Kelvin's Law for Economic Choice of Conductor Size

Kelvin’s Law:

The most economical size of a conductor for a transmission line is one where the annual interest and depreciation on the capital cost of the conductor are equal to the annual cost of energy loss due to the resistance of the conductor.

Mathematically, this can be expressed as:

Annual Cost of Energy Losses = Annual Capital Interest and depreciation Cost of the Conductor (Variable Part)

• Kelvin’s Law has several limitations:

1. Constant Load Assumption: Assumes a constant load, ignoring load variations.
2. Simplified Costs: Ignores other costs like maintenance and installation.
3. Line Length and Voltage: Doesn’t account for varying lengths and voltage levels.
4. Modern Technology: Doesn’t consider modern materials and technologies.
5. Environmental and Regulatory Factors: Omits environmental and regulatory considerations.
6. Fixed Financial Rates: Assumes constant interest and depreciation rates.
7. Network Complexity: Doesn’t address complex power system interactions.
8. Material Constraints: Doesn’t account for availability and properties of different materials.