TRANSFORMER MAGNETIZING CURRENT AND IRON-CORE LOSSES IN HARMONIC POWER-FLOW

The problem of modifying the harmonic power flow analysis to permit the inclusion of nonlinear anisotropic transformers and computation of their iron-core (and copper) losses so far neglected in power flow studies, constitutes the objective of this paper. The nonlinear model used for transformers is capable of simulating saturation of iron-cores, anisotropy laminations, and the iron-core and copper losses associated with anisotropic transformers, but simple enough to be included in the harmonic power flow algorithm without deteriorating its convergence properties. The dependency of iron-core losses on the maximum value of the total (fundamental and harmonic) flux density and the fact that iron-core losses are a function of the waveform of the induced voltage -that is its harmonic phase shifts with respect to the fundamental phase angle- are included. The induced voltage is transformed from frequency domain to time domain: the instantanenous induced voltage and the computed lambda-iota characteristics are employed to compute the instantaneous magnetizing and core-loss currents. Thereafter, a transformation is made from time domain back to frequency domain to compute the fundamental and harmonic components of the above-mentioned currents. Therefore, transformer harmonic couplings are properly modeled and included in the analysis. The modified harmonic load how formulation is applied to a balanced three-phase feeder consisting of a grounded-wye, grounded-wye nonlinear anisotropic transformer and Linear and nonlinear loads. The main contribution of this paper is the computation of iron-core (and copper) losses of transformers used in balanced three-phase and single-phase systems at (non)sinusoidal operation.