(\(R_{k}\)) usually have greater values than the nominal short-circuit resistances (\(R_{ccN}\)). However, the short-circuit resistances of [PERSON]. [PERSON] et al. have the same values in the three phases, since they are obtained based on the total load losses (\(P_{k}\)) and the combined currents of the three phases (\(I_{s}\)). This is a remarkable drawback of these short-circuit resistances, which also happens with the traditional \(R_{ccN}\), because the phase load losses (\(R_{k}\cdot I_{sZ}^{2},\;z=A,B,C\)) calculated with \(R_{k}\) have different values, in general, than those result ing from IEEE Standard C57.110-2018, applying Equation (8). That is, the short-circuit resistances of [PERSON]. [PERSON] et al. are not directly related and, therefore, do not characterize the load losses of each phase of three-phase transformers. To avoid the drawbacks of the short-circuit resistance of [PERSON]. [PERSON] et al. and to correctly characterize the load losses of each phase of three-phase transformers according to IEEE Standard C57.110-2018, reference [46] developed the effective short-circuit resistances of each phase of the transformer (\(R_{cc,z}\)), as follows:  
\[R_{cc,z}=\frac{P_{cc,z}}{I_{zz}^{2}} \tag{10}\]  
where \(P_{cc,z}\) is the load losses of each phase, defined by (8), and \(I_{sz}\) is the RMS value of the current of each secondary phase (\(z=A,B,C\)) of the transformer, as follows:  
\[R_{ccN}=\frac{P_{ccN}}{3\cdot I_{SN}^{2}} \tag{2}\]0  
where \(I_{hz}\) is the RMS value of the harmonic current of order \(h_{z}=f_{hz}/f_{1}\) of each secondary phase (\(z=A,B,C\)) of the transformer, and \(h_{z,max}\) is the order of the highest harmonic frequency used in the calculation. The effective short-circuit resistances of each phase (\(R_{cc,z}\)) have the following expressions, obtained after substituting Equations (8) and (11) into (10):  
\[R_{ccN}=\frac{P_{ccN}}{3\cdot I_{SN}^{2}} \tag{2}\]1  
where the factors due to the skin (\(F_{HL}^{z}\)) and other stray (\(F_{HL-STR}^{z}\)) losses of each phase [37] are calculated as follows:  
\[R_{ccN}=\frac{P_{ccN}}{3\cdot I_{SN}^{2}} \tag{2}\]2  
and  
\[R_{ccN}=\frac{P_{ccN}}{3\cdot I_{SN}^{2}} \tag{2}\]3  
are the nominal short-circuit resistances corresponding to the three phenomena defined by IEEE Standard C57.110-2018, namely the ohmic resistance of the coil conductors (\(R_{DCN}\)), the resistance caused by the skin effect (\(R_{ECN}\)), and the resistance caused by the currents induced in other metallic parts of the transformer (\(R_{OSLN}\)). The resistance \(R_{DCN}\) is obtained in the direct current, while \(R_{ECN}\) and \(R_{OSLN}\) are determined at the fundamental frequency (\(f_{1}=50-60\;Hz\)). The sum of these three resistances, shown below, is equal to the well-known nominal short-circuit resistance of the transformer (\(R_{ccN}\)), traditionally used in industrial practice, which is defined by (2):  
\[R_{ccN}=\frac{P_{ccN}}{3\cdot I_{SN}^{2}} \tag{2}\]4  
The effective short-circuit resistances of each phase (\(R_{cc,z}\)) calculated according to Equation (12) generally have different values in each phase, and they are physical parameters of the three-phase transformers since they are related to the load losses of each phase, according to the following expression:  
\[R_{ccN}=\frac{P_{ccN}}{3\cdot I_{SN}^{2}} \tag{2}\]5whose values match with those obtained according to (8), and the transformers' total load losses are obtained as follows:  
\[R_{ccN}=\frac{P_{ccN}}{3\cdot I_{SN}^{2}} \tag{2}\]6  
which satisfies Equations (4) and (7) deducted from IEEE Standard C57.110-2018.