3 phase Induction Motor frequency of induced emf current and power factor - problems

Three Phase Induction Motors
Contents :
Frequency of Rotor
Rotor EMF
Rotor Current and Power Factor
Related Problems
Kongunadu college of Engineering & Technology Three phase Induction – Frequency, Rotor EMF, Current and Power factor related Problems

Frequency of Rotor
• Assume rotor is stationary
– Relative speed between the rotor winding and
rotating magnetic field is Ns
• When the rotor speeds up
– Relative speed is (Ns – N)
• Rotor Frequency

Rotor EMF
• Under Standstill condition slip s=1
– Relative speed is maximum and maximum emf induced in
the rotor
– E2 = rotor induced emf under standstill condition
• When the motor speed increases (running condition)
– Relative speed increases, then induced emf in the rotor
decreases
– E2r = rotor induced emf under running condition

Rotor Current and Power Factor
• R2 = Rotor resistance per ph under standstill condition
• X2 = Rotor reactance per ph under standstill condition
In running condition
Rotor impedance per phase

Problem - 1
• A 3-phase induction motor is suppied at 50Hz and is
wound for 4 poles. Calculate (i) Synchronous speed,
(ii). Apeed when slip is 3%, (iii). Frequency of the
rotor emf when it runs at 1200 rpm
• Key:
• Answer:
Ns=1500rpm; N=1455rpm; fr=10Hz

Problem - 2
• The frequency of emf in the stator of a 4-pole, 3-
phase induction motor is 50Hz and that in the
rotor is 1.5Hz. Determine: i). The Slip, ii). Speed
of the motor.
• Key:
• Answer:
(i). Ns=1500rpm & s=0.03, (ii). N=1455rpm

Problem - 3
• For a 4pole, 3phase, 50Hz induction motor ratio of stator to rotor
turns is 3. On a certain load, its speed is observed to be 1450rpm,
when connected to 415V supply. Calculate:
– i). Frequency of rotor emf in running condition, (fr)
– ii). Magnitude of induced emf in the rotor at standstill, (E2ph)
– iii) Magnitude of induced emf in the rotor under running
condition.(E2r) Assume star connected stator.
• Key:
• Answer:
Fr=1.66Hz; E2ph=79.78V; E2r=2.63V
• Given: P=4, f=50Hz, EIL=415V=stator side line voltage ;
K=rotor turns / stator turns = 1/3 = 0.333; N=1450 rpm

Problem - 4
• A 4-pole three phase, 50Hz, induction motor has a star connected
rotor. The rotor has a resistance of 0.1 ohm per phase and
standstill reactance of 2ohm per phase. The induced emf between
the slip rings is 100V. If full load speed is 1460rpm, find i) Slip, ii).
Rotor frequency, iii). Rotor current, iv). Power factor on full load
condition. Assume slip rings are shorted.
• Key:
• Answer:
S=2.66%; fr=1.33Hz; I2r=13.15A; PF=0.887lagging
• Given: P=4, f=50Hz, R2=0.1ohm; X2=2ohm;
E2=100V, N=1460rpm

Problem - 5
• A 8-pole, 3-phase induction motor is supplied
from 50Hz AC supply. On full load, the
frequency of induced emf in rotor is 2Hz. Find
the full load slip and corresponding speed(N).
• Key:
• Answer:
S=0.04; Ns=750rpm; N=720rpm;
• Given: P=8, f=50Hz, fr=2Hz

Problem - 6
• A 3ph, 6pole, 50Hz induction motor has a slip of 1% at no
load and 3% at full load. Find (1) Synchronous speed(Ns).
(2). No load speed(Nnl). (3). Full load Speed(Nfl). (4).
Frequency of rotor current at standstill(frs). (5) Frequency
of rotor current at full load(frfl).
• Key:
• Answer:
Ns=1000rpm; Nnl=990rpm; Nfl=970rpm; frs=50Hz; frfl=1.5Hz
• Given: P=6, f=50Hz, slip at no load snl=1% or 0.01;
slip at full load sfl=3% or0.03; at standstill slip s=1;

Problem - 7
• If the emf in the stator winding of a 6 pole
induction motor has a frequency of 50c/s and
emf in the rotor has a frequency of 2c/s, find the
speed at which the motor is runing(N) and
percentage slip(s).
• Key:
• Answer:
S=4%; Ns=1000rpm; N=960rpm;
• Given: P=6, supply frequency f=50 c/s,
rotor frequency fr = 2c/s

Problem - 8
• A 3-phase induction motor is wound for 4poles
and is supplied from a 50Hz supply. Calculate the
synchronous speed(Ns), the speed of the
motor(N) when the slip is 3% and the rotor
frequency(fr).
• Key:
• Answer:
Ns=1500rpm; N=1455rpm; fr=1.5Hz;
• Given: P=4, supply frequency f=50Hz,
Slip=3% or 0.03

Problem - 9
• The induced emf between the slip ring terminals of a three phase
induction motor when the rotor is standstill is 100V. The rotor
winding is star connected and has resistance and standstill
reactance of 0.05ohms and 0.1 ohms per phase respectively.
Calculate the voltage and rotor current at (1) 4% slip and (2) 100%
slip(Standstill Condition).
• Key:
• Answer:
(1). For s=0.04, E2r=2.308V, Z2r=0.05ohm;
(2). E2=57.7V; Z2=0.111ohms; I2=519.8A ;
• Given: R2=0.05ohms; X2=0.1ohms;

Problem - 10
• A 3-ph, 50Hz, induction motor runs almost at 960rpm
on full load, when supplied with three-phase supply.
Calculate the following, (i).Number of poles(P), (ii).
Full load slip(s), (iii). Frequency of rotor emf(fr), (iv).
Speed of the motor at 8 percent slip(N).
• Key:
• Answer:
(i).P=6; (ii). S=0.04; (iii).fr=2Hz; (iv).N=920rpm;
• Given: Supply frequency f=50Hz; Speed N
=960rpm; therefore Ns=1000rpm;

Problem - 11
A 1100V, 50Hz delta connected induction motor has a star connected slip ring rotor with a
phase transformation ratio of 3.8. The rotor resistance and stand still leakage reactance
are 0.012ohm and 0.25ohms per phase respectively. Neglecting stator impedance and
magnetising current, determine:
(i). Rotor current at start with slip ring shorted.
(ii). The rotor PF at start with slip ring shorted.
(iii). The rotor current at 4% slip with slip ring shorted.
(iv). The rotor power factor at 4% slip with slip ring shorted.
(v). The external rotor resistance per phase required to obtain a starting current of 100A in
the stator supply lines.
• Key:
• Answer:
(i).I2=1157.2A; (ii). PF=0.048(lagging); (Starting)
(iii).I2r=742A; (iv).PF =0.77(lagging); (running s=4%)
(v). Ext Resistance r=0.707ohms
• Given: Supply voltage V =E1ph(due to delta connection in stator)= 1100V; f=50Hz;
Phase transformation ratio K = 1/3.8=0.263; R2=0.012ohms, X2=0.25ohms;

Problem - 12
• A 3-phase, 4-pole induction motor operates
from a supply whose frequency is 50Hz.
Calculate the frequncy of rotor current at
standstill and the speed at which the magnetic
field of the stator is rotating(Ns).
• Key:
• Answer:
Fr=50Hz; Ns=1500rpm;
• Given: P=4; f=50Hz; at standstill condition s=1;

Problem - 13
• A 4pole three phase squirrel cage induction
motor operates at supply frequency of 50Hz
at a speed at 1440rpm at full load. Find the
frequency of the EMF induced in the rotor(fr).
• Key:
• Answer:
Ns=1500rpm; s=0.04; Fr=2Hz;
• Given: P=4; f=50Hz; N=1440rpm;

Problem - 14
• A3phase 50Hz, 4pole induction motor has a slip of
4%. Calculate (i) Speed of the motor(N) (ii). Frequency
of rotor emf(fr). If the motor has a resistance of 1ohm
and standstill reactance of 4ohm, calculate(iii) power
factor at (a) standstill and (b) a speed of 1400rpm.
• Key:
• Answer:
(i).N=1440rpm; (ii).Fr=2Hz; (iii). (a).PF=0.242 (lagging);
(b).s=0.066; & PF=0.966(lagging)
• Given: P=4; f=50Hz; s=4% or 0.04; R2=1ohm;
X2=4ohm;

S.No Book s / Web Sources
1
A.E. Fitzgerald, Charles Kingsley, Stephen. D. Umans, ‘Electric Machinery’, Tata Mc Graw Hill publishing
Company Ltd, 2003.
2 D.P. Kothari and I.J. Nagrath, ‘Electric Machines’, Tata McGraw Hill Publishing Company Ltd, 2002.
3 P.S. Bhimbhra, ‘Electrical Machinery’, Khanna Publishers, 2003.
4 M.N.Bandyopadhyay, Electrical Machines Theory and Practice, PHI Learning PVT LTD., New Delhi, 2009.
5 K. Murugesh Kumar, ‘Electric Machines’, Vikas Publishing House Pvt. Ltd, 2002.
6
Syed A. Nasar, Electric Machines and Power Systems: Volume I, Mcgraw -Hill College; International ed Edition,
January 1995.
7 J. Ganavadivel, ‘Electrical Machines II’, Anuradha publications, Fourth edition, 2015.
8 U.A.Bakshi &M.V.Bakshi, ”Electrical Machines II,” Technical Publications, Second revised edition, 2016.
9 Google and Wikipedia
REFERENCES

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