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’s law in power system 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
Thanks for reading about kelvin’s law in power system.

Transmission and Distribution — 2 | MCQ

#1 The material generally used for armour of high voltage cables is


#2 Transmission line insulators are made of


#3 The material commonly used for sheaths of underground cables is


#4 The spacing between phase conductors of a 220 kV line is approximately equal to

6 m

#5 In a D.C. 3-wire distribution system, balancer fields are cross-connected in order to

equalize voltages on the positive and negative outer

#6 In a D.C. 3-wire distributor using balancers and having unequal loads on the two sides

balancer connected to lightly loaded side runs as a motor

#7 Transmitted power remaining the same, if supply voltage of a D.C. 2-wire feeder is increased 100 percent, saving in copper is

50 percent

#8 A uniformly-loaded D.C. distributor is fed at both ends with equal voltages. As compared to a similar distributor fed at One end only, the drop at the middle point is


#9 As compared to a 2 – wire D.C. distributor, in 3 – wire distributor with same maximum voltage to earth uses only

31.25 percent of copper

#10 Which of the following is usually not the generating voltage ?

8.8 kV

#11 For an overhead line, the surge impedance is taken as

100 – 200 ohms

#12 The presence of ozone due to corona is harmful because it

corrodes the material

#13 A feeder, in a transmission system, feeds power to


#14 The power transmitted will be maximum when

sending end voltage is more

#15 A 3-phase 4 wire system is commonly used on

secondary distribution

#16 Which of the following is not a constituent for making porcelain insulators?


#17 There is a great possibility of occurrence of corona during

humid weather

#18 Which of the following relays is used on long transmission lines?

Mho’s relay

#19 The steel used in steel cored conductors is usually

mild steel

#20 Which of the following distribution system is more reliable ?

Ring main system



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SARAVANAN · March 17, 2019 at 4:37 pm

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

    SARAVANAN · March 17, 2019 at 4:38 pm


    Ajay Sharma · March 18, 2019 at 4:48 pm

    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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