The \(P_{DCN}\) losses can be obtained through a direct current test [47] and the individual values of \(P_{ECN}\) and \(P_{OSLN}\) are defined by the IEEE Standard C57.90\({}^{\text{TM}}\)[48], which sets \(P_{ECN}=2/3\cdot P_{ACN}\), in oil-immersed transformers, and \(P_{ECN}=1/3\cdot P_{ACN}\), in dry-type transformers. Equation (4) is not explicitly expressed in IEEE Standard C57.110-2018, although it is used in many references [8; 9; 10; 11; 12] to refer to primary currents. However, the standard does not clearly indicate the meaning of the currents in Equation (4). That standard only establishes that \(I_{SR}\) is the RMS value of transformers' nominal secondary currents and \(I_{sh}\) are the RMS values of the harmonic secondary currents of order h.  
To clarify Equation (4), in [7], Equation (4) was adapted to indicate the meaning of the currents \(I_{sh}\) and \(I_{sR}\) used in IEEE Standard C57.110-2018. For Equation (4), to provide the values of the total load losses of the three-phase transformers, \(I_{sh}\) and \(I_{sR}\) must be, respectively, the combined RMS values of the harmonics and nominal currents of the three phases (\(z=A,B,C\)) of the secondary current, as follows:  
\[I_{sh}=\sqrt{I_{shA}^{2}+I_{shB}^{2}+I_{shC}^{2}}=\sqrt{\sum_{z=A,B,C}I_{lz}^{ 2}}\;I_{sR}=\sqrt{I_{sRA}^{2}+I_{sRB}^{2}+I_{sRC}^{2}}=\sqrt{3}\cdot I_{sN} \tag{6}\]  
The substitution of Expressions (6) in Equation (4) determines the following expression of the total load losses of the three-phase transformers, as follows:  
\[P_{cc}=\frac{1}{3}\cdot\sum_{z=A,B,C}\sum_{h_{z}=1}^{h_{z,max}}\Big{(}P_{DCN}+ P_{ECN}\cdot h_{z}^{2}+P_{OSLN}\cdot h_{z}^{08}\Big{)}\cdot\Big{(}\frac{I_{h_{z}}}{I _{sN}}\Big{)}^{2} \tag{7}\]  
where \(I_{h_{z}}\) is the RMS value of the harmonic current of order \(h_{z}=f_{hz}/f_{1}\) of each phase (\(z=A,B,C\)) of the secondary current of the transformer, and \(I_{sN}=I_{sR}\) is the nominal value of the secondary currents. The values of the total load losses (\(P_{cc}\)) obtained with this last expression are the same as those resulting from applying Equation (4), with the advantage that, in Equation (5), the load losses of each phase of the transformer (\(P_{cc,z}\)) are directly differentiated, as follows:  
\[P_{cc,z}=\frac{1}{3}\cdot\sum_{h_{z}=1}^{h_{z,max}}\Big{(}P_{DCN}+P_{ECN}\cdot h _{z}^{2}+P_{OSLN}\cdot h_{z}^{08}\Big{)}\cdot\Big{(}\frac{I_{h_{z}}}{I_{sN}} \Big{)}^{2} \tag{8}\]  
The separation of the load losses of each phase indicated by Equation (8) is not so evident from Equation (4). Short-Circuit Resistances of Three-Phase Transformers According to the Institute of Electric and Electronics Engineers (IEEE) Standard C57.110-2018  
Short-circuit resistances are the parameters that characterize the transformers' load losses, because its product times the square of the currents determines the value of those losses. [PERSON] et al. developed, in [45], a short-circuit resistance, referred to as the primary resistance, that determines the transformers' load losses established by IEEE Standard C57.110-2018. The short-circuit resistance of [PERSON] et al., referred to as the secondary resistance, is expressed as follows [45]:  
\[R_{k}=\frac{P_{k}}{I_{s}^{2}} \tag{9}\]  
where \(P_{k}=P_{cc}\) are the total load losses of the transformer obtained with Equation (4), and \(I_{s}\) is the combined RMS value of the currents of the three phases of the secondary winding, i.e., \(I_{s}^{2}=I_{sA}^{2}+I_{sB}^{2}+I_{sC}^{2}\). As the load losses established by IEEE Standard C57.110-2018 contain terms that are affected by the frequencies or the order of the harmonic currents, as observed in Equations (4) and (7), the short-circuit resistances \(R_{k}\) also depend on the harmonic frequencies. This is an important difference compared to traditional short-circuit resistance (\(R_{ccN}\)), which is independent of the frequencies of harmonic currents. For this reason, the short-circuit resistances of [PERSON]. [PERSON] et al.