# MATHEMATICAL MODEL OF ELECTROMAGNETIC PROCESSES IN LEHERA LINE AT OPEN-CIRCUIT OPERATION

## Authors

• A. V. Chaban Lviv National Agrarian University, Ukraine
• V. R. Levoniuk Lviv National Agrarian University, Ukraine
• I. M. Drobot Lviv National Agrarian University, Ukraine
• A. F. Herman Lviv National Agrarian University, Ukraine

## Keywords:

mathematical modeling, Hamilton-Ostrogradskiy principle, Euler-Lag¬range equation, electric power system, power line with distributed parameters

## Abstract

Purpose. The work proposed for the modeling of transients in Lehera line uses a modified Hamilton-Ostrogradskiy principle. The above approach makes it possible to avoid the decomposition of a single dynamic system that allows you to take into account some subtle hidden movements. This is true for systems with distributed parameters, which in the current work we are considering. Methodology. Based on our developed new interdisciplinary method of mathematical modeling of dynamic systems, based on the principle of modified Hamilton-Ostrogradskiy and expansion of the latter on the non-conservative dissipative systems, build mathematical model Lehera line. The model allows to analyze transient electromagnetic processes in power lines. Results. In this work the model used for the study of transients in the non-working condition Lehera line. Analyzing the results shows that our proposed approach and developed based on a mathematical model is appropriate, certifying physical principles regarding electrodynamics of wave processes in long power lines. Presented in 3D format, time-space distribution function of current and voltage that gives the most information about wave processes in  Lehera line at non-working condition go. Originality. The originality of the paper is that the method of finding the boundary conditions of the third kind (Poincare conditions) taking into account all differential equations of electric power system, i.e. to find the boundary conditions at the end of the line involves all object equation. This approach enables the analysis of any electric systems. Practical value. Practical application is that the wave processes in lines affect the various kinds of electrical devices, proper investigation of wave processes is the theme of the present work.

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2016-06-25

## How to Cite

Chaban, A. V., Levoniuk, V. R., Drobot, I. M., & Herman, A. F. (2016). MATHEMATICAL MODEL OF ELECTROMAGNETIC PROCESSES IN LEHERA LINE AT OPEN-CIRCUIT OPERATION. Electrical Engineering & Electromechanics, (3), 30–35. https://doi.org/10.20998/2074-272X.2016.3.05

## Section

Electrical Machines and Apparatus