## Equivalent circuit of a polyphase induction machine, Electrical Engineering

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Equivalent Circuit of a Polyphase Induction Machine

The inductionmachinemay be regarded as a generalized transformer inwhich energy is converted and electric power is transferred between stator and rotor, along with a change of frequency and a flow of mechanical power. At standstill, however, the machine acts as a simple transformer with an air gap and a short-circuited secondary winding. The frequency of the rotor-induced emf is the same as the stator frequency at standstill. At any value of the slip under balanced steady-state operation, the rotor current reacts on the statorwinding at the stator frequency because the rotating magnetic fields caused by the stator and rotor are stationary with respect to each other. The induction machine may thus be viewed as a transformer with an air gap and variable resistance in the secondary; the stator of the induction machine corresponds to the transformer primary, and the rotor corresponds to the secondary. For analysis of the balanced steady state, it is sufficient to proceed on a per-phase basis with some phasor concepts; so we will now develop an equivalent circuit on a per-phase basis. Only machines with symmetrical polyphase windings excited by balanced polyphase voltages are considered. As in other discussions of polyphase devices, let us think of three-phase machines as wye-connected, so that currents are always line values and voltages are always line-to-neutral values (on a per-phase basis).

The resultant air-gap flux is produced by the combined mmfs of the stator and rotor currents. For the sake of conceptual and analytical convenience, the total flux is divided into a mutual flux (linking both the stator and the rotor) and leakage fluxes, represented by appropriate reactances.

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