{1}\). Similarly, a reduction in  
Figure 9: Line flow for \(N_{2}\) in \(CS_{1}\). reactive power loss is 28.75%, which is 7.7% in \(S_{1}\) for use case 1. Likewise, results of use case 2 for \(S_{2}\) are better than that of \(S_{1}\), as shown in Table 7. Net savings for use case \(1\) is USD 10,511 and USD 38,101/year for \(S_{1}\) and \(S_{2}\), respectively. The same procedure is done for \(N_{2}\). The \(CS_{2}\) results of \(N_{2}\) for each scenario are shown in Tables 8 and 9, respectively. In \(S_{1}\), the annual cost is significantly reduced by placing optimal capacitors of sizes 150, 150, 203, 439, 295, 150,150, 150,161, and 286 at optimal locations (27, 29, 30, 64, 51, 50, 67, 19, 46, and 80). The active and reactive power losses are reduced to 55.85% and 55.68% for use case 1, respectively.