Electrical Engineering ⇒ Topic : Rotor Equivalent Circuit

 Equivalent Circuit of the Rotor:-

The rotor current I₂, when motor is loaded, is given by

From the above relation it appears that the rotor circuit which actually consists of a fixed resistance R₂, and a variable reactance sX₂ (proportion.al to slip) connected across E_r= sE₂ [Fig. (i)] can looked upon as equivalent to a rotor circuit having a fixed reactance X, connected in series with a variable resistance R₂s (inversely proportional to slip) and supplied with constant voltage E₂ as shown in [Fig.(ii)]

                               Figure (a) Equivalent circuit of a rotor.

Also, the resistance R₂/s can be written. as,

It consists of two parts : (i) The part R₂ is the rotor resistance itself and represents the rotor copper loss (ii) the second part is This is known as load resistance R_Land is the electrical equivalent of the mechanical load on the motor. In other words the mechanical load on an induction motor can be represented by a non-inductive resistance of the value

                                                  Fig(b). Equivalent circuit of a rotor with load resistance R_L

In Fig.(b) is shown the equivalent rotor circuit along with the load resistance R_L.

Rotor Equivalent Circuit

Figure (1) shows rotor equivalent circuit. The per phase rotor current is given by

                                .............. (1)

                                  .............. (2)

                                                           figure (1)  Rotor circuit

The complete equivalent circuit of induction motor is shown in Figure (2) where x'₂ and r'₂ are rotor leakage reactance and resistance referred to stator.

             figure (2) Complete equivalent circuit of three-phase induction motor

If prime notation used for referred quantities is dropped, Figure 3 (a) shows the equivalent circuit of three-phase induction motor and Figure 3 (b) shows the modified form of induction motor equivalent circuit.

From Figure 3 (b),

                                             ............ (3)

For s = 1, Figure 3 (b) becomes the equivalent circuit of the two short-circuited winding transformers and for s = 0, Figure 3 (b) becomes equivalent circuit of an open-circuited transformer.

                                                                    figure (3)  Equivalent circuit of induction motor

In Figure 3 (b), r₂ is the actual rotor resistance (referred to stator) whereas r₂[(1 - s) /s] is the electrical analogue of the variable mechanical load.

            The use of exact equivalent circuit is quite tedious. So some simplifications should be made. In transformers, it is possible to draw the approximate equivalent circuit by moving the shunt branch across the primary terminals because the no-load current is 2% to 5% of full load current and per unit leakage reactance is low. In induction motor, the no-load current is 30% to 50% of full-load current and per unit leakage reactance is high. So considerable error will be introduced if the shunt branch is neglected or moved towards stator terminals.

         During normal operating condition of constant voltage and frequency, the core loss ininduction motor is usually constant. So the core loss resistance R, representing  the motor core loss can be removed from the equivalent circuit. The equivalent circuit is redrawn in Figure (4).

                                  figure (4) Equivalent circuit of a three-phase induction motor without core loss

In Figure (4), z is the per phase impedance offered to the stator by the rotating air-gap field.

                                        ............ (4)

Impedance seen by the stator applied voltage is written as:

                                                       ............... (5)