Describe the voltage distribution along a transformer winding at power
frequency (50 Hz) and at high frequency (some 100s of kHz).
(ii) [5 marks] Figure 1 shows an example of cap-and-pin insulator strings for
mounting
...
Describe the voltage distribution along a transformer winding at power
frequency (50 Hz) and at high frequency (some 100s of kHz).
(ii) [5 marks] Figure 1 shows an example of cap-and-pin insulator strings for
mounting overhead lines onto the earthed tower. Explain two functions of the
overhangs (indicated by arrows) at the two ends of the insulator string.
Figure 1
(b) For measurement of the dielectric dissipation factor losses (tan), a precision high
voltage capacitor with very low loss must be used as one of the reference arms of the
Schering Bridge. For this purpose, a cylindrical coaxial electrode, gas-filled capacitor is
used. It has an inner conductor of diameter 20 mm and an outer coaxial cylinder of inner
diameter 150 mm. The axial length is 0.5 m for all component parts of the capacitor. The
insulating gas has a relative permittivity of 1.0.
(i) [5 marks] If the maximum allowable operating electric field in the gas layer is 50
kV(peak)/cm, what is the maximum possible operating RMS voltage that can be
allowed for this capacitor?
(ii) [5 marks] It is now required to increase the allowable operating voltage of the
capacitor. This is achieved by using the 20 mm diameter inner conductor with an
extruded layer of XLPE solid insulation over it. The thickness of the XLPE layer is
10 mm and its relative permittivity is 2.5. The outer electrode has the same
dimensions as before. What is the new maximum allowable operating voltage of the
modified capacitor? You can assume that the electric field in the XLPE is not a
limiting factor in any way in the calculation.
(iii) [5 marks] If tan of the XLPE is 0.001, determine the total power loss in the
modified capacitor at the maximum operating voltage?
Formulae: For a cylindrical coaxial capacitor with inner electrode of radius a, outer
electrode of radius b, dielectric material of relative permittivity r, and applied voltage V:
Capacitance:
2
ln
C o r
b a
F/m where: 8.85 10 F/m 12
o
Electric field at radial distance r:
ln
V
E r
r b a
V/m
Dielectric loss: P CV 2 tan W/mELEC4611: Final Examination - 2017 page 3
Question 2 [25 marks]
(a) Briefly answer the following questions:
(i) [7 marks] A fault on a typical low voltage circuit can be represented by a general
R-L circuit with a switch and a sinusoidal voltage source. The instantaneous fault
current for a fault initiating at t = 0, with no prior load current flow, is given by:
2
( ) ( ) ( )
t
V L R
i t sin t sin e
Z
where is power factor angle, is angle of voltage at switch closure and the other
quantities have their usual meanings.
Determine the condition that results in the worst-case DC offset and then derive the
formula for the peak instantaneous current
(ii) [5 marks] The comparative advantages and disadvantages of HRC fuses and circuit
breakers.
(b) A balanced three-phase 400V/50Hz distribution circuit comprises 3 parallel bus bars,
each phase carries a current of 500 A (rms). In this problem, we only consider the force
between 2 bars, the distance between them is 20 cm (i.e. we ignore the force associated
with the third phase conductor). Calculate:
(i) [5 marks] the peak magnitude of the repulsive force between the 2 bus bars.
(ii) [5 marks] the peak magnitude of the attractive force between the 2 bus bars.
(iii) [3 marks] the time it takes for the force to change from peak repulsive to peak
attractive.
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