Mathematical modell of mine electrotechnical complex with synchronous and induction motors

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 Authors:

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

Abstract:

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.

 

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ISSN (print) 2071-2227,
ISSN (online) 2223-2362.
Journal was registered by Ministry of Justice of Ukraine.
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