Mathematical model of the asynchronous machine in the coordinate system where the axes "oscillate" in space
DOI:
https://doi.org/10.33216/1998-7927-2023-277-1-38-42Keywords:
asynchronous machine, electromotive force, rotor, stator, current vector, coordinate system, squirrel-cage rotorAbstract
The article presents an analysis of the mathematical model of an asynchronous machine in a coordinate system, the axes of which "oscillate" in space. It is shown that the differential equations describing the processes in a real three-phase asynchronous machine contain periodic coefficients. The latter complicate the solution of such equations and require the search for approaches that make it possible to obtain an equation with constant coefficients.
It is shown that in a fully controlled asynchronous machine, both the magnitude and the phase of the additional electromotive force are adjustable and independent parameters, and in an asynchronously valve cascade, which can be considered as a dual-feed machine with limited control capabilities, only the magnitude of the additional electromotive force vector is an independent parameter; and its phase is determined: the counter-emf, which is introduced into the circuit of the rectified current of the rotor, is always in antiphase with the rotor current vector.
It has been established that the solution of the problem is simplified by the introduction of a new coordinate system, in which the axes rotate in space not at a constant speed, but with a variable that is a certain function of time. The essence of the transformations associated with the transition to a new coordinate system is to find such a function that allows in the plane of these coordinates to conditionally consider the fixed vector, the parameters of which are decisive for the given system. It is found based on the condition that the positive direction of the real axis of the system always coincides with the vector in relation to which the state of the asynchronous machine is considered.
The differential equations of the dual-feed machine in the "g-i" axes are given in vector form. It is shown that these equations are valid both for a motor with a squirrel-cage rotor and for any system of an asynchronous electric drive, the speed of which is controlled by introducing an additional emf. into the rotary chain.
An equation for the initial angular velocity of the vectors of currents and flux linkages in space relative to a fixed stator under zero initial conditions, regardless of the slip of the rotor, is derived for an asynchronous machine with a squirrel-cage rotor. Transient processes of starting an asynchronous machine with a squirrel-cage rotor are given.
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