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8/3/2019 Power System Engineering Lecture 24
http://slidepdf.com/reader/full/power-system-engineering-lecture-24 1/19
Review of Last Class
Electrical Characteristics of Cables Insulation resistance
Cable inductance (Empirical relations due presence of sheath, amour,
shields, etc.)
Cable capacitance Belted core cable (Empirical relations, measurement method)
Electrical stress inside insulation
Grading of cable
Capacitance grading
Inter-sheath grading
Dielectric losses and tan delta (loss tangent)
Sheath and armour losses
Breakdowns in cable insulations
8/3/2019 Power System Engineering Lecture 24
http://slidepdf.com/reader/full/power-system-engineering-lecture-24 2/19
Electric Stress in The Cable
Maximum stress occurs at the surface of conductor
Minimum stress occurs at the sheath surface
8/3/2019 Power System Engineering Lecture 24
http://slidepdf.com/reader/full/power-system-engineering-lecture-24 3/19
Electric Stress in The Cable
8/3/2019 Power System Engineering Lecture 24
http://slidepdf.com/reader/full/power-system-engineering-lecture-24 4/19
Electric Stress in The Cable
Optimal radius minimum stress
8/3/2019 Power System Engineering Lecture 24
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Grading of Cables
Electric field inside the cable is not uniform, maximum atconductor surface and minimum at the sheath.
Thus insulation material is not properly utilized.
The insulation near conductor surface is stressed more
while there is very less stress at the outer diameter of cable.
Grading is used to decrease difference between E max and
E min.
Grading can be broadly classified into two categories.
Capacitance Grading
Intersheath Grading
8/3/2019 Power System Engineering Lecture 24
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Capacitance Grading
Ideal condition for stress in cable
There fore the permittivity is
This can not be realized in practice
since it requires infinite number of
dielectric materials with varying
permittivity
In practice, this can be realized by
two or three layers of the dielectric
materials.
8/3/2019 Power System Engineering Lecture 24
http://slidepdf.com/reader/full/power-system-engineering-lecture-24 7/19
Capacitance Grading (With Same Safety Factor)
While designing cable
Let dielectric strengths of
material is G1 G2 and G3
corresponding to ε1 , ε2, and ε3 and F is safety factor same for
all materials.
Layer 1 (ε 1) Layer 1 (ε 2) Layer 1 (ε 3)
8/3/2019 Power System Engineering Lecture 24
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Capacitance Grading (With Same Safety Factor)
Since r < r 1<r 2
Therefore material having highest product of permittivity and
dielectric strength should be kept near to the conductor. The
operating voltage of Cable is given by
8/3/2019 Power System Engineering Lecture 24
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Capacitance Grading (With Same Maximum Stress)
If the materials are subjected to
same maximum stress at the r ,
r 1 , and r 2
Layer 1 (ε 1) Layer 1 (ε 2) Layer 1 (ε 3)
8/3/2019 Power System Engineering Lecture 24
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Capacitance Grading (With Same Maximum Stress)
Therefore same maximum stress
material having highest permittivity
needs to be kept at surface of
conductor.
Since r < r 1<r 2
8/3/2019 Power System Engineering Lecture 24
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Capacitance Grading
Without grading With capacitance grading
ε r = 4.4
ε r = 2.2
ε r = 4.4
ε r = 6.6
8/3/2019 Power System Engineering Lecture 24
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Intersheath Grading
Metal Sheaths having radii r 1
and r 2 are kept at potential V 1
and V 2. using auxiliary
transformer .
Layer 1 (V ) Layer 1 (V 1) Layer 1 (V 2)
8/3/2019 Power System Engineering Lecture 24
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Intersheath Grading
Since the material is same, the maximum stress is also same:
Without grading Intersheath grading
0 kV
33 kV
66 kV
110 KV
0 kV
110 KV
8/3/2019 Power System Engineering Lecture 24
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Grading of Cable
Generally not used for following reasons:
Non-availability of materials with required varying
permittivity materials
Change in permittivity with time
Damage of intersheath during cable laying
Charging current through the intersheath can damage the
cable due to overheating Resonance due to cable capacitance and transformers
inductance
8/3/2019 Power System Engineering Lecture 24
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Power loss in leakage resistance
For small angle δ
From phasor diagram
Therefore, dielectric power loss:
Dielectric Losses or Loss Tangent
8/3/2019 Power System Engineering Lecture 24
http://slidepdf.com/reader/full/power-system-engineering-lecture-24 16/19
Loss Tangent of Different Materials
Material Tan δ
Impregnated Paper 0.01
Oil filled paper insulation 0.004
PVC 0.1
XLPE 0.0004
The loss angle depends on the temperature.
Roughly it follows ‘V’ curve, i.e. Loss angle will be
minimum at certain temperature.
8/3/2019 Power System Engineering Lecture 24
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Other Topics
Breakdowns in Cable Insulation
Intrinsic Breakdown or puncture:
Thermal Breakdown:
Tracking:
Sheath and armour losses
8/3/2019 Power System Engineering Lecture 24
http://slidepdf.com/reader/full/power-system-engineering-lecture-24 18/19
HVDC Cables
Current Carrying Capacity: There is no charging current which will decrease copper losses.
Only loss due to leakage current. dielectric hysteresis loss will
be zero.
No voltage will be induced in sheath hence sheath losses due toinduced current will be zero.
Voltage Rating
DC breakdown stress is more than corresponding AC, hencecables can be used for higher DC voltages than AC.
Or, for same voltage rating DC cable can have smaller
insulation thickness than AC cable.
8/3/2019 Power System Engineering Lecture 24
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Underground Cable System
http://www05.abb.com/