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Electrical, Electronic and
Computer Engineering
ENEL4HA - High Voltage 1
Tutorial 2 - Conduction and Breakdown in Liquids and Solids
Theoretical Questions
- Describe the differences between mineral, natural ester and synthetic ester oils.
- Mineral oils consist of various hydrocarbons. What other additives (if any) could be added to the oil to improve its performance?
- Describe the ageing process in transformer or cable oil.
- What is a PCB?
- Comment on the use of an oil circuit breaker versus an SF6 circuit breaker.
- Describe what effect impurities have on the breakdown strength of a material (consider the energy bands).
- Describe tracking.
- Describe the components that make up an XLPE cable.
Question 1
A 6.35/11 kV single core PILC cable has a core conductor of 300 mm^2 and is insulated by oil impregnated paper of 7.5 mm thick and then covered in lead.
- Calculate the maximum stress on the insulation.
- Where does it occur?
Question 2
A rectangular section of solid insulation has a dimensions as shown. There is a small void 0.3 mm thick in the section. Assuming that the void is filled with air at 1 bar. Derive and solve an equation to determine the peak inception voltage. If the partial discharge occurs continuously, what are the long term effects?
εr = 2. 8
Cavity
D = 6cm
d = 4mm
Anode
Cathode
Further consider a second material with a relative permittivity was 2.3. Describe the difference the inception voltage. Why is there a difference and how this would influence the design of insulation?
Question 3
A motor slot has the dimensions shown in the figure where the relative permittivity is εr =
- Assuming the void is filled with air at 1 bar, by deriving the equations from first principles determine the value of the voltage in RMS that will cause partial discharge to start.
εr
Conductor 4 mm Insulation
- 3 mm Cavity
Question 4
A cable joint is often made up of different layers between the core conductor and the outer sheath with different permittivities including XLPE, mastic tape and stress control tubing. Assuming that the cable joint has a coaxial form with an inner conductor radius of ri = 10 mm and an outer conductor radius of R 0 = 20 mm, determine and sketch the electric field between the conductors when 6.35 kV is applied to the conductor.
Given that the breakdown strength of the materials are:
Material Breakdown Strength Thickness XLPE 550 kV/mm 6mm Mastic Tape 75 kV/cm 2mm Stress Control Tubing 140 kV/cm 2mm
Comment on the use of the different permittivity layers? Do they actually help in controlling the electric field? Repeat the question and comment on the effect of increasing the permittivity of the mastic tape to 15 and decreasing the stress control tubing to 5.
V
ri
Ro
E^ ~
Stress Control Tubing ε 3 = 15
Mastic Tape ε 2 = 5
XLPE ε 1 = 2. 3
Useful Formulae
Constants
Standard temperature: t 0 = 20oC Standard pressure: P 0 = 760 torr Permittivity of free space: ε 0 = 8. 85 × 10 −^12 F/m
Formulae
Relative air density:
δ =
P
P 0
273 + t 0 273 + t
Paschen’s law for air:
Vb = 6. 72
pd + 24.36(pd)
Electric field in a coaxial system:
E =
V
r ln R rio
Electric field in layer k in a coaxial system with multiple layers and permittivities:
Ek =
V
rk
[
εk ε 1 ln^
r 2 r 1 +^
εk ε 2 ln^
r 3 r 2 +^...
]
Electric field in layer k in a rectangular dielectric with multiple layers and permittivities:
Ek =
V
εk ε 1 d^1 +^
εk ε 2 d^2 +^...
Streamer breakdown criterion: ∫ (α − η)dx = 18
Ionisation and attachment coefficients for SF 6 are:
α − η = 0. 028 E − 249 × 103 p
Electrostatic force:
F =
ε 0 εr
V
d
Mechanical compressive strength of a dielectric:
F = Y ln
d 0 d
