The advent of high-temperature superconducting materials opens up a new possibilities for increasing the efficiency of the functioning of electric power systems. Their implementation can lead to qualitative changes in the modes of operation of transmission and distribution systems that are not observed in electrical circuits with losses. The aim of this work is to develop a mathematical model of the electric circuit, which includes a power line with distributed parameters and a superconducting power transformer in order to study the mode features in the long line, mainly in non-stationary mode. When constructing the equivalent circuit and the mathematical model, the serial circuit of the RLC type is used as the basic element. The parameters of the mathematical model are presented in a system of relative units. In solving the system of integro-differential equations describing the process in the circuit under consideration, the finite difference method is used. Mathematical models and modes in the circuit are considered in the case when several loads of the RLC type feeding through a step-down transformer and in the case when several sources of electric energy generation (distributed generation sources from a low voltage network) are connected to the transformer. Idling and load modes are considered for the case when the supply line and the transformer are presented as ideal (modeling the effect of superconductivity). The possibility of energy storage in the transformer and in the line under the existence of a wave mode is shown, as well as the transfer of power to the load through the transformer, even for the case of supplying the circuit from a direct current source.