How to use the Transformer Efficiency & Regulation Calculator
- 1. Enter the rating and losseskVA, core (iron) loss and full-load copper loss.
- 2. Set the loadLoad as % of full load, power factor and lagging/leading.
- 3. See the resultsEfficiency, load at maximum efficiency, regulation and a load table.
Transformer efficiency formula
At a fraction x of full load, output = x S cos φ, core loss Pi stays constant and copper loss is x² Pcu. So η = x S cos φ / (x S cos φ + Pi + x² Pcu). Maximum efficiency occurs when copper loss equals core loss, at x = √(Pi / Pcu).
Worked example: 25 kVA, Pi = 350 W, Pcu = 400 W, pf 0.8. At full load: η = 20,000 / (20,000 + 350 + 400) = 96.39%. At half load: η = 10,000 / (10,000 + 350 + 100) = 95.69%. Maximum efficiency is at x = √(350/400) = 0.935, that is 23.4 kVA, with η = 96.39%.
Voltage regulation and exam questions
Approximate regulation is x (εr cos φ ± εx sin φ) in percent, using + for lagging and − for leading loads. εr = Pcu / S × 100 comes from the copper loss, and εx is the leakage reactance in percent. In the example, εr = 1.6% and with εx = 4% at pf 0.8 lagging, regulation is 1.6 × 0.8 + 4 × 0.6 = 3.68%.
- Find efficiency at full and half load at unity and 0.8 pf.
- Find the kVA at which efficiency is maximum.
- Find the regulation at a leading power factor (it can be negative).
- Find copper loss at 75% load from the full-load value.
Frequently asked questions
Why does copper loss go with the square of load?
Copper loss is I²R, and current is proportional to load. At half load the current halves, so the copper loss falls to one quarter.
Why is regulation negative at leading pf?
With a leading load, the reactive drop can raise the secondary voltage above its no-load value, so the regulation formula gives a negative number.
Where do Pi and Pcu come from?
Pi comes from the open-circuit test at rated voltage. Pcu at full load comes from the short-circuit test at rated current.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.