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A static compensator (STATCOM) is a FACTS controller, whose capacitive or inductive output current can be controlled independently of the AC system voltage. A practical ±75 kVAr STATCOM has been designed, in which the phase difference between the converter voltage and the AC system voltage is controlled over a small region to obtain a nearly linear reactive power control. The converter voltage is synthesised using a PWM control with a fixed modulation index close to one. Here it is modelled using an averaging approach, by deriving the state-space equation of the STATCOM in the time domain. An average operator is defined, and applied to the state equation to get an averaged mathematical model. Expansion of this model will eventually lead to an average circuit model. An approximate averaged switching function represents the duty ratio as a continuous function of time. The solution is expandable as a Fourier series, which can be suitably truncated. Theoretical considerations show that the averaged model should agree well with the original system, and this is confirmed by MATLAB and PSpice simulations. Experimental results provide some practical waveforms that, compared to the corresponding simulations, validate the developed models.