Mathematical Modeling of Transition Processes in the High Voltage Transmission Line in Short Circuit Modes

2021;
: pp. 43 - 51
Authors:
1
Lviv National Agrarian University Department of Electrical Systems

The article analyzes the publications, which shows that two approaches to the analysis of transients in long power lines with distributed parameters are popular today: based on simplified methods of solving the equation of a long line, or equivalent to the known equation of a long line by circuit substitution schemes. In applying the first approach, the authors do not take into account the running resistance, phase and interphase conductivities, calculating the usually mentioned processes by the known methods of D’Alembert and “wandering waves”. The application of the second approach leads to the loss of the physical meaning of the equation of the long line, or requires the presence of boundary conditions to the mentioned equation, which is not always possible when modeling transients in complex electrical energy transfer systems.

In the present work, the analysis of transients in a long power line is based on the differential equation of a long line of the second order, which avoids the presence of two variables in the line equation and thus facilitate the implementation of the mathematical model in the form of program code in algorithmic programming languages. Thus, the article builds a mathematical model of a fragment of an electrical power transmission system, the key element of which is a long power line that combines two equivalent power systems for parallel operation.

The article presents a method for finding the functions of input and output voltages at the beginning and end of a long line, which significantly expands the scope of the developed mathematical model of the line as a stand-alone object in any general models of electrical power transmission systems.

Based on the developed mathematical model, algorithmization and computer simulation of transients in the power line during single-phase and two-phase short circuits 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.

1. Kotlan V., Benesova Z. Overvoltage Propagation from Transmission Line into Transformer Winding. Power engineering and electricalengineering. 2015. Vol. 13. No. 5. Р. 478-483. doi: https://doi.org/10.15598/aeee.v13i5.1421
2. Lobodzinsky V. Yu., Chibelis VI Mathematical model of a three-phase line with distributed parameters in electromagnetic transients. BULLETIN OF KNUTD. 2018. No. 4 (124). С. 96-102. doi: https://doi.org/10.30857/1813-6796.2018.4.10
3. Zakaryukin V. P., Kryukov A. V. Current distribution in wires of high-voltage power lines. News of higher educational institutions. Energy problems. 2010. P. 59-64. (Ukr). https://cyberleninka.ru/article/n/modelirovanie- tokoraspredeleniya-v-mnogoprovodnyh-liniyah-elektroperedachi.
4. Jung-Chien Li. Transient analysis of three-phase transmission lines with initial voltage and current distributions. Electric Power Systems Research. 1995. Vol. 35. Issue 3. P. 177-186.https://doi.org/10.1016/0378-7796(95)01006-8
5. Smolarczyk A., Chmielak W. PSCAD / EMTDC software as a convenient tool for modeling overhead lines. Works of the electrotechnical institute. 2016. No. 272. P. 31-48. (Pol). https://www.sciencedirect.com/science/article/ abs/pii/0378779695010068. https://doi.org/10.5604/00326216.1197255
6. Kirilenko O. B., Szegeda M. S., Butkevich O. F., Mazur T. A. Mathematical modeling in electric power industry. Lviv: Lviv Polytechnic University Island, 2010. 608 p. (Ukr).
7. Pruski P., Paszek S. Analysis of transient waveforms in a power system at asymmetrical short-circuits. Przeglad elektrotechniczny. 2020. No. 2. P. 26 - 29. doi: https://doi.org/10.15199/48.2020.02.05
8. Hermann W. Dommel. Digital Computer Solution of Electromagnetic Transients in Single- and Multiphase Networks. IEEE Transactions On Power Apparatus And Systems. 1969. P. 388-399. https://ieeexplore.ieee.org/ document/4073845. https://doi.org/10.1109/TPAS.1969.292459
9. Shimoni K. Theoretical electrical engineering. Moscow: Mir, 1956. 773 p. (Rus). https://doi.org/10.1109/EE.1956.6442120
10. Levoniuk V. Mathematical modeling of transients processes in thre-phase transmission line in two-phase short circuit mode. Electrical power and electromechanical systems. 2020. Vol. 2. P. 9-17. (Ukr). http://science. lpnu.ua/sites/default/files/journal-paper/2020/nov/22305/200864maket1-11-19.pdf.
11. Boglaev Yu. P. Computational Mathematics and Programming. Moscow: High School, 1990. 544 p. (Rus).
12. Chaban A. V. The Hamilton-Ostrogradsky principle in electromechanical systems. Lviv: Taras Soroka Island, 2015. 488 p. (Ukr).