Power System Engineering Lecture 23

8/3/2019 Power System Engineering Lecture 23

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Review of Last Class

Insulation materials for cable Different types of cable

Single core Cable

Three core cable

Belted Screened or shielded

H-Type cable

S.L. Type cable

Pressure cables

Oil pressure cable

Gas pressure cable >> Cryoresistive cable

Today: Electrical Characteristics of Cables


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Operating Range of the Cables

Gonen T., Electric Power Transmission System Engineering Analysis and Design, CRC Pres, 2010.


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Electric Field Intensity with Voids


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Effect of Void Permittivity

Air Voids Voids filled with oil


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Electrical Characteristics of Cables

Insulation resistance

Cable inductance

Cable capacitance

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


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Insulation Resistance

Resistance of small section dx is:

Therefore insulation resistance is

Insulation per unit length


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Conductor Inductance

For single core cable:

For three core cable:

D = separation distance between phase conductor

r= 0.7788rr= radius of the conductor

D = separation distance between

cores (equilateral spacing)

r= 0.7788r


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Inductance of Cable

http://www05.abb.com

Where

K=1 for equilateral spacingK=1.26 for flat spacing

D = distance between conductors

r= conductor radius

mH/kmln2.005.0r

DKL


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Capacitance of Single Core Cable

Therefore C=q/Vgives, capacitance between core to sheath

Therefore, voltage is


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Capacitance of Three Core Belted Cable

F/km

52.070.184.31log

0298.0

2

2

10

0

T

t

T

t

d

tTC r

If

r = the relative permittivity of the

insulation,

t = thickness of belt insulation,

d = diameter of the conductor and

T = conductor insulation thickness.


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Capacitance of Three Core Belted Cable

210 3CCC


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How to find C1 and C2Take following measurements:

1. All the three conductors joined together and

measure the capacitance between sheath and

conductors.

Cx =3C1 C1 = Cx/3

1. Connect two conductors and sheath together

and measure the capacitance between sheath

and remaining conductors

Cy = 2C2+C1

6222

12

xyy CCCCC

Therefore 62

3

623

33 210

xyxyx CCCCCCCC


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Electric Stress in The Cable

Maximum stress occurs at the surface of conductor

Minimum stress occurs at the sheath surface


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Optimal radius minimum stress


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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 ofcable.

Grading is used to decrease difference betweenEmax and

Emin.

Grading can be broadly classified into two categories.

Capacitance Grading

Intersheath Grading


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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.


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Capacitance Grading (With Same Safety Factor)

While designing cable

Let dielectric strengths of

material is G1G2 and G3

corresponding to

1,

2, and

3and Fis safety factor same for

all materials.

Layer 1 (1) Layer 1 (2) Layer 1 (3)


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Capacitance Grading (With Same Safety Factor)

Since r < r1


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Capacitance Grading (With Same Maximum Stress)

If the materials are subjected to

same maximum stress at the r ,

r1, and r2

Layer 1 (1) Layer 1 (2) Layer 1 (3)


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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 < r1


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Capacitance Grading

Without grading With capacitance grading

r= 4.4

r= 2.2

r= 4.4

r= 6.6


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Intersheath Grading

Metal Sheaths having radii r1

and r2 are kept at potential V1

and V2. using auxiliary

transformer .

Layer 1 (V) Layer 1 (V1) Layer 1 (V2)


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Intersheath Grading

Since the material is same, the maximum stress is also same:

Without grading Intersheath grading


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Intersheath Grading

Without grading Intersheath grading

0 kV

33 kV

66 kV

110 KV

0 kV

110 KV


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Grading of Cable

Generally not used for following reasons:

Non-availability of material with 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


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Power loss in leakage resistance

For small angle

From phasor diagram

Therefore, dielectric power loss:

Dielectric Losses or Loss Tangent


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Loss Tangent of Different Materials

Material Tan

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.


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Other Topics

Breakdowns in Cable Insulation

Intrinsic Breakdown or puncture:

Thermal Breakdown:

Tracking:

Sheath and armour losses


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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 to

induced current will be zero.

Voltage Rating

DC breakdown stress is more than corresponding AC, hencecables can be used for higher DC voltages than AC.


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Underground Cable System

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Power System Engineering Lecture 23