Characteristics of Cables

By Anu SinglaAnu SinglaAssociate ProfessorDepartment ofElectrical EngineeringChitkara University,Punjab Campus

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Insulation Resistance of a Single‐CoreCable

The cable conductor is provided with a suitable thickness of insulating materialin order to prevent leakage current. The path for leakage current is radialthrough the insulation. The opposition offered by insulation to leakage current isknown as insulation resistance of the cableknown as insulation resistance of the cable.

Consider a single‐core cable of conductor radius r1 and internal sheath radius r2 .

Let l be the length of the cable and ρ be the resistivity of the insulation.

Consider a very small layer of insulation of thickness dx at a radius x.

The length through which leakage current tends to flow is dx and the area of X‐section offered to this flow is 2π x l.

Insulation Resistance of a Single‐CoreCable contd.

Capacitance of a Single‐Core CableA single‐core cable can be considered to be equivalent to twolong co‐axial cylinders. The conductor (or core) of the cable isthe inner cylinder while the outer cylinder is represented bylead sheath which is at earth potentiallead sheath which is at earth potential.Consider a single core cable with conductor diameter d andinner sheath diameter D.Let the charge per metre axial length of the cable be Qcoulombs and ε be the permittivity of the insulation materialbetween core and lead sheath.

ε = ε0 εr where εr is the relative permittivity of the insulation.ε ε0 εr where εr is the relative permittivity of the insulation.

Capacitance of a Single‐Core Cable contd.

Dielectric Stress in a Single‐Core Cable

Under operating conditions, the insulation of a cable issubjected to electrostatic forces. This is known asdielectric stress.h d l bl f hThe dielectric stress at any point in a cable is in fact thepotential gradient (or electric intensity) at that point.Consider a single core cable with core diameter d andinternal sheath diameter D The electric intensity at ainternal sheath diameter D. The electric intensity at apoint x metres from the centre of the cable is

By definition, electric intensity is equal to potentialgradient. Therefore, potential gradient g at a point xmetres from the centre of cable is

P i l diff V b d d h h i

Dielectric Stress in a Single‐Core Cablecontd..

Potential difference V between conductor and sheath is

*potential gradient at any point is equal to the electric intensity at that point.

Dielectric Stress in a Single‐Core Cablecontd..

The variation of stress in the dielectric is shown in Fig.It is clear that dielectric stress is maximum at the conductorsurface and its value goes on decreasing as we move away fromg g ythe conductor.Maximum stress is an important consideration in the design of acable. For instance, if a cable is to be operated at such a voltagethat maximum stress is 5 kV/mm, then the insulation used musthave a dielectric strength of atleast 5 kV/mm, otherwisebreakdown of the cable will become inevitable.

Capacitance of 3‐Core Cablesh i f bl i h i h h f h dThe capacitance of a cable system is much more important than that of overheadline because in cables (i) conductors are nearer to each other and to the earthedsheath (ii) they are separated by a dielectric of permittivity much greater thanthat of air Fig shows a system of capacitances in a 3 core belted cable used forthat of air. Fig. shows a system of capacitances in a 3‐core belted cable used for3‐phase system.Since potential difference exists between pairs of conductors and between eachconductor and the sheath electrostatic fields are set up in the cable as shown inconductor and the sheath, electrostatic fields are set up in the cable as shown inFig. 1(i). These electrostatic fields give rise to core‐core capacitances Cc andconductor‐ earth capacitances Ce as shown in Fig. 1 (ii). The three Cc are deltaconnected whereas the three Ce are star connected, the sheath forming the stare , gpoint fig.1(iii).

Capacitance of 3‐Core CablesIt is reasonable to assume equality of each Cc and each Ce. The three deltaconnected capacitances Cc [See Fig. 2(i)] can be converted into equivalent starconnected capacitances as shown in Fig. 2 (ii). It can be easily shown that

l l h h d lequivalent star capacitance Ceq is equal to three times the delta capacitance Cci.e. Ceq = 3 Cc.

h f i h i i (iii) d h i l i iThe system of capacitances shown in Fig. 1 (iii) reduces to the equivalent circuitshown in Fig. 3 (i). Therefore, the whole cable is equivalent to three star‐connected capacitors each of capacitance [Fig. 3 (ii)],

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