We perform simulation and experimental investigation of transient processes emerging in a single-phase transformer when it is connected to the network. The transformer model constructed taking into account the saturation of the steel of the core differs from standard models in detailed accounting for the magnetic flux leakage, which is required, for example, for a correct description of inrush current. Universality of the model for the type of transformers under study is ensured by the allowance for eddy current losses and calculation of the magnetic hysteresis in the steel core. The latter makes it possible to estimate the effect of residual magnetization of the core on the form of a transient process, which is studied in detail. The methods for computing model parameters are described and its experimental verification is carried out.