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.
Chapter 5: Underground Power Cables
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.
Chapter 5: Underground 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.
Chapter 5: Underground Power Cables
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
5.4 Basics Of Insulated Power Cable Construction
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.
Chapter 5: Underground Power Cables
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.
5.4 Basics Of Insulated Power Cable Construction
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.
Chapter 5: Underground Power Cables
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.
Chapter 5: Underground Power Cables
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.
Chapter 5: Underground Power Cables
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).
Chapter 5: Underground Power Cables
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
Chapter 5: Underground Power Cables
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
Chapter 5: Underground Power Cables
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
Chapter 5: Underground Power Cables
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)
Chapter 5: Underground Power Cables
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:
Chapter 5: Underground Power Cables
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.
5.9 Thermal Characteristics and Current Rating of Power Cables
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
Chapter 5: Underground Power Cables
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
5.9 Thermal Characteristics and Current Rating of Power Cables
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.
Chapter 5: Underground Power Cables
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
5.9 Thermal Characteristics and Current Rating of Power Cables
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.
Chapter 5: Underground Power Cables
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)
5.9 Thermal Characteristics and Current Rating of Power Cables
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.
Chapter 5: Underground Power Cables
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).
Dielectric constant of XLPE insulation = 2.25.
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).
Dielectric constant of XLPE insulation = 2.25.
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.
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