An extensive s-domain tensor algebraic model of the transformer has been proposed. Unlike the traditional matrix-vector approach which relies on the conventional linear algebra, this model which in turn assumes the multilinear algebra that is of higher dimension thus more generic, is applicable to those recently often cited transformers which often employ the unconventional characteristics i.e. frequency variant parameters, time variant parameters and fractional impedance. The examples of such transformers are the on-chip monolithic transformer, the dynamic transformers and the fractional mutual inductance etc. The imperfect coupling has been considered and multiple winding transformer has also been assumed. The applications of the proposed model to the chosen recent transformers with those unconventional characteristics have been presented. The effects of failure of Kron’s postulate on power invariant and validity of duality invariant which are worthy of mentioned issues, have also been discussed. The proposed extensive model is more inclusive and up to date than the matrix-vector based model and those foregoing tensor algebraic models albeit it is more complicated.