CAPACITANCE OF SINGLE CORE CABLE

Presented by :-

Anant.k.momaya 45 Sumit.m.patil 53

Basics of cable :-

Front view :-

The core is provided with suitable thickness of insulation, depending upon the voltage to be withstood by the cable. The commonly used material for insulation are impregnated paper, varnished cambric or rubber mineral compound.

Insulation :-

A metallic sheath of lead or aluminum is provided over the insulation to protect the cable from moisture, gases or others damaging liquids

Metallic Sheath :-

A Core or Conductor cable may have one or more than one core depending upon the type of service for which it is intended. The conductor could be of aluminum or copper and is stranded in order to provide flexibility to the cable

What is core of cable?

A capacitor consists of two conducting plates separated by an insulating material called the dielectric.

What is capacitance in cable?

Formula for capacitance

A single core cable is equivalent to two long co-axial cylinders. The inner cylinder is the conductor itself while the outer cylinder is the lead sheath. The lead sheath is always at earth potential. Let d = Conductor diameter D = Total diameter with The co-axial cylindrical from of cable and its section are shown in the Fig. 1(a) and (b). Let Q = Charge per meter length of conductor in coulombs ε = Permittivity of material between core and sheath sheath

Now ε = εo εrThe Where εo = permittivity of free space = 8.854 x 10-12 F/m and εr = Relative permittivity of the medium Consider an elementary cylinder with radius x and axial length of 1 m. The thickness of the cylinder is dx. According to Gauss's theorem, the lines of flux emanating due to charge Q on the conductor are in parallel direction and total flux line are equal to the total charge possessed i.e. Q lines. As lines are in radial direction, the cross-sectional area through which lines pass is surface area. For a cylinder with radius x, the surface area is (2πx x axial length) m2. As axial length considered is 1 m, the surface area is 2 π x m2.

electric field intensity at any point P on the elementary cylinder is given by, gx = Dx/ε where Dx = Electric flux density

gx = Dx/ε where Dx = Electric flux density Hence the work done in moving a unit charge through a distance dx in the direction of an electric field is gx dx.

Therefore the work done in moving a unit charge from the conductor to sheath is the potential difference between the conductor and the sheath given by,

The capacitance of a cable is given by, Note that as length considered is 1 m, the capacitance is F/m. If required for length 'l' multiply c by 'l'. Substituting value of εo,

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Advantages .It increases the voltage of line at receiving end .It reduces voltage regulation of line .As voltage increases therefore line current decreases Disadvantages .Restricts the cable length in case of Dc transmission due to inrush of charging currents .For Ac transmission causes voltage rise at receiving end in low loaded condition. forces use of inductors at receiving end. .Because of capacitance you need to earth before touching after de energizing.

Advantages & Disadvantages of capacitence of cable

Capacitance causes current to flow even when no load is connected to the cable. This is called “line charging current”. Underground line capacitance for power cables is far higher than overhead line capacitance. . Wires are closer to each other . Wires are closer to the earth (within a few inches). . Underground lines have 20-75 times the line charging current that an overhead line has (depending on line voltage). . If a line is long enough the charging current could be equal to the total amount of current the line can carry. This will severely limit its ability to deliver power.

Effects of capacitence on line :-

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