A discrete time, linear time varying model of the three-phase voltage source converter (VSC) is developed. The model is employed to determine the steady state operating characteristics of a VSC taking all ac-dc side harmonic interactions into account. The procedure is based on an exact closed form solution of the system equations and does not rely on interative techniques. The steady state operating curves from the proposed model are compared with those derived from a conventional continuous time dq-frame model. The accuracy of the conventional continuous time model is shown to be highly dependent on the converter's duty cycle.