Electrical Engineering ⇒ Topic : Circuit Model and Phasor Diagram

Peter
 
Circuit Model and Phasor Diagram The net e.m.f. induced in the armature is the sum of the transformer e.m.f. and that due to leakage inductance x_{a}, which is given by
Since E_{t }is caused by crossflux whose origin is an armature current, the two must be in phase.
The net inductive e.m.f. in the armature circuit is:
The circuit model of the AC series motor is shown in Figure (a).
Figure (a) Circuit model of AC series motor for AC operation. Torque As stated earlier, the torque developed is pulsating in nature with an average value and a predominant second harmonic component. The average torque is given by
Being a series motor, Ea ∝ I_{a}, the torque is, therefore, proportional to the square of armature current, which becomes directly proportional at high armature current, because of saturation Phasor diagram and performance characteristics In AC series motor, there will be series drop in armature and field along with the reactance drop due to both in addition to rotational e.m.f. Vector diagram of AC series motor is shown in Figure (b)
Figure (b) Phasor diagram of AC series motor. where R_{a}, R_{f} are resistances of armature and field winding, respectively, and X_{a}, X_{f }are reactances of armature and field, respectively, and E_{b} is rotational back e.m.f. produced in the armature It will be seen that the field and armature reactances increase the angle of lag, and therefore, reduction in power factor. For a given value of torque and applied voltage, value of armature current will be constant as also the field flux. It may also be observed that the back e.m.f. in AC series motor is less than the back e.m.f. in DC series motor. Since field flux remains constant, reduction in e.m.f. in AC series motor would suggest that its speed for given developed torque is less than that of DC series motor. Figure (c) shows speedtorque characteristics of AC and DC series motors. It will be observed that whole performance revolves on the point that the back e.m.f. in AC series motor should be made as far as possible equal to the back e.m.f. in DC series motor. This would mean reducing the armature and field reactances. Field reactance can be reduced by employing less number of turns on the field, which will in turn reduce field flux. However, to develop the same torque, the number of turns on the armature has to be increased in the same ratio. This would reduce field reactance and increase armature reactance. To cancel the effect of armature reactance, compensating winding is used.
Figure (c) Performance characteristics of series motor for AC operation. The power factor of a series motor is rather poor because of the large reactances of field and armature (X_{f }and X_{a}). The p.f. at low speed is very poor. This is also due to the value of rotational back e.m.f. being small, and as such the applied voltage has to be balanced by the field and armature reactances which will now be high. However, p.f. of AC series motor is higher at higher speeds and is about 0.95. The arrangement of main field winding connected in series with the compensating winding for an AC series motor is shown in Figure (d). The axis of this winding is along the brush axis and the winding must be spread over the full pitch for effective neutralization of crossflux. Thearrangement also shows an interpole winding connected in series with the other two windings, whose effect is only over the interpolar region
figure (d) Series motor with compensating winding and interpole winding connected to AC mains The noload speed of a universal motor is very high (about 20,000 rpm). Hence the motor is smaller in size than other types for a given load. Universal motors are used where light weight is important as in vacuum cleaners, portable tools, etc.  
 
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