Influence of Harmonic and DC-Bias Coupling on Transformer Energization Inrush Current in Complex Power Grids

The methodological innovation of this study is a phase-domain separation-and-recombination framework that maps harmonic voltage to prospective flux, maps controlled quasi-DC winding current to magnetic operating-point displacement, and then resolves their nonlinear interaction through a shared-yoke three-limb model. A reduced nonlinear model informed by the measured major loops of a 50 kVA, 10 kV/400 V, Yyn0 transformer is evaluated over breaker-command angle and residual-flux sweeps. The operating matrix contains a sinusoidal baseline, a 0.15 p.u. negative-sequence second harmonic, a 0.08 p.u. negative-sequence fifth harmonic, their simultaneous application, and single-phase or asymmetric DC-current commands. Peak current, cycle-envelope decay, current total harmonic distortion, negative-sequence ratio, and a fourth-order three-phase current norm distinguish instantaneous from sustained stress. At the 60° command angle, the baseline, harmonic, DC-biased, and combined peaks are 21.30, 32.19, 35.15, and 41.67 A, respectively. Harmonic phase and sequence shift the knee-crossing instant and the dominant limb, whereas differential DC injection compresses one-directional saturation margin. The interaction contrast is interpreted as a model-output non-additivity statistic rather than an independent physical coupling constant. The conclusions are limited to the modeled distorted-source and differential-bias conditions; absolute prediction requires transformer-specific transient validation.