Mathematical Modeling of Transients Processes in Three-phase Transmission Line in Two-phase Short Circuit Mode

The article analyzes scientific publications, which showed that for most part of the study transients processes in the long power lines with distributed parameters is carried out by equivalent to the known equation of a long line with distributed parameters by a circular equivalent, or solve this equation using simplified approaches. These approaches require deterministic boundary conditions to the long line equation, which is not always possible when modeling transients processes in electrical networks. Also, in many works the authors do not take into account in the equations of the object linear active resistance, phase and interphase conductivities, calculating the usually mentioned processes by the known method of D’Alembert.

In the present work, the analysis of transients processes in a fragment of the electrical network is based on the modified Hamilton-Ostrogradsky principle, which made it possible to obtain the initial equations of state exclusively from a single energy approach, thus taking into account not only all energy transformations in the system, but also all distributed parameters of the long line. A mathematical model of a long power line is constructed, to which an equivalent asymmetric active- inductive load is connected, taking into account mutual inductive connections.

It is shown that the method of identification boundary conditions of the second and third genera to the differential equation of a long line increases efficiency construction of its model, since it does not require the creation of extended circuit substitution schemes, on the one hand; and makes it possible to take into account the course of electromagnetic processes at the field level, on the other hand. For further universal use of the developed line model, the parameter “output voltage” (voltage at the end of the line) is introduced into it.

Based on the developed mathematical model, algorithmization of dynamic processes and computer simulation of transient modes in the power line during a two-phase short circuit were performed. The research results are presented in the form of figures that are analyzed. All the results presented in this paper were obtained using numerical methods.