Transformers
Transformer voltage regulation at a given load
- where
- resistance voltage at the load (%)
- load as a fraction of rating
- load loss at rated current (kW)
- rated power (kVA)
- reactance voltage at the load (%)
- impedance voltage (%)
- voltage regulation (%)
- load power-factor angle (negative sin φ if leading)
Explain this equation
Gives the fall in secondary voltage from no load to a stated load and power factor. Use it to choose tap positions and to check the voltage delivered at the far end of a feeder.
εr is the resistive part of the transformer impedance, found from the load loss; εx is the reactive part, found from uk and εr. Both scale with the load fraction n. cos φ and sin φ resolve them against the load current.
The first two terms are the in-phase drop across R and X, as in a cable volt-drop. The squared term divided by 200 is the second-order correction for the quadrature drop, which lengthens the phasor slightly; 200 comes from expanding the square root with percentages rather than per-unit.
Sense check: a 5 % impedance, 1 % resistance transformer regulates by about 3.8 % at full load 0.8 pf lagging, only about 1 % at unity pf, and the voltage rises at 0.8 leading.
Watch out: uk is not the regulation. At unity power factor the drop is close to εr, which is much smaller.
Fall in secondary voltage from no load to a specified load and power factor, from the nameplate impedance and load loss.
Enter your values to see the result.
Good to know
εr is the load loss as a percentage of rating; εx follows from uk. Both scale with the load fraction. A negative result means the voltage rises under load (leading power factor). Typical distribution transformers (uk 4.75–6 %) regulate by 3–5 % at full load, 0.8 pf.
Common mistake
Treating uk as the regulation. At unity power factor the drop is roughly εr, much smaller than uk; at low lagging power factor it approaches uk.
Limits
The classical two-term series formula (J&P Appendix 4, IEC 60076-8 clause 7); the fourth-order term is neglected, which is negligible for uk below about 20 %. Two-winding transformer, principal tapping, constant-impedance load.
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.