Department of Electronics and Telecommunication Engineering
University of Moratuwa
EN5000 - Electronics Systems
Assignment 5
Date of Submission - 3rd April 2022
Q1
A 3ϕ, 460 V, 100 hp, 60 Hz, four-pole induction machine delivers rated output power at a slip of 0.05.
Determine the
1. Synchronous speed and motor speed.
2. Speed of the rotating air gap field.
3. Frequency of the rotor circuit.
4. Slip rpm.
5. Speed of the rotor field relative to the
ˆ rotor structure.
ˆ stator structure.
ˆ stator rotating field.
6. Rotor induced voltage at the operating speed, if the stator-to-rotor turns ratio is 1:0.5
Q2
Obtain an equivalent circuit for the induction motor model shown in Fig. 1 obtaining Thevenin equivalent
circuit of the section left to the AA′ line assuming R1 >> X1 + X2 and Xm >> X1 .
Figure 1: Equivalent circuit of the induction motor and its Thevenin equivalent circuit.
1. Determine Vth , Xth and Rth
1
2. Show that rotor induced torque (τind ) is given by (1).
τind =
2
3Vth
R2 /s
ωs [(Rth + R2 /s)2 + (Xth + X2 )2 ]
(1)
Q3
A 208 V/60 Hz Y-connected four-pole wound-rotor induction motor is rated at 15 hp. Its equivalent circuit
components are
R1 = 0.22 Ω
X1 = 0.430 Ω
Pv = 300 W
R2 = 0.127 Ω
X1 = 0.430 Ω
Pf = 200 W
Xm = 15 Ω
For a slip of 0.05, determine,
1. The line current
2. The stator copper losses
3. The air-gap power
4. The power converted from electrical to mechanical form
5. The induced torque
6. The load torque
7. The overall machine efficiency
Q4
Plot the torque-speed characteristics of the induction motor in Q3 using (1). Please do not use the simplified
expressions of Vth , Rth and Xth in part 1 of Q2.
Q5
The following test results are obtained for a 3-φ, 280 V, 60 Hz, 6.5 A, 500 W induction machine.
ˆ Blocked-rotor test: 44V, 60 Hz, 25 A, 1250 W
ˆ No-load test: 208 V, 60 Hz, 6.5 A, 500 W
The average resistance measured by a dc bridge between two stator terminals is 0.54 Ω.
1. Determine the no-load rotational loss.
2. Determine the parameters of the equivalent circuit.
3. Determine the output horsepower at s = 0.1.
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Q6
A 3-ϕ induction machine is mechanically coupled to a dc shunt machine. The rating and parameters of the
machines are as follows:
ˆ Induction machine:
3-ϕ, 5 kVA, 208 V, 60 Hz, four-pole
R1 = 0.25 Ω, X1 = 0.55 Ω, R2′ = 0.35 Ω, X2′ = 1.1 Ω, Xm = 38 Ω
ˆ DC machine: 220 V, 5 kW
The induction machine is connected to a 3-ϕ, 208 V, 60 Hz supply, and the dc machine is connected to a
220 V dc supply. The rotational loss of each machine of the M-G set may be considered constant at 225 W.
The system rotates at 1890 rpm in the direction of the rotating field of the induction machine.
1. Determine the mode of operation of the induction machine.
2. Determine the current taken by the induction machine.
3. Determine the real and reactive power at the terminals of the induction machine and indicate their
directions.
4. Determine the copper loss in the rotor circuit.
Q7
The M-G set in Q6 is rotating at 1710 rpm in the direction of the rotating field. The phase sequence of the
supply connected to the induction machine is suddenly reversed. Repeat parts (1) to (4) of Q6.
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