An undersized cable works, and that is why it is so often accepted. It carries the load without tripping and passes the commissioning test. The cost arrives afterwards, as heat in the conductor, paid for on every electricity bill for the life of the installation. This worksheet shows how to put a figure on that loss and compare it with the cost of the next conductor size.
The formula
For a three-phase circuit the power lost in the conductors, in watts, is 3 × (current per phase)² × (resistance of one conductor). Current is in amperes and resistance is in ohms for the full length of the run. For a single-phase circuit use 2 × (current)² × (resistance), because the current flows out and back. Resistance is the conductor resistance per kilometre multiplied by the length in kilometres.
Annual energy lost in kWh is the loss in kilowatts multiplied by the hours of load per year. The annual cost is that energy multiplied by the tariff.
Worked example: 16 mm² against 25 mm² copper
The figures use the IS 8130 maximum conductor resistance at 20°C: 1.15 ohm/km for 16 mm² copper and 0.727 ohm/km for 25 mm² copper. The circuit is three-phase, 100 m long and carries 60 A.
| Item | 16 mm² copper | 25 mm² copper |
|---|---|---|
| Resistance per conductor, 100 m | 0.115 ohm | 0.0727 ohm |
| Loss at 60 A (3 × current² × resistance) | 1,242 W | 785 W |
| Difference | 457 W saved by the larger size | |
| Energy saved over 8,000 hours a year | about 3,655 kWh | |
At an assumed tariff of ₹8 per kWh, used for illustration only, the saving is about ₹29,000 a year on one circuit. The right tariff is the plant’s own, so substitute it before drawing a conclusion.
How the loss grows with current
Loss rises with the square of the current, so a cable that is lightly loaded loses little, and one that runs near its limit loses a great deal.
| Current | Loss, 16 mm² (100 m) | Loss, 25 mm² (100 m) |
|---|---|---|
| 40 A | 552 W | 349 W |
| 60 A | 1,242 W | 785 W |
| 80 A | 2,208 W | 1,396 W |
Adjusting for real conditions
- Temperature. Conductor resistance rises as the cable warms, so the real loss at operating temperature is higher than the 20°C figures above, for both sizes.
- Load factor. Few circuits run at full current all year. Use the average of the squared current over the operating hours, not the peak.
- Hours. A feeder running continuously accumulates far more loss than one used a few hours a day, which is why continuous feeders gain most from the larger size.
- Cost of the extra copper. Obtain a quotation for both sizes and divide the extra cost by the annual saving to get a payback period.
When the check is worth running
Run it for long feeders, circuits that run continuously, and loads that sit near the top of the cable rating. The check on voltage drop is a separate one, covered by the kW to cable size chart, and both checks should be made before the size is fixed. APAR lists low-voltage power cables with copper and aluminium conductors on its LV XLPE insulated power cables page, and a higher-ampacity option on the high ampacity XLPE cables (105°C) page.