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A topology-correct transformer model, which covers core operation under heavy saturation conditions, is presented. A method of accounting for magnetic fluxes outside the core and windings is proposed. Representation of the magnetization curve at high flux densities is considered. The equivalent air gap in the core is taken into account. The model is capable of reproducing inrush currents accurately regardless of which transformer winding (LV or HV) is energized. The model is illustrated by calculating inrush currents produced by subsequent energizations of a single-phase transformer.