## Behaviour of Synchronous Motor on Loading

When a d.c. motor or an

induction motor is loaded, the speed of the motors drops. This is

because the load torque demand increases then the torque produced by the

motor. Hence motor draws more current to produce more torque to satisfy

the load but its speed reduces. In case of synchronous motor speed

always remains constant equal to the synchronous speed, irrespective of

load condition. It is interesting to study how synchronous motor reacts

to changes in the load condition.

In a d.c. motor, armature develops an e.m.f.after motoring action

starts, which opposes supply voltage, called back e.m.f. E

_{b}.

Hence if R

_{a }the armature resistance and V is the supply voltage, we have established the relation for the armature current as,
I

_{a }= (V- E_{b}) / R_{a }…… for a d.c. motor
where E

_{b }= ?PNZ / 60A ………for a d.c. motorIn case of synchronous motor also, once rotor starts rotating at

synchronous speed, the stationary stator (armature) conductors cut the

flux produced by rotor. The only difference is conductors are stationary

and flux is rotating. Due to this there is an induced e.m.f. in the

stator which according to Lenz’s law opposes the supply voltage. This

induced e.m.f. is called back e.m.f. in case of synchronous motor. It is

obtained as E

_{bph }i.e. back e.m.f. per phase. This gets

generated as the principle of alternator and hence alternating in nature

and its magnitude can be calculated by the equation,

**or**

**E**

_{bph }? ?As speed is always synchronous, the frequency is constant and hence

magnitude of such back e.m.f. can be controlled by changing the flux ?

produced by the rotor.

So back e.m.f. in case of synchronous motor depends on the excitation

given to the field winding and not on the speed, as speed is always

constant.

As

stator construction is similar to the armature of a three phase

alternator, the impedance of the stator is called synchronous impedance

of synchronous motor consisting of R

stator construction is similar to the armature of a three phase

alternator, the impedance of the stator is called synchronous impedance

of synchronous motor consisting of R

_{a }as the stator winding resistance and X_{s }as the synchronous reactance. All the values are generally expressed on per phase basis.
Z

_{s }= R_{a }+ jX_{s }? per phase
So similar to the d.c. motor, we can write voltage equation for a synchronous motor as,

The difference is that this equation is vector equation as each

quantity is alternating and has different phase. So addition is to be

performed vectorially to obtain the result.

The difference is that this equation is vector equation as each

quantity is alternating and has different phase. So addition is to be

performed vectorially to obtain the result.

where V

_{ph }is the supply voltage per phase. The magnitude of E_{bph }is adjusted almost equal to V_{ph}, on no load by controlling flux produced by rotor i.e. field winding.__1.1 Ideal Condition on No Load__

The ideal condition on no load can be assumed by neglecting various losses in the motor.

And V

_{ph }= E_{bph }Under this condition, the magnetic locking between stator and rotor is

in such a way that the magnetic axes of both, coincide with each other

as shown in the Fig.1. As this is possible only under no losses

condition, is said to be ideal in case of synchronous motor.

Fig. 1 Magnetic locking under no load condition |

As magnitude of E

_{bph }and V_{ph }is same and opposes the phasor diagram for this condition can be shown as in the Fig. 2.Fig. 2 Phasor diagram on no load losses |

In practice this is impossible. Motor has to supply mechanical losses

and iron losses alongwith small copper losses. Let us see how it can be

explained in case of synchronous motor.

__1.2 Synchronous Motor on No Load (With Losses)__

We have seen that E

_{bph }and V_{ph }are magnitudewise same, which is adjusted by controlling field current, in turn controlling the flux.Now due to the various losses practically present on no load, the

magnetic locking exists between stator and rotor but in such a way that

there exists a small angle difference between the axes of two magnetic

fields as shown in the Fig.3.

Fig. 3 Magnetic locking under practical condition |

So the rotor axis falls back with respect to stator axis by angle ‘?’

as shown in the Fig.3 This angle decides the amount of current required

to produce the torque to supply various losses.

Hence this angle is called load angle, power angle, coupling angle,

torque angle or angle of retardation and denoted as ? as mentioned

earlier.

The

magnetic locking still exists between the two and rotor rotates at

synchronous speed alongwith rotating magnetic field maintaining angle

difference between the axes of two fields, as shown in the Fig. 3(b).

The flux lines between the two get stretched due to such retardation of

rotor axis with respect to stator.

magnetic locking still exists between the two and rotor rotates at

synchronous speed alongwith rotating magnetic field maintaining angle

difference between the axes of two fields, as shown in the Fig. 3(b).

The flux lines between the two get stretched due to such retardation of

rotor axis with respect to stator.

Now though

**?**E_{bph }**?**_{}=**?**V_{ph }**?**, E_{bph }will not be located in exact opposition with V_{ph }, but will get displaced from its initial position by angle’?’ as shown in the Fig. 4(a).Fig. 4(a) Phasor diagram for no load condition with losses |

Hence the vector difference between the two, E

_{bph }and V_{ph }is not zero but give rise to a phasor ‘OB’ as shown.
This resultant decides the amount of current I

be drawn to produce the torque which meets the various losses present

in the synchronous motor. Under no load condition, ? is very small and

hence E

_{aph }tobe drawn to produce the torque which meets the various losses present

in the synchronous motor. Under no load condition, ? is very small and

hence E

_{Rph }is also very small.
So current drawn by the motor is also very small on no load which is the case in all the various type of motors.

__1.3 Synchronous Motor on Load__

As the load on the synchronous motor increases, there is no change in

its speed. But what gets affected is the load angle ‘?’ i.e. the angle

by which rotor axis retards with respect to stator axis.

Hence as load increases, ? increases but speed remains synchronous.

As synchronous impedance is constant, the magnitude of I

by the motor increases as load increases. This current produces the

necessary torque which satisfied the increased load demand. The magnetic

locking still exists between the rotor and stator.

_{aph }drawnby the motor increases as load increases. This current produces the

necessary torque which satisfied the increased load demand. The magnetic

locking still exists between the rotor and stator.

The phasor diagrams showing E

_{Rph }increases as load increases are shown in the Fig. 4(b) and (c).Fig. 4 |

So from the above discussion it is clear that on no load, current drawn

by the motor is very small. This is because the stator and the rotor

magnetic axes are almost matching transformer each other i.e. load

angle ? is very small. As load increases, rotor magnetic axis starts

retarding with respect to stator axis i.e. load angle ? increases

maintaining the magnetic locking condition. And hence in case of the

synchronous motor load affects the angle ? without affecting the speed.

As ? increases, the magnitude of E

_{Rph }increases which shows that motor draws more current from the supply. This satisfies the increased load torque demand.

So torque produced in the synchronous motor depends on the load angle

‘?’ for small values of and to be precise depends on ‘sin?’. The load

angle ‘?’ is measured in degrees electrical. As angle ? increases, the

magnetic flux lines producing the force of attraction between the two

get more and more stretched. This weakens the force maintaining the

magnetic locking, though torque produced by the motor increases. As ?

reaches upto 90

^{o}electrical i.e. half a pole pitch, the

stretched flux lines get broken and hence magnetic locking between the

stator and rotor no longer exists. The motor comes out of synchronism.

So torque produced at ? equal to 90

^{o}electrical is the

maximum torque, a synchronous motor can produce, maintaining magnetic

locking i.e. synchronism. Such s torque is called pull out torque. The

relationship between torque produced and load angle is shown in the Fig

5.

Fig. 5 Torque angle characteristic |

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