Analytical study of starting current of the induction motor stator
DOI:
https://doi.org/10.15587/1729-4061.2018.125801Keywords:
induction motor, three-phase coordinate system, state space method, characteristic equation, matrix of transfer functionsAbstract
In a three-phase coordinate system, the induction motor is described by a system of nonlinear differential equations of the eighth order, which in a general case does not have an analytical solution. The system of IM equations can be considerably simplified for the starting mode with a stationary rotor. When analyzing the specified operating mode, periodic coefficients in the IM equations that depend on the angular position of the rotor are transformed into constant magnitudes. Further simplification of the system of IM equations implies the exclusion of motion equations, which is also associated with the accepted assumption about the immobility of the rotor. We assume that the stator of IM is connected to a power line according to the circuit without a zero wire. This makes it possible to exclude from the common system two equations of electrical equilibrium of the windings, for one stator and one rotor winding, by applying the Kirchhoff's first law. As a result of the performed transformations, we obtained a simplified system of IM equations with a stationary rotor, which, in contrast to the complete system, is a system of linear differential equations of the fourth order and is presented in the Cauchy form, which can be solved analytically.
Using the methods of analysis of dynamic objects in a state space, we obtained expressions for the coefficients of IM characteristic equation and its roots, as well as for the matrix of IM transfer functions when the rotor is stationary. An analysis of expressions for the roots of the characteristic equation shows that the character of roots of the IM characteristic equation depends on the initial angular position of the IM rotor. This is explained by the fact that a change in the initial angular position of the rotor changes the magnitude of mutual inductance between separate windings of IM, which affects the processes of energy transfer between stator and rotor windings.
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Copyright (c) 2018 Valerii Tytiuk, Oleksii Chornyi, Aleksandr Pozihun, Mila Baranovskaya, Alexander Romanov
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