Insulated Cables | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) PDF Download

 Insulated Cables

INTRODUCTION

All the electric cables consist of three essential parts.

 The conductor for transmitting electrical power. 

• External protection against mechanical damage, chemical or electro-chemical attack, fire or any other dangerous effects external to the cable. 
• An insulation to isolate the conductors from each other and their surroundings.

General Construction of Cable The underground cable used for transmission of power at high voltage consists of one central core or a number of cores (two, three or four) of tinned stranded copper conductors (sometimes use of aluminium conductor is also made) insulated from each other by paper or varnished cambric or vulcanized bitumen or impregnated paper. A metallic sheath of lead or alloy or of aluminium is provided around the insulation to protect it against ingress of moisture. For the protection of metallic sheath against corrosion and from mechanical injury from the armouring a layer of bedding consisting of paper tape compounded with fibrous material is provided over the metallic sheath.

Requirements of cable

1. The conductor (usually annealed copper with about 99.95% purity or aluminium) used in cable should be stranded one in order to provide flexibility to the cable and should be of such x-sectional area that it may carry the desired load current without overheating and causeing voltage drop within limits.
2. The insulation  provided should be of such thickness that it may give high degree of safety and reliability at the working voltage for which it is designed,
   (iii) The cable should be provided with a mechanical protection so that it may withstand the rough usage in laying it.
   (iv) Materials used in manufacture of cable should be such as to give complete chemical and physical stability throughout.

Conductor Material Used  The materials employed for conductors generally are annealed copper and aluminium.

Copper  The used of copper is limited to cables used for control circuits, signalling and communications.

Aluminium  Power cables use standard or sector shaped aluminium conductors.

Insulation Main requirements of the insulating material :

• High dielectric strength.
• High insulation resistance.
• Good mechanical strength.
• Should be able to withstand temperatures from about–30°C to over 100°C.

Insulation Material

• Cross linked polythene (XLPE)
• Polyethylene thermoplastic
• Ethylene propylene (rubber)
• Butyl rubber
• Polyvinyl chloride (PVC)
• Oil impregnated paper

PARAMETERS OF CABLES

Insulation Resistance Figure shows a single core cable of conductor radius r and a sheath of radius R.

•  Insulation resistance

 Where r is the resistivity of the insulating material in W-m and l is the length of cable in metres. 

• Average value of r for impregnated paper varies from 5 × 10¹² to 8 × 10¹² ohm-metres at 15°C. 
• The change in resistivity of insulating materials with temperature is r_t = r₀e^–at Where r_t is resistivity at t°C. r₀ is resistivity at 0°C and a is constant.

Capacitance 

• Let the charge on the surface of the conductor be q Coulomb per metre length of cable. 
• The electric flux density D_x at a radius x

Capacitance 

• Let the charge on the surface of the conductor be q Coulomb per metre length of cable. 
• The electric flux density D_x at a radius x

Where Î_r is the relative permittivity (dielectric constant) of the cable insulation and Î₀ = 8.85 × 10^–12 F/m. 

• The potential difference between the core and the sheath

  Capacitance between core and sheath

THREE CORE CABLES

These are used only upto 11 kB. In these cables a potential difference exists between any two pairs of conductors and also between each conductor and sheath.

Measurement

Assumption: 

• The dielectric is uniform between the core and the sheath. 
• In the figure shown below C_c is the capacitance between any two pairs of conductors and C_s is the capacitance between each conductor and sheath.

•  The capacitances C_c and C_s are obtained by the following measurement. 
• Measurement 1 : Any two conductors are connected to the sheath and the capacitance C_x between this combination and the third conductor is measured.

•   Measurement 2 : All the three conductors are joined together and the capacitance C_y between this combination and sheath is measured.

•  Capacitance betw een any two pairs of conductors.

Capacitance between each conductor and sheath

The effective capacitance between each core and neutral (or capacitance per phase).

EXTRA HIGH VOLTAGE (EHV) CABLES

• Every dielectric material has certain dielectric strength which, if exceeded, will result in rupture of the dielectric. 
• Disruptive failure can be prevented by designing the cable such that the maximum electric stress (which occurs at the surface of the conductor) is below that required for short time puncture of the dielectric. 
• If the gradient is taken large to reduce the overall size of the cable the dielectric losses increase very much which may result in thermal breakdown of the cable.

Electrostatic stress Let r be the radius of the conductor, R the inner radius of the sheath, Î the permittivity of the dielectric, q the charge per unit length. 

• Gradient at a distance x
  
  where E is the electric field intensity.
  
• Potential of the conductor with respect to sheath.
  

• Gradient at distance x from centre

• The gradient is maximum at the surface of the conductor

• The gradient is minimum at the inner radius of the sheath

• The radius of conductor which gives minimum gradient at the surface of the conductor.

• For cable to be operates satisfactorily

GRADING OF CABLES

• Grading of a cable is meant the distribution of dielectric material such that the difference between the maximum gradient and the minimum is reduced, thereby a cable of the same size could be operated at higher voltages.

Methods of Grading Capacitance Grading

• This method involves the use of two or more layers of dielectrics having different primitivities, those with higher primitivities being nearer to the conducotor.
• If it were possible to vary permittivity with radius x such that
  

Thus E_x is constant throughout the thickness of insulations.

• Two or three dielectrics with different values of relative permittivity can be used as shown in figure.

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

• The operating voltage V
  

Intersheath Grading

• In this method only one dielectric is used but the dielectric is separated into two or more layers by thin metallic intersheaths maintained at appropriate potentials.

• A single core cable with two intersheaths is shown in above figure.
• The maximum voltage gradients in teh three sections

• If the values of maximum and minimum potential gradients in the three sections are kept the same.