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Sample Question Paper for 9210-114
Graduate Diploma in Electrical Engineering
Electrical energy systems
Duration: three hours
You should have the
following for this examination
• one answer book
• non-programmable calculator
• pen, pencil, drawing
instruments
General instructions
• This paper consists of nine questions.
• Answer any five questions.
• A non-programmable electronic calculator may be used but candidates must show
sufficient steps to justify their answers.
• Drawings should be clear, in good proportion and in pencil. Do not use red ink.
• All questions carry equal marks. The maximum marks for each section within a
question are shown.
1
a)
b)
How is a medium-length transmission line modelled? What simplifications can be
made if the line is of short-length category?
A 325 km, 500 kV, 50 Hz transmission line has the following per-phase, per-unit
length series reactance (x) and shunt susceptance (b):
x = j0.308 Ω/km;
b = j3.60x10–6 S/km
A load of 600 MW at 0.95 power factor lagging is connected to the receiving end
of the line. The voltage at load is equal to 500 kV.
i)
Calculate the surge impedance, propagation constant and wave length of
the line.
ii) Calculate voltage, current and power factor at the sending end of the line.
iii) If the load is disconnected from the line, determine:
– voltage at the receiving end,
– current and reactive power at the sending end.
2
a)
b)
(3 marks)
Briefly explain how an on-load tap changer of transformers is used for voltage
regulation at the consumer end. List two other methods used for voltage regulation.
A grid substation delivers power of 70 MW at 0.9 power factor lagging to a load
centre via a 132 kV, 105 km long transmission line and a 138 kV/11 kV transformer
(Figure Q2). Per-phase, per-unit length series resistance (r), series reactance (x)
and shunt susceptance (b) of the line are: r = 0.098 Ω/km, x = 0.429 Ω/km and
b = 2.64 x 10–6 S/km respectively. Leakage reactance of the transformer referred to
the HV side is 22.94 Ω. The voltage at the grid substation bus is maintained at 138 kV.
(3 marks)
(8 marks)
(6 marks)
(4 marks)
Figure Q2
i)
ii)
iii)
iv)
Calculate the voltage at the LV side of the transformer.
Find the active and reactive power delivered to the load.
Determine voltage regulation.
The transformer is built with an on-load tap changing facility and consists
of taps of ±9 x 1.78%. Check whether the voltage at the load centre can be
increased up-to 11.5 kV with the help of an on load tap changer. What is
the maximum voltage that can be achieved at the load centre?
2
(6 marks)
(4 marks)
(2 marks)
(4 marks)
3
a)
b)
A certain power system consists of many nodes and the system is often heavily
loaded. It is suggested to use a computer program based on a combination of
two methods: three iterations using Gauss-Seidel method and then using
Newton-Raphson method. What advantages over any single method can be
achieved by combining the two methods?
Consider the power system shown in Figure Q3. Data relevant to load flow
calculations are indicated in the figure. All the values are given in pu on a
common base.
(5 marks)
Figure Q3
i)
ii)
4
5
a)
b)
a)
b)
c)
Form the nodal admittance matrix.
Calculate the voltage at nodes 2 and 3 after the first iteration of
the Gauss-Seidel method.
Explain the term ‘flat start’ with respect to load flow calculation.
A generator delivers power to a load of (130 + j50) MVA via a 132 kV overhead
transmission line. The impedance of the line is 10 + j20 Ω. Generator voltage is
maintained at 138 kV. Voltage at the load is to be calculated using
Newton-Raphson method. Calculate
i)
power mismatch at the load bus
ii) elements of the Jakobian matrix
iii) voltage at load after the first iteration of Newton-Raphson method.
Explain the effects of an unusually low frequency supply on
i)
generating stations
ii) industrial loads.
How are active and reactive power outputs controlled in synchronous generators?
A generator delivers active power of 0.8 pu to a large system which can be
considered as an infinite bus. Excitation voltage and synchronous reactance
of the generator are 1.25 pu and 0.12 pu respectively. System voltage equals 1.0 pu.
i)
Calculate the power angle.
ii) Determine the reactive power delivered by the generator.
iii) If the field current of the generator is increased by 15%, determine the new
active and reactive power delivered by the generator.
3
(5 marks)
(10 marks)
(4 marks)
(5 marks)
(5 marks)
(6 marks)
(3 marks)
(2 marks)
(3 marks)
(2 marks)
(6 marks)
(4 marks)
See next page
6
A synchronous generator delivers power to a large system through a transformer
and a double circuit transmission line as shown in Figure Q6. Excitation voltage of
the generator and voltage at system bus are 1.07 pu and 1.05 pu respectively. The
prime-mover develops mechanical power of 0.9 pu. Energy constant of the machine
is 4 MJ/MVA. Sub transient reactance of the generator, transformer and transmission
lines are indicated in the figure. System frequency is 50 Hz. All the pu values are given
on a common base.
Figure Q6
a)
b)
i)
ii)
What is the initial power angle?
If one of the transmission lines is out of service, what is the new power angle
at the stable operation point of the generator?
While the system is operating with one line, a three-phase zero impedance fault
occurs at the generator bus bar (bus 1).
i)
Calculate the initial acceleration of the rotor.
ii) If the fault is self-extinguished after 2.5 cycles, determine whether the
generator could remain stable.
4
(4 marks)
(2 marks)
(4 marks)
(10 marks)
7
A single line diagram of a part of a power system is shown in Figure Q7. Positive, negative
and zero sequence reactance of generators (G1& G2) and transformers (T1, T2 & T3) are
given in Table Q7. Output voltages of the two generators G1 and G2 are equal to their
rated values. Generator G2 is earthed through a resistance of 700 Ω while generator
G1 and all star connected windings of transformers are solidly earthed.
Figure Q7
Positive
sequence
reactance
Negative sequence
Reactance
Zero
sequence
reactance
G1: 12 kV, 100 MVA
0.1 pu
0.9 pu
0.11 pu
G2: 11 kV, 125 MVA
0.1 pu
0.1 pu
0.1 pu
T1: 100 MVA, 12 kV/135 kV
0.09 pu
0.09 pu
0.09 pu
T2: 130 MVA, 12 kV/135 kV
0.1 pu
0.1 pu
0.1 pu
T3: 250 MVA, 132 kV/33 kV
0.08 pu
0.08 pu
0.08 pu
7.5 Ω
7.5 Ω
15 Ω
Equipment and rating
L
Table Q7
a)
b)
c)
Calculate all the parameters on a common base of 100 MVA for the system and a
base voltage of 132 kV for the transmission line.
Sketch,
i)
positive sequence network
ii) negative sequence network
iii) zero sequence network.
If a single line to ground fault occurs at point F, calculate the short circuit current
in amperes.
5
(5 marks)
(2 marks)
(1 mark)
(2 marks)
(10 marks)
See next page
8
a)
b)
c)
Explain the advantages of symmetrical components over phase components.
Explain the statement ‘Zero sequence current flows only for the faults
involving ground’.
A 33 kV/11 kV, ∆/Y, 100 MVA transformer with star point is solidly earthed on the
11 kV side and has the following currents in phases A, B and C on the 11 kV side
–I B = 100∠–85° A;
–I C = 150∠210° A;
–I A = 100∠85° A;
Calculate;
i)
symmetrical component of the currents on 11 kV side,
ii) current distribution in phases A, B and C in ∆ windings of the transformer.
9
a)
b)
c)
Explain why a distance relay is more suitable than a directional over current relay
for the protection of transmission lines.
Explain briefly three-zones as applicable to distance relays.
A transmission line having a length of 120 km is protected by a Mho relay installed
at the one end of the line. The relay has maximum reach of 60 Ω at angle of 60°
with R-X plane. Per unit length impedance of the line is 0.08 + j0.5 Ω/km.
i)
Sketch the Mho characteristic and show the transmission line and maximum
reach on the same graph.
ii) Calculate the fraction of the transmission line protected by the relay.
iii) If a resistive fault occurs at one third length of the line from the relay end
and the distance relay fails to detect the fault, show the minimum fault
resistance on your R-X plane.
6
(3 marks)
(3 marks)
(6 marks)
(8 marks)
(3 marks)
(3 marks)
(4 marks)
(6 marks)
(4 marks)