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A novel approach based on the finite element method is proposed to calculate accurately the winding losses and short circuit forces caused by harmonic currents in a furnace transformer. The technique derives the appropriate partial differential equation required to determine the harmonic currents. The technique is validated by its application to a benchmark furnace transformer where experimental results demonstrate the accuracy of the developed technique. The contribution of harmonic currents to winding losses is shown to be significant in the benchmark furnace transformer, whereas the contribution of harmonic currents to short-circuit forces is limited.