Electrical Engineering ⇒ Topic : Rotor Equivalent Circuit

Sachin
 
Equivalent Circuit of the Rotor: The rotor current I_{2}, when motor is loaded, is given by
From the above relation it appears that the rotor circuit which actually consists of a fixed resistance R_{2}, and a variable reactance sX_{2} (proportion.al to slip) connected across E_{r}= sE_{2} [Fig. (i)] can looked upon as equivalent to a rotor circuit having a fixed reactance X, connected in series with a variable resistance R_{2}s (inversely proportional to slip) and supplied with constant voltage E_{2} as shown in [Fig.(ii)]
Figure (a) Equivalent circuit of a rotor. Also, the resistance R_{2}/s can be written. as,
It consists of two parts : (i) The part R_{2} is the rotor resistance itself and represents the rotor copper loss (ii) the second part is This is known as load resistance R_{L}and 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 noninductive 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}.  
 
Samual
 
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 threephase induction motor If prime notation used for referred quantities is dropped, Figure 3 (a) shows the equivalent circuit of threephase 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 shortcircuited winding transformers and for s = 0, Figure 3 (b) becomes equivalent circuit of an opencircuited transformer.
figure (3) Equivalent circuit of induction motor In Figure 3 (b), r_{2} is the actual rotor resistance (referred to stator) whereas r_{2}[(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 noload current is 2% to 5% of full load current and per unit leakage reactance is low. In induction motor, the noload current is 30% to 50% of fullload 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 threephase induction motor without core loss In Figure (4), z is the per phase impedance offered to the stator by the rotating airgap field. ............ (4) Impedance seen by the stator applied voltage is written as: ............... (5)  
 
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