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Accurate modeling of power system components for the purpose of electromagnetic transient calculations requires the frequency dependence of components to be taken into account. In the case of linear components, this can be achieved by identification of a terminal equivalent based on rational functions. This paper addresses the problem of approximating a frequency dependent matrix H(s) with rational functions for the purpose of obtaining a realization in the form of matrices A, B, C, D as used in state equations. It is shown that usage of the Vector Fitting approach leads to a realization in the form of a sum of partial fractions with a residue matrix for each pole. This can be directly converted into a realization in the form A, B, C, D in which B is sparse and each pole is repeated n times with n by n being the size of H. The number of repetitions can be strongly reduced and sometimes completely avoided by reducing the rank of the residue matrices, thereby producing a compacted realization which is physically more correct and also permits faster time-domain simulations. The error resulting from the rank-reduction can be reduced by subjecting the realization to a nonlinear least-squares procedure, e.g., Gauss-Newton as was used in this work.