charecteristics of electric cables and fault localization
DESCRIPTION
cables, XLPETRANSCRIPT
Characteristics of Electric Cables
and Fault Localization
Shashidhar kasthalaAsst.professor
Indian Naval Academy,Ezhimala, kerla
Shashidhar kasthala
Table of contents
Abstract
Chapter 1: Basics of power cable Engineering
1.1 Introduction
1.2 Underground System Designs
1.3 Cable conductors
1.4. Medium and High voltage power cables
Chapter 2: Materials in cables
2.1 Material used in cables
2.2 Cable Insulation
2.3 Paper Insulated cables
2.4 Polymer Insulated cables
2.5 Electrical stress distribution and calculation
2.6 Electrical shielding
2.7. Protection against fire
2.7.1 Levels of cable fire performance
2.7.2 Material Considerations
2.8. System Protection Devices
Chapter 3: Characteristics of Power cables
3.1 General basis of rating determination
3.2. Mathematical Treatment
3.3. Ambient and cable operating temparature
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3.3.1 Ambient Temparature
3.3.2 Maximum Cable operating Temparature
3.4. Effect of Installation condition on Cables
3.4.1 Thermal resistivity of soil
3.5. Calculation of losses
3.5.1 Conductor Resistance
3.5.2 Dielectric Losses
3.5.3 Sheath Loss Factor
3.5.4 Armor Loss Factor
3.6. Standard operating conditions & Rating Factors
3.6.1. Cables installed in air
3.6.2. Cables installed in ducts
Chapter 4: Mathemetical Analysis
4.1: The Cable and Insulator Parameters
4.2 Localization of cable faults
4.3 Example for fault localization
Conclusion
References
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List of Figures
Figure 1.1(a): Radial System
Figure 1.1(b): Looped System
Figure 1.2: Voltage distribution in the insulation with the cable shield removed.
Figure 1.3: Four core MV Cables
Figure 2.1: single core paper insulated lead sheath cable with PVC oversheath
Figure 2.2: 4 core, paper insulated lead sheath cable with STA and bituminous finish.
Figure 2.3: 3 –core screened PLIS cable with PVC oversheath
Figure 2.4: 3-core 19/33 kV SL cable
Figure 2.5: 3-core, circular stranded conductors, XLPE insulated, collective copper wire
screen,MDPE oversheathed, 6.35/11 kV cable
Figure 2.6: Paper insulated belted cable with top conductor at peak potential
Figure 3.1: Circuit diaram to represent heat generated in a 3-core metal sheathed cable
Figure 3.2: Heat flow for a circuit of single core cables installed in trefoil
Figure 3.3 (a): The ladder diagram for steady state computations on single core cable
Figure 3.3(b): The ladder diagram for steady state computations on three core cable
Figure 3.4(a) Diagrammatic representation of a cross bonded cable system, when cables
are not transposed
Figure 3.4(b) Diagrammatic representation of a cross bonded cable system when Cables
are transposed.
Figure 4.1 Typical High volatge cable
Figure 4.2 Faults in underfround cable
Figure 4.3: Ground fault of a single cable
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List of Tables
Table 2.1: Physical properties of metal used in cables
Table 2.2: Electrical properties of metals
Table 2.3: Permittivity, Dielectric constant, and SIC
Table 2.4: Insulation Thickness and stresses on polymeric cables
Table 2.5: Levels of fire performance for different types of cables
Table 3.1: Ambient air and ground temparature
Table 3.2: Conductor temparature limits for starnded cable types
Table 3.3: Soil thermal resistivities
Table 3.4: Material properties
Table 3.5: Values of skin and proximity effect
Table 3.6: Values of dielectric constant and loss factor
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Abstract
Underground cables are far expensive to install and maintain than overhead lines.
This is due to the large capital cost associated with cable installations making it necessary
that particular care be applied in selecting the proper cable type and size to serve the load
for the life of installation. In power cable engineering and operation it is extremely
important to know the maximum current carrying capacity in which a cable can tolerate
through out its life without risking deterioration or damage for which the cable and
insulation properties should be properly analyzed.
In this project in addition to the evaluation of cable and insulation properties, the
location of cable faults are estimated. Underground lines are susceptible to being
damaged by excavations and it being more expensive to repair and maintain, there is an
utmost importance to localize the cable fault. The mathematical analysis is carried out
using MATLAB Programming.
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Chapter 1
Basics of Power Cable Engineering
1.1. Introduction
Aesthetics is primarily the major reason for installing power cables underground,
providing open views of the landscape free of poles and wires. One could also argue that
underground lines are more reliable than overhead lines as they are not susceptible to
weather and tree caused outages, common to overhead power lines. This is particularly
true of temporary outages caused by wind, which represents approximately 80% of all
outages occurring on overhead systems.
However, underground lines are susceptible to being damaged by excavations.
The time required to repair a damaged underground line may be considerably longer than
an overhead line. Underground lines are typically ten times more expensive to install than
overhead lines. The ampacity, current carrying capacity, of an underground line is less
than an equivalent sized overhead line. Underground lines require a higher degree of
planning than overhead, because it is costly to add or change facilities in an existing
system. Underground cables do not have an infinite life, because the dielectric insulation
is subjected to aging; therefore, systems should be designed with future replacement or
repair as a consideration.
1.2 Underground System Designs
There are two types of underground systems
A. Radial —The transformers are served from a single source as in Figure 1.1(a).
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B. Looped—where the transformers are capable of being served from one of two
sources. During normal operation an open is located at one of the transformers,
usually the midpoint as in Figure 1.1(b).
Figure 1.1(a): Radial System
Figure 1.1(b): Looped System
A radial system has the lowest initial cost, because a looped system requires the
additional facilities to the second source. Outage restoration on a radial system requires
either a cable repair or replacement, whereas on a looped system, switching to the
alternate source is all that is required.
Underground cable can be directly buried in earth, which is the lowest initial cost,
allows splicing at the point of failure as a repair option and allows for maximum
ampacity. Cables may also be installed in conduit, which is an additional cost, requires
replacement of a complete section as the repair option, reduces the ampacity, because the
conduit wall and surrounding air are additional thermal resistances, but provides
protection to the cable.
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Underground power cables have three classifications.
1. Low voltage—limited to 2 kV. Primarily used as service cables
2. Medium voltage—2–11 kV. Primarily used to supply distribution transformers
3. High voltage—above 11 kV. Primarily used to supply substation transformers
1.3 Cable conductors
The conductors of cables is usually stranded, i.e, it consists of a number of strands
of wire of circular cross-section so that it may become flexible and carry more current. In
the stranded conductor each wire lies on helix the pitch of which is so adjusted that the
cross-section of the cable at right angle to its axis if practically circular. To avoid the
bending and deformation of the cable conductor under normal condition the alternate
layers have right and left spirals.
In general the total number of conductors N in a n layer cable is given as
N = 1+3n(n+1) … (1.1)
Note: It should be remembered that the central conductor is not counted as layer.
The overall diameter D of a stranded cable with n layers is given as
D = (1 + 2n)d …(1.2)
Where d is the diameter of single strand conductor
1.4. Medium and High voltage power cables
Medium and high voltage power cables, in addition to being insulated, are
shielded to contain and evenly distribute the electric field within the insulation.
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Since medium- and high-voltage cables are shielded, special methods are required
to connect them to devices or other cables. Since the insulation shield is conductive and
effectively grounded, it must be carefully removed a specific distance from the conductor
end, on the basis of the operating voltage. Once the insulation shield has been removed,
the electric field will no longer be contained within the insulation and the highest
electrical stress will be concentrated at the end of the insulation shield.
Figure 1.2: Voltage distribution in the insulation with the cable shield removed.
The general construction of cable is given below:
(a) Core: All cables have one central core or a number of cores of stranded copper
or aluminum conductors having highest conductivity.
(b) Insulation: The different insulations used to insulate the conductors are paper,
varnished, cambric and vulcanized bitumen for low voltages. But mostly
impregnated paper is used which is an excellent insulating material.
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(c) Metallic sheath: It is provided over the insulation so as to prevent the entry of
moisture into the insulating material. The metallic sheath is usually of lead or lead
alloy and in case of cables having copper as conductor sometimes aluminum is
used for providing metallic sheath.
Figure 1.3: Four core MV Cables
(d) Bedding: Over the metallic sheath comes the layer of bedding which consists of
paper tape compounded with a fibrous material to protect it from mechanical
injury from armoring. Also sometimes jute strands or Hessian tape is also used for
bedding.
(e) Armoring: Armoring is provided to avoid mechanical injury to the cable and it
consists of one or two layers of galvanized steel wires or two layers of steel tape.
(f) Serving: Over and above armoring a layer of fibrous material is again provided
which is similar to that of bedding but is called as serving.
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Chapter 2
Materials in cables
2.1 Material used in cables
Electrical properties
The table 2.1 indicates the electrical properties of the common metals used in
cables. Copper and aluminum are clearly the best choice for conductors till date for
various reasons. But in the recent days there has been some experience with sodium.
Table 2.1: Physical properties of metal used in cables
Physical Properties
The physical properties of metals used for conductors and sheaths are given in
Table 2.2. Except for the conductors of self supporting overhead cables, copper is
invariably used in the annealed condition. Aluminum sheaths are now extruded directly
onto cables and hence of soft temper but a small amount of work hardening occur during
corrugation.
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Table 2.2: Electrical properties of metals
2.2 Cable Insulation
Electrical conductors must be covered with some form of electrical insulation.
Cables are usually classified according to the type of insulation used. An ideal insulating
material for this purpose should have the following characteristics
1. It should have a high specific resistance
2. It should have high dielectric strength
3. It should be tough and tensile
4. It should not be hygroscopic i.e, it should not absorb moisture from air
5. It should be capable of standing high temperature without deterioration
6. It should be non-inflammable
7. It should be capable of withstanding high rupturing voltages.
The selection of a particular insulation to be used is dependent upon the purpose
for which the cable is required and qualities of the insulation to be aimed at. The
following are the chief types of insulation groups which can be used are tabulated along
with their dielectric constants:
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Material Range TypicalButyl Rubber 3.0 – 4.5 3.2PVC 3.4 – 10 6.0Varnished Cambric 4.0 – 6.0 5.0Impregnated Paper 3.3 – 3.7 3.5Rubber-GRS or Natural 2.7 – 7.0 3.5HMWPE 2.1 – 2.6 2.2XLPE or TR-XLPE 2.1 – 2.6 2.3XLPE, filled 3.5 – 6.0 4.5EPR 2.5 – 3.5 3.2Silicone Rubber 2.9 – 6.0 4.0
Table 2.3: Permittivity, Dielectric constant, and SIC
2.3 Paper Insulated cables
For distribution and transmission purposes impregnated paper insulated cables
have had an impressive record of reliability in the 20th century. Impregnated-paper
insulation provides the highest electrical breakdown strength, greatest reliability, and
longest life of any of the materials employed for the electrical insulation of conductors. It
will safely withstand higher operating temperatures than either rubber or varnished-
cambric insulations. On the other hand, it is not moisture-resistant and must always have
a covering which will protect the insulation from moisture, such as a lead sheath.
Paper-insulated cables are not so flexible and easy to handle as varnished-cambric
or rubber-insulated cables and require greater care and time for the making of splices.
They are available in the following types:
1. Solid-type insulation
2. Low-pressure gas-filled
3. Medium-pressure gas-filled
4. Low-pressure oil-filled
5. High-pressure oil-filled (pipe enclosed)
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6. High-pressure gas-filled (pipe enclosed)
7. High-pressure gas-filled (self-contained)
Construction
Paper cables in the 1-33 kV range are often referred to as ‘solid type’ as they are
designed to operate without internal or external pressure.
The insulation consists of helically applied paper tapes with a small gap between
turns. The registration of tapes in relation to each other is important to avoid successive
butt gaps in a radial direction.
Figure 2.1: single core paper insulated lead sheath cable with PVC over sheath
The conductors in multi core cables are usually sector shaped upto 11 kV and oval
for 33 kV. Solid aluminum is used extensively at 1 kV.
Belted construction
The cable design with a belt of insulation over the laid-up cores (Figure 2.2) is the
most economical in terms of total material cost. Such cables are nearly always used upto
6.6 kV and are most common type at 11 kV.
The spaces between the cable cores under the belt are filled with jute or paper.
Whereas the main insulation consists of paper tapes precisely applied, the filler insulation
has to be softer and less dense so as to compress into the space available and is weaker
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electrically. Stresses in the filler have to be limited to an acceptable level and therefore
belted cables are not generally used at voltages greater than 11 kV.
Figure 2.2: 4 cores, paper insulated lead sheath cable with STA and bituminous finish.
Screened cable
The dielectric strength of impregnated paper is weaker in the tangential direction
than in the radial direction and for cables at voltages above 11 kV it is necessary to
ensure that the electrical field is radial. As operating temperature were raised with 3-core
cable in the early 1920’s, non radial fields were the cause of extensive cable failures of
belted cables.
Screening consists of a thin metallic layer in contact with the metallic sheath
(Figure 2.3). As it carries only a small charging current, the thickness is unimportant but
it is necessary to have smooth contact with the insulation together with an ability to
withstand cable bending without damage.
Figure 2.3: 3–core screened PLIS cable with PVC over sheath
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At voltage levels where it is necessary to adopt insulation screening a screening
layer over the conductor is also required. This provides a smooth interface between the
wires of a stranded conductor and the insulation, thus limits discharge which may rise
due to electrical stress enhancement on the strands or voids at the interface. Conventional
practice is to apply two semiconductor carbon paper tapes over the conductors.
SL and SA screened cables
These are radial field single core metallic sheath cables with electrostatic type
acting as the insulation screen. SL and SA refer to sheathing with lead and aluminum
respectively. The three corrosion protected cores of SL cables are laid up together,
armored and finished with further corrosion protection (Figure 2. 4). SA cables are laid
up similarly with a PVC over sheath on each core but are not normally armored.
Figure 2.4: 3-core 19/33 kV SL cable
Although the amount of metal in the three individual sheaths is little different
from that in the cable having three core within a single sheath, the greater diameter
results in extra bedding and armoring material, thereby increasing the total cable cost.
However, jointing and terminating is more convenient.
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2.4 Polymer Insulated cables
The conductors of polymeric cables are generally circular with either stranded
copper, stranded aluminum or solid aluminum. For three-core cable in the range 3.6/6.0
kV to 8.7/15 kV some use has been made of both sector. shaped stranded and solid
conductors.
At 3.6/6kV and above, as a means of containing the electrical field within the
insulation, semi conducting screens are applied over the conductor and insulation. By
this means it is possible to eliminate any electrical discharges arising from air gaps
adjacent to the insulation. The coefficient of thermal expansion of polyethylene and
EPR is approximately ten times greater than that of either aluminum or copper, and
when the conductor is at its maximum operating temperature of 90°C a sufficiently large
gap is formed between the insulation and conductor to enable electrical discharges to
occur. This discharge site and any others which are formed around a conductor when
the cable is bent can be eliminated by applying a semi conducting layer over the
conductor. Similarly, any discharges arising from air gaps between laid-up cores can be
nullified by the use of a screen over the insulation.
The insulation thicknesses for the three insulants PE, XLPE and EPR are identical
at each voltage level above 3.6/6 kV; at this voltage EPR is thicker. The radial
thicknesses and electrical stresses are given in table 24.1. The outer semiconducting
screen is normally an extruded layer of semiconducting material. The extruded screen can
be a compatible material which bonds itself to the insulation or a compound, such as
ethylene-(vinyl acetate) (EVA), which is strippable from the insulation.
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In order for the strippable screen to have sufficient tear strength during removal
from the insulation, it is necessary for the thickness to be approximately 1.0mm, but it
may be thinner for harder materials. There are no such constraints with a bonded screen
and, because semiconducting materials are very expensive, thickness is kept to a
minimum, 0.5 mm being a typical figure.
Rated Voltage (kV)
Insulation Thickness (mm)
Electrical stress (kV/mm) 185 mm2 PE XLPE EPR Maximum Minimum
3.6/6 2.5 2.5 3.0 1.63 1.286/10 3.4 3.4 3.4 2.07 1.528.7/15 4.5 4.5 4.5 2.38 1.6012/20 5.5 5.5 5.5 2.79 1.7418/30 8.0 8.0 8.0 3.12 1.67
Table 2.4: Insulation Thickness and stresses on polymeric cables
The manufacture of single core cables is generally completed by the application
of a layer of copper wires to provide an earth envelope with a cross-sectional area of 16
to 50mm 2, depending upon the phase to earth fault level existing on the network. The
cable is finished with an extruded oversheath. For networks with a very much higher fault
level, or where increased mechanical protection is required, a copper tape is applied over
the semiconducting layer, followed by an extruded bedding, then a helical application of
aluminum armour wires and finally an extruded over sheath.
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Figure 2.5: 3-core, circular stranded conductors, XLPE insulated, collective copper wire screen,MDPE oversheathed, 6.35/11 kV cable to IEC 502: (1) circular stranded conductor; (2) conductor
screen; (3) XLPE insulation; (4) extruded semiconducting screen; (5) non-hygroscopic fillers;(6) semiconducting tapes; (7) copper wire screen; (8) synthetic tape; (9) MDPE oversheath
2.5 Electrical stress distribution and calculation
The current in the conductor, in the sheath and dielectric loss increases the
temperature of the cable, and this heat produced is dissipated to the soil and when the
temperature becomes constant at that instant the heat generated is equal to the heat
dissipated. The flux distribution in a.c belted cable insulation is complex and is shown
diagrammatically. The path of heat dissipation in through the dielectric, sheath, cable and
serving to the soil and is represented in figure 2.5. The electric field in case of single
cable is radial but in 3-phase cables the electric field is no longer radial.
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Figure 2.6: Paper insulated belted cable with top conductor at peak potential
The direction and intensity of the electric stress constantly changes of potential.
The field within the dielectric is rotating and during the different instants the parts of the
dielectric are subjected to tangential stress. The distorted nature of the electric stress will
have a component parallel to the layers of the insulation.
2.6 Electrical shielding
Electrical shielding is often necessary on power cable to confine the dielectric
field to the inside of the cable insulation so as to prevent damage from corona or
ionization. The shield usually consists of a thin (3-mil, or 0.076-mm) conducting tape of
copper or aluminum applied over the insulation of each conductor. The shielding tape
sometimes is perforated to reduce power losses due to eddy currents set up in the shield.
Sometimes semiconducting tapes consisting of specially treated fibrous tapes or braids
are used. These semiconducting tapes are frequently employed for the shielding of aerial
cable, since they adhere more closely to the insulation and thus tend to prevent corona.
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2.7. Protection against fire
The bedding materials used over the sheath make the cable inflammable, in
certain indoor works such as substations, factories etc. To avoid fire hazard, the wire
armoring is used directly over the sheath. Also the outer serving is omitted.
Sometimes asbestos tape or fire-resiting paint is provided over the armoring which
perfectly makes it fireproof.
2.7.1 Levels of Cable Fire Performance
A wide spectrum of fire performance is available from the many types of
cables on the market. This can range from cables at one extreme which have no
enhanced for properties, which are readily ignitable and burn with ease, to, at the
other extreme fire survival mineral insulated cables which contain no
combustible materials and which present no hazard in a fire. The choice of cable
for a given application depends on the degree of hazard which can be tolerated
and the level of performance required. The level of fire performance and the
potential hazard resulting from the combustion of a given cable depend on the
materials from which the cable is made and the cable construction. Table 2.4
summarizes the different levels of performance that can be achieved by different
categories of cables, along with typical areas of application.
S.No Cable Type Fire Characteristics
Application
1.Mineral insulated (copper sheathed)
Fire survival and circuit integrity up to the melting point of copper
For maintaining essential circuits such as emergency lighting and fire alarms, circuits for the safe shutdown of critical processes, etc.
Negligible fire hazard
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2.
Limited circuit integrity,low fire hazard, zerohalogen
Limited fire survival As above but circuit integrity maintained for shorter time periods. Reduced hazard fromcable combustion.
Flame retardant
Low smoke and acidgas emission
3.
Limited circuit integrity, reduced hazard (halogen containing)
Limited fire survivalAs above, but increased hazard from smoke and acid gas emission.
Flame retardantReduced acid gas emissionReduced smoke emission4. Low fire hazard,
low, smoke, Flame retardant, low smoke and acid gas
For installation in areas where smoke and acid gas
5.
Low emission PVC based(or chlorinated polymer)
Flame retardantgrades possible
In situations where reduced levels of smoke and corrosive gases are needed, compared toordinary PVC or chlorinated polymer based cables.
Reduced smokeand/or acid gas
Reduced flamepropagation possible
6.PVC or chlorinated polymer
Flame retardant
Where flame retardance is desirable, but smoke and acid gas evolution is not considered to pose a serious hazard.
7. Fluor polymer based
Inherently flameretardant
Where cables are exposed to high temperatures or aggressive environments in normal use.
8.
Non-flame retarded(e.g. polyethylene orEPR based)
Readily combustible
In situations when fire performance requirements are low and where cable combustion poses little hazard.
Table 2.5: Levels of fire performance for different types of cables
2.7.2 Material Considerations
The range of flammability is wide however and many polymeric cable
components are formulated so as to reduce their tendency to burn. It should be
noted that polymeric materials overall are no more hazardous in their combustion
behavior than other flammable materials such as wood, paper, cotton or wool.
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There are several factors that describe a material's flammability and
combustion behavior, although how these are measured and their relevance is
often a cause of debate. The major factors are:
1. Ease of ignition (flammability)
2. Resistance to propagation (flame spread)
3. Heat of combustion (heat release)
4. Smoke emission
5. Toxic gas evolution
6. Corrosive gas evolution.
2.8. System Protection Devices
Two types of protecting devices are used on cable systems.
A. Overcurrent—fuses or circuit breakers. These devices isolate the cable from its
source, preventing the flow of damaging levels of current during an overload, or
remove a faulted cable from the system allowing restoration of the unfaulted parts.
B. Overvoltage—surge arrester. This device prevents damaging overvoltages caused
by lightning or switching surges from entering the cable by clamping the voltage to a
level tolerated by the cable insulation.
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Chapter 3
Characteristics of Power cables
3. Current carrying capacity
The current-carrying capability of a cable system will depend on several
parameters. The most important of these are:
1. The number of cables and the different cable types in the installation under study
2. The cable construction and materials used for the different cable types
3. The medium in which the cables are installed
4. Cable locations with respect to each other and with respect to the earth surface
5. The cable bonding arrangement
Selection of optimum size of conductor is an important aspect to achieve
maximum economy in first cost and subsequent operation of cables. In addition to this
the voltage drop, cost of losses and ability to carry short circuit currents must also be
estimated.
To establish a rating for a particular cable design, the most convenient way is to
calculate amperage (sustained rating) which can be carried continuously under prescribed
standard conditions.
3.1 General basis of rating determination
During service operation, cables suffer electric loss which appear has heat in the
conductor, insulation and metallic components. The current rating is dependent on the
way this heat is transmitted to the cable surface and then dissipated to the surroundings.
A maximum temperature is fixed, which is commonly the limit for insulating material
without undue aging for a reasonable maximum life.
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Figure 3.1: Circuit diagram to represent heat generated in a 3-core metal sheathed cable
The figure 3.1 explains the heat flow corresponding to current, temperature,
difference to voltage and the total thermal resistance to the cable and the surroundings to
electrical resistance. The heat flow within the cable is radial but externally must be made
for the method of installation. Figure 3.2 shows the pattern of heat flow for three buried
single core cables.
Figure 3.2: Heat flow for a circuit of single core cables installed in trefoil
Mathematical treatment is most conveniently expressed for steady state
conditions, i.e for continuous (sustained) ratings. A small cable in air will heat up very
quickly to a steady state condition but a large buried power cable takes some time.
3.2. Mathematical Treatment
The temperature rise in the cable is due to the heat generated in the conductors
(I2R), in the insulation (W) and in the sheath and armour (λ2R), with allowance being
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made by multiplying each of these by the thermal resistance of the layers through which
the heat flows(T).
Since losses occur at several positions in the cable system (for this lumped
parameter network), the heat flow in the thermal circuit shown in Figure will increase in
steps. Thus, the total joule loss WF in a cable can be expressed as
… (3.1)
Figure 3.3 (a): The ladder diagram for steady state computations on single core cable
Figure 3.3(b): The ladder diagram for steady state computations on three core cable
The temperature rise in AC cables is given by
…. (3.2)
Where, Δθ = Conductor temperature rise (k)I = Current flowing in one conductor (A)R = alternating current Resistance per unit length of the conductor at maximum
operating temperature.WC = I2RWd = dielectric strength/ unit length for insulation surrounding the conductorn = number of load carrying conductors in cableT1 = Thermal resistance per unit length between one conductor and the sheath
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T2 = Thermal resistance per unit length of the bedding between sheath and armor, T3 = Thermal resistance per unit length of the external serving of the cable, and T4 = Thermal resistance per unit length between the cable surface and the surrounding medium.
λ1 = sheath loss factor and is equal to the ratio of the total losses in themetallic sheath to the total conductor losses. λ 2 = the armor loss factor and is equal to the ratio of the total losses in the metallic armor to the total conductor losses.
The unknown quantity is either the conductor current / or its operating
temperature 6C (°C). In the first case, the maximum operating conductor temperature is
given, and in the second case, the conductor current is specified. The obtainable
permissible current limit is written as
…. (3.3)
This formula accounts needs to be taken of the fact that it only provides rating for
the prescribed representative conditions.
Note: In case of 1 kV 4-core cables, n may be assumed to be 3 if the fourth conductor is
neutral or is a protective conductor. This assumes that the neutral conductor is not
carrying currents which are due to the presence of harmonics.
3.3. Ambient and cable operating temperature
3.3.1 Ambient Temperature:
Representative average ambient temperature may vary within any individual
country, according to whether the cables are buried or in air outdoors or within a building
and between counties according to the geographical climate.
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For convenience, the normal tabulated ratings in UK are based on 15oC for cables
in the ground, 250C outdoors in air, 300C in air within buildings and 450C for conditions
in ships.
ClimateAir temperature Ground Temperature
(at 1M depth)Minimum Maximum Minimum Maximum
Tropical 25 55 25 40Subtropical 10 40 15 30Temperate 0 25 10 20
Table 3.1: Ambient air and ground temperature
3.3.2 Maximum Cable operating Temperature:
Maximum cable operating temperature according to the insulation material, cable
deign and voltage has been agreed in IEC and the standard values are almost universally
accepted throughout the world for continuous operation.
In using these values an important proviso is that attention must be given to soil
resistivity. Continuous operation at cable surface temperature above 500C will cause
movement of moisture away from the cables and with many types of cable drying out of
the backfill may occur and the cable could exceed the permissible temperature.
Insulation Cable Design Max Conductor temp (0C)Impregnated paper (U0/U)
0.6/1, 1.8/3, 3.6/6 6/10 6/10,8.7/15 12/20,18/30 MIND
BeltedBelted
ScreenedScreened
80657065
Polyvinyl Chloride All 70Polyethylene All 70Butyl Rubber All 85Ethylene Propylene Rubber All 90Cross-linked polyethylene All 90Natural Rubber All 60
Table 3.2: Conductor temperature limits for stranded cable types
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3.4. Effect of Installation condition on Cables
3.4.1 Thermal resistivity of soil:
It is of not much importance for distribution cables to consider thermal resistivity,
unless because of fully continuous operation there is a danger of the soil drying out.
The presence of moisture has a predominant effect on resistivity of any type of
soil ans so it is necessary to take the weather conditions into account. IEC 287 gives
guidance and ignores the make up of particular ground types.
Thermal Resistivity(Km /W)
Soil conditions Weather Conditions
0.7 Very moist Continuously moist1.0 Moist Regular rainfall2.0 Dry Seldom rains3.0 Very dry Little or no rain
Table 3.3: Soil thermal resistivity
3.5. Calculation of losses
3.5.1 Conductor Resistance
Conductor resistance is calculated in two stages. First, the dc value R' (ohm/m) is
obtained from the following expression:
…. (3.4)
In the second stage, the DC value is modified to take into account the skin and proximity
effects. The resistance of a conductor when carrying an alternating current is higher than
that of the conductor when carrying a direct current. The principal reasons for the
increase are: skin effect, proximity effect, hysteresis and eddy current losses in nearby
ferromagnetic materials, and induced losses in short-circuited non ferromagnetic
materials nearby. The degree of complexity of the calculations that can economically be
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justified varies considerably. Except in very high voltage cables consisting of large
segmental conductors, it is common to consider only skin effect, proximity effect, and in
some cases, an approximation of the effect of metallic sheath and/or conduit. The
relevant expressions are:
…. (3.5)
For cables in magnetic pipes and conduits:
…. (3.6)
Material properties and the expressions for the skin and proximity factors are:
Material Resistivity. (ρ20).10-8 Ω.m at 200C
Temperature coefficient (α20).10-3 per K at 200C
Copper 1.7241 3.93Aluminum 2.8264 4.03
Table 3.4: Material properties
Skin and proximity factors are computed from the following expressions:
… (3.7)
Where,
The proximity factor is obtained from
For sector-shaped conductors:
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For oval conductors:
…(3.8)
The above expressions apply when x<= 2.8
3.5.2 Dielectric Losses
When paper and solid dielectric insulations are subjected to alternating voltage,
they act as large capacitors and charging currents flow in them. The work required to
effect the realignment of electrons each time the voltage direction changes (i.e., 50 or 60
times a second) produces heat and results in a loss of real power that is called dielectric
loss, which should be distinguished from reactive loss. For a unit length of a cable, the
magnitude of the required charging current is a function of the dielectric constant of the
insulation, the dimensions of the cable, and the operating voltage. For some cable
constructions, notably for high-voltage, paper-insulated cables, this loss can have a
significant effect on the cable rating. The dielectric losses are computed from the
following expression:
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Table 3.5: Values of skin and proximity effect
…. (3.9)
where the electrical capacitance and the phase-to-to-ground voltage are obtained from
…. (3.10)
The dielectric constants and the loss factor tanδ are taken from Table 3.6
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.Table 3.6: Values of dielectric constant and loss factor
3.5.3 Sheath Loss Factor
Sheath losses are current dependent, and can be divided into two categories
according to the type of bonding. These are losses due to circulating currents that flow in
the sheaths of single-core cables if the sheaths are bonded together at two points, and
losses due to eddy currents, which circulate radially (skin effect) and azimuthally
(proximity effect). Eddy current losses occur in both three-core and single- core cables,
irrespective of the method of bonding. Eddy current losses in the sheaths of single-core
cables, which are solidly bonded are considerably smaller than circulating current losses,
and are ignored except for cables with large segmental conductors.
Sheath Bonding Arrangements
Sheath losses in single-core cables depend on a number of factors, one of which is
the sheath bonding arrangement. In fact, the bonding arrangement is the second most
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important parameter in cable ampacity computations after the external thermal resistance
of the cable. For safety reasons, cable sheaths must be earthed, and hence bonded, at least
at one point in a run. There are three basic options for bonding sheaths of single-core
cables. These are: single-point bonding, solid bonding, and cross bonding.
In a single-point-bonded system, the considerable heating effect of circulating
currents is avoided, but voltages will be induced along the length of the cable. These
voltages are proportional to the conductor current and length of run, and increase as the
cable spacing increases. Particular care must be taken to insulate and provide surge
protection at the free end of the sheath to avoid danger from the induced voltages. One
way of eliminating the induced voltages is to bond the sheath at both ends of the run
(solid bonding). The disadvantage of this is that the circulating currents that then flow in
the sheaths reduce the current-carrying capacity of the cable.
Cross bonding of single-core cable sheaths is a method of avoiding circulating
currents and excessive sheath voltages while permitting increased cable spacing and long
run lengths. The increase in cable spacing increases the thermal independence of each
cable and, hence, increases its current-carrying capacity. The cross bonding divides the
cable run into three sections, and cross connects the sheaths in such a manner that the
induced voltages cancel. One disadvantage of this system is that it is very expensive and,
therefore, is applied mostly in high-voltage installations. Figure 3 gives a diagrammatic
representation of the cross connections. The cable route is divided into three equal
lengths, and the sheath continuity is broken at each joint. The induced sheath voltages in
each section of each phase are equal in magnitude and 120° out of phase. When the
sheaths are cross connected, as shown in Figure 1-11, each sheath circuit contains one
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section from each phase such that the total voltage in each sheath circuit sums to zero. If
the sheaths are then bonded and earthed at the end of the run, the net voltage in the loop
and the circulating currents will be zero and the only sheath losses will be those caused
by eddy currents.
Figure 3.4(a) Diagrammatic representation of a cross bonded cable system, when cables are not transposed.
Figure 3.4(b) Diagrammatic representation of a cross bonded cable system when Cables are transposed.
This method of bonding allows the cables to be spaced to take advantage of
improved heat dissipation without incurring the penalty of increased circulating current
losses. In practice, the lengths and cable spacings in each section may not be identical,
and, therefore, some circulating currents will be present. The length of each section and
cable spacings are limited by the voltages that exist between the sheaths and between the
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sheaths and earth at each cross-bonding position. For long runs, the route is divided into a
number of lengths, each of which is divided into three sections. Cross bonding as
described above can be applied to each length independently.
The cross-bonding scheme described above assumes that the cables are arranged
symmetrically; that is, in a trefoil pattern. It is usual that single-core cables are laid in a
flat configuration. In this case, it is a common practice in long-cable circuits or heavily
loaded cable lines to transpose the cables as shown in Figure 3(b) so that each cable
occupies each position for a third of the run.
3.5.4 Armor Loss Factor
Armored single-core cables for general use in ac systems usually have
nonmagnetic armor. This is because of the very high losses that would occur in closely
spaced single-core cables with magnetic armor. On the other hand, when magnetic armor
is used, losses due to eddy currents and hysteresis in the steel must be considered. The
armoring or reinforcement on two-core or three-core cables can be either magnetic or
nonmagnetic. These cases are treated separately in what follows. Steel wires or tapes are
generally used for magnetic armor.
When nonmagnetic armor is used, the losses are calculated as a combination of
sheath and armor losses. The equations set out above for sheath losses are applied, but the
resistance used is that of the parallel combination of sheath and armor, and the sheath
diameter is replaced by the misvalue of the mean armor and sheath diameters.
For nonmagnetic tape reinforcement where the tapes do not overlap, the resistance
of the reinforcement is a function of the lay length of the tape. The advice given in IEC
60287 to deal with this is as follows:
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1. If the tapes have a very long lay length, that is, are almost longitudinal tapes, the
resistance taken is that of the equivalent tube, that is, a tube having the same mass
per unit length and the same internal diameter as the tapes.
2. If the tapes are wound at about 54° to the axis of the cable, the resistance is taken
to be twice the equivalent tube resistance.
3. If the tapes are wound with a very short lay, the resistance is assumed to be
infinite; hence, the reinforcement has no effect on the losses.
4. If there are two or more layers of tape in contact with each other and having a
very short lay, the resistance is taken to be twice the equivalent tube resistance.
This is intended to take account of the effect of the contact resistance between the
tapes.
3.6. Electromagnetic Fields
Insulated distribution and transmission cables have an advantage over overhead
lines; the external electrostatic field is zero because of the shielding effect of the
conducting insulation screen within the cable. The magnetic field external to a three-core
distribution cable carrying balanced load currents rapidly reduces to zero because the
vector sum of the spatial and time resolved components of the field is zero. A useful
degree of ferromagnetic shielding is achieved for three-core cables by the application of
steel wire amour which helps to contain the flux. The shielding effect can be significantly
increased by eliminating the air gaps with steel tape amour (suitable for small diameter
cables) or by the installation of the cable within a steel pipe (as employed with high
pressure fluid-filled and high pressure gas-filled cables) The magnetic field external to
single-core cables laid in flat formation does not sum to zero close to the cables because
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of the geometric asymmetry. The distribution of flux. density can be calculated
analytically by the application of the Biot-Savart law to each individual current carrying
conductor and metallic sheath and by making a vectorially and temporally resolved
summation (equations (3.11) and (3.12)). The simple analytical method can be used in
those applications which have one value of permeability and which do not use eddy
current shielding. For more complex application, such as those employing ferrous
materials, specialized computer programs are required which usually employ a finite
element algorithm with the ability to model a non-linear B-H hysteresis curve. It is usual
in calculations to use the peak value of current. The waveform of the resultant flux
density is complex, comprising both sinusoidal and bias components and with a polarized
vector rotating about an axis and pulsating in magnitude. In consequence it is usual to
quote either the r.m.s, value or the mean value of flux density, the preferred unit being µT
(1 µT = 10 mG).
… (3.11)
… (3.12)
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For comparative purposes it has become practice to calculate the magnetic flux
density above a buried cable circuit at a height of 1 m above ground level. At this height
the ratio of distance to cable center-line spacing is comparatively large such that the
maximum magnitude of the flux density is low and, compared with an overhead line,
rapidly reduces in magnitude on both sides of the cable circuit, i.e. within the width of a
roadway (fig. 2.12). Should it be required, significant further reduction in flux density
can be achieved; however this is in varying degrees detrimental to the cable thermal
rating and to the cost of the circuit.
Fig 3.5: Horizontal flux density distribution I m above ground level for 400kV underground double cable circuits carrying 1000 A.
Examples of flux density distributions are shown in fig. 3.5 for the 400kV double
circuit configuration given in table 3.7. The simplest methods are to lay the cables closer
together and at greater depth, the most effective compromise being to lay the cables in an
open trefoil formation.
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Configuration(Double Circuit)
Cable Spacing
(mm)
Circuit spacing (mm)
Depth (mm)
Flux density at 1000 A
Rating per
circuit (A)Max Fig
Flat – XBa 300 1500 900 30 a 2432Flat – XBb 300 1500 900 23 b 2432Flat - XB 200 800 900 13 c 1934Flat - XB 300 1500 1800 11 d 1886Trefoil - XB 300 1500 900 11 e 2248Flat -SB 300 1500 900 2 f 1370
Table 3.7: of installation configuration on magnetic flux density and cable rating
A degree of cancellation of the magnetic field is obtained by solidly bonding the
metallic sheaths of single core cables thereby permitting the induced voltages to drive a
current which, in ideal theoretical circumstances, would be of equal magnitude and in
antiphase to the conductor current. In practice the finite resistances of the metallic sheath
and earth return wires, if present, reduce the magnitude and alter the phase of the sheath
current thereby achieving only partial magnetic screening and with the disadvantage of
generating sheath heat loss of comparatively high magnitude.
3.7. Standard operating conditions & Rating Factors
3.7.1. Cables installed in air:
Standard conditions
(a) Ambient air temperature is taken to be 250C for paper insulated cables for XLPE cables above 1.9/3.3 KV. 300C is chosen for PVC insulated cables ans for XLPE cabled of 1.9/3.3 KV and below in order to be in conformity with IEE wiring regulations.
(b) Air Circulation is not restricted significantly. e.g. if cables are fastened to a wall they should be spaced at least 20mm from it.
(c) Adjacent circuits are spaced at least 160mm apart and suitable disposed to prevent mutual heating.
(d) Cables are shielded from direct sunshine.
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3.7.2. Cables installed in ducts
Standard conditions
(a) Ground temperature 150C
(b) Soil Thermal resistivity 1.2 Km/W
(c) Adjacent circuits at least 1.8m distance
(d) Depth of laying 0.5m for 1KV cables0.8 m for cables above 1kV and upto 33kV
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Chapter 4
Mathematical Analysis
4.1 The Cable and Insulator Parameters
The following figure shows a typical high-voltage cable.
Figure 4.1 Typical High volatge cable
The variables used in the equations below are:
N: The number of cables
n: the number of strands contained in the phase conductor.
d: the diameter of one strand (m)
f: the nominal frequency of the cable application
r: the radius of the phase conductor
µr: the relative permittivity of phase conductor
rint, rext: the internal and external radius of phase-screen insulator
GMD: Geometric mean distance between the phase conductors.
ρ: Resistivity of the phase-screen insulator
ɛrax: Relative permittivity of the phase-screen insulator
ɛrxe: Relative permittivity of the outer screen insulator
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dax,Dax: the internal and external diameter of phase-screen insulator
dxe,Dxe: the internal and external diameter of the outer screen insulator
Self-Impedance of Phase Conductor(s)
The self-impedance of the copper phase conductor is calculated as follow
The DC resistance of phase conductor is given by
The resistance of earth return is given by
The frequency factor is given by
The distance to equivalent earth return path is given by
The geometric mean radius of phase conductor is given by
Self Impedance of Screen Conductor(s)
The self-impedance of the screen conductor is calculated as follow
The DC resistance of phase-screen insulator is given by
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The geometric mean radius of phase-screen insulator is given by
Mutual Impedance between the Phase and Screen Conductors
The mutual impedance between the phase conductor and its corresponding screen
conductor is calculated as follow
Dn corresponds to the distance between the phase conductor and the mean radius of the
phase-screen insulator.
Mutual Impedance between the Phase Conductors
If more than one cable is modeled (N>1), the mutual impedance between the N phase
conductors is calculated as follow
In general, the Geometric Mean Distance (GMD) between the phase conductors of a
given set of cables can be calculated as follow
where n is the total number of distances between the conductors.
However the GMD value is not calculated by the function and need to be specified
directly as an input parameter.
Capacitance between the Phase and Screen Conductors
The capacitance between the phase conductor and its corresponding screen conductor is
calculated as follow
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The cross-linked polyethylene (XLPE) insulator material is assumed in this equation.
Capacitance between the Screen Conductor and the Ground
The same equation is used to calculate the capacitance between the screen conductor and
the ground.
4.2 Localization of cable faults
The faults which are most likely to occur in the cables are:
Figure 4.2 Faults in underfround cable
1. Ground or Earth faults: When the insulation of the cable gets damaged, the
current starts flowing from the core to earth or to the cable sheath. Such faults
are known as ground or earth faults.
2. Cross or short-circuited fault: When the insulation between twoc ables or
between two cores of a multi-core cable gets damaged, the current starts flowing
from one cable to another cable or from one core to another core of multicore
cable directly. Such faults are known as short-circuit faults.
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3. Open-circuit faults: When the conductor of a cable is broken or joint is pulled
out there is no current in the cable. Such faults are known as open circuit faults.
The nature of fault is determined and then the point of fault is located. For
determination of nature of faults, the insulation resistance of each core to ground and
between cores is measured with help of megger. The low value of insulation resistance
between any core and earth indicates the ground fault whereas the low value of insulation
resistance indicates short-circuit fault.
Ground fault of a single fault
Blavier’s test is used to locate the ground fault of a single cable i.e when no other
cables run along with the faulty one.
This test is performed wih the aid of a low-voltage supply and either an ammeter or
voltmeter or a bridge network. In this test resistance between one end of the cable T1 and
earth is measured first with the far end T2 isolated from earth and then with the far end T2
earthed. Let the two readings be R1 and R2 respectively.
If r1 and r2 are the conductor resistance of the lengths of cable “Far end” to fault
and “Test end” of fault respectively and r is the resistance of fault to earth then
R1 = r2 + r …..(1)
…. (2)The total resistance of conductor,
R = r1 + r2 …. (3)
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(a) (b) (c)
Figure 4.3: Ground fault of a single cable
Substituting r = R1 - r2 from eq (1) in eq (2) we have
or,
since r2 is obviously less than R2 (eq 2), the positive sign is rejected and therefore,
… (4)
If the total length of the cable is L meters, the length of cable between far end and
fault is L1 meters, length of cable between test end and fault is L2 meters and cross-
section of conductor is uniform then
and
or … (5)
Thus the distance from the fault can be determined.
Earth overlap test:
It is also performed to locate the ground fault of a single cable. In this test two
measurements are made one between line and earth, measured form testing end, with far
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end ground and second between line and earth, measured from far end, with testing end
grounded. Let the two readings be R1 and R2 respectively.
Then …. (6)
…. (7)
and R = r1 + r2 as before
By elimination, as blavier test, we have
…. (8)
…. (9)
Knowing the values of r1 or r2, the distance of fault from test end can be
determined, as discussed in case of Blavier test.
4.3 Example for fault localization
Input data:
Feeder cable length – 500 Mts
Fault type – fault to earth
Resistance measurements between earth and one of the cable
Distant end insulated : 7.0 Ohm
Distant end earthed : 1.7 Ohm
The cable has total resistance : 1.8 Ohm
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Calculation:
R1 = 7.0 Ω, R2 = 1.7 Ω, R = 1.8 Ω
If r1 and r2 are the conductor resistance of the length of cable for end to fault and test
end to fault respectively and r is the resistance of fault to earth then
r1 + r2 = R = 1.8 Ω … (i)
r + r2 = R1 = 7.0 Ω … (ii)
R2 = = 1.7 Ω … (iii)
Solving the above equations ,
Resistance of fault, r = 6.0275 Ω
Resistance per meter length = 1.8 / 500 = 0.0036 Ω
Therefore, distance from testing end = r2 / Resistance per meter length
= 0.9725 / 0.0036 = 270.14 Ω
4.4 Matlab Programclc;disp(' ')%% Input parameters% Nominal frequencyf = 50; % [Hz]% Soil resistivityrho_e = 100; % [ohm*m]% Phase conductor - number of strandsn_ba = 58; % []% Phase conductor - diameter of one strandd_ba = 2.71e-3; % [m]% Phase conductor - resistivitydisp('The material is assumed as Aluminium ')disp(' ')rho_ba = 2.8e-8; % [ohm*m]% Phase conductor - permittivity50
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mu_r_ba = 1; % []% Phase conductor - external diameterD_a = 20.90e-3; % [m]% Screen - resistivityrho_x = 17.8e-9; % [ohm*m]% Screen - total section% Ecran - Section du conducteurS_x = 169e-6; %[m*m]% Screen - Internal diameterd_x = 65.80e-3; % [m]% Screen - External diameterD_x = 69.80e-3; % [m]% GMD between phase conductorsGMD_phi = 1.1225 * 22e-2; % [m] % See theorical examples% Insulator phase to screen - Internal diameterd_iax = 23.30e-3; % [m]% Insulator phase to screen - External diameterD_iax = 60.60e-3; % [m]% Insulator phase to screen - Permittivityepsilon_iax = 2.3; % []% Insulator screen to soil - Internal diameterd_ixe = 69.80e-3; % [m] %(Protection anti-corrosion + Gaine en PE)% Insulator screen to soil - External diameterD_ixe = 77.80e-3; % [m] %(Protection anti-corrosion + Gaine en PE)% Insulator screen to soil - Permittivityepsilon_ixe = 2.25; % []%% Computed parameters% Phase conductor - external radiusR_a = D_a/2; % [m]% Phase conductor - sectionS_a = n_ba * pi * d_ba^2 / 4; % [m*m]% Phase conductor - R_phiR_phi = rho_ba * 1000 / S_a; % [ohm/km]% Current path return resistanceR_e = pi^2*10^(-4)*f; % [ohm/km]% Frequency coefficient k_1k_1 = 0.0529 * f / (0.3048*60); % main work unit: ohm/km% Current path return depthD_e = 1650*sqrt(rho_e/(2*pi*f)); % [m]% Phase conductor - GMRGMR_phi = R_a * exp(-mu_r_ba/4); % [m]% Screen resistanceR_N = rho_x * 1000/S_x; % [ohm/km]% Screen - GMRGMR_N = d_x/2+(D_x-d_x)/4; % [m]% Distance between phase conductor and screen mean radiusDN_2 = d_x/2 + (D_x/2-d_x/2)/2; % [m]%% Impedance matrix ZZ_aa = R_phi + R_e + j*k_1*log10(D_e/GMR_phi); % [ohm/km]Z_xx = R_N + R_e + j*k_1*log10(D_e/GMR_N); % [ohm/km]51
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Z_ab = R_e + j*k_1*log10(D_e/GMD_phi); % [ohm/km]Z_ax = R_e + j*k_1*log10(D_e/DN_2); % [ohm/km]fprintf(' Self Impedence of Phase conductor is %g ', Z_aa);disp(' ')fprintf(' Self Impedence of screen conductor is %g ', Z_xx);disp(' ')fprintf(' Mutual Impedence between phase and screen conductor is %g ', Z_ax);disp(' ')fprintf(' Mutual Impedence between phase conductors is %g ', Z_ab);%% Capacity matrix% Calcul des CC_ax = 1/0.3048 * ((0.00736 * epsilon_iax) / (log10(D_iax/d_iax))); % [muF/km]C_xe = 1/0.3048 * ((0.00736 * epsilon_ixe) / (log10(D_ixe/d_ixe))); % [muF/km]C_ax = C_ax * 1e-6 % [F/km]disp(' ')fprintf('Capacitance between phase and screen conductor is %g ', C_ax);disp(' ')fprintf('Capacitance between screen conductor and the groundis %g ', C_xe);C_xe = C_xe * 1e-6 % [F/km]S_ax = C_ax * (2*pi*f); % [S/km]S_xe = C_xe * (2*pi*f); % [S/km]%% For a three phase system (three radial electromagnetic field cables) Z = [Z_aa Z_ax Z_ab Z_ab Z_ab Z_ab ; ... Z_ax Z_xx Z_ab Z_ab Z_ab Z_ab ; ... Z_ab Z_ab Z_aa Z_ax Z_ab Z_ab ; ... Z_ab Z_ab Z_ax Z_xx Z_ab Z_ab ; ... Z_ab Z_ab Z_ab Z_ab Z_aa Z_ax ; ... Z_ab Z_ab Z_ab Z_ab Z_ax Z_xx] % [ohm/km] Y = [0+j*S_ax 0-j*S_ax 0 0 0 0 ; ... 0-j*S_ax 0+j*S_xe 0 0 0 0 ; ... 0 0 0+j*S_ax 0-j*S_ax 0 0 ; ... 0 0 0-j*S_ax 0+j*S_xe 0 0 ; ... 0 0 0 0 0+j*S_ax 0-j*S_ax ; ... 0 0 0 0 0-j*S_ax 0+j*S_xe] % [S/km]% In [Y], with SimPowerSystem, it's possible to use epsilon instead of 0 for avoiding errorsdisp(' Wish to find the fault location ');Cont = input(' if yes press Y or N :', 's');error = 0;switch Cont case {'Y', 'y','Yes','yes','ye','Ye'} Len = input(' The length of the cable in mts is : '); ResIns = input(' Resistance measured for the distant end insulated is : '); ResEart = input(' Resistance measured for the distant end earthed is : '); TotRes = input(' Total resiatnce of the cable is :' ); Rtemp1 = ((ResIns *(TotRes - ResEart))/( ResEart *(TotRes - ResIns))); Rtemp2 = ((TotRes - ResIns)/(ResEart - ResIns)); r1 = ResEart*Rtemp2*(1- sqrt(abs(Rtemp1))); case {'NO','No','n','no','N'} error =1;52
Shashidhar kasthala
endif error disp(' ') fprintf(' \t\t Thank You') else disp(' ') r2 = TotRes - r1; r = ResIns - r2; disp(' ') fprintf('conductor resistance of the length of cable far end to fault is %g Ohm',r1); disp(' ') fprintf('conductor resistance of the length of cable test end to fault is %g Ohm',r2); disp(' ') fprintf('conductor resistance of the fault to earth is %g Ohm',r); disp(' ') ResperLen = TotRes/Len; DistTestEnd = r2/ResperLen; fprintf('The resistance per meter length is %g Ohm', ResperLen); disp(' ') fprintf('The distance from testing end is %g mts', DistTestEnd); disp(' -------------------------')end
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Conclusion
In this project the characteristics of Electric power cables and its insulation is
studied and evaluated as per the standard IEC 187 and IEC 287. A mathematical analysis
is performed to analyze the cable and its insulation parameters. In addition to it
localization of ground fault in cables is evaluated using Blavier’s test and earth overlap
test.
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References
1. Electrical Cable Handbook by George F.Moore, BICC cables Ltd.
2. Rating of Electric power cables: Ampacity computations by George J.Anderson
3. Electric Power Cable Engineering by William A.Thue.
4. Switchgear Manual. 10th revised edition,ABB
5. Insulated power cables used in Underground applications by Michael J.Dyer, Salt
river project.
6. Review of Power cable Standard Rating Methods
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