## 3 Results
### Short-Circuit Resistances and Load Losses for Each Phase Harmonic Current  
Table 5 summarizes the values of the short-circuit resistances \(R_{cc,h}\), calculated using Equation (20) for the first 25 harmonics of the secondary currents at 6:55 a.m. and 8:55 p.m. (Table 3), using the values of the nominal short-circuit resistances, \(R_{DCN}=2.622\) m\(\Omega\), \(R_{ECN}=0.089\) m\(\Omega\), and \(R_{OSLN}=0.178\) m\(\Omega\), obtained by substituting the nominal values of the transformer losses, indicated in Table 1, on Equation (14). ### Short-Circuit Resistances and Load Losses for Each Phase Harmonic Current  
Table 5 summarizes the values of the short-circuit resistances \(R_{cc,h}\), calculated using Equation (20) for the first 25 harmonics of the secondary currents at 6:55 a.m. and 8:55 p.m. (Table 3), using the values of the nominal short-circuit resistances, \(R_{DCN}=2.622\) m\(\Omega\), \(R_{ECN}=0.089\) m\(\Omega\), and \(R_{OSLN}=0.178\) m\(\Omega\), obtained by substituting the nominal values of the transformer losses, indicated in Table 1, on Equation (14). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**Load Losses (W)**} & \multicolumn{6}{c}{**6:55 a.m. (Low Consumption)**} & \multicolumn{6}{c}{**8:55 p.m. (High Consumption)**} \\ \cline{2-10}  & **A-Phase** & **B-Phase** & **C-Phase** & **Total** & **A-Phase** & **B-Phase** & **C-Phase** & **Total** \\ \hline \(P_{cc,t}\), \(p_{cc}\) & 70.450 & 109.158 & 77.548 & 257.156 & 463.131 & 444.443 & 495.611 & 1403.186 \\ \hline \(P_{cc,t,t}\), \(P_{cc,t}\) & 33.887 & 63.598 & 34.456 & 131.941 & 432.139 & 393.279 & 455.172 & 1280.590 \\ \hline \(P_{cc,t,t_{x}}\), \(P_{cc,H}\) & 36.563 & 45.560 & 43.091 & 125.214 & 30.992 & 51.164 & 40.439 & 122.596 \\ \hline \end{tabular}
\end{table} 
Table 4: Transformer’s load losses according to IEEE Standard C57.110-2018 at 6:55 a.m. and 8:55 p.m. on 10 November 2022. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multirow{2}{*}{**Freq. (Hz)**} & \multirow{2}{*}{\ \begin{tabular}{c} **Harmon. Order** \\ **(h)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **\(R_{cch}\)** \\ **(mf)** \\ \end{tabular}  } & \multicolumn{6}{c}{**6:55 a.m. (Low Consumption)**} & \multicolumn{6}{c}{**8:55 p.m. (High Consumption)**} \\ \cline{3-11}  & & & **A-Phase** & **B-Phase** & **C-  
Likewise, Table 5 shows the values of the losses corresponding to each harmonic (\(P_{cc}(h_{z})\)) and each phase (\(P_{cc,z}\)), obtained with the use of the values of the short-circuit resistances \(R_{cc,h}\) in Equations (18) and (19), respectively. From the results indicated in Table 5, the following findings about the short-circuit resistances of each harmonic (\(R_{cc,h}\)) are verified:  
1. They are characteristic parameters of each transformer, since they have the same values for each frequency, regardless of the load consumptions;
2. Their values increase strongly with the frequencies of the harmonics of the currents;
3. They identify the losses caused by harmonic currents in each phase (\(P_{cc}(h_{z})\)), since the sum of losses obtained with the short-circuit resistances (\(R_{cc,h}\)) determine the same values of total (\(P_{cc}\)) and phase (\(P_{cc,z}\)) load losses, and their components for the fundamental (\(P_{cc,1},~{}P_{cc,12}\)) and non-fundamental (\(P_{cc,H},~{}P_{cc,H_{2}}\)) frequencies than those resulting from applying IEEE Standard C57.110-2018, indicated in Table 4.  
Short-Circuit Resistances and Load Losses of Each Phase at the Fundamental and Non-Fundamental Frequencies  
Table 6 summarizes the values of the effective short-circuit resistances (\(R_{cc,z}\)) and the load losses (\(P_{cc,z}\)) of each phase for the two analyzed consumption periods (6:55 a.m. and 8:55 p.m.).