In modern tokamaks, plasma with a vertically elongated cross section is created; however, this configuration is unstable with respect to the vertical position of the plasma, and control systems for the vertical position of the plasma are necessary for the operation of such tokamaks. An important parameter characterizing the capabilities for controlling the vertical position of the plasma is the controllability region. This article assesses the controllability region of the plasma in the KTM tokamak using an HFC coil, taking into account limitations from the power supply. To obtain this assessment, the plasma equilibrium was reconstructed from experimental signals of the tokamak, and a model of plasma motion was constructed on the basis of the reconstructed equilibria. Subsequently, a current control system was simulated for the HFC powered by a voltage inverter in a pulse-width modulation (PWM) mode. The calculated lower estimate of the plasma controllability region was 23 cm, which is sufficiently large for a tokamak with a small plasma radius of 45 cm, and demonstrates the potential for creating an effective plasma position control system using the HFC coil in the KTM tokamak.