A method for modeling the time-varying magnetic geometry in a low-aspect-ratio tokamak is developed. The model includes mutual inductance effects of an arbitrarily shaped (toroidally symmetric) conducting shell, poloidal field (PF) coils, a saddle coil with finite gap resistance, and a single element, distributed plasma current. The plasma current distribution is specified using EFIT results and remains unchanged during the simulation, while the magnitude of the plasma current is ramped up linearly over time. The resulting simulation code is used to predict power supply requirements and tracking capabilities of an arbitrarily chosen feedback mechanism employed to operate the PF coils of the tokamak.