ПОРІВНЯЛЬНИЙ АНАЛІЗ МЕТОДІВ РОЗРАХУНКУ ПЕРІОДИЧНИХ ПРОЦЕСІВ НЕЛІНІЙНИХ ЕЛЕКТРОМЕХАНІЧНИХ СИСТЕМ
COMPARATIVE ANALYSIS OF CALCULATION METHODS OF PERIODIC PROCESSES OF NONLINEAR ELECTROMECHANICAL SYSTEMS
Сторінки: 93-96. Номер: №1, 2021 (293) 
Автори:
Л.А. БІЛИЙ, О.С. ПОЛІЩУК, С.П. ЛІСЕВИЧ, А.О. ПОЛІЩУК, М.А. ЛУЧИНСЬКИЙ
Хмельницький національний університет
L. A. Bily, O.S. Polishchuk, S. P. Lisevych, A. O. Polishchuk, M.A. Luchynskyi
Khmelnytskyi National University
DOI: https://www.doi.org/10.31891/2307-5732-2021-293-1-93-96
Рецензія/Peer review : 17.01.2021 р.
Надрукована/Printed : 10.03.2021 р.
Анотація мовою оригіналу
В роботі обґрунтовано доцільність використання методу модулів чутливості до початкових умов для аналізу періодичних процесів нелінійних електромеханічних пристроїв.
Ключові слова: диференціальні рівняння, матриця чутливості, прискорений пошук, періодичні процеси .
Розширена анотація англійською мовою
The analysis of processes of the basic methods of calculation of periodic (stationary) processes (stationary) processes of nonlinear electromechanical systems is carried out. Modeling of steady-state electromechanical processes of electrical devices, covering both power energy converters (electric machines, transformers, electromagnetic devices) and automation devices (actuators, selsyn, position sensors, tachogenerators, rotary transformers, etc.) is one of the most difficult problems due to reproduction of physical processes of different nature that take place in them. Nominal operating modes of most of them are fixed or periodic, that is, their coordinates (currents, voltages, angular displacements, etc.) are periodic functions of time. The problem of finding periodic solutions of nonlinear differential equations is more difficult than the Cauchy problem of integrating these equations from the initial conditions to the establishment, because it imposes another condition on the solution – the periodicity condition. The main methods of analysis of periodic processes in continuous time are the method of models of sensitivity to initial conditions, extrapolation and gradient methods. This article is devoted to the comparison of these methods, which is based on their suitability for algorithmization of the computational process and the possibility of using them to solve other problems, such as determining the static stability of the periodic process.
Modern methods of studying static stability, in particular determining the limits of stability of periodic processes, are based on the algebraic criteria of Nyquist, Hurwitz and others. These methods are not subject to the ideology of building a single mathematical apparatus and creating on its basis a single algorithm for calculating periodic processes.
The practical use of the method, which is based on the model of sensitivity of system variables to their initial conditions, was hampered by the difficulty of determining the elements of the sensitivity matrix. In this paper, this problem is solved by representing the specified matrix by the product of two other matrices obtained on the basis of the functional relationship between electrical and magnetic parameters.
Keywords: differential equations, sensitivity matrix, accelerated search, periodic processes
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