The mathematical model of a fragment of a high-voltage electric network is developed in this paper. The network consists of a long power line with distributed parameters and an equivalent three-phase active-inductive load. Neumann and Robin-Poincare boundary conditions were used to identify the boundary conditions for the long line equation. The parameter output voltage (voltage at the end of the line) is introduced into the paper for further universal use of the developed line model. On the basis of the developed mathematical model, the program code is written in the algorithmic language Visual Fortran. By means of it, oscillograms of transient electromagnetic processes of voltages and currents in the form of spatial, temporal and temporal-spatial distributions during remote two-phase short circuits in the transmission line of high voltage are obtained. Two transient electromagnetic processes are analyzed in the present work. The first one was analyzed during the switching on of the line to the normal mode of operation with the subsequent transition to the emergency mode. The second one was analyzed during the switching on the line in the mode of a remote two-phase short circuit to the ground. The results of transient electromagnetic process simulation in the form of analyzed figures are shown. All the results presented in this paper were obtained exclusively using numerical methods.
Keywords: Hamilton–Ostrogradskii principle; boundary conditions; electrical network; long power line; mathematical simulation; short circuit; transient electromagnetic processes.