This article validates the possibility of a piecewise linear approximation with one breakpoint of the magnetizing characteristic of a power transformer for studying the processes of unilateral saturation of a magnetic system during periods of a high geomagnetic activity, which is caused by space-weather disturbances. An integral quantitative characteristic of a piecewise linear approximation is proposed that takes the features of the main magnetization curve of electric steel and the structural features of the power-transformer magnetic system into account. An analytical model is developed that allows determination of the instantaneous values and the harmonic structure of the magnetizing current at different intensities of quasi-direct currents. Two specific levels of the geomagnetic activity are determined. At one of them, the even harmonics of the magnetizing current are maximized, while at the second level the fundamental harmonic of the magnetizing current reaches a maximum that exceeds the certified value of the open-circuit current of the power transformer by several times.