Electrical Power Engineering ELE2019



SECTION A

Q1. A four-pole Y-connected, 415 V, 50 Hz, induction motor has phase-
equivalent circuit parameters of 1 = 1.5 Ω, 2 = 1.2 Ω, 1 = 2 = 3.0 Ω,
and = 80 Ω. Under rated condition, the rotor slip is 4%.

(i) What is the rotor speed and rotor electrical frequency under rated
conditions?
[3 Marks]
(ii) Calculate the stator input current, power factor, and
electromagnetic torque under these conditions.
[11 Marks]
(iii) What is the maximum torque of this machine?
[5 Marks]
(iv) How much additional resistance (referred to the stator) would it
be necessary to add to the rotor to make the maximum torque
occur under starting conditions?
[4 Marks]
(v) Suggest how the additional rotor resistance would be added to a
wound rotor induction machine, and what effect does the
additional rotor resistance have on the starting current.
[2 Marks]


Electrical Power Engineering ELE2019



Q2. (a) A ferromagnetic core as shown in Figure Q2 has a mean path length l1
of 25 cm. There is a small gap g of 0.1 cm in the structure of the otherwise
whole core. The cross-sectional areas of both the core and the air gap are
14 cm2, the relative permeability of the core is 3000 and the coil of wire on
the core has 350 turns. If the current flowing to the coil is 1.33 A, what is
the flux density in the air gap?
Note: the permeability for free space is given as H/m104 70
−=  .
[8 Marks]


Figure Q2
(b) A 3-phase, 4-pole, 50 Hz alternator has a double-layer winding in
36 slots and produces 415 V when star connected. Each coil has 2 turns
and is short-chorded by 60° (i.e. kwc = 0.866), the distribution factor kwd is
0.96, and the specific magnetic and electric loadings are respectively
0.56 T and 38000 Amp Cond/m. Use the voltage and output equations to
calculate the length and inside diameter of the stator core if a rating of
200 kVA is to be achieved. [11 marks]
(c) Show how short-chording by 60° will eliminate the 3rd harmonic, and
explain why the line voltage is affected. [4 marks]
(d) Briefly describe what the distribution factor, kwd, is and how it might
be derived? [2 marks]


i
g
l1 = mean length
Electrical Power Engineering ELE2019


Q3. (a) State the various sources of losses in a DC machine and explain, briefly,
how they arise. [6 Marks]
(b) When DC machines are loaded, armature reaction occurs. What are the
causes of armature reaction and explain its consequences. [6 Marks]
(c) A shunt DC motor is supplied by 240 V DC. The armature resistance of
the motor is Ra = 0.16 , and the field resistance Rf is 50 . The field
winding has 600 turns. An adjustable resistance Radj is connected in series
to the field and is currently set at 22 . Armature reaction may be ignored
in this machine. The magnetization curve for this motor, taken at a speed
of 900 rpm, is given in the table below:
Ea (V) 95 150 188 212 229 243
mmf (A·turns) 500 1000 1500 2000 2500 3000

(i) What is the speed of the motor when it is running at an armature
current of 50 A? [6 Marks]

(ii) If the terminal voltage is reduced to 180 V and the armature
current stays at 50 A, calculate the required Radj in order to
restore the speed of the motor to the value in (i). [7 Marks]


END OF SECTION A







Electrical Power Engineering ELE2019





SECTION B


Q4. (a) Describe the advantages of using per-unit quantities in power
system analysis.

[5 Marks]
(b) Show that the per-unit impedance of a transformer is the same on
both the primary and the secondary side.

[5 Marks]
(c) Using a 100-MVA base, derive an equivalent circuit for the single-
line diagram of the 3-phase power system shown as Figure Q4.

[5 Marks]
(d) Calculate the required voltage at the terminals of the generator, ,
and the complex power, , delivered by the generator.

[10 Marks]










Figure Q4


ZL = 100 + j200 
20 : 200 kV 200 : 20 kV
VR = 18 kV
50 MVA
X1 = 0.1 pu
50 MVA
X2 = 0.1 pu
45 MVA
0.85 pf, lagging
Vt
Electrical Power Engineering ELE2019


Q5. (a) Sketch the circuit diagram for the nominal-Π representation of a
transmission line and use Kirchhoff’s Laws derive the A, B, C and D
parameters of the corresponding 2-port network.


[10 Marks]
(b) A three-phase, 132–kV, transmission line supplies a load of 49 MW
at 0.85 lagging power factor, at rated voltage. The total series
impedance and shunt admittance are Z = 20 + j 93  and Y = j 0.001 S
respectively. Using the nominal- Π representation, calculate:
(i) The A, B, C and D parameters [7 Marks]
(ii) The sending-end voltage [2 Marks]
(iii) The sending-end current [2 Marks]
(iv) The sending-end power factor [2 Marks]
(v) The efficiency of transmission. [2 Marks]


Electrical Power Engineering ELE2019


Q6. (a) List any two reasons why performing load flow analysis is essential
in power systems.

[2 Marks]
(b) Explain why it is important to be able to control the flow of real
and reactive power in a power system. List any four
equipment/methods which allow us to implement these controls. [4 Marks]
(c) The single-line diagram of a three-bus power system is presented
in Figure Q6. All line impedances are marked in per unit (pu) on a
100 MVA base. Line resistances and shunt capacitances are ignored.

(i) Using a single iteration of the Gauss Seidel method,
calculate the complex voltages (pu) at Buses 2 and 3, i.e., V2
and V3 respectively. [14 Marks]
(ii) Determine the losses (MW and Mvar) in line 2–3.

Bus 1
(Slack)
Bus 2Bus 3
V1 = 1 0° pu
|V2| = 1.05 pu
P2 = 100 MW
P3 = 300 MW
Q3 = 120 Mvar
Z13 = + j0.05 pu
Z23 = + j0.04 pu
Z12 = + j0.04 pu


Figure Q6


Hint: The voltage of the ith node in a power system consisting of N nodes can be
estimated using the following equation (corresponding to iteration cycle p+1):


+1 = (
1

×

∗

∗
) + (
1

∑ ( ∗
)

=1,≠
)


[5 Marks]












END OF EXAMINATION