Electrical World

The rotor input P 2 , rotor copper loss P c and gross mechanical power developed P m are related through the slip s. Let us derive this relationship.        Let            T = Gross torque developed by motor in N-m.        We know that the torque and power are related by the relation,                          P = T x ω       where          P = Power and                    ω = angular speed                               = (2πN)/60 , N = speed in r.p.m.    ...

Induction motor converts an electrical power supplies to it into mechanical power. The various stages in this conversion is called power flow in an inductor motor.        The three phase supply given to the stator is the net electrical input to the motor. If motor power factor is cos Φ and V L , I L are line values of supply voltage and current drawn, then net electrical supplied to the motor can be calculated as,        This is nothing but the stator input.        The part of this power is utilised to supply the losses in the stator which are stator core as well as copper losses.        The remaining power is delivered to the rotor magnetically through the air gap with the help of rotating magnetic field. This is called rotor input denoted as P 2 .       The rotor is not able to convert its entire input to the mec...

The various power losses in an induction motor can be classified as, i) Constant losses ii) Variable losses i) Constant losses :        These can be further classified as core losses and mechanical losses.       Core losses occur in stator core and rotor core. These are also called iron losses. These losses include eddy current losses and hysteresis losses. The eddy current losses are minimised by using laminated construction while hysteresis losses are minimised by selecting high grade silicon steel as the material for stator and rotor.       The iron losses depends on the frequency. The stator frequency is always supply frequency hence stator iron losses are dominate. As against this in rotor circuit, the frequency is very small which is slip times the supply frequency. Hence rotor iron losses are very small and hence generally neglected, in the running condition.   ...

It is shown that in slip ring induction motor, externally resistance can be added in the rotor. Let us see the effect of change in rotor resistance on the torque produced.       Let                                   R 2 = Rotor resistance per phase       Corresponding torque,      T α   (s E 2 2 R 2 )/√(R 2 2 +(s X 2 ) 2 )        Now externally resistance is added in each phase of rotor through slip rings.       Let        R 2 ' = New rotor resistance per phase       Corresponding torque        T ' α   (s E 2 2 R 2 ' )/√(R 2 ' 2 +(s X 2 ) 2 )        Similarly the starting torque at s =...

Uptill now, we have seen torque - slip characteristics of an induction motor. To compare the performance of induction motor with d.c. shunt and series motors, it is possible to plot speed-torque curve of an induction motor.        At N = T s , the motor stops as it can not produce any torque, as induction motor can not rotate at synchronous motor.       At N = 0, the starting condition, motor produces a torque called starting torque. Fig. 1   Speed Torque characteristics        For low slip region, i.e. speeds near the region is stable and the characteristics is straight in nature. Fall in speed from no load to full load is about 4 to 6 %. The characteristics is shown in the Fig.1. It can be seen from that the figure that for the stable region of operation, the characteristics is similar to that of d.c. shunt motor. Due to this, three phase induction motor is practically s...

The performance of the motor is sometimes expressed in terms of comparison of various torques such as full load torque, starting torque and maximum torque. The comparison is obtained by finding out ratios of these torques. 1.1 Full load and Maximum Torque Ratio In general,        T α (s E 2 2 R 2 )/(R 2 2 +(s X 2 ) 2 )   Let                     s f  = Full load slip . . .                        T F.L.   α (s f  E 2 2 R 2 )/(R 2 2 +(s f  X 2 ) 2 )   and                    s m = Slip for maximum torque T m  . . .                       ...

As the induction motor is located from no load to full load, its speed decreases hence slip increases. Due to the increased. load, motor has to produce more torque to satisfy load demand. The torque ultimately depends on slip as explained earlier. The behaviour of motor can be easily judged by sketching a curve obtained by plotting torque produced against slip of induction motor. The curve obtained by plotting torque against slip from s = 1 (at start) to s = 0 (at synchronous speed) is called torque-slip characteristics of the induction motor. It is very interesting to study the nature of torque-slip characteristics.        We have seen that for a constant supply voltage,  E 2 is also constant. So we can write torque equations as,        Now to judge the nature of torque-slip characteristics let us divide the slip range (s = 0 to s = 1) into two parts and analyse them independently. i) Low slip region...

From the torque equation, it is clear that torque depends on slip at which motor is running. The supply voltage to the motor is usually rated and constant and there exists a fixed ratio between E 1 and E 2 . Hence E 2 is also consatnt. Similarly R 2 , X 2 and n s are constants for the induction motor.         Hence while finding the condition for maximum torque, remember that the only parameter which controls the torque is slip s.        Mathematically for the maximum torque we can write,                  dT/ds = 0 where        T = (k s E 2 2 R 2 )/(R 2 2 +(s X 2 ) 2 )        While carrying out differential remember that E 2 , R 2 , X 2 and k are constants. The only variable is slip s. As load on motor changes, its speed changes and hence slip changes. This sl...

The torque produced in the induction motor depends on the following factors : 1. The part of rotating magnetic field which reacts with rotor and is responsible to produce induced e.m.f. in rotor. 2. The magnitude of rotor current in running condition. 3. The power factor of the rotor circuit in running condition.        Mathematically the relationship cab be expressed as,                        T α Φ I 2r cos Φ 2r                                             .........(1) where              Φ = Flux responsible to produce induced e.m.f.                   ...

We know that, transformer is a device in which two windings are magnetically coupled and when one winding is excited by a.c. supply of certain frequency, the e.m.f. gets induced in the second winding having same frequency as that of supply given to the first winding. The winding to which supply is given is called primary winding while winding in which e.m.f. gets induced is called secondary winding. The induction motor can be regarded as the transformer.        The difference is that the normal transformer is an alternating flux transformer while induction motor is rotating flux transformer. The normal transformer has no air gap as against this an induction motor has distinct air gap between its stator and rotor.        In an alternating flux transformer the frequency of induced e.m.f. and current in primary and secondary is always same. However in the induction motor frequency of e.m.f. and current on the sta...

Effect of Slip on Rotor Parameters 4. Effect on Rotor Power factor        From rotor impedance, we can write the expression for the power factor of rotor at standstill and also in running condition.        The impedance triangle on standstill condition is shown in the Fig1. From it we can write,                         cos Φ 2 = Rotor power factor on standstill                                     = R 2 /Z 2 =R 2 /√ ( R 2 2 + X 2 2 )        The impedance in running condition becomes Z 2r and the corresponding impedance triangle is shown in the Fig.2. From Fig. 2 we can write,    ...