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Aim. Development of a method for calculating mechanical characteristics of three-phase induction motors with single-phase power supply. Methods. The developed algorithm is based on the high-adequacy mathematical model of motor and projection method for solving the boundary problem for equations of electrical circuits balance presented in the three-phase coordinate system. As a result of asymmetry of power supply to the stator windings, in steady state, flux-linkage and current change according to the periodic law. They are determined by solving the boundary problem. Results. The developed mathematical model allows determining periodic dependence of coordinates as a function of slip and, based on them, mechanical characteristics of motors. Academic novelty. The developed method relies on a completely new mathematical approach to calculation of stationary modes of nonlinear electromagnetic circuits, which allows obtaining periodic solution in a timeless domain. Practical value. Using the developed calculation algorithm, one can select capacitance required to start an induction motor with single-phase power supply and calculate static mechanical characteristics at a given capacitance. References 5, figures 3. Key words: mechanical characteristic, induction motor, single-phase power supply, boundary problem, projection method, capacitor.Предложен метод расчета механических характеристик трехфазных асинхронных двигателей, которые питаются от однофазной сети. Вращающееся магнитное поле создается за счет включения последовательно в одну фазу кон-денсаторов. Задача решается как краевая в трехфазной системе координат. В математической модели двигателя учитывается насыщение магнитопровода и вытеснение тока. Библ. 5, рис. 3. Ключевые слова: механическая характеристика, асинхронный двигатель, однофазное питание, краевая задача, проекционный метод, конденсатор.Introduction. Induction motors (IM) are mainly produced with three-phase windings that are powered symmetrical three-phase system voltages. However, in practice may need to switch to a single-phase network [1], which use capacitors that create shifting the phase current in a coil and a magnetic field motor becomes pulsating and rotating, causing electromagnetic torque. Also developed and are widely used capacitor electric motors, which are designed to operate on single-phase network [5]. And in the first and second cases, there is a problem of calculation of their starting characteristics and capacitors' capacitance choice.In technical literature since the calculation method for different values of capacitors are known [1,2], but these methods are not sufficient accuracy, since not adequately take into account factors such as asymmetry of power magnetic saturation and displacement current. Problems of analysis of operation modes of IM by mathematical modeling needs to solve two problems: the choice of a mathematical model of the motor and the method of calculation. These problems are interrelated, since using a simplified mathematical model of IM can not adequately tak...

Goal. Development of methods and mathematical models, based on them, for the calculation of transients and steady-state modes of induction electric drives operating in periodic load mode. Methodology. The developed algorithms are based on a mathematical model of an induction motor, which takes into account the saturation of the magnetic core and the displacement of current in the rotor bars. The processes are described by a system of nonlinear differential equations in the orthogonal axes x, y, which enables the results to be obtained with the smallest amount of calculations. The magnetization characteristics by the main magnetic flux and the leakage fluxes are used to calculate the electromagnetic parameters of the motor. To account for the current displacement in the rotor bars, the short-circuited winding is considered as a multilayer structure formed by dividing the bars in height by several elements. Results. Due to the variable load on the motor shaft, electromagnetic processes in both transient and steady state modes of the electric drive in any coordinate system are described by a system of nonlinear differential equations. The result of the calculation of the transients is obtained as a result of their integration time dependencies of coordinates (currents, electromagnetic torque, etc.) at a given law of change of the moment of loading. The proposed method of calculating steady-state mode is based on algebraization of differential equations on the mesh of nodes of the process cyclicity period and allows to obtain periodic dependencies in the time domain. Originality. The problem of calculating a steady-state periodic mode is solved as a boundary problem for a system of first-order differential equations with periodic boundary conditions, which allows to obtain instantaneous dependences during the period of currents, electromagnetic torque, capacities and other coordinates. Practical significance. Using the developed algorithm, it is possible to calculate the static characteristics of periodic processes as dependencies on different parameters of the cycle of periodic load or other coordinates, which is the basis for the choice of the motor for overload, power, heating, etc., as well as to detect the possibility of resonance. References 9, figures 4.

Розглядається проблема математичного моделювання динамічних режимів асинхронних двигунів з поздовжньоємнісною компенсацією реактивної потужності. В основу алгоритму розрахунку покладено математичну модель асинхронного двигуна високого рівня адекватності, в якій враховується насичення та витіснення струму. Бібл. 4, рис. 1. Ключові слова: асинхронний двигун, компенсація реактивної потужності, характеристики пуску, резонанс, конденсатори, субгармонічні коливання. математического моделирования динамических режимов асинхронных двигателей с продольно-емкостной компенсацией реактивной мощности. В основу алгоритма расчета положена математическая модель асинхронного двигателя высокого уровня адекватности, в которой учитывается насыщение и вытеснение тока. Библ. 4, рис. 1. Ключевые слова: асинхронный двигатель, компенсация реактивной мощности, характеристики пуска, резонанс, конденсаторы, субгармонические колебания. Рассматривается проблема

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