## 5 Conclusions  
The load losses of electrical transformers are of great practical interest since they allow monitoring to ensure correct operation and make it possible to carry out preventive maintenance, identifying possible causes of failures. One of these causes is current distortions, which increase the load loss values. In this article, the effects of current harmonics on the load loss values of three-phase distribution transformers are obtained indirectly using their short-circuit resistances, obtained according to IEEE Standard C.57.110-2018. Specifically, new expressions of the short-circuit resistances for each harmonic (\(R_{cc,h}\)) are developed according to the standard. Based on those resistances, the expressions of the effective short-circuit resistances for each phase (\(R_{cc,z}\)) and combinations of all non-fundamental harmonics (\(R_{cc,Hz}\)) are established. These short-circuit resistances characterize load losses  
Figure 3: Transformer’s C-phase harmonic loss factor (\(HLF_{C}\)%) based on IEEE Standard C57.110-2018 and traditional procedures, and A-phase total harmonic distortion (\(THD_{iC}\)%) on 10 November 2022. Figure 2: Transformer’s B-phase harmonic loss factor (\(HLF_{B}\)%) based on IEEE Standard C57.110-2018 and traditional procedures, and A-phase total harmonic distortion (\(THD_{B}\)%) on 10 November 2022.  
of three-phase transformers according to IEEE Standard C57.110-2018 and are a novelty in the technical literature. The harmonic loss factor of each phase (\(HLF_{z}\)%) is another novelty of the article. This parameter determines the relative importance of non-fundamental harmonics in the load losses of each phase of the three-phase transformers. The comparison of the load loss values obtained in the transformer of an actual residential distribution network with the use of these resistances and those resulting from applying the traditional procedure in industrial practice, using the nominal short-circuit resistance (\(R_{cN}\)), has allowed us to verify the following findings:  
* The values of the new effective short-circuit resistances (\(R_{cc,z}\) and \(R_{cc,Hz}\)) are usually different in the three phases of the transformer and vary with the frequencies and the RMS values of the harmonics of the currents, as happens with the phenomena associated with load losses in transformers. For this reason, these resistances are physical parameters of three-phase transformers, which accurately determine the total (\(P_{cc}\)) and phase (\(P_{cc,z}\)) load losses, as well as the load losses of the set of all non-fundamental harmonics (\(P_{cc,H}\) and \(P_{cc,Hz}\)), providing exactly the same values as IEEE Standard C57.110-2018. * Using the nominal short-circuit resistance (\(R_{ccN}\)), which is traditional in industrial practice, is not advisable for correctly measuring load losses of transformers feeding non-linear loads. In the practical application of this article, it has been verified that the traditional procedure determines load loss values in the phases of up to 48.75% (6:55 a.m., phase C) lower than those calculated with the IEEE Standard C57.110-2018. This result is because the traditional procedure underestimates the losses caused by current harmonics of non-fundamental frequency, as deduced by comparing the values of the harmonic loss factor of each phase (\(HLF_{z}\)%). At that same time (6:55 a.m.), the value of this factor in phase C was only 13.3%, using the traditional procedure, as opposed to 55.57%, as measured in that phase by the IEEE Standard C57.110-2018. * The previously indicated errors of the traditional procedure in measuring transformer load losses increase with current distortion rates (\(THDiz\)%) and are due to the inadequate definition of the nominal short-circuit resistance (\(R_{ccN}\)), whose values are obtained for the fundamental frequency and under load balanced conditions and does not include the energy phenomena caused by non-fundamental frequency currents.