# RESONANT PROCESSES IN STARTING MODES OF SYNCHRONOUS MOTORS WITH CAPACITORS IN THE EXCITATION WINDINGS CIRCUIT

## DOI:

https://doi.org/10.20998/2074-272X.2017.4.04## Keywords:

salient-pole synchronous motor, capacitors, excitation winding, resonance, static characteristics## Abstract

*Purpose**. Development of a mathematical model that enables to detect resonance modes during asynchronous startup of salient-pole synchronous motors, in which capacitors are switched on to increase the electromagnetic moment in the circuit of the excitation winding.*

**Methodology**. The asynchronous mode is described by a system of differential equations of the electric equilibrium of motor circuits written in orthogonal coordinate axes. The basis of the developed algorithm is the mathematical model of the high-level adequacy motor and the projection method for solving the boundary value problem for the equations of the electric equilibrium of the circuits written in orthogonal coordinate axes, taking into account the presence of capacitors in the excitation winding. The coefficients of differential equations are the differential inductances of the motor circuits, which are determined on the basis of the calculation of its magnetic circuit. As a result of the asymmetry of the rotor windings in the asynchronous mode, the current coupling and currents change according to the periodic law. The problem of its definition is solved as a boundary one.**Results**. A mathematical model for studying the asynchronous characteristics of synchronous motors with capacitors in an excitation winding is developed, by means of which it is possible to investigate the influence of the size of the capacity on the motor's starting properties and the resonance processes which may arise in this case.**Scientific novelty**. The developed method of mathematical modeling is based on a fundamentally new mathematical basis for the calculation of stationary dynamic modes of nonlinear electromagnetic circuits, which enables to obtain periodic coordinate dependencies, without resorting to the calculation of the transients. The basis of the developed algorithm is based on the approximation of state variables by cubic splines, the projection method of decomposition for the boundary value problems of the calculation of the established periodic modes and the differential method of calculating static characteristics.**Practical value**. Using the developed algorithm of calculation it is possible to determine the required capacitances of the capacitors in the excitation winding to start the synchronous motor and to investigate the possibility of occurrence of the resonance at startup with the selected capacitance value of the capacitors by calculating the static characteristics as a sequence of asynchronous modes.## References

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*Electrical Engineering & Electromechanics*, (4), 21–25. https://doi.org/10.20998/2074-272X.2017.4.04

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Copyright (c) 2017 V. S. Malyar, V. S. Maday, I. R. Kens

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