ch5 underground power cables 2[1]

5

UNDERGROUND POWER CABLES

5.1 INTRODUCTION

Though, the underground transmission facilities are more costly as compared with

the O.H.T.L, the electric power transmission by underground power cables is popular,

because it offers number of advantages:

i) It can be used to transmit electric power, where construction of O.H.T.L is

undesirable technically or economically. For example, the use of U.G.C in

crossing under seawater, highways or railways, in approaches to transformer

substations, on the territories of high density populated areas, etc.

ii) Underground power transmission has freedom from above ground weather and

traffic problems (e.g. wind storms, thick ice layers, lightning discharges, dust,

etc.), and thus experience fewer interruptions than O.H.T.L

5.2 CORE CONDUCTOR

The core conductor is the current carrying conducting material of the underground

power cable. The most commonly used conductor materials for power cables are

harddrawn copper or aluminum that are characterized with high conductivity

i) To decrease cross-sectional area of extra high voltage cable, hard drawn copper

core conductors are used (Aluminum conductivity = 60% Copper conductivity).

ii) The hard drawn copper conductors are preferred in low-voltage networks, as

copper material can withstand thermal stress during overloading operations

compared with aluminum conductors.

iii) The hard drawn aluminum conductors are commonly used in medium-voltage

and high-voltage distribution networks to decrease costs where the three-phase

load balancing and hence overloading problem is minimized.

Core conductors are made of one solid conductor or multi stranded wires (Fig.5.1).

The primary reason for stranded conductors is improved flexibility.

Chapter 5: Underground Power Cables

160

Fig.5.1 Stranded wires core conductors

Multi-core power cables uses circular stranded non-compacted conductors or

sector-shaped stranded compacted conductors (Fig.5.2). Sector-shaped (either soild

tpye or stranded compacted type) core conductors are used to reduce the inter space

between three-phase core conductors and hence increase the rigidness of the power

cable.

(a) Circular stranded non-

compacted conductors

(b) Sector-shaped stranded

compacted conductors

Fig.5.2 Core conductors configuration for three-core power cables

5.3 CABLE INSULATION

There are many insulations (or dielectric materials) used in producing the various

cables to deliver electric power. Cable insulation materials include oil impregnated-

paper, rubber , and extruded (or polymetric) insulations.

5.3.1 Oil Impregnated-paper Insulation (OIP)

Paper has little insulation value alone. However, when impregnated with a high

grade of mineral oil, it serves as a satisfactory insulation for extremely high-voltage

cables (relative permittivity 8.3~3.3r ). The paper must be thoroughly saturated

with the oil. The thin paper tape is wrapped in many layers around the conductors, and

then soaked with oil. The OIP insulation has the following merits:

i) The oil has the highest dielectric strength among all cable insulation materials.

ii) Reliable in operation since 1800s (some cables are installed 60 years or more).

iii) Long lifetime.

5.3 Cable Insulation

161

OIP cables are calssified into the following types:

1. Lead-sheathed solid-type OIP insulation cables.

2. Oil filled cables.

3. Gas pressure cables.

5.3.2 Lead-sheathed Solid-type OIP Insulation Cables

Lead-sheathed solid-type OIP insulation cables (also called mass- impregnated

paper insulating cables) (Fig.5.3a) are used in heavy-duty environments requiring good

anti-chemical characteristics, protects cable insulation from water and damaging

substances. Disadvantage of solid type cables is the possibility of void formation

inside OIP insulation layers. Voids can be formed as a result of poor quality control in

cable manufacuring and/or heating and cooling of the cable during loading cycle of

operation. Void formation can decrease the dielectric strength of cables and the cable

become susceptible to internal breakdown especially in the case of extra high voltage

operation. Void formation can be overcomed by the use of oil-filled under pressure

type cables.

5.3.3 Oil Filled Cables

The oil filled cables permit the use of higher maximum stress values at reduced

dielectric thickness. Figure 5.3b shows the section of a three-core oil filled cable.

Perforated oil ducts are located within the filling space. The oil channels are filled with

oil in the factory and they are dispatched in length over drums provided with tanks

having oil under pressure. Thus even for transportation a good pressure of oil is kept to

maintain good impregnation.

5.3.4 Gas pressure Cables

For extra high-voltage cables, the dielectric strength of oil can be increased by

increasing the hydraulic pressure of oil via the use of gas pressure cables. The gas

pressure cables are classified into two main types:

i) Direct gas pressure cables. Figure 5.3c shows how to increase the pressure of

OIP insulation layers directly by the insertion of inert gas under pressure via

perforated gas pressure ducts.

ii) Indirect gas pressure cables. In these types the three-core OIP insulation cables

are put inside steel pipe that is filled with Nitrogen gas at 12 ~ 15 atmospheres.


162

Sector-shaped & Solid-type Aluminum Conductor

OIP Insulation layers Lead sheath

Jacket

(a) OIP Solid-type Insulation Cable

Perforated oil filled duct

Lead-sheath

OIP insulation layers Conductor core

Jacket

(b) Section of 66-kV Oil-filled Cable

Perforated gas pressure duct

OIP insulation layers Conductor core

Jacket

Steel pipe

(c) Section of Extra High-voltage Direct Gas Pressure Cable

Fig.5.3 Thee-core OIP and Oil-filled Cables

5.3 Cable Insulation

163

Advantages of gas pressure cables are:

i) Increasing temperature of continuous operation up to 80oC compared with less

than 60oC in case of solid-type OIP insulation cables.

ii) The maximum dielectric strength can be increased up to 100 kV/cm.

iii) Increasing the current carrying conductor rating by 40% ~ 50% with the

possibility of increasing operating voltage.

iv) Decreasing no-load power factor up to 0.5% and hence decreasing dissipation

power losses of the cable.

v) The inert nitorogen gas is used as an extenguishing medium for the arc that can

be formed by short-circuit faults.

However, the main disadvantage of gas pressure cables is the high cost compared with

soil type OIP insulation cables.

5.3.5 Polymeric Materials Insulated Cables

Polymeric insulations (known also as Extruded insulations) are long chain

hydrocarbon thermoplastic materials which are produced by the polymerization of

petrochemical products like ethylene gas under high pressure and temperature.

Extruded insulations used for wire and cable are classified into two main types:

i) Thermoplastic materials that tend to lose their form upon subsequent heating.

Polyethylene (PE) and Polyvinyl chloride (PVC) are the most common

thermoplastic type extruded insulations.

Thermosetting materials that tend to maintain their form upon subsequent

heating. These extruded insulations range from Crosslinked Polyethylene

(XLPE) and Ethylene-Propylene Rubber (EPR) to the most recent advances in

Tree-retardent Crosslinked Polyethylene (TR-XLPE).

5.3.6 Advantages of Extruded Insulated Cables as Compared with OIP Insulated Cables:

i) Reduced weight vs. OIP insulated cables.

ii) No hydraulic pressure or pumping requirements as that needed for oil

impregnations in OIP insulated cables.

iii) Easier to repaire faults.

iv) Reduced risk of flammability and fire propagation.

v) More economical (in both initial costs and lifetime) compared with OIP

insulated cables.

Table-5.1 illustrates by comparison the different characteristics of PVC, XLPE, and

EPR type extruded insulation power cables.


164

Tab

le 5

.1 C

hara

cter

isti

cs o

f P

oly

meri

c M

ate

ria

ls I

nsu

lati

on

s (E

xtr

ud

ed I

nsu

lati

on

s)

EP

R

90

130

250

Sli

ghtl

y H

igher

than

XL

PE

wit

h

r =

2.5

Sli

ghtl

y L

ow

er t

han

PV

C

Chan

ge

slig

htl

y a

s te

mper

ature

incr

ease

s an

d

does

not

mel

t at

105

oC

More

fle

xib

le

com

par

ed w

ith X

LP

E

Pre

dom

inan

t fo

r

indust

rial

pow

er

cable

s fr

om

5 ~

35 k

V

XL

PE

90

130

250

Low

er t

han

PV

C

wit

h

r =

2.2

5

Har

d t

o b

end

Pri

mar

y f

eed

ers

in M

V

and i

n H

V &

EH

V

syst

ems

PV

C

70

120

160

Hig

h

wit

h

r >

2.8

Rel

ativ

ely H

igh

Deg

rad

ed m

uch

wh

en

hea

ting o

ver

105

oC

Fle

xib

le

Wir

ing i

nst

alla

tions

insi

de

buil

din

gs

Ch

ara

cter

isti

cs

Rec

om

men

ded

Con

tinuous

Wo

rkin

g T

emper

ature

at

Conduct

or

Su

rfac

e in

oC

Inte

rmit

tent

Tem

per

atu

re R

atin

g D

uri

ng O

ver

load

ing i

n o

C

Max

imum

Tem

per

ature

Duri

ng

Short

-cir

cuit

in o

C

Per

mit

tivit

y a

nd D

issi

pat

ion P

ow

er L

oss

es

Die

lect

ric

Str

ength

Mec

han

ical

and E

lect

rica

l P

roper

ties

at

Hig

h T

emper

ature

Duri

ng O

ver

load

ing a

nd L

ong S

hort

-cir

cuit

Per

iods

Fle

xib

ilit

y

Appli

cati

ons

5.4 Basics Of Insulated Power Cable Construction

165

5.4 BASICS OF INSULATED POWER CABLE CONSTRUCTION

An insulated power cable appears to be a relatively simple electrical device. In fact,

this cable is an electrically sophisticated system of components. To understand it, let

us examine its components and basics of operation. For simplicity, the following

discussion shall be confined to a single-conductor cable. However, these fundamentals

also apply to multiple-conductor cables.

5.4.1 Non-Shielded Cables

There are two basic components in a nonshielded cable. They are the conductor and

the electrical insulation. A third component used in some cable designs is an outer

jacket (See Figure 5.4).

Conductor

Insulation

Jacket

(Optional)

Fig.5.4 Construction of Low-Voltage

Nonshielded Cable

5.4.1.1 Conductor:

The conductor can be copper or aluminum with either a solid or stranded cross

section.

5.4.1.2 Electrical Insulation or Dielectric:

The electrical insulation must provide adequate physical and electrical properties

between the energized conductor and the nearest electrical ground to prevent electrical

breakdown. For low-voltage cables, 600 volts and below, the insulation thickness

required to provide the necessary physical protection against damage is more adequate

to provide the necessary dielectric strength.

5.4.1.3 Jacket:

For special applications, a jacket is applied over the insulation. There are several

materials available for use as jackets to provide the necessary chemical, physical, or

thermal protection required by the application.


166

5.4.1.4 Dielectric Field:

Another consideration in the design and application of cables is the dielectric field.

In all electrical cables, irrespective of their voltage ratings, there is a dielectric field

present when the conductor is energized. This dielectric field is typically represented

by electrostatic flux lines and equipotential lines between the conductor and

electrical ground. Figure-5.5 represents the electrical field of a nonshielded cable in

contact with a ground plane. It does not take into account the difference in the

dielectric constants of the insulation and the surrounding air. Observe that the

electrostatic flux lines are crowded in the insulation area closet to the ground. Also, the

equipotential lines are eccentric in their relationship to the conductor and cable

dielectric surface. This distortion of the field is acceptable if the dielectric strength of

the cable insulation is adequate to resist the concentration of the dielectric stresses.

Low-voltage nonshielded cables are designed to meet this requirement.

Electrostatic Flux Lines Equipotential Lines

Fig.5.5 Dielectric Field of Low-Voltage Nonshielded Cable

in Contact with Electrical Ground

5.4.2 Shielded Cables

A fundamental difference between nonshielded and shielded cable is the inclusion

of conducting components in the cable system. The basic components of a shielded

cable are shown in Fig. 5.6.

Conductor

Insulation

Fig.5.6 Construction of Shielded Power Cable

Conductor Shield

Auxiliary Insulation Shield

Using semi-conducting

Non-metallic material

Primary Insulation Shield

Using metallic (wire or tape)

material


167

5.4.2.1 Conductor:

The conductors used in shielded cables are comparable to those used in nonshielded cables.

5.4.2.1 Conductor Shield or Screen:

The conductor shield is usually a semiconducting material applied over the

conductor circumference to shield out the conductor contours. Due to the presence of

this shield, the resulting dielectric field lines will not be distorted by the shape of the

outer strands or other conductor contours. This layer also provides a smooth and

compatible surface for the application of the insulation, and may also be used to

facilitate splicing and terminating of the cable.

5.4.2.2 Insulation Shield or Screen:

The insulation shield or screen is a two-part system composed of an auxiliary and

a primary shield:

An auxiliary shield is usually a semiconducting nonmetallic material over the

dielectric circumference. It must be smooth, compatible with the insulation, and

exhibit an acceptably low voltage drop through its thickness. A commonly used

auxiliary shield consists of an extruded semiconducting layer partially bonded to the

insulation.

A primary shield is a metallic shield over the circumference of the auxiliary shield.

The primary shield may consist of metal tape; drain wires, or concentric neutral

(CN) wires. It must be capable of conducting the summation of "leakage" currents

to the nearest ground with an acceptable voltage drop. In some cases it must be

capable of conducting fault currents. The grounding of the insulation shield is the

electrical connection between the metallic component of the insulation shield and

the system ground. This grounding of the insulation shield results in the

symmetrical dielectric fields previously discussed. In addition, grounding promotes

personnel safety by minimizing potentials on the outer surface of the cable and its

accessories.

5.4.2.3 Dielectric Field:

The insulation shield should be effectively at ground potential. There is no

resulting distortion of the electrostatic flux or equipotential lines. electrostatic flux

lines are spaced symmetrically and perpendicular to equipotential lines. The

equipotential lines are concentric and parallel with respect to each other, the conductor

shield, and the insulation shield. The presence of the shielding results in field lines as

depicted in Fig.5.7.


168

Fig.5.7 Dielectric Field of Shielded Power Cable

Insulation

Conductor

Insulation Shield

Conductor Shield

(a) Electrostatic Field Lines (b) Equipotential Lines

5.4.3 Sheathing, Armoring, and Jacketing

5.4.3.1 Metallic Sheaths:

Sheathing may also include various forms of metallic armoring, tapes, or wires

to enhance the physical properties of the cable and to provide a built-in protective

electrically grounded conduit for the insulated conductors. The term "sheathing" is

typically used to identify tubular metallic coverings. Materials of metalic sheaths

recommended by IEEE 635 specifications are:

a) Lead Sheathing:

Lead is one of the oldes sheathing materials used on power cables, dating back to

the early 1900s. Use of lead sheaths has proven to be a very effective moisture

barrier contributing to long-term reliability of cable systems. Disadvantage of lead

sheaths is that:

i) They add a great deal of weight to the cable.

ii) Lead sheaths are prone to deformation under continuous load conditions due to

the creep characteristics of the material.

iii) Also, lead sheaths are susceptible to failure due to metal fatigue caused by

mechanical vibration or thermal cycling.

b) Aluminum Sheathing

Aluminum sheathing began to appear in the late 1940s. Aluminum is attractive

because it is much lighter than lead and has good mechanical properties. However,

extra sheath losses caused by eddy cuurents can be generated because Aluminum

metal has higher conductivity compared with lead sheath type.


169

5.4.3.2 Armoring:

Armoring is primarily used to protect the cable mechanically and add strength to

the cable. Hazards to the cable include penetration by sharp objects, crushing forces,

and damage from gnawing animals or boring insects. High pulling or application

tensions such as submarine, riser, and down-hole installations also may cause

damage. A flat galvanized steel metal tape is helically wrapped around the cable

core. The tape is typically protected by an outer covering. Applications include

commercial or industrial installations in conduit, ducts, troughs, and raceways.

5.4.3.3 Nonmetallic jackets:

Jackets, also called sheaths, are external covering layers that can serve several

purposes:

i) They provide mechanical, thermal, chemical and environmental protection to

the insulated conductors they enclose.

ii) They may act as electrical insulation when used over shields or armor.

iii) They ease installation and routing concerns by enclosing multiple insulated

conductors.

iv) They may also protect the characteristics of the underlying insulation, for

example, a thin nylon jacket over PVC enhances the abrasion and fluid

resistance of a 600v cable.

Commonly used jacketing materials include thermoplastic extrusions of PE, PVC, and

Nylon.


170

5.5 CABLE CONSTRUCTION

5.5.1 H-type Three-core Cables

The H-type cable has derived its name after its designer Hothstadter. These are used

up to 66 kV. Functional operations of the different layers (Fig. 5.8) are as follows:

i) Core Conductor

Three core conductors circular or sector-shaped (solid and stranded) wires are used,

depending on voltage-level and power capability. Filler materials made of oil

impregnated paper are used to fill in interspaces between circular shaped core

conductors.

ii) Insulation Layers

Each core is insulated with multi layers of oil impregnated paper (OIP) insulation. The

OIP consists of the finest electrical grade paper made from coniferous wood pulp and

the purest grade polybutene dielectric fluid.

iii) Lead sheathing (Optional)

A metal sheathing layer made of lead is used as an insulation shield (or screen) over

the OIP insulation layer. The lead screen provides moisture barrier to the OIP

insulation

iv) Metal Screen

Each of the conductor core is covered by screen thin layer of copper or aluminum

metalized paper over its OIP insulation layers so that there is not much power

dissipation in them. The paper is perforated to facilate the process of oil impregnation

with the same coefficient of contraction and expansion of the dielectric (i.e. the cable

becomes homogenous mass). The screen layer, as an equipotential surface, forces flux

lines distribution to be spaced symmetrically and perpendicular to equipotential lines

(i.e. in radial directions). An outer screen is wrapped round with copper woven fabric

(cotton tape into which is woven copper wire). This outer screen is in contact with the

inner screens and is earthed.

v) Bedding

It is an inner sheath of bituminous paper over the lead metal sheath to provide a

protective layer against mechanical crakes caused by the pressure of the steel tape

armoring layers

vi) Steel-tape armoring

One or more layers of galvanized steel tape is used as an external layer for increasing

the mechanical strength of the cable that can be directly buried in ground.

5.5 Cable Construction

171

vii) Servicing

It is an external protective layer made of bituminous jute to provide anti-rusting

protection to steel-tape armoring layers.

The other layers are as shown in Fig.5.8.

Fig.5.8 a Cross-sectional View of the Three-core H-Type Cable

5.5.2 Separated Lead (or Aluminum) Screened Three-core Cable (SL-cable or

SA-cables)

In this type of cable each core is first insulated with an OIP and then each of them

is separately lead (or aluminum) sheathed. Each lead (or aluminum) screen layer is

grounded, and hence the three-cores are just equivalent to three separate single-core

cables (see Fig.5.9). The dielectric field is uniformly radially distributed for each

cable-core, and the electric field stresses are distributed uniformly for the OIP

insulation layers.

Fig.5.9 a Cross-sectional View of the SL-type Cable

The electrical and thermal advantages of H-type cables are also enjoyed by the S.L.

type cables. These cables are suitable for hilly routes, as the absence of oil in the filler

spaces lessens the risk of oil drainage.


172

5.5.3 Mass-impregnated Paper Insulating Submarine Cables

Fig.5.10 A Cross-sectional View of the mass OIP Submarine Cable

1 Conductor core 5 Lead sheath 9 Steel-wire armour

2 Conductor shielding 6 Plastic jacket 10 PVC outer jacket

3 OIP insulation 7 Steel-tape armouring

4 Insulation shielding 8 Optical fiber (optional)

5.5.4 Single-core EPR-insulated Shielded Power Cable

1 Circular stranded compacted copper (or

aluminum) conductors

2 Conductor Shield (or Screen) using

Extruded Semiconducting EPR material

3 EPR Insulation layer

4 Insulation Shield (or Screen) using Extruded

Semiconducting EPR material

5 Metallic Sheath using 5 Mil Uncoated

Copper Tape.

6 PVC external Jacket

Fig.5.11 Typical 66kV Single-core EPR-insulated Shielded Power Cable

5.5 Cable Construction

173

5.5.5 Four-core XLPE-insulated Low Voltage (0.6/1.0kV) Power Cable

Fig. 5.12 Four-core XLPE -insulated Shielded Power Cable

1 Conductor Concentric stranded or compact stranded annealed copper wires

2 Insulation Cross-linked polyethylene (XLPE)

Insulation identification: Red, Yellow, Blue and Black color

3 Filler Polypropylene (Non-hygroscopic material)

4 Binding tape Polyester / Spunbond tape

5 Inner Sheath Polyvinyl chloride (PVC), Black color

6 Armor Galvanized steel wire

7 Binding tape Polyester / Spunbond tape

8 Outer Sheath Polyvinyl chloride (PVC), Black color

Application:

It is used for general purpose power distribution in dry or wet location.


174

5.6 CABLE PARAMETERS

5.6.1 Effective Cable Resistance

The resistance of the core conductor of a power cable is very important in

evaluating the efficiency of the transmitted power and economy study. The dc

resistance (in ohms) of a solid round core conductor at a specified temperature is given

by

ARdc

(5.1)

= conductor resistivity in (.m)

= conductor length in (m)

A = conductor cross-sectional area in (m2)

The conductor resistance is affected by four factors: (i) spiraling and cable transposition, (ii)

temperature effect, (iii) skin effect, (iv) proximity effect, and (v) eddy currents in metallic

sheaths.

5.6.1.1 Spiraling and cable transposition:

For stranded wires type core conductors, there is about 2% increases in dc

resistance due to spiraling. Also, for three-core type cables an additional 2% increase

in dc resistance by the effect of three-phase core transposition.

5.6.1.2 Temperature effect:

The dc resistance of the core conductor increases as temperature increases. This

change can be considered linear over the range of temperature normally encountered

and may be calculated from (2.34): Chapter-2.

5.6.1.3 Skin effect

When AC flows in a conductor, the current distribution is not uniform over the core

conductor cross-sectional area and the current density is greatest at the outer shells.

This causes a decrease in the effective conductor cross-sectional area (A) and hence an

increase of the ac resistance over the dc resistance by the percentage value o. The

behavior is known as skin effect as explained in detail in section 2.9.3.1: Chapter-2.

The value of o increases by the increase of conductor cross-sectional area and

frequency.

5.6.1.4 Proximity effect

For three-phase power cables, each core conductor lie within the alternating

magnetic fields of the other near-by cores that produces eddy currents and hence an

increase in power losses (called proximity effect: Section-2.9.3.2: Chapter-2). The

5.6 Cable Parameters

175

percentage increase of the ac resistance that counts for the extra power losses caused

by proximity effect can be taken as p.

Finally, the ac resistance of the core conductor becomes

)1(RR podcac (5.2)

Therefore, it is recommended to determine the ac core resistance from manufacturer’s data that

takes into account all of the above effects.

5.6.2 Cable Inductance

The inductance of a single-core or approximately of each core in the three-

phase core cable is calculated from

GMR

GMDln102L 4 (5.3)

Where GMD : is the geometric mean distance between centeres of core conductors.

GMR : is the geometric mean radius (GMR = 0.7788 r, r is the outer conductor radius for

solid round conductor).

5.6.3 Capacitance of single-core type cable

The capacitance of core to grounded metallic sheath for single core (or H-type, SL and

SA three-core cables), see Fig.5.13, is calculated from

km/Fμ

r

Rln

ε005.0C r

N

(5.4)

Conductor

Insulation

Fig.5.13 Capacitance of Shielded Single-core Cable

Conductor Shield

MetallicInsulation Shield

r

R

5.6.4 Capacitance of Three-core Belted type Cables

Three-core belted-type cables are old technology for cable manufacturing. Each

core is insulated with multi layers of the OIP insulated material. An insulation belt is

wound over the three cores for increasing dielectric strength of the cable As these

types of three-core cables has no separate screening (like SL or SA cables), then non-

uniform distributed electric field flux with capacitance between cores and core-to-

sheath capcitances are existed (see Fig.5.14).


176

Cs

Cc

Cs

Cc

Cs

Cc

Fig. 5.14 Capacitances of three-belted core cables

As the core conductor is always not round in shape and insulation layers are non-

uniform, it can not be easily to derive a mathematical expression for the core

conductor-to- neutral capacitance (CN) in terms of capacitances between cores (Cc) and

core-to-sheath capcitances (Cs). Instead the value of CN is detemined experimentally as

follows:

Using delta-to-star transformation of Cc capacitive reactances, as shown in Fig.5.14,

the value of CN can be represented as

cscablesbeltedcore3N C3CC

(5.5)

A measurement for determining the value of CN is illustrated in Fig.5.15.

Cs

Cs

Cc

Cc

Cc

One core is connected to sheath

To a

c bri

dge

mea

sure

men

t ci

rcuit

Cc

Cc Cc

Cc Cc

A

B

A

B

Fig.5.15 AC bridge measurement circuit for capaitance-to-neutral capacitance

of three-core Belted type Cable

alsminterABbetweenmeasuredcetanCapaci2C

C)C3C(

C)CC(C

N

N21

cs21

ccs21

AB

(5.6)

5.7 Dielectric Stress in a Single Core Cable

177

5.7 DIELECTRIC STRESS IN A SINGLE CORE CABLE

The potential gradient Ex at the different insulation layers distant radial length x (refer

to Fig.16a) is defined as the dielectric stress and equals to

xεεπ2

λ

dx

dVE

ro

xx

Where : is the electric line charge in C/m.

Integration of the above equation through insulation thickness yields

r

Rln

εεπ2

λ

x

dx

εεπ2

λV

ro

R

rro

ph

Now, by substitution of roεεπ2

λ in terms of the operating voltage Vph from the above

equation, the expression of the electric stress xE (show Fig.5.16) becomes

rR

phx

lnx

VE (5.7)

Therefore, the maximum dielectric stress maxE at conductor surface and the minimum dielectric

stress at metallic sheath layer are obtained from

rR

phmax

lnr

VE (5.8)

rR

phmin

lnR

VE (5.9)

Since it is required that this maximum stress in the dielectric should be as low as

possible, differentiating with respect to r for minimum maxE gives 0rd

Ed max

718.2er

Ror

0r

1r

rRln

rRlnr

V.e.i

2

Thus if the overall diameter of the cable is kept fixed, then R/r = e is the condition for

minimum maxE . This value of radius of conductor will generally be larger than would

be required for current carrying capacity.

Since er

R , the minimum value of maxE is given by


178

r

VEmin

phmax (5.10)

Since the radius of the conductor that would be given from the above expression is

larger than is necessary for current carrying capacity, this value of radius may be

achieved by using Aluminum or hollow conductors.

Generally, the insulation thickness is designed such that the maximum allowable electric stress

at conductor surface is 5

1 of the dielectric breakdown strength of cable insulation.

Fig.5.16 Electric Stress Distribution

Example 5.1:

An XLPE single-core, 3 km long UGC is used as a single-phase in a three phase 220

kV, 50 Hz power system, has the following data:

Copper core: 600 mm2 (127 strands/2.25 mm).

Dielectric constant of XLPE insulation = 2.25.

Maximum working electric stress = 15 kV/mm.

Calculate:

(i) Insulation thickness.

(ii) Electric stress at conductor surface when a surge voltage of 1000-kV peak is

applied and energy dissipation if the insulation breaks down at that voltage.

Solution 5.1:

The stranded core conductor is arranged in six layers with outer radius r as 6.5×2.25 =

14.625 mm.

5.7 Dielectric Stress in a Single Core Cable

179

784.1er

R

579.0ln

ln625.14

3220

15

lnr

VE

579.0

r

R

r

R

r

R

phmax

Insulation thickness (t) = mm47.11rR

peakkV09.118579.0625.14

1000

lnr

VE

r

R

phmax

F100583.0km3579.0l

25.2005.0km/F

r

Rln

005.0C 6r

N

Dissipated energy at breakdown voltage surge

= s.W10029145.0101000100583.0VC 6236

2

12N2

1

Example 5.2:

Calculate the insulation thickness in Example 5.1 for minimum electric stress at conductor

surface.

Solution 5.2:

mm75.39R718.2625.14

R yields

Insulation thickness (t) = mm126.25rR


180

5.8 POWER LOSS IN HIGH VOLTAGE CABLES

High voltage cables are generally single cored, and hence have their separate

insulation and mechanical protection by sheaths. The presence of sheath increases

cable power loss. This is due to the fact that sheaths of the conductors cross the

magnetic field set up by the conductor currents. At all points along the cable, the

magnetic field is not the same. Hence, different voltages are induced at different points

on the sheath.

Power loss in the cable can occur due to a variety of reasons (Figure 5.17). They

may be caused by the conductor current passing through the resistance of the

conductor - conductor loss (also sometimes called the copper loss on account of the

fact that conductors were mainly made out of copper), dielectric losses caused by the

voltage across the insulation, sheath losses caused by the induced currents in the

sheath, and intersheath losses caused by circulating currents in loops formed between

sheaths of different phases. The dielectric loss is voltage dependant, while the rest is

current dependant.

Fig. 5.17 - Heat Transfer in a Cable due to Losses

5.8.1 Dielectric Losses of Metallic-sheathed Power Cables

The path for leakage current (Il) in metallic-sheathed cables is radial through

insulation layers (as shown in Fig.5.18).

R r

x

c

dx

(a) Incremental cylindrical

shell for calculation dRin

phV Rin CN

lI cI

phV

lI

cI

oφ

(b) No-load equivlent circuit

and phasor diagram

oδ

oI

oI

Fig. 5.18 Calculation of Insulation Resistance for metallic-sheathed cable

5.8 Power Loss in High Voltage Cables

181

The incremental insulation resistance can be calculated as

Lxπ2

dxρdR in

in

Where inρ : is the specific resistance of the insulating material (in ohm.m)

L : is the cable length (in m)

Integration of the above equation through insulation thickness yields

r

Rln

Lπ2

ρR in

in (5.11)

Dielectric power loss Pdis is then equals:

oN2phoophin

2ldis tanCVcosIVRIP (5.12)

Where otan is defined as the dissipation factor

Values for the permittivity and dissipation factor are given in Table 5.2.

Table 5.2 Nominal Values for Permittivity and Loss Factor

Cable Type Permittivity r otan

Solid type OIP 4 0.01

Fluid-filled OIP

Up to Vo = 36 kV 3.6 0.0035

Up to Vo = 87 kV 3.6 0.0033

Up to Vo = 160 kV 3.5 0.0030

Up to Vo = 36 kV 3.5 0.0028

High Pressure OIP

Fluid-pressure, pipe type OIP 3.7 0.0045

External gas pressure OIP 3.6 0.0040

Internal gas pressure OIP 3.4 0.0045

Butyl rubber 4 0.05

Polymeric-

Insulated Cables

EPR Up to 18/30 (36) kV 3 0.02

Above 18/30 (36) kV 3 0.005

PVC 8 0.1

PE (HD and LD) 2.3 0.001

XLPE 18/30 (36) kV (unfilled) 2.5 0.004

> 18/30 (36) kV (unfilled) 2.5 0.001

> 18/30 (36) kV (filled) 3 0.005

Vo/V (Vm) Vo is the rated power frequency voltage between conductor and

earth or metallic screen

V is the rated power frequency voltage between conductors

Vm Is the maximum continuously operating voltage of a cable at

time or in any part of the network


182

It can be concluded that the dielectric power losses are directly proportional to the

square of the operating voltage and the loss angle. Therefore, in high-voltage cables

the dielectric loss angle must be kept very small. Generally, high quality of high-

voltage cables is measured in terms of a small loss angle less than 2o.

The no-load power factor of high-voltage cable is

inNNph

in

ph

o

loloadno RCω

1

CωV

R

V

I

IφcosF.P

(5.13)

5.8.2 Conductor Loss

The conductor power loss is given by

ac2

c RIP (5.14)

Where acR is the resistance of the conductor and I is the current in the cable.

5.8.3 Sheath Loss

The losses occurring in the sheath of a cable is usually obtained by the empirical

formula of Arnold. Arnold's formula for the sheath loss shP is given by

wattd

r

R

I107.7P

2m

sh

23

sh

(5.15)

Where

rm = mean radius of sheath

d = distance between cables (centre to centre)

Rsh = resistance of full length of cable sheath

I = current in cable

The sheath loss is usually about 2 to 5 % of the conductor loss.

5.8.4 Intersheath Loss

Intersheath losses are caused by the induced emf between the sheaths causing a

circulating current. This loss is thus present only when the sheaths of adjacent cables

are connected together. The sheaths need to be connected together in practice, as

otherwise sparking could occur causing damage to the sheaths. The intersheath loss

ishP can be calculated as follows.

The mutual inductance shM between a core of one cable and the sheath of an adjacent

cable is given by

5.8 Power Loss in High Voltage Cables

183

r

dln

2Msh

(5.16)

The voltage induced ishE is given by

shish MIE (5.17)

And the induced current ishI is given by

2sh

22sh

ishish

MR

EI

(5.18)

Therefore the intersheah loss ishP is given by

2sh

22sh

sh2sh

22

sh2ishish

MR

RMIRIP

Generally, the sheath resistance shsh MR so that

sh

2sh

22

ishR

MIP

(5.19)

The intersheath loss is larger than the sheath loss and may range from 10% to 50% of

the copper loss. Thus the total power loss (exclusive of the dielectric loss) is given as

ishshctotal PPPP (5.20)

Since the whole expression is dependant on 2I , we may express the loss in terms of an

effective resistance effR . This gives the total power loss in terms of the effective

resistance as

eff2

total RIP (5.21)

sh

2sh

22m

sh

3

ceffR

M

d

r

R

107.7RR

Since the sheath loss is usually very small, the effective conductor resistance can be

written as

sh

2sh

2

ceffR

MRR

(5.22)


184

5.8.5 Cross-bonding of Cables

When three single phase cables are used in power transmission, currents are

induced in the sheaths and lead to sheath circulating currents and power loss. These

may be substantially reduced, and the current rating of the cable increased by cross

bonding of the cables (Fig.5.19). Cross bonding of cables are done except for very

short lengths of cable.

Fig.5.19 Cross Bonding of Sheaths

The continuity of each cable sheath is broken at regular intervals; the cables

between two adjacent discontinuities being a minor section. 3 minor sections make up

a major section, where the sheaths are solidly bonded together and to earth. A residual

sheath voltage exists, and the desired balance, giving negligible sheath voltage

between the solid grounded positions is achieved by transposing the cables at each

cross bonded section.

To prevent excessive voltage build up at the cross bonded points, especially during

faults, these points are earthed through non-linear resistors (i.e. surge arrestor) which

limit voltage build up. The cable is also transposed (Fig.5.20).

Fig.5.20 Nonlinear Resistor Earthing

5.9 Thermal Characteristics and Current Rating of Power Cables

185

5.9 THERMAL CHARACTERISTICS AND CURRENT RATING OF POWER

CABLES

The power losses in cable resistance produced by cable current ( ac2 RI ) in addition

to dielectric losses disP and the eddy current losses in metallic sheath and steel

armouring layers increases the cable operating temperature. Now, if the heat generated

by power losses balances the heat dissipation from core conductor to air via the

different cable layers and ground, then the cable temperature becomes steady at the

recommended insulation value (for example as 70oC for PVC insulation).

Figure 5.19 shows paths of the heat dissipation from conductor surface to air

via the different cable layers and ground.

Cable of outer diameter d

Burried

depth ls

Ground Surface

Air medium

Fig.5.19 Radial paths of heat power flow from conductor

surface to air invironment

An analogy of the Ohm’s law in electric circuit and law of heat flow in thermodynamics yields

SRInSHT ac2 (5.13)

Where T : is the temperature rise of core conductor over soil temperature.

H : is the rate of heat flow in oC/m

n : is the number of core conductors

Rac : is the ac resistance of 1-m cable length

I : is the cable current rating

S : is the sum of thermal resistances of the different cable layers and ground

The thermal resistances of the different cable layers (refer to Fig.5.20) are derived as follows:


186

dc

dis

dm

d

External Jacket

Metallic Sheath

Insulation layers

Conductor core

Fig. 5.20 Calculation of thermal resistivity for different cable layers

If gis : is the thermal resistivity of the insulation material, then the thermal resistance of the

insulation layer for one-meter length of the single-core cable (Fig.18) is

W/mCd

dln

π2

g

0.1xπ2

dxgS o

c

isis

R

rx

isis

(5.14)

Similarly, the thermal resistance of the insulation screen, metallic sheath, armouring, textile

servicing layers and outer jacket (Fig.5.20) will be

W/mCd

dln

π2

gS o

m

mm

(5.15)

If it is assumed that the surface of the ground is an isothermal and the ground is homogeneous, the

thermal resistance of soil layers can be given by the imperical formula

W/mCd

l4ln

π2

gS ose

e

(5.16)

Finally, the total thermal resistance of the different cable layers and ground is obtained as

emis SSSS (5.17)

Table 5.2 shows the thermal resitivity of typical materials that are used in cable manufacturing and

installation, while Table 5.3 shows the thermal resitivity of soil under different weathering

conditions.


187

Table 5.2 Thermal Resistivity of the Different Materials

that are used in Cable Manufacturing and Installation

Material Thermal Resitivity

in oC m/W

Insulation

OIP 5.5 ~ 6.5

PVC

3-kV 5.0

> 3-kV 6.0

EPR

3-kV 3.5

> 3-kV 5.0

PE & XLPE 3.5

Natural rubber 5.0

External

Covering

Jute and Textile Materials 6.0

PVC

35-kV 5.0

> 35-kV 6.0

Ducts

Armoured concrete 1.0

Fiber 4.8

PVC 7.0

Table 5.3 Thermal Resistivity of Soil

Thermal Resitivity ge

in oC m/W

Soil Condition Weathering

Conditions

0.7 Very wet Always humid

1.0 Wet Rains fall regularly

2.0 Dry Rains fall very rare

3.0 Very Dry No rains normally

Example 5.3:

A 10-km long single-core cable has a core made of stranded copper wires specified as

150 mm2 (37 strands with 2.25 mm diam/strand). The cable is insulated with OIP

insulation (r = 3.5) to a radial thickness of 25 mm. The cable has the following

specifications:

Core resistivity = 2.98×10-8

Ohm.m with skin factor as 7% and sheath effect

with armour as 13%.

Insulation resistivity = 5×109 Ohm.m

Thermal resitivity of insulation = 5.5 moC/W

Thermal resitivity of ground = 2.5 moC/W

Soil temperature = 15oC

Recommended cable temperature = 85oC


188

Determine:

i) The cable rated current if the cable is burried directly in ground to a depth of

0.75 m.

ii) The no-load power factor and the dielectric losses if the cable is used in three-

phase 66-kV subtransmission system.

Solution 5.3:

DC resistance of cable m/10987.110150

1098.2

A

0.1ρR 4

6

8cu

dc

AC resistance of cable m/10384.22.1RR 4dcac

The stranded core conductor is arranged in three layers (1 + 6 + 12 + 18) with outer

diameter dc as 7 × 2.25 = 15.75 mm

Diameter over insulation layers dis = 15.75 + 2×25 = 65.75 mm

Overall diameter of cable d dis (by neglecting outer servicing layer thickness)

Sum of thermal resistances

d

l4ln

π2

g

d

dln

π2

gSSS se

c

isiseis

W/Cm77.275.65

7504ln

π2

5.2

75.15

75.65ln

π2

5.5SSS o

eis

A6.325I:currentratedCable

77.210384.2I11585

SRInT

42

ac2

Dielectric resistance

5

9in

in 10137.175.15

75.65ln

10000π2

105

r

Rln

Lπ2

ρR

Capacitance of conductor core-to-neutral

)F(10362.11010

2/75.15

2/75.65ln

5.3055.0km/Fμ

r

Rln

ε005.0C 66r

N

Loss angle o

56

1

inN

1 18.110137.110362.1502

1tan

RC

1tan

No-load power factor %)2or(02.0)18.190cos(φcos o

Dielectric power losses = )W(103.3810137.1

103

R

V33

5

23

3

66

in

2ph


189

5.9.1 Cable Ampacity

Cable ampacity (or current carrying capacity) is defined as the continuous

maximum current the cable can carry at its maximum operating temperature. The

calculation of cable ampacity is a complicated problem and always provided by cable

manufacturers as data in the technical information tables. The given data of cable

ampacities are based on specified installation conditions. If the installation conditions

are not specified, then designer engineer has to follow the standard installations

conditions in cable ampacities calculations.

5.9.2 Standard Cable Installation Conditions

Standard installation conditions for cables that are installed in free air includes:

i) Ambient air temperature is 25oC for transmission and distribution cables, 30

oC

for indoor wiring and 35oC for wiring installations in ships. .

ii) Minimum distance between cable and wall is 20 mm.

iii) Minimum distance between the cable and neighbouring one is 150 cm.

iv) Cable is isolated from direct sun rays.

While the standard installation conditions for cables that are directly burried in ground

includes:

a) Soil temperature is 15oC.

b) Thermal resistivity of soil is 1.2 oC m/W.

c) Minimum distance between the cable and neighbouring one is 1.8 m.

d) Burried depth is 0.5 m for 1-kV cables and 0.8 m for cables higher than 1-kV.

5.9.3 Cable Ampacity and Derating Factors

In the technical information tables that are prepared by cable manufacturers the

cable conductor current carrying capacity (or cable ampacity) is calculated either under

specified installation conditions or it follows the standard ones mentioned in section

5.9.1. In Tables 5.4 through 5.9 the following installation conditions that fit Alexandria

Mediterranean weathering conditions are:

a) Ambient temperature = 40oC.

b) Ground temperature = 35oC.

c) Ground thermal resitivity = 120 oC m/W.


190

Table 5.4- Ground temperature derating factor

Ground temperature oC 25 30 35 40 45 50 55

PVC cables rated 70oC 1.13 1.07 1.00 0.93 0.85 0.76 0.65

XLPE cables rated 90oC 1.09 1.04 1.00 0.95 0.90 0.85 0.80

Table 5.5- Air temperature derating factor

Air temperature oC 25 30 35 40 45 50 55

PVC cables rated 70oC 1.22 1.15 1.08 1.00 0.95 0.82 0.71

XLPE cables rated 90oC 1.09 1.04 1.00 1.00 0.90 0.89 0.84

Table 5.6- Burial depth derating factor

Depth laying (m) Cable cross-section

Up to 70mm2

95 Up to 240mm2

300mm2 & above

0.50 1.00 1.00 1.00

0.60 0.99 0.98 0.97

0.80 0.97 0.96 0.94

1.00 0.95 0.93 0.92

1.25 0.94 0.92 0.89

1.50 0.93 0.90 0.87

1.75 0.92 0.89 0.86

2.00 0.91 0.88 0.85

Table 5.7- Trefoil or flat formation derating factor for three single core cables

laid direct in ground

Number of

Circuits

Touching Spacing = 0.15 m Spacing = 0.30 m

Trefoil Flat Trefoil Flat Trefoil Flat

2 0.77 0.80 0.82 0.85 0.88 0.91

3 0.66 0.69 0.73 0.76 0.80 0.83

4 0.60 0.63 0.68 0.71 0.74 0.77

5 0.56 0.59 0.64 0.67 0.72 0.75

6 0.53 0.57 0.61 0.64 0.70 0.73


191

Table 5.8- Trefoil or flat formation derating factor for multi-core cables

laid direct in ground

Number of

Circuits

Touching Spacing = 0.15 m Spacing = 0.30 m

Trefoil Flat Trefoil Flat Trefoil Flat

2 0.81 0.81 0.87 0.87 0.91 0.91

3 0.69 0.70 0.76 0.78 0.82 0.84

4 0.62 0.63 0.72 0.74 0.77 0.81

5 0.58 0.60 0.66 0.70 0.73 0.78

6 0.54 0.56 0.63 0.67 0.70 0.76

Table 5.9- Soil resistivity derating factor

Soil thermal resistivity in oC.cm/W

80 90 100 120 150 200 250

Derating factor 1.17 1.12 1.07 1.00 0.91 0.80 0.73

Example 5.4:

Wiring design and installation for an industrial plant requires the use of four 0.6/1

(1.2) kV multi-core cables with stranded copper conductors, XLPE insulated, steel

wire armoured and PVC sheathed to feed a total load of 800-A . Installations

conditions are

Cables are laid directly in ground at depth of 1.25-m.

Cables are laid in trenches with flat configurations of spacing 30 cm.

Soil temperature = 40oC.

Soil type condition is very dry with rarely falling rains.

Using the technical information tables 5.4 through 5.9 to calculate:

i) The augmented derating factor under practical installation conditions of cable

circuits.

ii) Cable ampacity and corresponding nominal cross-sectional area under practical

installation conditions of cable circuits.

Solution 5.4:

Nominal copper conductor cross-sectional area for a current ampacity of 200-A per

cable circuit under specified installation conditions by the manufacturer =

3×70+35mm2.

Derating factor (K1) @ soil temperature of 40oC for XLPE cable using Table 5.4 =

0.95.


192

Derating factor (K2) for 1.25 mm depth of burial and nominal cross-sectiona area up to

70 mm2 using Table 5.6 = 0.94.

Derating factor (K3) for thermal resistivity of 200 oC cm/W (very dry soil with rarely

falling rains) using Table 5.9 = 0.8.

Derating factor (K4) for multi-core cable grouping in four circuits using flat formation

with 0.3 m spacing as indicated in Table-7 = 0.81.

Augmented derating factor is then equals:

5787.081.08.094.095.0KKKKK 4321

Cable Ampacity = A6.3455787.0

200

Nominal cross-sectional area under practical installation conditions of cable circuits is

3× 185 + 95 mm2.

5.9.4 Cable Short Circuit Capacity

The wiring design and installation of cable circuits requires an adequate selction of

the nominal cross-sectional area based on:

i) Continuous current loading under practical installation conditions of cable

circuits.

ii) Cable short-circuit capacity at duration starts from short-circuit instant until

complete interruption by automatic circuit-breakers.

Cable insulations among other cable layers that are affected much with heat dissipation

during short-circuit, where the maximum recommended temperature max not to exceed

160oC for PVC-insulation, 250

oC for XLPE-insulation and 250

oC for OIP insulation.

The maximum short-circuit current period (T) in seconds changes in an inverse

relationship to the cable r.m.s short circuit capacity (Isc) in amperes as shown in the

following imperical formula:

βθ

βθln

T

SαI

o

max22

2sc (5.18)

S is the nominal cross-sectional area of core conductor in mm2

o is the recommended cable temperature for continuous operation (70oC for PVC-

insulation, 90oC for XLPE-insulation and 60

oC for solid-type OIP insulation

& are constants depending upon materials of core conductor and metallic sheath layer

(as indicated in Table 5.10 below)


193

Table 5.10 Values for and constants in eq.5.18

Material

Copper 226 234.5

Aluminum 148 228

Lead 32 230

Steel 78 202

It is recommended to select an adequate nominal cross-sectional area of core

conductor to carry short-circuit current less than short-circuit current capacity during 1

or 3 seconds standard interrupting duration to release the short-circuited cable length.

Example 5.5:

If the selected cable of Example 5.4 is installed as main feeder in an industrial

distribution power system network. The cable is susceptible to maximum three phase-

to-ground short circuit of 30 kA. Check that the selected cable size (3× 185 + 95 mm2)

can withstand the short circuit current. Comment on result.

Solution 5.4:

For 1 sec interrupting time, the cable short circuit capacity is calculated as

kA47.26I

5.23490

5.234250ln

1

185226ln

T

SI

sc

22

o

max22

2sc

The cable size cannot withstand the maximum short circuit current of 30 kA.

The short-circuit capacity of the cable can be increased by increasing the cable size.

Selecting higher cable size 3× 240 + 120 mm2 of then the cable short circuit capacity is

kA34.34I185

240

47.26

I

kAI

5.23490

5.234250ln

1

185226ln

T

SI

scyieldssc

sc

22

o

max22

2sc

This can withstand the maximum short circuit current of 30 kA.


194

5.10 ASSIGNMENT OF CHAPTER-5

P5.1 What is the main difference between non-shielded and shielded type cables?

Draw a schematic cross-section in a shielded type cable and state the functional

operation of each layer. What are the functional operations of metallic armoring

and non-metallic jacket layers in power cables?

P5.2 Why the non-shielded type cables are limited in use for low-voltage networks?

P5.3 State the different types of polymeric type insulations that are used in power

cables. Make a comparison between these types of power cables. The

comparison should include recommended continuous working temperature,

dielectric strength, mechanical and electrical properties at high temperatures

during short-circuit faults, flexibility for installations, and fields of practical use.

P5.4 An XLPE single-core, 3 km long UGC is used as a single-phase in a three phase

220 kV, 50 Hz power system, has the following data:

Copper core: 600 mm2 (127 strands/2.25 mm).


Maximum working electric stress = 15 kV/mm.

Calculate:

(iii) Insulation thickness.

(iv) Electric stress at conductor surface when a surge voltage of 1000-kV peak is

applied and energy dissipation if the insulation breaks down at that voltage.

P5.5 Give reasons for the followings:

(i) Use of separate lead screening layers for three-core high-voltage OIP power cables.

(ii) Use of steel armoring layers for power cables that are directly buried in ground.

(iii) Use of conductor and insulation shield layers beddings under and above

XLPE or EPR insulation layers.

P5.6 An XLPE single-core, 11 km long UGC is used as a single-phase in a three

phase 400 kV, 50 Hz power system, has the following data:

Copper core: 600 mm2 (127 strands (6-layers)/2.25 mm per strand).


Calculate:

(i) The insulation thickness for maximum working electric stress of 15 kV/mm.

(ii) The dielectric power loss for no-load power factor of 2%.

P5.7 Show how to decrease the sheath and intersheath power loss for high-voltage

three-phase single core cables?

5.10 Assignment of Chapter-5

195

P5.8 A 66 kV, 50 Hz, and 50 km long lead-sheathed SL-cable is insulated with oil-

impregnated paper (r = 3.5) to a radial thickness of 10 mm and the cable is

armored with steel band. The lead sheath over electrical insulation is 3-mm

thickness, the outer jacket over the sheath is 3-mm thick and the armour is 2-

mm thick.

The cable has the following specifications:

Aluminum conductor: 400 mm2 (61 strands/2.89 mm).

Overall diameter = 55 mm.

DC-aluminum resistivity as 0.030310-6

.mm2/m with skin effect factor

as 7% and the sheath effect with armor as 13%.

Insulation resistivity = 1.341010

.m.

Thermal resistivitie of impregnated-paper insulation is 5.5 oC.m/W and that

of outer insulation, armouring and PVC jacket is 6 oC m/W and that of

ground is 1.3 oC.m/W.

Ground temperature = 15oC.

Recommended cable temperature = 65oC.

The cable is directly buried at a depth of 1 m with derating factor as 0.92

and laid side by side with a similar one at group derating factor of 0.8.

Determine the following:

(i) The cable rated current.

(ii) The no-load power factor and the dielectric losses.

(iii) Charging kVAR of the cable.

(iv) Electric stresses at in kV/mm.

(v) Electric stress at conductor surface when a surge voltage of 1000-kV peak

is applied and energy dissipation if the insulation breaks down at that

voltage.

P5.9 A 11 kV, 3-core, 5 km long copper 240 mm2 (61/2.24 mm) power cable. The

PVC insulation has a thickness of 7 mm and the aluminum sheath over

electrical insulation is 3 mm in thickness and having a relative permittivity of

2.26. The outer jacket over the sheath is 3 mm thick and the armor is 2 mm

thick. Determine:

(i) The AC core resistance at recommended cable temperature of 70oC if the DC-

aluminum resistivity at 20oC as 0.030310

-6 .mm

2/m with skin and armor effect

factor as 20%. Temperature coefficient of electric resistance for aluminum is

o.00403 per oC.

(ii) The electric sress at conductor surface and at outer shell of the insulation.

ch5 underground power cables 2[1]

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