How to Calculate Transmission Line Losses

Electricity is transmitted at high voltage to reduce power loss.

As electrical transmission lines span hundreds of miles, there will be some load loss incurred. The longer the line, the more electricity will be lost to the resistance inherent in the line material. Joule's Law states that energy losses are proportional to the square of the current; therefore, if the voltage is kept high, the power lost will be comparatively low. The equation for line losses is defined as P(loss) = (I^2)(R) where I is the current and R is the resistance in the wire.

Things You'll Need

• Power demand (P)
• Resistance (R)
• Line Voltage (V)

Instructions

1. Calculate the resistance of the wire by multiplying the cross sectional area by the length and multiplying by the resistivity of the material. The resistivity of copper is typically 0.000999 ohms per foot, so the resistance of a 14 gauge copper line (a cross section of 2.081 square millimeters) 1 mile long would be 13.6 ohms, according to Jeff Lucius's resistance calculator.

2. Determine the voltage produced by the source. This is the output voltage of the transformer; long distance transmission is often stepped to 400 kV, according to Enmax, a Canadian electricity provider.

3. Determine the power being produced by the power station. Nine Mile Point, for example, supplies 1,758 MW of electricity.

4. Determine the current by dividing the voltage by the resistance. Square this result and multiply it by the resistance in the line, and the result will be the load loss, measured in watts.

References

• Jeff Lucius: Wire Resistance and Voltage Drop Calculator
• Enmax: How is Electricity Transmitted?
• Nuclear Street: Nine Mile Point Nuclear Station Unit 2 Completes Scheduled Refueling Outage
• Power Logic: Transformer Line Loss Calculations