Revisited Concept of Three-Phase Transformers' Short-Circuit Resistances in Light of the Institute of Electric and Electronics Engineers (IEEE) Standard C57.110-2018  
[PERSON]  
[PERSON]  
[PERSON]  
networks. The article's authors have managed to register \(THDi\)% values greater than 70% in highly distorted industrial distribution networks. The load loss values (\(P_{cc}\)) of three-phase distribution transformers can be obtained directly, by applying the IEEE Standard C57.110 [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17] and other well-known standards [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32], or, indirectly, based on their short-circuit resistances referred to as the secondary resistance (\(R_{cc}\)), according to the following expression:  
\[P_{cc}=R_{cc}\cdot\sum_{z=A,B,C}\sum_{h_{z}=1}^{h_{z,max}}I_{hz}^{2} \tag{1}\]  
where \(I_{hz}\) is the RMS value of the harmonic current of frequency \(f_{hz}\), order \(h_{z}=f_{hz}/f_{1}\) of the secondary phases (\(z=A,B,C\)), \(f_{1}\) is the fundamental frequency (50-60 Hz), and \(h_{z,max}\) is the order of the highest harmonic frequency used in the calculation. Short-circuit resistances are, therefore, parameters that characterize transformers' load losses. In industrial practice, the load losses of three-phase transformers have traditionally been calculated according to Equation (1), using the nominal value of the short-circuit resistance referred to as the secondary resistance (\(R_{ccN}\)), which is obtained as follows:  
\[R_{ccN}=\frac{P_{ccN}}{3\cdot I_{SN}^{2}} \tag{2}\]  
according to the load losses (\(P_{ccN}\)) and secondary current (\(I_{SN}\)) nominal values, determined after performing a short-circuit test at the industrial frequency (50-60 Hz) [33; 34; 35; 36] or, by any of the procedures described in references [37; 38; 39; 40; 41; 42; 43; 44]. The nominal short-circuit resistance (\(R_{ccN}\)) defined by Equation (2) is a parameter independent of the frequency of the winding current harmonics and has the same values in each phase of the three-phase transformers. However, its application in Equation (1) provides lower load loss values than those calculated with IEEE Standard C57.110-2018 [6] when the loads are non-linear. This fact is explained because Equation (2) does not include the effects of skin phenomena and eddy currents induced in other metallic parts of the transformer, defined by IEEE Standard C57.110-2018, for harmonic currents of non-fundamental frequency. To avoid the errors that \(R_{ccN}\) usually introduces in the calculation of load losses of three-phase transformers, two types of short-circuit resistances were developed in [45; 46], based on the expressions of the load losses included in the IEEE Standard C57.110-2018 [6; 7], which have been included in Section 1.1. These are the short-circuit resistances of [PERSON] et al. (\(R_{k}\)) [45] and the effective short-circuit resistances of each phase (\(R_{cc,z}\)) [46], and their expressions are indicated in Section 1.2 of this article. However, the short-circuit resistance of [PERSON] et al. is inappropriate, since its application determines values of the load losses that are different in each transformer's phases than those obtained from the IEEE Standard C57.110-2018, as was verified in reference [46]; therefore, [PERSON] et al. 's short-circuit resistance is not the object of study of this work. The article's main objective is to study the effects of the harmonics of the winding currents on the load losses of three-phase transformers, using their short-circuit resistances referred to each secondary phase of the transformer.