electric power cables1 pdf

8/10/2019 Electric Power Cables1 PDF

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ELECTRIC POWER CABLES All electric cables consist of the following essential parts:

1. The conductors for transmitting electrical power.2. An electrical insulating medium required to insulate the conductor from direct contact

with earth or other line conductors inside the cable.3. External protective coverings for protection against mechanical damage, chemical or

electrochemical attack, fire or any other dangerous effects external to the cable.

Copper (Cu) conductors have extensively being used for cables but of late Aluminum (Al) isbeing used in place of copper to reduce both the cost and weight of the cable for the samecurrent capacity. To obtain flexibility a number of wires are made up into a strand which makesit easier to handle, less flexible to kink and break and to a large extent eliminates the risk of theconductor breaking through the dielectric. The wire in a stranded conductor are twisted togetherto form lays. The successive layers usually are stranded in opposite direction. The strandedconductor is expressed as 19/0.1, where the first number stands for the number of strands used

second number given corresponds to the gauge of the strand used; e.g. 3/20, which means acable with three strands each of 20 SWG (1.0 mm ).

TYPES OF CABLES AND CABLE COMPONENTS

The conductors of a cable have to be covered by an insulation to isolate the conductors from

each other and from their surroundings. The insulating material should have high dielectricstrength, high insulation resistance, good mechanical strength and should be able to withstandtemperatures from about -30 C to over 100 C. Many insulating materials have beendeveloped and are used in cable manufacture. Typical properties of few cable insulations areshown below:

Temperature rating C

# Material DielectricStrength(KV/mm)

Power

factor Maxcontinuous

Short-timeoverload

Short-circuit

1 XLPE 2.5 18 0.008 90 130 250

2 P l h h l i 2 3 21 0 0004 75 95 150


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6 Oil impregnated Paper 3.6 21 0.008 80 110 200

Different types of Cables:1. VIR Cables

Vulcanized Indian Rubber (VIR) insulation was developed in 1870 and has a dielectricstrength of around 10 ~ 20 KV/mm and a dielectric constant of about 2.5. Sulfur (S) ismainly used as the vulcanizing agent. This insulation is limited to wiring cables for lowcost lighting and minor power installations.

2. Elastomer Insulated Cables

Elastomeric insulation includes many types of rubber, e.g. butyl rubber, silicone rubber,and ethylene propylene rubber. Elastomers have rubber like characteristics which isachieved by compounding the basic polymer with selected additives. Since natural beendevoted for the development of synthetic elastomeric compounds with superior

properties.

PolyChloroPrene (PCP) or Neoprene is obtained by polymerization of ChloroPrene. Theraw polymer contains about 35% chlorine as a result of which PolyChloroPrene (PCP)or Neoprene is self extinguishing, if ignited externally. Neoprene compounds can beused up to a conductor temperature of 60 C and are more resistant to outdoorweathering and to deterioration by oil than natural rubber.

Butyl rubber, a co-polymer of isobutylene and a small quantity of isoprene, is moreresistant to oxidation and ozone than natural rubber and can be used up to a conductortemperature of 85 C.

Ethylene propylene rubber (EPR) is a saturated co-polymer of ethylene and propylenein approximately equimolecular preparations. It has good electrical properties, and isresistant to ozone, heat and chemicals. Cables with this insulation can be buried directlyand exposed to weather and contaminated atmospheres and are, therefore, suitable forservice industry. They can be used up to a conductor temperature of 85 C.

3. PVC Cables


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The thickness of insulation depends on the mechanical and electrical requirements which it hasto withstand in service. The low voltage cables (< 1 KV rating) should have sufficient insulation

thickness to meet the mechanical treatment which the cable may undergo during manufacture,installation and service. At higher voltages the insulation thickness is determined by electricalrequirements.

7. Sheath, Armor and Covering

A metal sheath is provided over the cable insulation so that moisture may not be able to affectthe insulation and may also protect the insulation from mechanical damage. A metallic sheath isessential because no organic material is sufficiently impervious to moisture. Previously, manyyears back, lead was established as a suitable material for sheathing. The main advantages oflead sheaths are the comparative ease with which they are made in lead presses, their flexibilityand high corrosion resistance. Some of the disadvantages of lead are its large mass (sp.gr. oflead is 11.37), low mechanical strength, fluidity and small resistance to vibrations. Thehardness, mechanical strength and resistance to vibrations of lead sheaths may beconsiderably increased by adding alloying mixtures. Many alloys of lead having around 1% ofcopper (Cu), tin (Sn), Bismuth (Bi), etc. may be used for sheathing.

Aluminum (Al) is now being increasingly used as a sheathing material. Aluminum sheaths havea much greater mechanical strength than lead sheaths, low weight (sp.gr. of Al is 2.71) and lowfluidity. The Aluminum sheaths cost about 3.5 times less than the lead sheaths.

Steel tape or wire armor is necessary to protect the sheath against mechanical damage. Steeltape armor consists of two steel tapes coated with preservative compounds, applied helically inthe same direction over fibrous bedding, the outer layer covering the spaces between the turnsof the inner layer. This provides a good protection against mechanical damage but Steel wirearmor is recommended where additional longitudinal stresses may occur during installation or inservice. Steel wire armor consists of galvanized steel wires applied over compounded bedding.Double wire armors are used for high degree of mechanical protection. Single core cables for

AC systems are usually not provided with armor because of its effect in increasing the losses. In

these cables a plastic or PVC over-sheath is used for mechanical protection. Aluminumsheathed cables, owing to the comparative hardness of the sheath, are not required to bearmored in the same way as the lead sheathed cables but for special conditions armoring isprovided for these cables too. As an anticorrosion measure, power cables are usually protectedby Bitumen impregnated fibrous wrapping (or covering for serving). Generally two layers of such


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(a) Solid Type Cables: In these cables, the pressure within the cable does not go aboveatmospheric pressure and may even fall below it locally, e.g., in voids. This can lead to

cable breakdown when the electrostatic stress is high. The cables for voltages up to 33KV belong to this category.

(b) Pressurized Cables: In these cables pressure is maintained above atmospheric eitherby oil, in oil filled cables or by gas in gas filled pressurized cables. Gas pressures cablesare used up to 275 KV while oil filled ones are used up to 500 KV or so.

Either of these may be single core or multi-core. A solid single core cable has a central

conductor, with an insulation of impregnated paper, a metallic sheath and a plastic over-sheath. Fig. 8.1 shows such cable. A multi-core cable may have 3 cores (for 3-phase, 3-wire system) or 4 cores (for 3-phase, 4-wire systems) and may be a belted type cable orH type cable.

A multi-core cable is designated as S L cable if each of the core has a separate leadsheath and also an overall covering of lead sheath. Similarly, it is designated as S Acable if each of the core has a separate Aluminum sheath and also an overall coveringof Aluminum sheath. In H S L cable the individual cores are also covered with a layer of

Aluminum foil or Copper tape under the lead sheath. The lead sheaths over the threecores and the overall lead sheath should make good electrical contact with each other.

Solid type cables are suitable only up to 33 KV. At higher voltages the chances ofinsulation breakdown in cables due to ionization in voids become quite high. Inpressurized cables voids are eliminated by maintaining higher pressure thanatmosphere. Pressurized cables are either oil filled or gas-pressure cables.

(i) Oil filled Cables: Single core or 3 core oil filled cables are suitable for 33 KV aswell as higher voltages up to 500 KV. An oil filled cable is kept constantlysupplied with low viscosity mineral oil through ducts in the cable, the ducts beingconnected to oil reservoirs. The expansions and contractions merely producechanges in the oil level of the reservoirs and, therefore, do not result in voids.

Another advantage is that any space formed by the distortion of lead sheath or

by relative movement of paper dielectric is immediately filled with oil.

The breakdown inception stress, for oil filled cables, is 300 400 KV/cm which ismuch higher than that for a solid type cable. Therefore, the normal operatingstresses are raised considerably. The insulation thickness is mainly governed byrequirement of withstand voltage at power frequency Maximum stresses up to


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(ii) Gas filled Cables: In these cables paper dielectric is impregnated withpetroleum jelly so that it may not have any free compound. The intersticesbetween the layers of the paper are then filled with gas, generally dry nitrogen, ata pressure up to 1380 KN/m2, forming a composite dielectric. Pressure isretained by lead sheath. The gas flows throughout the cable via the filler spaces,butt-gaps in the dielectric and conductor strands. In single core cables a smallclearance to the sheath is left for allowing the axial flow of gas. In case of multi-core cables, such a clearance is not necessary because the filler spaces andstrands provide sufficient path for the flow of the gas. The advantage of gas filled

cable over the oil filled cable is that the oil pressure reservoirs and otherextraneous apparatus are unnecessary and still the ionization is avoidedbecause the voids are filled by gas at high pressure.

Another type of cable used for high voltages is external pressure cable. In thesecables, the conductor cores, after being insulated, impregnated and covered withsheath, are placed inside a steel pipe which is filled with gas, generally, nitrogen,at a pressure of about 12 15 atmospheres.

Because of external gas pressure, the voltage required to set up ionization insidethe voids is increased. Moreover the external pressure tends to close the voids.In comparison with the solid type cable, this construction gives twice the workingvoltage and about one and half times the working current. The increased cost ismore than justified by the increased operating voltage and current. In addition thesteel pipe provides an ideal mechanical protection for the cable.

9. Effective Conductor Resistance

The effective conductor resistance R eff of each conductor of a cable has to becalculated by taking into account the dc resistance, skin effect, proximity effect, sheathloss and armor loss.

(a) DC Resistance: In calculating the dc resistance, the increase in resistance due totemperature, effects of stranding and laying should be taken into account. Theconductor temperature must not exceed 85 C for pressurized cables. For othercables, the specified temperatures vary from 50 C to 75 C. The dcresistance at the maximum temperature may be about 20% more than that at 20C. The resistance is multiplied by 1.02 to account for stranding and in case of multi-core cables again multiplied by 1.02 to account for additional length of conductorresulting from the lay of strands and of core in manufacture.


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resistance at the operating temperature as modified by stranding, laying, skin effectand proximity effect is termed as ac resistance, i.e.; R ac .

(d) Sheath Losses: When alternating current flows in the core of a cable, the core andthe sheath act as the primary and secondary of an air core transformer. An emf isinduced in the sheath leading to flow of eddy currents and longitudinal circulatingcurrents. These currents give rise to sheath losses. The losses due to eddy currentin the sheath are usually negligible except in very large cables.

For three phase cables, circulating currents are important only when 3 separatesingle core cables or a three core cable with each core having separate sheath (SL

or SA cable) are used. In 3-core belted cable or 3-core screened cable with only asingle sheath covering all the three cores, the magnetic fields of the three cores arepartially mutually compensated and the circulating currents are reduced. Sheathlosses are greater in aluminum sheathed cables than in lead sheathed cables.

When the sheaths of the three single core cables are not bonded or bonded at oneend only, circulating currents cannot flow but induced voltages appear between onesheath and another. The magnitude of these voltages may be 50 200 Volts/Km(and much more at short circuits). In order to avoid the risk of damage or danger

arising from the presence of these sheath voltages especially adjacent to theterminals, sheaths have to be bonded at both ends. If this is done, circulatingcurrents flow and sheath losses occur. As the spacing between the cores increasesthe loss also increases. Methods of cross-bonding at joints have been developed bywhich circulating current sheath losses can be virtually eliminated and the inter-sheath voltages kept small. Cross-bonding employs a transposition method involvingsystematic interruption and cross-connection of sheaths at each interruption (i.e.; thesheath of conductor 1 connected to that of conductor 2, sheath of conductor 2connected to that of conductor 3 and sheath of conductor 3 connected to that ofconductor 1) at suitable intervals. Since the sheath voltages are equal and displacedby 120 (for balanced loads), the circulating currents are eliminated. Forunbalance loads as well, the circulating currents are very small. Inter-sheath voltageis limited to that of each section.

(e) Armor Losses: These losses are partly due to eddy currents in the armor and partlydue to hysteresis. The losses due to eddy currents are of greater importance. It is nota standard practice to provide single core cables with armor of magnetic materials

because of large armor losses and larger inductive line reactance. In multi-corecables the armor losses are generally negligible for conductor sections less than 200sq. mm but may be high as 20% of conductor resistance loss for some 3-corecables.

If sheath loss = 1 x conductor loss; and armor loss = 2 x conductor loss, then


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10. Conductor Inductive Reactance

For small changes in temperature, the resistance increases linearly with temperature andthe resistance at a temperature t is given by: R t = R 0 (1 + 0 t ) (1)

Where R t = resistance at t C

R 0 = resistance at 0 C

0 = temperature co-efficient of resistance at 0 C

Using equation (1) the resistance R 2 at a temperature t 2 C can be found if theresistance at a temperature of t 1 C is known.

R2 / R 1 = (1 / 0 + t 2 ) / (1 / 0 + t 1 ) (2)

The constant 1 / 0 equals to 228 for Aluminum.

11. The inductance of three phase line with un-symmetric spacing D12 , D23 , D31

The inductance of phase a is:

La = a /Ia = 2 x 10 -7 ln ( 3(D12 D23 D31 ) / r) H/m (3)

Where r = GMR = 0.7788 r (r being the radius of conductor.

Or, La = 2 x 10 -7 ln (D eq / r) H/m (4)

= 0.465 log (D eq / r) H/m (5)

The quantity 3(D12 D23 D31 ) is called equivalent spacing and is denoted by D eq . It is thegeometric mean of the three distances of the line.

[Example: A three phase transmission line has its conductors at the corners of anequilateral triangle with side 3 m. The diameter of each conductor is 1.63 cm. Find theinductance per phase per kilometer of the line.

Solution:

r = 0.7788 x 0.5 x 1.63 = 0.635 cm.

Hence, L = 0.465 log (300/0.635) = 1.2315 mH/km ]


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(b) Reduction due to lower effective spacing between cables with conductors of cross-section other than circular.

(c) Increase due to mutual coupling with the armor of 3-core cables. This may be to anextent of 10%.

Because of the need of modification due to reasons given above, it is better to determinethe inductance experimentally.

Example 1:Calculate the inductance per conductor per km of a 3-core belted cable with 37/0.238 cmconductor and core insulation 0.5 cm thick. Neglect the effect of mutual coupling withsheath and armor.

Solution:

A 37-strand conductor has a central strand surrounded by 3 layers containing 6, 12 and 18strands respectively. The overall conductor radius is, 0.238 x 3.5 = 0.834 cm.

Geometric mean radius r = 0.7788 x 0.834 = 0.6495 cm.The distance between conductor centers is uniform and, therefore,

Deq = 2(0.5 + 0.834) = 2.668 cm.

Using Eq. (5)L = 0.465 log (D eq / r) = 0.465 log (2.668 / 0.6495) = 0.2825 mH/km.

12. Parameters of Single core cables

12.1 Insulation Resistance

The Fig. 12.1 shows a single core cable of conductor radius r . The cable has a sheath of insideradius R. The insulation resistance d R ins of an annulus of thickness dx at radius x is:

dx d R ins = ---------- Ohms/metre (12.1)

2 xWhere, is the resistivity of the insulating material in Ohm-metres.

The insulation resistance per metre length is

R dx R ( / 2 ) l (R/ ) Oh / t (12 2)


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Average value of for impregnated paper varies from 5 x 10 12 to 8 x 10 12 Ohm-metres at15 C. The change in resistivity of insulating materials with temperature is described by the

equation: t = 0 - t (12.4)

Where, t is resistivity at t C, 0 is resistivity at 0 C and is a constant.

12.2 Capacitance

Since the single core cable (Fig. 12.1) has an earthed metallic sheath, there is an electric fieldbetween the conductor and the sheath. Let the charge on the surface of the conductor be qcoulomb per metre length of the cable. The electric flux density D x at a radius x is

D x = (q / 2 x ) C / m 2

The electric field intensity E x at a radius x is

E x = ( D x / r . 0 x ) V/m

Where, r is the relative permittivity (dielectric constant) of the cable insulation and

0 = 8.85 x 10

-12

F / mThe potential difference between the core and the sheath is

R

V = E x dx = q / ( 2 r . 0 ). l n (R/r) Voltsr

Capacitance between core and sheath is

C = (q/v) = ( 2 r . 0 ) / l n (R/r) F / m


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12.2.1 Dielectric Loss

A cable has a capacitance between the core and the sheath. If a voltage is applied to anunloaded cable between the core and the sheath a capacitive current (or the charging current)flows through it. Since the resistivity of insulation is not infinite, leakage current flows and apower loss occurs. With AC voltages the phenomenon of dielectric absorption also contributesto the power loss. Thus the cable behaves like an imperfect capacitor and the total current, evoltage not by 90 but by an angle (90 ) as shown in Fig. 12.2. The angle is termed asloss angle of the dielectric.

The dielectric loss P d is

= V. I. cos = V. I. cos (90 ) = V. I. sin

= C V 2 sin = C V 2 Watts

Where C is the capacitance of the cable and V is the applied line to neutral voltage; is thedielectric loss angle (radians) and is the power supply frequency (measured in radians / sec).Since, is normally very small, sin = . Hence, P = V 2 C Watts, where is in radians.

ALTERNATIVELY

The cable is a sort of capacitor with core and the sheath forming two plates of the capacitorseparated by the dielectric material in between. The equivalent circuit for this system isrepresented by a parallel combination of leakage resistance R and a capacitance C. Theequivalent circuit with its phasor diagram is shown in Fig 12.3. The loss in dielectric is due to theloss in the equivalent leakage resistance.

P = V 2 / R

From phasor diagram: (V / R) / (V C ) = tan

Or, V / R = V C / tan

P = V 2 / R = V 2 C tan

Where, is the dielectric loss angle (radians) and is the power supply frequency (measured

in radians / sec). Since, is normally very small,tan =

Hence, P = V 2 C Watts, where is in radians.


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12.3 Grading of Cables

The value of E max has to be kept within limits which depend on the margin of safety and thepermissible degree of dielectric heating. Since the insulation away from the core is understressed, there is an avoidable waste of insulation. It seems attractive to use methods whichreduce the amount of insulation by redistribution of stress so as to increase stress in outerlayers of insulation without increasing it at the conductor surface. Two methods for such agrading of insulation have been suggested. These are:

(a) Capacitance grading

(b) Inter-sheath grading

12.3.1 Capacitance grading

The method involves the use of two or more layers of dielectrics having different permittivity,those with higher permittivity being nearer to the conductor.

The electric field intensity E x at any radius x is given by equation:

E x = D 1 / ( r 0 ) = q / (2 r 0 x).

If it were possible to vary permittivity with radius x such that:

r 1 / x = m / x

Then, Ex

= q / {2 0

(m / x) (x)} = q / (.2 0

m )

Thus E x is constant throughout the thickness of insulation. Such a gradation is evidently notpossible. However, two or three dielectrics with different values of relative permittivity can beused as shown in the Fig. 8.6.

From x = r to x = r 1 , the dielectric with relative permittivity 1 is used.

At x = r, E = q / (2 0 1 r)

At x = r 1 , E = q / (2 0 1 r 1)

From x = r 1 to x = r 2 , the dielectric relative permittivity 2 is used.


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If all the three dielectrics are operated at the same maximum electric intensity, then:

1 / ( 1 r) = 1 / ( 2 r 1 ) = 1 / ( 3 r 2 )

Or, ( 1 r) = ( 2 r 1 ) = ( 3 r 2 )

The variation of electric field intensity with radius is shown the above Fig. 8.6. The operatingvoltage V is:

r 1 r 2 r 3

V = E x dx + E x dx + E x dx

r r 1 r 2

r 1 r 2 r 3

= {q / (2 0 1 x)} dx + {q / (2 0 2 x)} dx + {q / (2 0 3 x)} dx

r r 1 r 2

= {q / (2 0 1) ln (r 1 / r)} + {q / (2 0 2) ln (r 2 / r 1 )} + {q / (2 0 3) ln (R / r 2 )}

= { q / (2 0 1 r)} r l n (r 1 / r) + {q / (2 0 2 r 1)} r 1 ln (r 2 / r 1 ) + {q / (2 0 3 r 2)} r 2 ln (R / r 2 )

= E max [ r l n (r 1 / r) + r 1 ln (r 2 / r 1 ) + r 2 ln (R / r 2 )

12.3.2 Inter-sheath Grading

In this method, only one dielectric is used but the dielectric is separated into two or more layersby thin metallic inter-sheaths maintained at appropriate potentials by connecting them to thetappings on the winding of the transformer feeding the cable. There is a fixed voltage betweenthe inner and outer radii of each sheath.

Fig. 8.7 shows a single core cable with two inter-sheaths. The different radii are r, r 1, r 2 and R.The potential difference between conductor and first inter-sheath is (V V 1), that between the


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If the values of maximum and minimum potential gradients in the three sections are kept thesame, we get: (r 1 / r) = (r 2 / r 1) = (R / r 2) =

Then,

(V V 1) / r l n = (V 1 V 2) / r 1 ln = V 2 / r 2 ln

If the cable does not have any inter-sheath, the maximum voltage gradient is:

Emax3 = V / {r l n (R / r)}

Using the above equations, the ratio of maximum stress with and without inter-sheath can be

calculated. The radii of inter-sheaths may be found from the ratio .Both the methods of grading of cables involve practical difficulties. With Capacitance gradingthe difficulty exists in obtaining different permittivity. The use of rubber ( r = 4 - 6) andimpregnated paper ( r = 3 - 4) have been suggested by reputed cable manufacturers. However,the possible change of permittivity with time may alter the stress distribution and lead toinsulation breakdown even at the working voltage. With inter-sheath grading it may be difficult toarrange for proper voltages of inter-sheaths. The jointing of cables having inter-sheaths alsoposes problems. The possibility of damage to the thin inter-sheaths during cable laying alsoexists. Moreover, the charging current may cause overheating of inter-sheaths especially in verylong cables.

12.4 Capacitance of three core belted cables

Three core belted cables were used previously up to 11 KV and are now used up to 33 KV. Inthis cable a potential difference exists between any two pair of conductors and also betweeneach conductor and the outer sheath. Thus, there is an electric field between any two pairs ofconductors and also between each conductor and the outer sheath. Consequently, there isCapacitance C c any two pairs of conductors and Capacitance C s between each conductor andthe outer sheath, as shown in Fig. 8.8. The overall field pattern is very complicated and may bestudied experimentally in an electrolytic tank. The Capacitances may be more easily obtainedby measurement.

The three delta connected Capacitance C c in Fig. 8.8 can be replaced by three star connectedcapacitances each of value 3 C c using delta / star transformation as shown in Fig.8.9. TheCapacitance to sheath can be assumed to be in series with star connected capacitance of eachcore to earthed neutral, i.e. C = 3 C c + C s

Th i C d C b i d b h f ll i


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(c) All the three conductors are joined together and the capacitance C a between thiscombination and the sheath is measured. This measured value is:

Cb = 3 C s

From the above two equations:

C s = C b / 3 and C c = (C a / 2) (C b / 6)

The effective capacitance between each core and earthed neutral is:

C = 3 C c + C s = 1.5 C a 0.167C b

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