UNIVERSITY OF SURREY
School of Electronics and Physical Sciences
ELECTRONIC ENGINEERING PROGRAMMES
For BEng and MEng Degrees
Level HE2 Modular Examination
Module EE2.pwc
POWER CONVERSION
Duration: 2 Hours
READ THESE INSTRUCTIONS
Attempt ALL questions.
Candidates must write their full solutions in the answer books provided
AND complete the answer sheets provided at the end of this examination paper.
Both the answer book AND the examination paper with the answer sheets
must be handed in.
1
A permanent magnet d.c. motor has a continuous maximum rating of 25 V, 125 W and an armature
resistance of 0.85 Ω, and is connected to a 25 V supply. Mechanical losses are negligible. When the
motor runs with no mechanical load it reaches a speed of 1500 rev/min.
(a)
Find the starting torque of the motor.
(b)
Find the maximum output power of the motor.
(c)
Find the two values of armature current which give a mechanical output of 125 W, and the
corresponding values of torque and speed.
(d)
The thermal resistance between the case and ambient is 3 °C/W, the maximum permitted
winding temperature is 180 °C and the ambient temperature is 25 °C. Taking the more
efficient operating point for a mechanical output of 125 W, determine the maximum
acceptable thermal resistance between the windings and the case.
(e)
2
Closed part of question.
(i) A resistor of 41.5 Ω and an inductor of 76.4 mH are connected in series and supplied at 240 V,
50 Hz. The circuit is switched on and any transients are allowed to die away.
(a)
Sketch curves for applied voltage, current and the instantaneous power consumed by the
circuit for one cycle of the supply voltage. Calculate the maximum and minimum
instantaneous power consumption and also the average value.
(ii) A 2 pole, a.c. series (universal) motor is rated at 240 V, 50 Hz, 3A, 4000 rev/min, and has an
air gap of 0.3 mm at each side of the armature.
(b)
Assuming the iron has infinite permeability calculate the total number of field turns required
to give an r.m.s. air gap flux density of 0.9 T under rated conditions.
(c)
The face of each pole measures 30 mm by 40 mm. Calculate the inductance of the field
winding.
Taken together the field and armature have an inductance of 76.4 mH and a resistance of 41.5 Ω.
(d)
Calculate the rated power and torque of the motor.
(iii)
(e) Closed part of question.
3
(i) A transformer has a primary - to - secondary turns ratio of 5 : 1. The primary has a winding
resistance of 30 Ω and is supplied, at normal working frequency, by a signal generator of internal
impedance 50 Ω. The secondary has a winding resistance of 1 Ω and is loaded by a 3 Ω resistor.
(a)
Calculate the input resistance of the loaded transformer measured at the primary terminals
with the generator removed.
(b)
Calculate the output resistance of the transformer measured at the secondary terminals with
the generator connected.
(ii) In the design of large transformers the effect of winding resistance and leakage reactance can be
neglected. Figure Q3 shows the iron core of a transformer with the windings around the centre limb.
The transformer is designed to have a peak flux density in the iron of 1.7 T and an r.m.s. current
density in the windows of 1.5 A / mm2.
60mm
75mm
50mm
25mm
25mm
70mm
Figure Q3
(c)
Derive a formula for the volt-ampere rating of the transformer as a function of the supply
frequency, f Hz.
(iii) In the design of small transformers the effect of winding resistance and leakage reactance
cannot be neglected. One such transformer has a rating of 240 V : 30 V for a resistive load and a
turns ratio of 5 (five) :1.
The transformer has the following parameters,
4
Primary resistance
100 Ω
Primary leakage reactance
50 Ω
Secondary resistance
3Ω
Secondary leakage reactance
2Ω
Magnetising current
Negligible
(d)
Determine the secondary terminal voltage when the transformer is unloaded.
(e)
Determine the rated secondary current of the transformer.
(i) A three-phase induction motor is required to drive a load at 910 rev/min with an efficiency of at
least 80 %. Two supplies are available, 50 Hz & 60 Hz.
(a)
Specify the only supply frequency and pole number for which this efficiency might be
possible.
(ii) Another three-phase induction motor has a starting torque of 150 Nm and a synchronous speed
of 3000 rev/min. When the motor is very lightly loaded the speed falls by 1.5 rev/min for each
additional 1 Nm of torque. The motor has negligible stator impedance and can be represented by the
equivalent circuit shown in Figure Q4.
jX
R
R(1-s)/s
E
s = slip
Figure Q4
(b)
Calculate the speed for maximum torque.
(c)
Calculate the maximum torque that can be delivered without the motor stalling.
(iii)
(d) & (e) Closed part of question
5
(i) A three-phase, 6 pulse, controlled rectifier is connected to a 50 Hz supply of 400 V r.m.s. (line)
as shown in Figure Q5. Each supply line has an inductance, L1 equal to 0.4 mH. The load is a
resistance R, in series with a very large smoothing inductance L. The waveform of the voltage E is
observed on an oscilloscope during the commutation period and the result is shown in Figure Q5
for a firing angle delay of 75°.
E
400 V line
(r.m.s)
V2
R
L1
E
L1
33s
L
L1
O
L1=0.4mH
t
V1
Figure Q5
(a) Determine the voltages V1 and V2.
(b) Calculate the average value of the current in the resistance R.
(c) Calculate the value of the resistance R.
(ii) (d), (e), (f) Closed part of question
URN:
ANSWER SHEET
Please copy numerical answers (with units) from your answer book.
Make sketches and put descriptive answers on this sheet and not in your answer book.
Question 1
(a)
Starting torque
4.67 Nm………………...…/ 3
(b)
Maximum output power
184 W ................................../ 2
(c)
Armature current
23 A ..................................../ 2
Torque
3.65 Nm ............................../ 2
Speed
327 rev/min ......................../ 1
Armature current
6.39 A ................................./ 2
Torque
1.01 Nm ............................../ 2
Speed
1174 rev/min ....................../ 1
(d)
Maximum thermal resistance
1.466 oC/W ........................./ 2
(e)
Closed part
........................................./ 3
points for question 1
/20
Question 2
(i) (a)
Waveforms...... 1 A/div, 40 V/div, 200 W/div, and 30°/div
/ 4
Maximum power
2239 W ................................./ 2
Minimum power
-161 W ................................../ 2
Average power
1039 W ................................./ 1
(ii) (b) Number of field turns
143 turns.............................../ 2
(c) Field winding inductance
51 mH .................................../ 2
(d) Rated power of motor
312 W ................................../ 2
Rated torque of motor
0.745 Nm ............................./ 1
(iii) (e) Closed part of question
……………………………./ 4
question 2
/20
Question 3
(i) (a) Input resistance
(b) Output resistance
130  .................................../ 3
4.2  .................................../ 3
(ii) (c) Volt-ampere rating as a function of supply frequency f, Hz.
f VA ............................../ 5
(iii) (d) Secondary terminal voltage when transformer is unloaded
48 V .................................../ 2
(e)
Rated secondary current
2.43 A................................./ 7
points for question 3
/20
Question 4
(i) (a) Suitable supply frequency
Suitable pole number
(ii) (b) Speed for maximum torque
(c) Maximum torque
(iii) (d) (e) Closed part
50 Hz ................................../ 2
six ....................................../ 2
2178 rev/min ....................../ 5
274 Nm ............................../ 5
…………………………… / 6
points for question 4
/20
Question 5
(i) (a) Voltage V1
-146.5 V ............................/ 3
Voltage V2
+ 400 V ............................/ 3
(b) Average current in R
22.5 A ............................../ 2
(c) Resistance R
6.2  ................................/ 2
(ii) (d) (e) (f)
…………………………./ 10
points for question 5
Total points
/20
/100