Insulation of Electrical Cables (with Problems and Solutions) - Conductors, Insulation, Extra High Voltage Cables, Grading of Cables


Here's a general introduction to the concepts which will be introduced in this tutorial

Electric cables generally have 3 essential parts

  1. Conductor to transmit power

  2. Insulation, a medium to avoid direct contact with earth or other objects

  3. External protection against mechanical damage, chemical damage or electro-chemical attack, fire or other dangerous effects.


Copper conductors have been extensively used for cables. But late aluminium is being replaced for the same. Number of wires are used to make into a strand in-order to obtain flexibility.

Apart from flexibility other uses are

  1. Easy to handle

  2. Less liable to break or kink

  3. Risk of conductor breaking through the dielectric can be reduced

Wires in stranded conductor are twisted together to forms lays and also the successive layers are stranded in opposite direction. If one layer is right handed lay, then the next layer will be left handed lay.

Standard stranding is done with 6 wires around 1, 12 around 6, 18 around 12, and so on. These conductors specifications are expressed as 19/0.1. The number ‘19’ above represents number of strands and the number ‘0.1’ represents diameter of each strand. Sometimes these specifications can be given as 3/20, which means a cable has 3 strands and number 20 represents gauge of strand used.


Requirements of insulation

  1. High insulation resistance

  2. High dielectric strength

  3. Good mechanical properties (tenacity and elasticity)

  4. Immune to chemicals around it

  5. Non Hygroscopic (Di-electric strength decreases very much with moisture content)


  1. Vulcanized rubber

Rubber used in

  1. Natural form :-  absorbs moisture readily and gets oxidized into resinous material and hence loses insulating properties

  2. Mixed with sulphur and chosen ingredients :- When the mixture is subjected to particular temperature, it changes to vulcanized rubber. It doesn’t absorbs moisture and has better insulation properties than natural rubber, elastic and resilient

Expected electrical properties of rubber insulation are

  1. High break down strength

  2. High insulation resistance

         Insulation strength of vulcanized rubber is so good for lower voltages and its radical thickness is limited due to mechanical consideration.

Expected physical properties of rubber insulation are

  1. Withstand normal hazards of installation

  2. Trouble free service

Vulcanized rubber insulated cables are used for low power applications like

  1. Wiring of houses

  2. Buildings

  3. Factories

Two main groups of synthetic rubber material are

  1. General purpose synthetics which have rubber like properties

  2. Special purpose synthetics which have better properties than rubber

e.g. fire resisting and oil resisting properties

Four main types of rubber

  1. Butyl rubber

  2. Silicon rubber

  3. Neoprene

  4. Styrene rubber

  1. Butyl Rubber: The processing of butyl rubber is similar to that of natural rubber except that butyl rubber is subjected to continuous temperature of 85oC whereas for natural rubber it is 60o. Current ratings for butyl rubber and paper or PVC insulated cables are approximately same. This compound can also be manufactured such that it has low water absorption and also has possibilities for a non-metallic sheathed cable suitable for direct burial in the ground.

  2. Silicon Rubber: is mechanically weak and needs external protection but has high heat resistant properties (can be operated above 150oC.

Raw materials used: sand, marsh gas, salt, coke and magnesium.

  1. Neoprene: is polymerized chloro butadiene. Neoprene does not have good insulating properties and is used upto 660V a.c, but has very good fire resisting properties and therefore can be extensively used as a sheathing material.

  2. Styrene Rubber: is used both for insulating and sheathing of cables which has properties similar to natural rubber

  1. Polyvinyl Chloride (PVC)

  • Polymer derived from acetylene

  • Produced in different grades depending on polymerization process

  • Compounded with plasticizer which makes it plastic over a wide range of temperature to use in cable industry

  • PVC material has many grades which depends on plasticizer.

PVC is inferior to vulcanized in respect of elasticity and insulation resistance.

  1. General Purpose Type: used for sheathing and as an insulating material. In this compound, monomeric plasticizers are used. V.R insulated PVC sheathed cable is not good to use. Due to monomeric plasticizer which volatilizes at 80-100oC, these compounds become stiff.

  2. Hard Grade PVC: Less amount of plasticizer than general purpose type. These are used for high temperature for short duration of time but not for low continuous temperature.

  3. Heat Resisting PVC: By making use of polymeric plasticizers, it is possible to operate cables continuously at 100oC.

           PVC compounds are more costlier than rubber compounds. Polymeric plasticized compounds are more expensive than mono meric plasticized ones. PVC is more useful than rubber where the environment contain oxygen, oils, alkalis and acids as PVC is inert to these things.

  1. Polythene

  • Used for high frequency cables

  • Thermal dissipation properties are better than those of impregnated paper

  • Impulse strength compares favourably with an impregnated paper- insulated cable

  • Max operating temperature- 100oC

  • Inert to chemicals reactions as it does not have double bonds and polar groups

  • Polythene can be cross linked only through special condition e.g. by irradiating polythene with electrons

Cross linked polythene:

  • Polythene has limited use because of low meting point

  • By cross linking the molecules, new material is produces which does not melt but carbonizes at 250oC  to 300oC.

  • Properties of cross linking such as change of tensile strength and better temperature stability.

  • Many irradiation techniques are developed which involves high energy radiations and procedure is expensive

  1. Impregnated Paper

  • Depending upon operating voltage, suitable layer of paper is lapped on the conductor

  • It is then dried by the combined application of heat and vacuum.

  • This is carried out in a hermetically sealed steam heated chamber.

  • Temperature of 120oC-130oC before vacuum is created.

  • After cable is dried, an insulated compound having the same temperature as that of the chamber is forced into the chamber.

  • All the pores are filled with this compound.

  • After impregnation, the cable is allowed to cool under the compound so that the void formation due to compound shrinkage is minimized.

  • After this metal sheath is applied

  1. Protective Coverings

  • Cotton braid is applied over the insulated conductor and is then impregnated with a compound which is water and weather proof.

  • Rubber insulated cables are covered with a lead alloy sheath and is used for fixed installation inside or outside buildings

  • By armouring the cables with steel tapes or galvanized steel wires, cables are protected against mechanical damage.

  • If at all armouring is necessary, non magnetic materials should be used. This reduces the losses but they still remain quite large.

  • Steel tape is the cheapest material for armouring a cable and is useful for damage against direct blows or abrasion.

  • Galvanized steel wires are used for longer length and suitable where longitudinal stress is involved.

  • Lead sheaths are used where cables are subjected to vibrations.

  • Both lead and aluminium sheaths are prone to corrosive attack which maybe caused by chemical, bacteriological and/or electrolytic action.


            The electric material surrounds the conductor and we know that every dielectric material has certain dielectric strength which, if exceeded, will result in rupture of the dielectric. In general the 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. In case the potential gradient is taken a low value, the overall size of the cable above 11kV becomes relatively large. Also, 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. So a compromise between the two has to be made and normally the value of working stress is taken about one-fifth of the breakdown value for design purpose.

Electrostatic Stress in Single Core Cable - discussed in detail in the tutorial document provided at the end of the page.



Grading of cable is meant the distribution of dielectric material such that the differences between the maximum gradient and the minimum is reduced, thereby a cable of same size could be operated at higher voltages or for the same operating voltage a cable of relatively smaller size could be used.

Two methods of grading:

  1. Capacitance grading where more than one dielectric material is used

  2. Intersheath grading where the same dielectric material is used but potentials at certain radii are held to certain values by interposing thin metal sheaths.

Single core cable with three materials

Let the dielectric strength and working stress of this material be G1, G2, G3 and g1, g2, g3 respectively

Our objective is find out the locations of  these materials with respect to the conductor of the cable. We can’t keep them anywhere we like. There must be some criterion; otherwise the results of grading may be offset.

There are two possibilities (discussed in detail in the tutorial document provided at the end of the page).

  1. The factor of safety for all the materials be same, thereby the working stress of the various materials different.

  2. The same working stress for different materials

INTERSHEATH GRADING (discussed in detail in the tutorial document provided at the end of the page).

     An auxiliary transformer is used to maintain the metal sheath and the power conductor on certain potentials; thereby the stress distribution is forced to be different from the one which it would be without the intersheaths. The objective now here is to show that the gradient with intersheath will be smaller than the gradient without intersheath for the same overall radius and the operating voltage. Since a homogeneous material is being used, the maximum values of the stress at various intersheaths is same.

INSULATION RESISTANCE OF CABLE (discussed in detail in the tutorial document provided at the end of the page)

The usual load current flows through the core of the cable whereas leakage current flows radially from the conductor to the sheath through the dielectric material.

It can be seen that resistance of core is directly proportional to length of the cable whereas leakage resistance is inversely proportional to the length of cable.

CAPACITANCE OF CABLE (this topic has been discussed in detail in the tutorial document provided at the end of the page).

Capacitance of single cable

A single core cable has 2 electrodes, the core of the cable and sheath. Insulator behaves as dielectric material, thus a cable is in effect an electrostatic capacitor.

Let λ be the charge per unit length. By definition capacitance is the ratio of the charge on one of the electrodes to the potential difference between the electrodes.

Capacitance of cables is important than the overhead line because of nearness of the conductors to one another and earthed sheath. And also permittivity of dielectric material is higher than that of air.

Capacitance of a 3-Core Cable

If the dielectric is uniform between core and the sheath, it is possible to calculate the capacitance of the 3 core cable. But practically it is not so, therefore, capacitance is desirable to find by measurements. In a 3 core cable, sheath is at earth potential and the three conductors at supply potentials. 3 capacitances are formed between, sheath and conductors and other 3 between conductors forming total 6 capacitors. (this topic has been discussed in detail in the tutorial document provided at the end of the page).

Here are some of the problems solved in this tutorial :

Problem : Determine the economic overall diameter of a 1-core cable metal sheathed for a working voltage of 85kV if the dielectric strength of the insulating material is 65kV/cm.

Problem : A conductor of 1cm diameter passes centrally through a porcelain cylinder of internal diameter 2cms and external diameter 7 cms. The cylinder is surrounded by a tightly fitting metal sheath. The permittivity of porcelain is 5 and peak voltage gradient in air must not exceed 34kV/cm. Determine the maximum safe working voltage.

Problem : The capacitance of a 3-core cable lead sheathed cablel measured between any two of the conductors with sheath earthed is 0.19µF per km. Determine the equivalent star connected capacity and he kVA required to keep 18kms of the cable charged when connected to 20kV,50Hz supply

A single core lead covered cable is to be designed for 66kV to earth. Its conductor radius is 0.5cm and its three insulating materials A,B,C have relative permittivities of 4, 2.5 and 4.0 with maximum permissible stresses of 50, 30 and 40kV/cm respectively. Determine the minimum internal diameter of the lead sheath. Discuss the arrangement of the insulating materials.

Complete Tutorial Document with Problems and Solutions :