This paper presents a linear state-space model of a static VAr compensator. The model consists of three individual subsystem models: an AC system, a SVC model and a controller model, linked together through d-q transformation. The issue of non-linear susceptance-voltage term and coupling with a static frame of reference is resolved using an artificial rotating susceptance and linearising its dependence on firing angle. The model is implemented in MATLAB and verified against PSCAD/EMTDC in the time and frequency domains. The verification demonstrates very good system gain accuracy in a wide frequency range f<150 Hz, whereas the phase angle shows somewhat inferior matching above 25 Hz. It is concluded that the model is sufficiently accurate for many control design applications and practical stability issues. The model's use is demonstrated by analyzing the dynamic influence of the PLL gains, where the eigenvalue movement shows that reductions in gains deteriorate system stability.