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 are discussed. The nonlinear model used for transformers is capable of simulating saturation of iron-cores, anisotropy of 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 instantaneous induced voltage and the computed λ-i 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 flow formulation is applied to a balanced three-phase feeder consisting of a grounded-wye, grounded-wye nonlinear anisotropic transformer and linear and nonlinear loads