power system engineering lecture 24

8/3/2019 Power System Engineering Lecture 24

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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



Electric Stress in The Cable

Maximum stress occurs at the surface of conductor

Minimum stress occurs at the sheath surface




Optimal radius minimum stress



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



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.



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)



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



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)



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



Capacitance Grading

Without grading With capacitance grading

ε r = 4.4

ε r = 2.2

ε r = 4.4

ε r = 6.6



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)



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



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



Power loss in leakage resistance

For small angle δ

From phasor diagram

Therefore, dielectric power loss:

Dielectric Losses or Loss Tangent



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.



Other Topics

Breakdowns in Cable Insulation

Intrinsic Breakdown or puncture:

Thermal Breakdown:

Tracking:

Sheath and armour losses



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.



Underground Cable System

http://www05.abb.com/

power system engineering lecture 24

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