Kelvin’s Law In Power System

The cost of conductor material is a vital part of the total cost of a transmission line. Therefore, calculation of conductor size of a transmission line is very important.
Kelvin’s law in power system is used to find out the most economical area of x-section of a conductor for which the total annual cost of the transmission line is minimum.
Kelvin’s law can be stated as: The most economical area of x-section of a conductor is that for which the variable part of annual charges (i.e. annual charges on account of interest and depreciation) is equal to the cost of energy wasted per year.

Practical Limitations of Kelvin’s Law in Power System

Although theoretically, Kelvin’s law holds good but in actual practice, an economical x-section of the conductor determined by Kelvin’s law may not suit because of the following factors:

  • Interest and depreciation on the capital cost outlay cannot be determined so accurately.
  • It is difficult to estimate the energy loss in the line without load curves, which are not available at the time of estimation.
  • It is also not easy to estimate the cost per unit of energy wasted in the line. In fact, the cost per unit of the energy wasted is not the same as that of the cost of generation per unit since their cost per unit depends upon load factors which are different for the generation and the line losses.

  • Kelvin’s law does not take into account various physical factors such as current density, mechanical strength, corona loss etc.
  • The conductor size determined by Kelvin’s law may not be practicable one because it may be so small that
  • (a) It may cause too much voltage drop in the line.
    (b) It may cause high corona loss.
    (c) It may be too weak from mechanical considerations.
    Thus it is advisable to go to the higher conductor size irrespective to the economy.

To understand the kelvin law for economic size of conductor properly, look at the following example.
Example A 2-conductor cable 1 km long is required to supply a constant current of 200 A throughout the year. The cost of cable including installation is Rs. (20 a + 20) per metre where ‘a’is the area of X-section of the conductor in cm2.
The cost of energy is 5 Paisa per kWh and interest and depreciation charges amount to 10%. Calculate the most economical conductor size. Assume resistivity of conductor material to be 1·73  micro ohm cm.

kelvin's law in power system numericals
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3 thoughts on “Kelvin’s Law In Power System”


    I tried to find conductor size for aluminium and copper both. Cancelled the Length of cable on the both capital cost and resistance. For Aluminium – a^2 = I^2*0.1393, For copper – a^2=I^2*0.091.
    Is it possible ???? I tried but it didn’t work. Please suggest

    1. Ajay Sharma

      This formula is used to design the transmission lines only. If you are doing that then you are much level higher than me. If you are trying else then you are on wrong track.

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