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Answer ALL Questions.
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PAPER CODE NO. EXAMINER: Dr. A. Al-Ataby
ELEC209 DEPARTMENT: EE&E Email: aliataby@liverpool.ac.uk

1. a) The switch in the circuit shown in Figure Q1-1 has been closed for a long time and is
opened at = 0.
Figure Q1 – 1
i) Calculate the initial value of the current . 3
ii) Calculate the initial energy stored in the inductor. 2
iii) What is the time constant of the circuit for > 0 2
iv) What is the mathematical expression for ( ) for ≥ 0 4
v) What percentage of the initial energy stored in the inductor has been dissipated
in the 2 resistor at 5 ms after the switch has been opened.
4
b) There is no energy stored in the circuit shown in Figure Q1-2 at the time the switch is
closed. Find the mathematical expressions for ( ), ( ), 1
( ) and 2( ) for ≥ 0.
2 H i i1 4 H i2
18 H +
_
vo 100 V +
–
(50/3)
t = 0
Figure Q1-2
10
Total
25
120 V 6
8 mH
i +
–
3
30 2 t = 0

2. a) A balanced three-phase Y-connected generator has an internal impedance of 0.2 +
0.5 per phase and an internal voltage of 120 V per phase. The generator feeds a
balanced three-phase -load having an impedance of 118.5 + 85.8 per phase.
The impedance of the line connecting the generator to the load is 0.3 + 0.9 per
phase. Assume the system has a positive phase sequence.
i) Calculate the three line currents. 3
ii) Calculate the three phase voltages at the load. 3
iii) Calculate the three phase currents of the load. 3
iv) Calculate the efficiency of the given three-phase system. 2
b) A balanced three-phase load requires 600 kW at a lagging power factor of 0.7. The
load is fed from a line having an impedance of 0.003 + 0.02 per phase. The line
voltage at the terminal of the load is 500 V.
i) Calculate the magnitude of the line current 2
ii) Calculate the magnitude of the line voltage at the sending end of the line. 4
iii) Calculate the power factor at the sending end of the line. 2
iv) Calculate the transmitted (i.e. the sending end) power. 2
c) Two sets of measurements are made on a two-port resistive circuit. The results are
as follows:
Port 2 Open Circuited
Port 2 Short Circuited
1 = 10 mV 1 = 24 mV
1 = 10 μA 1 = 20 μA
2 = -40 V 2 = 1 mA
Use a suitable two-port network parameters to represent the circuit.
4
Total
25

3. a) A power transmission line is represented by a series impedance = 5 + 40
. Assuming the base voltage is 140 kV (line) and the base power is 20 MVA
(three-phase power),
i) Express transmission line impedance in per unit. 3
ii) Find the base current of the system. 3
b) A power system is shown in Figure Q3 below. Draw a simpler representation
(i.e. equivalent circuit) for this system using the per unit concept. Show all the
necessary steps (Note: Use 30 kVA and 240 V as your base values for the
entire system. Reactances X1 and X2 are expressed in per unit, pu).
Figure Q3
10
Question continues overleaf.
Line T1 T2
30 kVA X1 = 0.1 pu 20 kVA X2 = 0.2 pu
ZL = 0.8 + j0.3 240 V 480 V 460 V 115 V j5 Load VS = 230∠0o V

Question continued.
c) It is required to replace a fossil fuel power plant by a wind farm, and you have
been hired as the engineer to carry out this task. After studying the site, you
have found out that the average wind speed is 13 m/s. You have decided to use
wind turbines with 42% efficiency and 50 m blade length. Design the farm
(i.e. determine the number of wind turbines needed to replace the power
plant), assuming the density of air is 1.25 kg/m3
and the fossil fuel power plant
generates 750 MW on average. [Note: the number of turbines must be an
integer].
6
d) A three-phase synchronous generator with terminal line voltage of 60 kV is
required to have line current of 6.5 -40 kA. Determine the complex power
supplied by the generator and the power factor.
3
Total
25

4. a) A three-phase 4-pole induction machine, with rated frequency of 50 Hz and rated
voltage of 380 V, has the following parameters: 1 = 0.5 , 2
′ = 0.2 , 1 = 0.4
and 2
′ = 0.4 . (Assume the rated speed is 1455 rpm).
i) Calculate the rated slip. 3
ii) Calculate the starting and rated stator currents. 4
iii) Calculate the input power and the power factor of the machine under rated
condition.
2
b) A three-phase, 10 kV, 750 MVA, star-connected synchronous generator has a per
phase reactance of 2 pu and supplies 1.2 pu per phase real power at the rated
voltage, with a leading power factor of 0.75 to the load.
i) Calculate the actual excitation voltage and the power angle. 4
ii) Calculate the actual complex power consumed by the load. 4
iii) Is the generator overexcited or under excited Explain your answer. 2
c) When filling the fuel tank of a truck with an internal combustion engine, it takes 3
minutes to put 100 litres into the tank. Given that the density of petrol is 730 kg m-3
and its heat value 45 MJ kg-1
, calculate the effective energy flow rate while filling
the tank.
4
d) The turns ratio of a transformer is 20:3. Calculate the referred load to the primary
side of this transformer when the load connected to the secondary winding is 10 +
5 .
2