Electrical Power and Machines
Date: May 2015

Time allowed: 3 hours
Instructions to Candidates:

This is an unseen examination.

This exam paper is made up of eight questions.

Candidates should answer any five out of the eight questions.

All questions are marked out of 20.
Materials provided:
Graph Paper.
Materials allowed:
A scientific calculator may be used in this exam.

Unannotated paper versions of general bi-lingual dictionaries only may be used by overseas students whose first language is not English. Subject-specific bi-lingual dictionaries are not permitted. Electronic dictionaries may not be used.

Access to any other materials is not permitted.

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Question 1

A three-phase, 50 Hz, 11kV/415V, transformer with a star connected secondary is used to supply a balanced delta connected inductive load of 30 kW. This load draws a line current (IL) of 60 A.

a) Calculate the system phase to neutral voltage. (Van) (3 marks)
b) Calculate the load phase current (IP). (3 marks)
c) Calculate the values of R and L in each branch of the load. (4 marks)

The ‘two-wattmeter method’ for measuring real and reactive power in the load is being used. One wattmeter (W1) has its current coil in the ‘a-phase’ line and its voltage coil connected between the ‘a-phase’ and ‘c-phase’ lines. The other wattmeter (W2) has its current coil in the ‘b-phase’ and its voltage coil connected between the ‘b-phase’ and the ‘c-phase’ lines. The phase sequence is abc.

d) Sketch a phasor diagram of the voltages and currents supplied to the load highlighting the phasors relevant to the two wattmeters.
(5 marks)

e) Calculate the individual wattmeter readings and thus show that their sum is equal to the total Power supplied to the load.
(5 marks)

[20 MARKS]
Question 2

A factory is supplied at 415 V, 50 Hz and the load at the factory comprises two items. Load one draws a power of 300 kW at a power factor of 0.85 lagging. Load two draws an apparent power of 200 kVA and a reactive power of 175 kVAr. The overall power factor at the factory is to be improved by the installation of capacitor banks totalling 100 kVAr.

a) Explain how the capacitor banks should be connected and why. (3 marks)

Now calculate:

b) The total power supplied. (3 marks)

c) The power factor prior to correction. (4 marks)

d) The power factor following correction. (4 marks)

e) The per-phase value of capacitance (Farads) required to improve the power factor of the original uncorrected system to 0.95.
(6 marks)

[20 MARKS]

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Question 3

An 11kV overhead line is fed from a busbar with a fault level of 180 MVA. The line is 9 km long with an impedance of (0.1 + j0.6) Ω per km and feeds an 11 kV/415 V, 750 kVA, transformer with an impedance of (0.1 + j0.4) pu based on its own rating.

a) Calculate the source impedance as seen from the 11 kV busbars in:

i) Per Unit (Sb = 50 MVA) (3 marks)
ii) Ohms (3 marks)

b) Convert the overhead line and transformer impedances to per unit values (Sb = 50 MVA).
(4 marks)

c) If a three-phase short circuit is applied to the transformer secondary terminals, calculate:

i) The fault current (IF) at the short circuit (4 marks)
ii) The fault level in MVA at this point (3 marks)
iii) The voltage at the 11kV busbars during the fault
(3 marks)

[20 MARKS]
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Question 4

R1, R2 and R3, shown in Figure Q4 below, are over-current IDMT relays having a time/psm characteristic given by:

a) Using the tabulated data, given in table Q4, calculate appropriate Plug Settings and Time Multiplier Settings to ensure minimum relay operate times and a minimum grading margin of 0.4 seconds for the fault conditions given. Show all relevant relay operate times in your working.
(12 marks)

b) Recalculate the relay operate times and the grading margin for all relevant faults with only one transformer in service.
(5 marks)

c) Discuss the advantages and disadvantages of ‘Time-Graded’ and ‘Current-Graded’ protection systems.
(3 marks)

Figure Q4
Maximum Feeder Load
(Amperes) Fault Level
T1 & T2 in Service
(MVA) Fault Level
One Transformer in Service
(MVA)
R1 380 240 130
R2 290 180 110
R3 190 180 110

Table Q4

[20 MARKS]
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Question 5

Tests on a three-phase, 100 kW, 2 kV, 4-pole, 50 Hz induction motor produced the results shown in table Q5:

No load test @ 50 Hz Locked rotor test @ 15 Hz DC Test
Voltage(V) 2000 250 20
Current (A) 5.0 27 3.7
Power (W) 1620 9100
Table Q5

a) Draw the approximate equivalent circuit for this induction motor and calculate the relevant component values from the data given in table Q5 above.
(10 marks)

b) For the above motor, using the component values determined in (a) above, calculate the following parameters when slip = 2.5%:

i) Rotor current referred to stator (Is) (3 marks)
ii) Gross electromagnetic torque (Te) (3 marks)
iii) Motor losses (2 marks)
iv) Motor efficiency (2 marks)
[20 MARKS]

Question 6

a) Using diagrams and appropriate graphs, explain briefly how a single-phase, full-wave half-controlled rectifier bridge, can be used to effect speed control of a permanent magnet dc motor.
(5 marks)

b) A 150 V, shunt connected, dc motor has an armature resistance of 0.17 Ω and a field resistance of 75 Ω. At no load the motor runs at 1000 rpm taking a line current of 5A. At full load the electrical power input to the motor is 7.5 kW. If armature reaction is considered negligible, calculate for full load conditions:

i) Motor speed (3 marks)
ii) Speed regulation (2 marks)
iii) Gross torque (3 marks)
iv) Gross mechanical power developed (3 marks)

c) If armature reaction reduces the air gap flux by 6% when full load current flows in the armature recalculate the values for part (b) above.

(4 marks)

[20 MARKS]
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Question 7

a) Explain how two 3-phase, fully-controlled, 6-pulse rectifier bridges, operating in circulating current mode, may be used as a 4-quadrant drive to control the speed of a dc machine. Illustrate your answer with appropriate sketches.
(8 marks)
For a p-pulse, controlled rectifier bridge, without a flywheel diode, the average dc voltage presented to the load, is given by:

Where VS = the supply voltage
IL = the line current
L = the source inductance (per phase)
P = the number of pulses per cycle
α = the delay angle beyond the natural commutation point

It is required to provide variable speed control of a 400 V, separately excited, dc motor using a
6-pulse converter. The motor armature current rating is 600 A, its speed rating is 1200 rpm and the armature resistance is 20.0 mΩ. The supply frequency is 50 Hz and the source impedance is
j0.06 Ω per phase.

b) Calculate the minimum line voltage required to operate the motor at its rating with the above arrangement.
(6 marks)

c) Determine the value of α when the motor is operated at 700 rpm drawing two thirds rated current with a supply voltage of 350 V.
(6 marks)

[20 MARKS]

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Question 8

a) Explain fully, using circuit diagrams and appropriate graphs of voltage and current waveforms, how the speed of a permanent magnet, dc motor may be controlled from a dc supply using a chopper drive.
(10 marks)

b) A simple chopper circuit is used to control the speed of a permanent magnet dc motor. The dc supply voltage is 48V and the motor armature resistance is 0.5 . The motor drives a constant torque load which takes an average current of 10 A. The motor torque constant KM is 0.27 Nm/A. If the motor current is continuous determine:

i) The duty cycle (on /off ratio) of the chopper such that the motor rotor just starts to turn.
(6 marks)
ii) The speed of the motor when the duty cycle is 2:3.

(4 marks)

[20 MARKS]