Characteristics of Electric Cables and Fault Localization
Shashidhar kasthala Asst.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 Butyl Rubber PVC Varnished Cambric Impregnated Paper Rubber-GRS or Natural HMWPE XLPE or TR-XLPE XLPE, filled EPR Silicone Rubber
Range 3.0 – 4.5 3.4 – 10 4.0 – 6.0 3.3 – 3.7 2.7 – 7.0 2.1 – 2.6 2.1 – 2.6 3.5 – 6.0 2.5 – 3.5 2.9 – 6.0
Typical 3.2 6.0 5.0 3.5 3.5 2.2 2.3 4.5 3.2 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 varnishedcambric 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) 3.6/6 6/10 8.7/15 12/20 18/30
Insulation Thickness (mm) EPR PE XLPE 2.5 2.5 3.0 3.4 3.4 3.4 4.5 4.5 4.5 5.5 5.5 5.5 8.0 8.0 8.0
Electrical stress (kV/mm) 185 mm2 Maximum Minimum 1.63 1.28 2.07 1.52 2.38 1.60 2.79 1.74 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
1.
Fire Characteristics Fire survival and circuit integrity up to the melting point Mineral insulated of copper (copper sheathed) Negligible fire hazard Cable Type
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Application For maintaining essential circuits such as emergency lighting and fire alarms, circuits for the safe shutdown of critical processes, etc.
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Limited fire survival Flame retardant
2.
Limited circuit integrity, low fire hazard, zerohalogen
3.
Limited circuit integrity, reduced hazard (halogen containing)
4.
Low fire hazard, low, smoke,
5.
Low emission PVC based (or chlorinated polymer)
6.
PVC or chlorinated polymer
Flame retardant
7.
Fluor polymer based
Inherently flame retardant
8.
Non-flame retarded (e.g. polyethylene orEPR based)
Low smoke and acid gas emission Limited fire survival Flame retardant Reduced acid gas emission Reduced smoke emission Flame retardant, low smoke retardant and acid gas Flame grades possible Reduced smoke and/or acid gas Reduced flame propagation possible
Readily combustible
As above but circuit integrity maintained for shorter time periods. Reduced hazard from cable combustion. As above, but increased hazard from smoke and acid gas emission. For installation in areas where smoke and acid gas In situations where reduced levels of smoke and corrosive gases are needed, compared to ordinary PVC or chlorinated polymer based cables. Where flame retardance is desirable, but smoke and acid gas evolution is not considered to pose a serious hazard. Where cables are exposed to high temperatures or aggressive environments in normal use. 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 = I2R Wd = dielectric strength/ unit length for insulation surrounding the conductor n = number of load carrying conductors in cable T1 = 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 the metallic 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. Air temperature Climate Tropical Subtropical Temperate
Minimum 25 10 0
Maximum 55 40 25
Ground Temperature (at 1M depth) Minimum Maximum 25 40 15 30 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 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
Cable Design
Max Conductor temp (0C)
Belted Belted Screened Screened
80 65 70 65
All All All All All All
70 70 85 90 90 60
Polyvinyl Chloride Polyethylene Butyl Rubber Ethylene Propylene Rubber Cross-linked polyethylene Natural Rubber
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) 0.7 1.0 2.0 3.0
Soil conditions Very moist Moist Dry Very dry
Weather Conditions Continuously moist Regular rainfall Seldom rains 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 Aluminum
1.7241 2.8264
3.93 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) Flat – XBa Flat – XBb Flat - XB Flat - XB Trefoil - XB Flat -SB
Cable Spacing (mm) 300 300 200 300 300 300
Circuit spacing (mm) 1500 1500 800 1500 1500 1500
Depth (mm)
Flux density at 1000Fig A Max
900 900 900 1800 900 900
30 23 13 11 11 2
a b c d e f
Rating per circuit (A) 2432 2432 1934 1886 2248 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 cables 0.8 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 crosssection 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 Program clc; disp(' ') %% Input parameters % Nominal frequency f = 50; % [Hz] % Soil resistivity rho_e = 100; % [ohm*m] % Phase conductor - number of strands n_ba = 58; % [] % Phase conductor - diameter of one strand d_ba = 2.71e-3; % [m] % Phase conductor - resistivity disp('The material is assumed as Aluminium ') disp(' ') rho_ba = 2.8e-8; % [ohm*m] % Phase conductor - permittivity
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Shashidhar kasthala mu_r_ba = 1; % [] % Phase conductor - external diameter D_a = 20.90e-3; % [m] % Screen - resistivity rho_x = 17.8e-9; % [ohm*m] % Screen - total section % Ecran - Section du conducteur S_x = 169e-6; %[m*m] % Screen - Internal diameter d_x = 65.80e-3; % [m] % Screen - External diameter D_x = 69.80e-3; % [m] % GMD between phase conductors GMD_phi = 1.1225 * 22e-2; % [m] % See theorical examples % Insulator phase to screen - Internal diameter d_iax = 23.30e-3; % [m] % Insulator phase to screen - External diameter D_iax = 60.60e-3; % [m] % Insulator phase to screen - Permittivity epsilon_iax = 2.3; % [] % Insulator screen to soil - Internal diameter d_ixe = 69.80e-3; % [m] %(Protection anti-corrosion + Gaine en PE) % Insulator screen to soil - External diameter D_ixe = 77.80e-3; % [m] %(Protection anti-corrosion + Gaine en PE) % Insulator screen to soil - Permittivity epsilon_ixe = 2.25; % [] %% Computed parameters % Phase conductor - external radius R_a = D_a/2; % [m] % Phase conductor - section S_a = n_ba * pi * d_ba^2 / 4; % [m*m] % Phase conductor - R_phi R_phi = rho_ba * 1000 / S_a; % [ohm/km] % Current path return resistance R_e = pi^2*10^(-4)*f; % [ohm/km] % Frequency coefficient k_1 k_1 = 0.0529 * f / (0.3048*60); % main work unit: ohm/km % Current path return depth D_e = 1650*sqrt(rho_e/(2*pi*f)); % [m] % Phase conductor - GMR GMR_phi = R_a * exp(-mu_r_ba/4); % [m] % Screen resistance R_N = rho_x * 1000/S_x; % [ohm/km] % Screen - GMR GMR_N = d_x/2+(D_x-d_x)/4; % [m] % Distance between phase conductor and screen mean radius DN_2 = d_x/2 + (D_x/2-d_x/2)/2; % [m] %% Impedance matrix Z Z_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]
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Shashidhar kasthala 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 C C_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 errors disp(' 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;
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Shashidhar kasthala end if 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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