Uncontrolled switching of transformers on the network is accompanied by a large asymmetry of currents in the iron core. As a result of such asymmetrical currents, large harmonic distortions of voltage and magnetizing current occur. Problems caused by inrush currents can cause failures in the transformer itself and can cause incorrect operation of protective relays, fuses and other types of protection in the power system. Finally, all of the above contributes to a significant reduction in the quality of the supplied electricity. This paper describes a mathematical model of a three-phase three-pole transformer. The hysteresis loop is also modeled using a simple analytical expression. With the help of this model, a simulation was made on a digital computer, taking into account the effect of saturation, residual magnetic flux and the selection of the moment of switching. For the purpose of experimental verification of the results, a laboratory model of a system for controlled switching of transformers was made. It was shown that the inrush current when using a controlled switching system is several times smaller than the inrush current that occurs during uncontrolled switching.