Mathematical modell of mine electrotechnical complex with synchronous and induction motors

User Rating:  / 0


V.F. Syvokobylenko, Dr. Sci. (Tech.), Professor, State Higher Educational Institution «Donetsk National Technical University», Head of the Department “Power Stations”, Donetsk, Ukraine

S.V. Vasylets, Cand. Sci. (Tech.), State Higher Educational Institution «Donetsk National Technical University», Senior Lecturer of the Department “Mining Electrotechnology and Automation named after R.M. Leibov”, Donetsk, Ukraine


Purpose. To substantiate the mathematical model of mine electrotechnical complex, which includes synchronous and induction motors.

Methodology. Technique of researches includes formulation of topological description for power network equivalent circuit using graph theory that provides a matrix of the principal cross-sections and allows the formulation of the matrix equation of state for resistive and reactive elements of equivalent circuit for mine electrotechnical complex, moreover in the latter case the state variables method is used, according to which the differential equations are formed regarding currents of inductive links and voltages of capacitive edges. Synchronous and induction motors, which are represented in the equivalent circuit of electrical complex by voltage-controlled current sources, described by the matrix differential equations, which are combined with the state equations of RLC-systems into a single system state matrix differential equation, for numerical solving of which expediency of using a stiff-stable Gear-Nordsieck method with variable step of integration was substantiated.

Findings. The mathematical model of mine electrotechnical complex, that includes electrical sources, transformers, switching units, power cables, synchronous and induction motors was grounded as matrix differential equation in the form of Cauchy

Originality. The mathematical model of mine electrotechnical complex, which grounds on using of matrix differential state equations of equivalent circuit reactive elements, synchronous and induction motors, that differs from known models in taking into account mutual influence of electric motors in power network of any configuration and by the possibility of complex research into system state during any emergency states, was further developed.

Practical value consists in development of the application program with graphical interface „MinePowerNet“, using of which allows to explore the steady states and transients in mine electrotechnical complexes of particular configuration in case of commutations, changes in operating parameters and emergency states of synchronous and induction motors in the mine electric drive.


1. Вареник Е.А. Проблемное поле создания взрывозащищенного электрооборудования в контексте развития отраслей-потребителей / Е.А. Вареник, А.Н. Омельченко, Р.М. Лазебник // Взрывозащищенное электрооборудование: сб. науч. тр. УкрНИИВЭ. – Донецк: ООО „Юго-Восток, Лтд“, 2011. – С. 7–13.
Varenik, E.A. Omelchenko, A.N. and Lazebnik, R.M. (2011), “The problem field of explosionproof electrical equipment development in context of consumer-branches evolution”, Vzryvozashchishchyennoe elektrooborudovanie: collected articles of UkrNIIVE, “Yugo-Vostok”, Ltd., Donetsk, pp. 7–13.
2. Справочник энергетика угольной шахты: в 2 т. / [Дзюбан В.С., Ширнин И.Г., Ванеев Б.Н. и др. ]; под ред. Б.Н. Ванеева. – [2-е изд., перераб. и доп.]. - Донецк: ООО „Юго-Восток, Лтд“, 2001. -  Т.1.: (Гл. 1-21). - 447 с.;  Т.2.: (Гл. 22-44). - 440 с.
Dzyuban, V.S., Shirnin, I.G., Vaneev, B.N. and Gostishchev, V.M. (2001), Spravochnik energetika ugolnoy shakhty [Mine Power Engineering Reference Book], 2nd revised ed., Donetsk: “Yugo-Vostok”, Ltd., Vol.1.: (Ch. 1–21). – 447 p.; Vol.2.: (Ch. 22–44), 440 p.
3. Анализ параметров и процессов в шахтных электрических сетях / [Шкрабец Ф.П., Шидловская Н.А., Дзюбан В.С. и др. ]. - Днепропетровск: Нац. горный ун-т, 2003. - 151 с.
Shkrabets, F.P., Shydlovskaya, N.A., Dziuban, V.S. and Varenik, Y.A. (2003), Analiz parametrov i protsessov v shakhtnykh elektricheskikh setyakh [Parameters and Processes Analysis in Power Network of Mines], National Mining University, Dnepropetrovsk, Ukraine. 
4. Перехідні процеси в системах електропостачання / [Півняк Г.Г., Винославський В.М., Рибалко А.Я. и др. ]; за ред. академіка НАН України Г.Г. Півняка. - Дніпропетровськ: Національний гірничий університет, 2002. – 597с.
Pivniak, G.G., Vynoslavski, V.M., Rybalko, A.Ya. and Nesen, L.I. (2002), Perekhidni protsesy v systemakh electropostachahhia [Transients in Power-Supply Systems], National Mining University, Dnepropetrovsk, Ukraine. 
5. Krause, P.C. Oleg Wasynczuk, Scott D. Sudhoff (2002), Analysis of Electric Machinery and Drive Systems, 2nd ed., John Wiley & Sons, Inc., New York.
6. Murthy P.S.R. (2007), Power System Analysis, BS Publications, Hyderabad.
7. Hairer, E. and Wanner, G. (2010), Solving Ordinary Differential Equations II, 2nd revised ed., Sprinter, London – New York, (Sprinter series in computation mathematics, 14). Part II Stiff and differential-algebraic problems.
Date 2013-12-24 Filesize 624.11 KB Download 554


This Month
All days

Guest Book

If you have questions, comments or suggestions, you can write them in our "Guest Book"

Registration data

ISSN (print) 2071-2227,
ISSN (online) 2223-2362.
Journal was registered by Ministry of Justice of Ukraine.
Registration number КВ No.17742-6592PR dated April 27, 2011.


D.Yavornytskyi ave.,19, pavilion 3, room 24-а, Dnipro, 49005
Tel.: +38 (056) 746 32 79.
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
You are here: Home Archive by field of science Electrical engineering Mathematical modell of mine electrotechnical complex with synchronous and induction motors