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This paper presents the mathematical modelling and simulation study of three phase squirrel cage induction machine. This is achieved, using the dot convention technique for magnetically coupled circuit applicable to circuit elements of electrical machines. When two loops (coils), with or without contacts between them affect each other through the magnetic field generated by one of them, they are said to be magnetically coupled when such loops are in a close proximity to each other, the magnetic flux caused by current in one coil links with the other loop, thereby inducing voltage in the later by mutual induction. Based on the notion of mutual induction, we then introduce the circuit element known as transformer. A close examination of the fluxmmf interactions in a poly-phase squirrel cage induction motor shows that, electrically, the machine is a form of transformer. The synchronously-rotating air-gap flux wave in the induction machine is the counterpart of the mutual core flux in the transformer. The rotating field induces emf’s of stator frequency in the stator windings and of slip frequency in the rotor windings (for all rotor speeds other than synchronous speed). The induction machine transforms voltages and at the same time changes frequency. When viewed from the stator, all rotor electrical and magnetic phenomena are transformed to stator frequency. The rotor mmf reacts on the stator windings in the same manner as the mmf of the secondary current in a transformer reacts on the primary. Pursuit of this line of reasoning leads to per-phase equivalent circuit for 3-phase induction machines which closely resemble that of the transformer (A.E. Fitzgerald et al (2003)). In terms of operation, the squirrel cage induction machine can be relatively seen as a short-circuited rotating transformer, having much similarity in their steady state equivalent circuits. In the course of developing this paper, the equivalent circuit of the squirrel cage induction machine, from which its steady-state characteristics via simulation/matlab plots could be predicted, is obtained using the magnetically coupling effect of transformer elements. Keyword: Magnetic coupling, mutual induction, self induction, short-circuited rotating transformer, squirrel cage induction machine.

iosr journal of electrical and electronics engineering

Mathematical Modelling And Steady-State Simulation Study of Three Phase Squirrel Cage Induction Machine, Using The Dot Convention Technique for Magnetically Coupled Circuit.