Transformers
Transformer losses and efficiency at a load
- where
- output power (kW)
- load as a fraction of rating
- rated power (kVA)
- load power factor
- total losses (kW)
- no-load loss (kW)
- load loss at rated current (kW)
- efficiency (%)
- load fraction for maximum efficiency
Explain this equation
Works out the losses and efficiency of a transformer at any load, and the load at which efficiency peaks. Use it for loss capitalisation, comparing tenders and judging whether to run one or two units at light load.
P0 is the core loss, present whenever the transformer is energised regardless of load. Pk is the winding loss at rated current; it scales with the square of current, hence n². Pout is the real power delivered.
Efficiency is output divided by output plus losses. It peaks when the variable loss equals the fixed loss, n²Pk = P0, which gives nmax = √(P0/Pk). The calculator’s maximum-efficiency figure uses 2P0 as the total loss at that point.
Sense check: a 1 MVA unit with 1.7 kW no-load and 10.5 kW load loss is about 99.05 % efficient at half load 0.9 pf and peaks at about 40 % load.
Watch out: efficiency alone hides the no-load loss of a lightly loaded unit, which runs 8760 hours a year.
Losses and efficiency of a transformer at any load fraction, and the load at which efficiency peaks (where load loss equals no-load loss).
Enter your values to see the result.
Good to know
No-load (iron) loss is constant whenever the transformer is energised; load (copper) loss varies with the square of current. Take P0 and Pk from the test certificate or the EU Ecodesign (Regulation 548/2014) tier values. Distribution transformers are designed to peak at 30–50 % load, which matches their typical average loading.
Common mistake
Scaling load loss linearly with load rather than with load squared, or using the input instead of output power in the efficiency.
Limits
Uses rated-voltage no-load loss and load loss at reference temperature (75 °C); real load loss also varies with winding temperature and harmonics (IEC 60076-7 for loading, IEC TS 60076-20 for efficiency indices).
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.