Wide frequency range representation of power system components such as power transformers, reactors and rotating machines is mainly needed for the analysis of electromagnetic transients in power systems. In this paper, a method is presented for state space formulation of machine windings. The described procedure is completely based on external terminal impedance measurements and data related to the internal structure is not required. First, the wide frequency behavior of machine windings is reviewed and the nonlinearity effects of the iron core are discussed. A numerical method is given for calculation of the state equation parameters directly from the measured terminal impedance characteristics. The presented modeling method is applicable to any transformer, reactor or rotating machine in service where sufficient information on the internal design is not available. Besides, the canonical structure of the model offers advantages in terms of computer memory and computation effort in time domain analyses of complex power systems.