The study investigates the features of the operation of off-the-grid power systems. Such power systems are commonly used for supplying power to consumers spread throughout the Arctic zone of the Russian Federation, and their unique operating conditions are due to the effect of geomagnetically induced currents (GICs) resulting from geomagnetic disturbances. We argue that the cause of stator current deviations from the pure sine wave are unit transformers. Their low-voltage windings are directly connected to stator windings of synchronous generators, and GICs run through grounded high-voltage windings. To support our claim, we simulated the effect of a test GIC event. Its amplitude in each of high-voltage phase windings of the unit transformer was 100 A, and the duration was 20 seconds (power transformers of the Hydro-Québec power grid were exposed to geomagnetically induced currents of a similar intensity during the geomagnetic storm on March 13-14, 1989). The spike targeted the "generator (TVF-100-2) - transformer (TDTs-125000/220/10.5)" unit that fed a major consumer node (Рnom = 83.125 MW, Qnom = 29.75 Mvar, cosφ=0.95) through a 160 km long double-circuit overhead line. Our study demonstrated that the effect of GICs on the operation of synchronous generators started from the moment of saturation of the unit transformer's core due to the inverse transformation of magnetizing current harmonics in the stator winding circuit. The harmonics introduced significant deviations from the pure sine wave into the curve of instantaneous stator currents. We calculated the nonlinear distortion factor of the stator current, which reached an unacceptably high value of THD=55.59%, 10 seconds into the test GIC event. The study showed that the 2nd and 4th harmonics of the unit transformer magnetizing current were responsible for the great bulk of deviations from the pure sine wave of the stator current.