Two kinds of loss, one yearly bill
Even when it supplies nothing, a transformer consumes active power whenever it is energized. As the load rises, winding and stray load losses add to it. A simple loss-and-cost calculation estimates the energy impact of keeping a transformer energized through the year.
1. Two principal categories of loss
No-load loss P0 (core or iron loss) is measured at rated voltage and frequency with the secondary unloaded. It is present whenever the transformer is energized, even at zero load. Load loss Pk is measured at rated current and a reference temperature and includes the winding I²R and other load-dependent losses; for a first comparison it scales with the current squared. Both are test-report or nameplate values: the kVA rating alone is not enough to know them.
2. The operating-point equation
At x = 0.5 the load loss is about 25 % of Pk, not 50 %. The model ignores the winding temperature, part of the stray-loss behaviour, harmonics and cooling fans or pumps.
3. Annual energy and cost
H is the number of energized hours, c your energy rate. No tariff is correct everywhere: enter your own, and your own currency label.
4. Worked example
| Quantity | Value |
|---|---|
| P0 (test report) | 1.4 kW |
| Pk (test report) | 10.0 kW |
| Loading x | 0.5 |
| Load loss | 10.0 × 0.5² = 2.5 kW |
| Total loss while energized | 3.9 kW |
| No-load energy | 1.4 × 8760 = 12,264 kWh |
| Load-loss energy | 2.5 × 8760 = 21,900 kWh |
| Total | 34,164 kWh per year |
| Cost at 0.15 per kWh | 5,124.60 per year |
These are illustrative values. A real result needs the actual losses of your transformer and your loading.
5. The average-loading trap
A transformer that runs at 0 % for half of the year and at 100 % for the other half has an average loading of 50 %, but the average of x² is 0.5, not 0.25. Squaring the average halves the load-loss energy in that case: 21,900 kWh instead of 43,800 kWh. For several periods with loadings xj and hours Hj:
The calculator offers one constant loading and, in Advanced, up to three intervals; it then shows the average and the RMS-equivalent loading side by side. A load that rises steadily from 0 % to 100 % gives yet another value (one third, 29,200 kWh in the example).
6. Comparing transformers
A cheaper unit with a higher no-load loss can cost more over long energized periods even at light load; in heavily loaded installations the load loss dominates. Compare only with the same energized hours, load profile, energy rate and loss reference temperature: never a 20 °C winding loss against a 75 °C nameplate loss.
7. Common mistakes
- Assuming the loss follows from the kVA rating.
- Assuming P0 is zero when the LV side has no load.
- Squaring the arithmetic mean of a strongly varying load.
- Counting hours when the transformer is actually isolated.
- Forgetting fans and pumps, harmonics and temperature.
- Treating a loss comparison as proof of IEC energy-efficiency compliance.
Related: the Transformer fundamentals guide · the result is an energy estimate, not a guaranteed utility bill.