In this paper, a piece-wise linearized transformer winding model is proposed for transient internal voltage distribution computations. In particular, the model is based on the linearization of the primitive non-linear, frequency dependent and invariant matrix of voltage distribution factors. This primitive matrix is utilized as a pattern from which, for any specific switching event and its frequency spectrum, the piecewise linearized matrix of voltage distribution factors can be computed. In this manner, a unified black-box to lumped-parameters combined transformer model successfully bypasses the need of geometrical data. The computations are also significantly reduced. The model is verified by measurements on a three-phase distribution transformer.