Home » POWER SYSTEM » ECONOMICS OF POWER TRANSMISSION, KELVIN’S LAW.

By transmission and distribution system, electrical power transmitted from power plant to local load centre.
At generating station usually 11 kv voltage is generated by 3 phase alternator. This voltage then stepped up to 132 kv or more by 3 phase step up transformer.
Primary transmission: High voltage power in the range of 66 kv, 132 kv, 220 kv or 400 kv is transmitted by 3 phase 3 wire a.c. system to the major distribution substation.
Secondary transmission: At receiving substation the high voltage is lowered by step down transformer, usually it makes 33 kv. By 3 phase 3 wire system it transmitted at various sub-station.
Primary distribution: 33 kv secondary transmission voltage again reduced to 11 kv voltage by step down transformer at substation near locality.
Secondary distribution: From primary distribution 11 kv line distributed to different pole mounted substation near the consumer where it step down at 400volt 3 phase 4 wire secondary distribution. The voltage between two phases is 400 volt and between any phase and neutral is 230 volt.

ECONOMICS OF POWER TRANSMISSION:
Economic choice of conductor size and economic choice of transmission voltage are the two basic economic principles by which economics of power transmission depends.

Economic choice of conductor size: The cost of conductor material plays a vital role of the total cost of transmission line. In 1981, Lord Kelvin stated that the most economical area of conductor is that for which the total annual cost of transmission line is minimum. This is known as Kelvin’s law.
The total annual costs are divided by two parts (i) annual charge on capital outlay and (ii) Annual cost of energy wasted in the conductor.
(i) Annual charge on capital outlay: For a particular transmission voltage, current to be carried is fixed. The charge will be the annual interest and depreciation on the capital cost of conductors, supports, insulators and the cost of their erection. It is clear that insulators cost are constant. The conductor costs vary directly to the cross-section of the conductor. The costs of supports and their erection is partly constant and partly proportional to the area of cross section of the conductor.
So, annual charge on an overhead transmission line can be expressed as
Annual charge = P1+P2a………………..eqn-(i)
Here = P1 and P2 are constants and a is the area of cross section of the conductor.
(ii) Annual cost of energy wasted in a conductor: Energy wasted in a conductor due to its ohmic resistance i.e., I2R losses in insulating material and in metallic sheaths. For a constant current in the conductor throughout the year, the energy lost in the conductor is proportional to resistance. The resistance of conductor being inversely proportional to its area of cross-section,
The energy loss due to ohomic resistance is let P3/a……eqn(ii) where P3 is a constant.
So, the total annual cost is P1+ P2a+ P3/a.
Its value should be minimum for most economical condition.
So, this condition occur when, d/da(P1+ P2a+ P3/a)=0,
Or, P2– P3/a2=0,
Or, P2= P3/a2.
Or, P2a= P3/a.
i.e., variable part of annual charge = Annual cost of energy wasted.

So, as per Kelvin’s law the most economical area of conductor size is that, for which the variable part of annual charge is equal to the cost of energy losses per year.

Limitations of Kelvin’s law:
(i) Without load curve it is not easy to estimate the energy loss in the line.
(ii) The assumption that annual charge is of the form P1+P2a is not true.
(iii) This law does not consider physical aspects like temperature rise, mechanical strength, corona loss etc.
(iv) Determined conductor size by this law always not be practical because sometimes it too small to carry of necessary current.
(v) Interest and depreciation on the capital outlay is not valid in maximum time. It cannot be determined accurately.