A new aging calculation method for three-phase three-leg power transformers under (un) balanced and (non) sinusoidal operating conditions is proposed where the impacts of magnetic saturation, couplings, and hysteresis are accurately included. The aging estimation is carried out through a recently developed and validated time-domain model of a nonlinear three-phase three-leg transformer. The model outputs are used to compute aging based on Arrhenius' thermal reaction theory. The combined aging effects from transformer core asymmetry and load nonlinearity, as well as current and voltage harmonic interactions from nonsinusoidal input excitations and nonlinear loading are considered in the calculation. The model improves upon the conventional weighted harmonic factor (WHF) approach of aging estimation by direct evaluation of additional fundamental and harmonic losses generated by the iron-core, nonlinear loads, and terminal voltage distortions. The main contribution is a new transformer aging estimation method with wider applicability to three-phase transformers considering harmonic current-voltage interactions from unbalanced nonlinear loads, terminal voltage distortions and imbalances, as well as magnetic hysteresis and flux-coupling effects in asymmetric iron-core structures. Several case studies are presented for comparing the proposed model based aging method with the conventional WHF approach.