## 3 Results
### Short-Circuit Resistances and Load Losses for Each Phase Harmonic Current
The values of \(R_{cc,z}\) have been obtained by substituting into Equation (25) the RMS values of the currents of each phase (\(I_{zz}\)) and each harmonic (\(I_{hz}\)), indicated in Tables 2 and 3, respectively, as well as the short-circuit resistances of each harmonic (\(R_{cc,h}\)), shown in Table 5. The values of the load losses of each phase (\(P_{cc,z}\)) have been obtained by substituting into Equation (16) the values of \(R_{cc,z}\) from Table 7 and the RMS values of the secondary phase currents (\(I_{zz}\)) from Table 2.  
The values of the short-circuit resistance (\(R_{cc,1}\)) and the load losses of each phase (\(P_{cc,12}\)) and total (\(P_{cc,1}\)) for the fundamental frequency are those indicated in Table 5 for the harmonic of order \(h=1\). It is noted in these tables that the fundamental frequency short-circuit resistance has the same value, \(R_{cc,1}=2.889\) m\(\Omega\), in the three phases of the transformer for the two analyzed consumption periods (6:55 a.m. and 8:55 p.m.). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Hour**} & \multicolumn{3}{c}{**Effective Short-Circuit Resistances of Each Phase (m\(\Omega\))**} & \multicolumn{3}{c}{**Load Losses**} \\  & **A-Phase** & **B-Phase** & **C-Phase** & **A-Phase** & **B-Phase** & **C-Phase** & **Total** \\ \hline
6:55 a.m. & 5.285 & 4.577 & 5.637 & 70.449 & 109.158 & 77.548 & 257.156 \\ \hline
8:55 p.m. & 3.049 & 3.168 & 3.083 & 463.131 & 444.443 & 495.611 & 1403.186 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Transformer’s effective short-circuit resistances (\(R_{cc,z}\)) and load losses (\(P_{cc,z}\)) of each phase 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} \hline \hline \multirow{2}{*}{**Hour**} & \multicolumn{3}{c}{**Non-Fundamental Short-Circuit Resistances (m\(\Omega\))**} & \multicolumn{3}{c}{**Non-Fundamental Load Losses**} \\  & **A-Phase** & **B-Phase** & **C-Phase** & **A-Phase** & **B-Phase** & **C-Phase** & **Total** \\ \hline
6:55 a.m. & 2.743 & 1.910 & 3.132 & 36.562 & 45.560 & 43.091 & 125.214 \\ \hline
8:55 p.m. & 0.204 & 0.364 & 0.251 & 30.992 & 51.165 & 40.439 & 122.596 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Transformer’s short-circuit resistances (\(R_{cc,H_{2}}\)) and phase (\(P_{cc,H_{2}}\)) and total (\(P_{cc,H}\)) load losses for the non-fundamental harmonic currents at 6:55 a.m. and 8:55 p.m. on 10 November 2022. The values of the combined short-circuit resistances of all non-fundamental frequency harmonics of each phase (\(R_{cc,Hz}\)) and the values of the losses in each phase (\(P_{cc,Hz}\)) and total (\(P_{cc,H}\)) that these resistances characterize are obtained by applying Equations (26) and (27), respectively, and are summarized in Table 7. From Tables 6 and 7, the following statements are verified:  
1. Equation (25) is suitable for calculating the effective short-circuit resistances of each phase (\(R_{cc,z}\)) from the individual resistances of the harmonics (\(R_{cc,h}\)), since the product of the short-circuit resistances obtained with that equation determines the same load loss values in each phase (\(P_{cc,z}\)) as the IEEE Standard C57.110-2018, indicated in Table 4 for the two consumption periods. 2. The effective short-circuit resistances of each phase (\(R_{cc,z}\)) are not equal to the sum of the short-circuit resistances of the harmonics of that phase (\(R_{cc,h}\)), as can be seen in Table 5, due to the high values that the resistances \(R_{cc,h}\) acquire as the order \(h\) of the current harmonics increases. 3. The short-circuit resistances \(R_{cc,Hz}\) defined by (26) identify the phase (\(P_{cc,Hz}\)) and total (\(P_{cc,H}\)) load losses caused by the set of harmonics of non-fundamental frequency, since the values of these losses (Table 7) are the same as those determined using IEEE Standard C57.110-2018 (Table 4), and satisfy \(P_{cc,Hz}=P_{cc,z}-P_{cc,12}\).