UNIT 4

Electrical Machines

Que1) The stator of a 3-phase induction motor has 5 slots per pole per phase. If supply frequency is 50Hz. Calculate a) number of stator poles produced and total number of slots in stator. b) Speed of rotating stator flux.?

Sol: a) P=2n=2*5=10 poles

Total number of slots= 5 slots/pole/phase * 10 poles * 3 phase=150

a) Ns==120x50/10=600rpm

Que2) A 3-phase induction motor is wound for 5 poles and is supplied from 50 Hz. Calculate a) synchronous speed b) rotor speed when slip is 4% c) rotor frequency when rotor runs at 500 rpm?

Sol: a) Ns==120x50/5=1200 rpm

b)rotor speed N=Ns(1-s)=1200(1-0.04)=1152 rpm

c)when rotor speed is 500 rpm, slip s=(Ns-N)/Ns=(1200-500)/1200=0.58

rotor current frequency f’=sf=0.58x50=29.17 Hz

Que3) A 3-phase, 50 Hz,3-pole induction motor has a slip of 4%.Calculate a)speed of rotor. B) frequency of rotor emf. If the rotor as a resistance of 2ohm, and standstill reactance of 4ohm,calculate the power factor c)at standstill and d)at a speed of 1200rpm?

Sol: Ns==120x50/3=2000 rpm

a) Speed of rotor N=Ns(1-s)=2000(1-0.04)=1920 rpm

b) Frequency or rotor = f’=sf=0.04x50=2Hz

R2=2ohm, X2=4ohm

Z2=R2+jX2=2+j4=4.4763.43o ohm

c)Power factor cosφ2=0.44(lag)

slip at speed 1200rpm s=2000-1200/2000=0.4

Rotor impedance at slip s=0.4 is

Z2s=R2+jsX2=2+jx0.4x4=2.56oohm

Power factor at 1200rpm is cos φ2s=cos38.66o=0.78(lag)

Q4) A 3-phase induction motor star connected rotor has an induced emf of 70volts between slip rings at standstill on open circuit. The rotor has a resistance and reactance per phase of 1ohm and 5ohm respectively. Calculate current/phase and power factor when slip rings are short circuited?

Sol: Standstill emf/rotor phase=70/

Rotor impedance/phase= ohm

Rotor current/phase=40.4/5.09=7.92A

Power factor cosφ=0.99

Que5) A 3-phase induction motor star connected rotor has an induced emf of 70volts between slip rings at standstill on open circuit. The rotor has a resistance and reactance per phase of 1ohm and 5ohm respectively. Calculate current/phase and power factor when slip rings are connected to star connected rheostat of 2ohm?

Sol: Rotor resistance/phase=2+1=3 ohm

Rotor impedance/phase==5.83 ohm

Rotor current/phase= (70/)/5.83=6.93A

Cosφ=3/5.83=0.514

Que6) A 6-pole, 3-phase induction motor operates from a supply whose frequency is 50Hz. Calculate i) speed at which the magnetic field of stator is rotating. Ii)speed of rotor when slip is 4%. Iii)frequency of rotor current when slip is 3%?

Sol: i) Stator revolves at synchronous speed. So, Ns=120f/P=120 x 50/6=1000rpm

Ii)rotor speed N=(1-s) Ns= (1-0.04) x 1000=960rpm

Iii)frequency of rotor current f’=sf=0.03 x 50=90rpm

Que7) The power input to a rotor of 440V, 50Hz, 6-pole, 3-phase, induction motor is 60kW. The rotor force is observed to make 80 alterations per minute. Calculate i) slip ii) rotor speed iii) rotor cu loss per phase?

Sol: 80 alterations per minute=80/60 cycles per second=1.333Hz=sf

i)slip=1.333/50=0.027 P.u.=2.7%

Ii)Rotor speed N=(1-s) Ns=(1-0.027) x 1000=973.33rpm

Ns=120f/P=120 x 50/6=1000rpm

Iii)rotor cu loss/phase===0.54kW

Que8) The power input to a 3-phase induction motor is 80kW. The stator loss is total 1kW. Find the mechanical power developed and the rotor cu loss per phase if the slip is 3%?

Sol: P2= stator input – stator losses=80-1=79kW

Pm=(1-s)P2==(1-0.03) x 79=76.63kW

Total rotor cu loss=sP2=0.03 x 79=2.37kW

Rotor cu loss per phase=2.37x1000/3=790W

Que9) The power input to a rotor of a 400V, 50hz,6-pole, 3-phaseinduction motor is 15kW. The slip is 4%. Calculate i) frequency of rotor current. i)rotor speed. Iii)rotor cu loss iv) rotor resistance/phase if rotor current is 50A?

Sol: i) frequency of rotor current=sf=0.04 x 50=2Hz

Ii) Rotor speed N=(1-s) Ns=(1-0.04) x 1000=960rpm

Ns=120f/P=120 x 50/6=1000rpm

Iii) rotor cu loss=s x rotor input=0.04 x 15=0.6kW

Iv)rotor cu loss/phase=0.6 x 1000/3=200W

602R2=200

R2=0.055Ω

Q10) Explain operation of synchronous generator?

Sol: The synchronous generator or alternator is an electrical machine that converts the mechanical power from a prime mover into an AC electrical power at a particular voltage and frequency.

The synchronous motor always runs at a constant speed called synchronous speed.

It works on the principle of Faraday laws of electromagnetic induction. The electromagnetic induction states that electromotive force induced in the armature coil if it is rotating in the uniform magnetic field.

The EMF will also be generated if the field rotates and the conductor becomes stationary. Thus, the relative motion between the conductor and the field induces the EMF in the conductor. The wave shape of the induces voltage always a sinusoidal curve.

Construction of Synchronous Generator

The rotor and stator are the rotating and the stationary part of the synchronous generator. They are the power generating components of the synchronous generator.

The rotor has the field pole, and the stator consists the armature conductor. The relative motion between the rotor and the stator induces the voltage between the conductor.