Course: EE211 – Electrical Machines
School of Engineering & Physics
Electrical and Electronics Engineering
Final Examination
Semester 2 2020
(F2F Mode)
Duration of Exam: 3 hours + 10 minutes
Reading Time: 10 minutes
Writing Time: 3 hours
Instructions:
1.
2.
3.
4.
5.
6.
7.
8.
This paper has two sections:
Section A: Answer ALL questions (compulsory)(QA1-QA4)
Section B: Answer any 4 questions out of 6 (QB1-QB6 )
This exam is worth 50% of your overall mark. The pass mark is 40/100.
Where applicable, state all assumptions with clear justifications.
Write your answers in the answer booklet provided.
Start each question on a new page.
Unless otherwise stated, all other symbols have their usual meanings.
Only non-programmable calculators are permitted.
Closed book
n
(60 marks)
(40 marks)
Total 100
SECTION A (Compulsory Questions)
Solve the following 4 questions
Question A1 (15 marks):
Consider the following diagram of Heyland-Ossana of an induction machine working in point M:
Consider the point B (intersect of the segment AM with the straight line in bold passing in P1), the
point C (intersect of the segment AC with the straight line in bold passing in s=±∞), then:
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
Define the lines of mechanical power and torque line
What does the segment BM represent?
What does the segment CM represent?
What does the segment AM represent?
What does the segment P1D represent?
What does the segment AC represent?
What does the segment CB represent?
Does the induction motor work as a motor or as a brake at point M?
What does the point s=0 represent?
Page 2 of 6
(1 mark)
(2 marks)
(2 marks)
(2 marks)
(2 marks)
(2 marks)
(2 marks)
(1 mark)
(1 mark)
Question A2 (15 marks):
A ferromagnetic core with a relative permeability of 1500 is shown in the figure shown below. The
dimensions are as shown in the diagram, and the depth of the core is 7cm. the air gaps on the left and
right sides of the core are 0.07 cm and 0.05 cm, respectively. Because of fringing effects, the effective
area of the air gaps is 5 percent larger than their physical size. If there are 400 turns in the coil wrapped
around the center leg of the core and if the current in the coil is 1.0 Amps,
i.
ii.
iii.
iv.
What is the flux in the center core?
What is the flux in the left core?
What is the flux in the right core?
What is the flux density in each air gap?
(4 marks)
(4 marks)
(4 marks)
(3 marks)
Question A3 (15 marks):
The following test data were taken on a 10 hp, 4 pole, 415 V, 50 Hz, design A, Y connected induction
motor at a rated current of 28 A.
DC Test
VDC = 15 V
IDC = 32 A
i.
ii.
No load test
VT = 415 V
IA = 10 A
IB = 10.1 A
IC = 9.9 A
PIN = 450 W
f = 50 Hz
Locked rotor test
VT = 28 V
IA = 30 A
IB = 30.1 A
IC = 29.9 A
PIN = 950 W
f = 12.5 Hz
Compute and sketch the per-phase equivalent circuit for this motor.
(11 marks)
Find the slip at the pullout torque, and find the value of the pullout torque itself. (4 marks)
Page 3 of 6
Question A4 (15 marks):
A 1000-VA, 230/115V transformer has been tested to determine its equivslent cicuit. The results of
the test are as follows
Open-circuit test
Voc = 230 V
Ioc = 0.95 A
Poc = 80 W
i.
ii.
iii.
Short-circuit test
Vsc = 11.2 V
Isc = 5 A
Psc = 20.1 W
Find the equivalent circuit of this transformer referred to the primary.
Find the transformers voltage regulation at 0.8 PF lagging
Determine the transformers efficiency at 0.8 PF lagging
Page 4 of 6
(8 Marks)
(3 Marks)
(4 Marks)
SECTION B
Answer ANY 4 out of the following 6 questions
Question B1 (10 marks):
Find the magnitude and angles of each line and phase voltage and current on the load shown in the
figure
Question B2 (10 marks):
Consider a synchronous generator (SG) moved by a motor that supplies constant mechanical power.
i.
ii.
How can you regulate the production of reactive power of a SG? Does this affect the
production of active power?
(5 marks)
How can you regulate the production of active power of a SG? Does this affect the
production of reactive power?
(5 marks)
Question B3 (10 marks):
i.
ii.
iii.
Consider a 600 V DC motor with separate excitation. Its rated speed is n= 1500 rpm and
the rated current In= 40 A. Determine rated torque (neglect the resistance of the
armature winding)
(4 marks)
Imagine that this motor is supplied before with V1=500 V and then with V2=600 V. How
do the speeds change?
(3 marks)
How do you regulate the speed with a DC motor with separate excitation by reducing the
excitation field?
(3 mark)
Page 5 of 6
Question B4 (10 marks):
Consider a 3-phase induction motor with 6 poles supplied with a sinusoidal voltage at 50Hz and slip s
= 0.06
i.
ii.
iii.
iv.
v.
Determine the synchronous speed
(2 marks)
Determine the speed of the rotor
(2 marks)
Determine the pulsation of the rotor currents
(2 marks)
What is the pulsation of the rotor currents if the rotor rotates exactly at the synchronous speed?
(2 marks)
What is the value of the torque when the rotor rotates exactly at the synchronous speed?
(2 marks)
Question B5 (10 marks):
A 415 V, 50 kVA, 0.8 PF leading, Delta connected, 50 Hz synchronous machine has a synchronous
reactance of 3 ohms and a negligible armature resistance. Its friction and windage losses are 1.5 kW,
and its core losses are 1 kW. Initially, the shaft is supplying a 16 hp load, and the motors power factor
is 0.8 leading.
i)
ii)
iii)
iv)
Find the values of IL
Find the values of IA
Find the values of EA
Sketch the phasor diagram of this motor
(2 marks)
(2 marks)
(3 marks)
(3 marks)
Question B6 (10 marks):
A square magnetic core has a mean path length of 66 cm and a cross-sectional area of 200 cm2. A 300
turn coil of wire is wrapped around one leg of the core. The core is made of a material having the
magnetizing curve shown in the figure below.
i.
ii.
iii.
How much current is required to produce 0.028 Wb of flux in the core?
What is the core’s relative permeability at that current level?
What is the reluctance?
Page 6 of 6
(6 marks)
(2 marks)
(2 marks)