## 4 Results
### Reduction of Power Losses in Peak Hours
#### 4.1.2 Distribution System of 69 Nodes  
In the 69-node system, when there is no type of generation by a PV system, the power losses at peak hour are 224.9519 kW. Through this power, it is possible to quantify the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & \(\mathbf{P_{loss}}\) **(kW)** & **Nodes Localization** & **Sizing** (MW) \\ \hline MSSA & 69.4077 & \(\{11,\ 18,\ 61\}\) & \(\{0.5260,\ 0.3800,\ 1.7180\}\) \\ CBGA-VSA & 69.4077 & \(\{11,\ 18,\ 61\}\) & \(\{0.5268,\ 0.3801,\ 1.7190\}\) \\ DSCA-SOCP & 69.4077 & \(\{11,\ 18,\ 61\}\) & \(\{0.5268,\ 0.3801,\ 1.7190\}\) \\ CHVSA & 69.4088 & \(\{11,\ 17,\ 61\}\) & \(\{0.5284,\ 0.3794,\ 1.7186\}\) \\ MINLP & 69.4090 & \(\{11,\ 17,\ 61\}\) & \(\{0.5300,\ 0.3800,\ 1.7200\}\) \\ KHA & 69.5730 & \(\{12,\ 22,\ 61\}\) & \(\{0.4962,\ 0.3113,\ 1.7354\}\) \\ AHA & 69.6669 & \(\{12,\ 21,\ 61\}\) & \(\{0.4710,\ 0.3120,\ 1.6890\}\) \\ QOTLBO & 71.6345 & \(\{18,\ 61,\ 63\}\) & \(\{0.5334,\ 1.1986,\ 0.5672\}\) \\ MOHTLBOGWO & 71.7400 & \(\{18,\ 61,\ 62\}\) & \(\{0.5230,\ 1.0000,\ 0.7730\}\) \\ GAMS & 72.0900 & \(\{12,\ 61,\ 64\}\) & \(\{0.8131,\ 1.4447,\ 0.2896\}\) \\ LSFSA & 77.1000 & \(\{18,\ 60,\ 65\}\) & \(\{0.4962,\ 0.3113,\ 1.7354\}\) \\ GA-IWD & 80.9100 & \(\{20,\ 61,\ 64\}\) & \(\{0.9115,\ 1.3926,\ 0.8059\}\) \\ TLDO & 81.0000 & \(\{25,\ 60,\ 63\}\) & \(\{0.7574,\ 1.0188,\ 1.1784\}\) \\ SOS & 82.0800 & \(\{57,\ 58,\ 61\}\) & \(\{0.5288,\ 0.2000,\ 1.5247\}\) \\ PSO & 83.2000 & \(\{17,\ 61,\ 63\}\) & \(\{0.9925,\ 1.1998,\ 0.7956\}\) \\ HSA & 86.6600 & \(\{63,\ 64,\ 65\}\) & \(\{1.6283,\ 0.1416,\ 0.0149\}\) \\ PBIL-PSO & 86.9000 & \(\{26,\ 61,\ 66\}\) & \(\{0.1789,\ 1.0532,\ 0.4209\}\) \\ GA & 89.0000 & \(\{21,\ 62,\ 64\}\) & \(\{0.9297,\ 1.0752,\ 0.9925\}\) \\ PMC & 91.6000 & \(\{63,\ 68,\ 69\}\) & \(\{1.2000,\ 0.0577,\ 0.3954\}\) \\ \hline DCVSA & 69.4077 & \(\{11,\ 18,\ 61\}\) & \(\{0.5268,\ 0.3801,\ 1.7190\}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Location and sizing of PV systems in the 69-node system.  
reduction in power losses of each of the methods reported by the specialized literature, as shown in Table 4.  
The results of the numerical validation shown in Table 4 state that:  
* Unlike the 33-node system, there are four methods among the most efficient for reducing power losses, with a location vector of {11, 18, 61}, of which one is the method proposed in this article. The reduction percentage of the power, the MSSA, DCVSA, CBGA-VSA, and DSCA-SOCP methods present 69.1455%, with the difference that the first proposes a total of 2.624 MW of installed power for the PV systems, while the three other systems rise to 2.6259 MW.
* The DCVSA method proposed in this article presents a reduction in power losses for the peak hour of 69.1455% with a power injection in the nodes {11, 18, 61} of {0.5268, 0.3801, 1.7190} MW. This result presents a higher reduction in power losses than 84% of the methods represented in the comparative Table 4.
* It validates the performance of the proposed algorithm concerning the presented lower reduction in power losses, which, unlike the 33-node system, is not HSA but PMC, which implies that the DCVSA is 9.8654% better.