Mathematical Simulation Of The Magnetic Field Occurred By The Armature Reaction Of The Synchronous Machine

KEYWORDS As experience shows while studying the magnetic field, it can be assumed that the machine's magnetic field is plane-parallel. Mathematical simulation, synchronous machine, magnetic field. It is appropriate to substitute the electromagnetic field equations system with one equation which depends on the magnetic vector potential, having only one (axial) component z A A in a plane-parallel field. In such equation A is spatial coordinates x, y and time t function, which means that the equation (1) describes space and time alternating magnetic field (Voldek 1978) ABSTRACT Using proposed methodology and mathematical simulation parameters of the armature winding, magnetic system geometry is estimated, as well as the saturation's influence on the mentioned parameter is evaluated. Methods are based on magnetic field mathematical simulation, solving partial derivatives of the differential equation comparatively to the vector magnetic potential A and using one of the most efficient methods – the finite element method (FEM) (Voldek 1978). There is theoretically justified and described method of obtaining the armature winding phase magnetic-flux linkage, i.e.,) t (Z < , from the vector potential which, as a function of spatial coordinates , is received by mathematical simulation of the stationary magnetic field.) , (y x A a j y A x A P w w w w 2 2 2 2 , (1) where P-magnetic permeability; and – the external field source's current density. a j Solving this type of equation is rather difficult, therefore, it is appropriate to reduce it to number of simpler tasks. In this case, the task is based on the fact that in time varying process (0 z w w t) can be viewed as a single fixed process set of different consecutive time points. So, for example, if the field source current density is in time varying sinusoidal function n i t t t t ,. 1 t j t j am a Z sin) (, then equation (1) must be solved n times, each time in the right side of that equation define moment of time that corresponds to current densities moment value i t i a t j i am t j Z sin) (. Solving such a task as the results receive vector potentials, which are essentially a table formed functional dependence) (t f A. A similar approach is used solving non-stationary field equations, when rotor speed 0 z Q. In this case, it is possible to solve …