Consequently the circuit can be simplified by eliminating the ideal transformer and referring the rotor's resistance and reactance to the primary (denoted by ′). The equivalent circuit shown above has removed the dependence on slip for determining the secondary voltage and frequency. The above equality allows the equivalent circuit to be drawn as: The rotor circuit, the current I 2 is given by:
The rotor resistance and reactance are represented by R 2 and X 2 with X 2 being dependant on the frequency of the inductor rotor emfs. For the rotor side, the induced emf is affected by the slip (as the rotor gains speed, slip reduces and less emf is induced). Magnetising reactance required to cross the air gap is represented by X m and core losses (hysteresis and eddy current) by R c.Īn ideal transformer of N1 and N2 turns respectively represents the air gap. In the equivalent circuit R 1 represents, the resistance of the stator winding and X 1 the stator leakage reactance (flux that does not link with the air gap and rotor). Induction Motor Equivalent Circuitįrom the preceding, we can utilise the equivalent circuit of a transformer to model an induction motor. This is the same as in a transformer and allows us to model the behaviour of an induction as a transformer with an air gap. The rotational speed of the stator flux and rotor flux are identical. However, the rotor itself is rotating at n r, giving a total rotor flux speed of: The quantity n s is the speed at which the flux rotates relative to the stator and sn s the speed of the rotor flux relative to the rotor. The synchronous speed in revolutions per second is: Which when combined with the above equation for slip, gives: Within the rotor, the frequency (f r) is given by the speed difference between that of the rotor and stator: Slip can be expressed as either a fraction or percentage:įrom magnetic winding theory, the relationship between frequency in the stator ( f), number of pole pairs ( p) and the synchronous speed is given by: The difference between the motors synchronous speed ( n s) and actual rotor speed ( n r) is known as the slip ( s). The difference between the motors synchronous and actual asynchronous speed is known as the slip
Motor winding resistance calculator full#
Typically the rotor full speed will between 2 and 6% that of the synchronous speed. The rotor can never rotate at synchronous speed, otherwise there would be no induced current. The stator magnetic field rotates at the motors synchronous speed ( n s). Before jumping into the equivalent circuit, a few concepts are useful. One way to analyse and understand the operation of an induction motor is by the use of an equivalent circuit. The rotor current produces it's own magnetic field, which then interacts with the stator field to produce torque and rotation. Within the induction motor, an electrical current in the rotor is induced by a varying magnetic field in the stator winding. Induction motors are frequently used in both industrial and domestic applications.
0 kommentar(er)
