Transformer is a key component in power transmission by the electric power system. The stability and security of the transformer protection operation are vital for the power system operation and control. The main topic of this paper is the investigation of the power transformer behaviour under the switching condition. The inrush current phenomena has been particularly discussed including the stabilization of the transformer differential protection and identification of the transformer internal faults condition. When a transformer is switched on, it may draw a high-magnitude transient current from the power grid. The power transformer energizing is accompanied by a high asymmetry of the flux in the iron core. Due to the flux asymmetry, significant distortion of the magnetizing current waveform, very high inrush currents, and a very high DC component of the inrush currents occur. The inrush currents may result in malfunction of the protective relays in the electric power system and a mechanical damage of the transformer. The magnitude and duration of the transient inrush current of the transformer depends on the switching angle and position of the voltage waveform when the transformer is energized. It also depends on the power grid impendence to which the transformer is switched, the value and the sign of the residual flux linkage in the transformer core, and the non-linear magnetic saturation characteristics of the transformer core. This paper addresses the issues caused by the transient inrush current of the transformer and presents the results obtained by measuring the inrush currents on the characteristic transformers from the power transmission grid. Taking into account the negative effect of the inrush current on differential protection and the relay stabilization, the inrush current waveforms have been analyzed.