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A comprehensive time domain model of a synchronous three-phase static compensator (STATCOM) is presented in this paper. The STATCOM model comprises the voltage source converter (VSC), which incorporates pulse width modulation (PWM) control techniques, and the coupling transformer, which includes the nonlinear, magnetizing branch. The switching pattern used in this model is a unipolar PWM scheme. The coupling transformer is modelled as an equivalent circuit connected in a delta-star configuration. Besides saturation, core losses are also included in the transformer model. The model is applied to study the interactions that take place between the different components of the STATCOM, namely the VSC, the coupling transformer, the DC-link capacitor and the control system. The model is developed from first principles and the ensuing formulation is coded in C++ using a UNIX platform.