Faculty of Electrical Engineering
Electric Drives (ENME 503)
Dr. Eng. Noha Shouman
Eng. Kareem Noureldin, M.Sc. - Eng. Ahmed AlKhatib
Sheet (8)
Induction Motors (cont.)
1) A three-phase Y-connected 220-V, 7.5-kW 60-Hz six-pole induction motor has the following
parameters per phase and referred to the stator:
Solution:
a) The maximum torque and the corresponding speed.
b) Starting Torque: 𝐹𝑜𝑟 𝑠 = 1
Faculty of Electrical Engineering
Electric Drives (ENME 503)
Dr. Eng. Noha Shouman
Eng. Kareem Noureldin, M.Sc. - Eng. Ahmed AlKhatib
Starting Current: (s = 1)
Faculty of Electrical Engineering
Electric Drives (ENME 503)
Dr. Eng. Noha Shouman
Eng. Kareem Noureldin, M.Sc. - Eng. Ahmed AlKhatib
2) A 50-kW, 440-V, 50-Hz, two-pole induction motor has a slip of 6 percent when operating at
full-load conditions. At full-load conditions, the friction, windage losses and the core losses
are 1020 W. Find the following values for full-load conditions:
Solution:
a) The synchronous speed:
b) The full-load speed in rpm
c) The rotor frequency in hertz
𝒇𝒓 = 𝒔𝒇𝒍 𝒙 𝒇𝒔 = 𝟎. 𝟎𝟔 ∗ 𝟓𝟎 = 𝟑 𝑯𝒛
d) The output power in watts
𝑷𝒇𝒍 = 𝟓𝟎, 𝟎𝟎𝟎 𝒘𝒂𝒕𝒕𝒔
e) The load torque in newton-meters
f) The power converted from electrical to mechanical form Pconv.
𝑷𝒄𝒐𝒏𝒗 = 𝑷𝒐𝒖𝒕 + 𝑷𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏+𝑪𝒐𝒓𝒆 = 𝟓𝟎. 𝟎𝟎𝟎 + 𝟏𝟎𝟐𝟎 = 𝟓𝟏𝟎𝟐𝟎 𝑾𝒂𝒕𝒕𝒔
g) The induced torque in newton-meters
h) The rotor copper loss.
Faculty of Electrical Engineering
Electric Drives (ENME 503)
Dr. Eng. Noha Shouman
Eng. Kareem Noureldin, M.Sc. - Eng. Ahmed AlKhatib
i) The air-gap power.
3) A 208-V, two-pole, 60-Hz, V-connected wound-rotor induction motor is rated at 15 hp. Its
equivalent circuit components are: R1 = 0.2 Ω, = 0.12 Ω, X1 = 0.41 Ω, = 0.41 Ω, Xm =15 Ω.
Solution:
a) How much additional resistance (referred to the stator circuit) would it be necessary to be
added to the rotor circuit to make the maximum torque occur at starting conditions?
b) If the motor is to be operated on a 50-Hz power system, what must be done to its supply
voltage? Why? What will the equivalent circuit component values at 50 Hz?
Faculty of Electrical Engineering
Electric Drives (ENME 503)
Dr. Eng. Noha Shouman
Eng. Kareem Noureldin, M.Sc. - Eng. Ahmed AlKhatib
J 0.34 J 0.34
Faculty of Electrical Engineering
Electric Drives (ENME 503)
Dr. Eng. Noha Shouman
Eng. Kareem Noureldin, M.Sc. - Eng. Ahmed AlKhatib
1) The following test data were taken on a 7.5 hp, four-pole, 208 V, 60-Hz, Y-connected induction
motor:
DC test:
VDC=13.6 V IDC=28 A
No load test:
IA=8.12 A IB=8.2 A IC=8.18 A
VT=208 V f=60 Hz Pin=420 W
Locked rotor test:
IA=28.1 A IB=28 A IC=27.6 A
VT=25 V f=15 Hz Pin=920 W
Solution:
a) Sketch the per-phase equivalent circuit for this motor.
Faculty of Electrical Engineering
Electric Drives (ENME 503)
Dr. Eng. Noha Shouman
Eng. Kareem Noureldin, M.Sc. - Eng. Ahmed AlKhatib
∴ 𝜽 = 𝟒𝟎. 𝟒 °
𝒁𝑳𝑹𝒙𝒄𝒐𝒔(𝜽) = 𝟎. 𝟓𝟏𝟕 𝒙 𝟎. 𝟕𝟔 = 𝑹𝟏 + 𝑹𝟐′
∴ 𝑹′𝟐 = 𝟎. 𝟑𝟗𝟑 − 𝟎. 𝟐𝟒𝟑 = 𝟎. 𝟏𝟓 𝛀
𝑨𝒏𝒅 𝒁𝑳𝑹 𝐬𝐢𝐧(𝜽) = 𝟎. 𝟓𝟏𝟕 𝒙 𝟎. 𝟔𝟒𝟖 = (𝑿𝟏 + 𝑿′𝟐) = 𝟎. 𝟑𝟑𝟓 𝒂𝒕 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 = 𝟏𝟓 𝑯𝒛
∴ 𝑹𝟏 = 𝟎. 𝟐𝟒𝟑 𝑹′𝟐 = 𝟎. 𝟏𝟓 , 𝑿𝟏 = 𝟎. 𝟔𝟕 , 𝑿𝟐 = 𝟎. 𝟔𝟕 , 𝑿𝒎 = 𝟏𝟒. 𝟎𝟑
b) Find the slip at the pullout torque and the pullout torque value.
Faculty of Electrical Engineering
Electric Drives (ENME 503)
Dr. Eng. Noha Shouman
Eng. Kareem Noureldin, M.Sc. - Eng. Ahmed AlKhatib
