Machines 3 - Lec_002 [Compatibility Mode]

Lecture Outlines1. Slip and Rotor Frequency

2. Induced Voltage

3. Induction Motors and Transformers

4. Armature Windings

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

4. Armature Windings

Slip and Rotor Frequency

Let Nm is the rotor speed at a certain load.

With respect to the rotor, the revolving field is moving

a head at a relative speed of

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Nr = Ns- Nm , rpm

This speed is called slip speed, and can be expressed in

terms of slip (s), which is the ratio of the slip speed andsynchronous speed

s

ms

s

r

NNN

NN

s

==

At starting or blocked rotor, S=1, the rotor appears

exactly like a short circuited secondary winding of the

transformer

Hence, the frequency of the induced emf in the rotor

Slip and Rotor Frequency

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Hence, the frequency of the induced emf in the rotorwindings is the same as that of the revolving field.

However, when the rotor rotates, it is the relative speed

of the rotor (Nr) that is responsible for the induced emfin its coils.

Thus, the frequency of the induced emf in the rotor is

( )NNPPNf msrr ==

Slip and Rotor Frequency

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

( )

s fN

NNPN

f

s

mss

r

=

=

==

120

120120

What would be the frequency of the rotors induced

voltage at any speed Nm?

sr s ff =

Slip and Rotor Frequency

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

When the rotor is blocked (s = 1) , the frequency of the induced voltage is equal to the supply frequency

On the other hand, if the rotor runs at synchronous

speed (s = 0), the frequency will be zero

a flux linkage of phase a

a = N p cos(t) By Faradays law, induced voltage in a phase coil aa is

tsinNdt

de pa =

=

Induced voltage

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

dtpa

p

p

rms Nf44.42

NE =

=

In actual machine with distributed and short-pitch windings

induced voltage is LESS THAN this by a winding factor Kw

wp

p

rms KNf44.42

NE =

=

Induction Motors and Transformers Both IM and transformer works on the principle of induced

voltage Transformer: voltage applied to the primary windings

produce an induced voltage in the secondary windings

Induction motor: voltage applied to the stator windingsproduce an induced voltage in the rotor windings

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

produce an induced voltage in the rotor windings

The difference is that, in the case of the induction motor, thesecondary windings can move

Due to the rotation of the rotor (the secondary winding of theIM), the induced voltage in it does not have the samefrequency of the stator (the primary) voltage

No of stator slots, S =12 No of phases, m = 3 No of poles, P = 4 No of stator slots per pole = 3 electrical slot angle = (360/S)* (P/2) = 60

Armature WindingsExample:

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

electrical slot angle = (360/S)* (P/2) = 60

Phase- A

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Phase- A and phase-B

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Phase- A and phase-B and phase-C

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

At = 0

Ia +veIb & Ic -ve

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Ia +ve

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Ib -ve

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Ic -ve

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Pattern of four pole at = 0

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

At = 60

Ia & Ib +veIc -ve

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Ia +ve

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Ib +ve

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Ic -ve

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Pattern of four pole at = 60

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

Pattern of four pole at = 0 and 60

= 0

Tanta University Faculty of EngineeringElectrical Power and Machines Engineering Department EPM3215 Electrical Machines (3) Dr. Said M. Allam

= 60