Winding resistance calculator: correction to 75 °C and phase imbalance
Correct a measured winding resistance to 75 °C, 85 °C or 20 °C and calculate the imbalance between the three phases.
Correction to reference temperature and phase imbalance
Enter the resistances measured on the three phases and the winding temperature. The tool corrects them to the reference temperature and calculates the imbalance between phases, which is what reveals a loose connection, a shorted turn or a dirty tap-changer contact.
Result
R(Tref) = R(T) × (Tref + k)/(T + k), with k = 234.5 for copper and 225 for aluminium.
Indicative result. The calculation runs in your browser and is not sent to any server. This website may contain errors or omissions: before making any decision about an installation, the information must be checked and validated by a qualified engineer. Legal notice and terms of use
What this calculator does
It brings the resistances measured on the three phases to the reference temperature and works out how far apart they are. Those two numbers are what actually gets interpreted: the first allows comparison against the factory test report and the history, the second reveals a problem even when no earlier figure exists.
The temperature correction
The resistivity of metals grows almost linearly with temperature over a transformer’s working range, and the relation is written as
R(Tref) = R(T) × (Tref + k) / (T + k)
where k = 234.5 for copper and k = 225 for aluminium, temperatures in degrees Celsius. The constant is the reciprocal of the material’s temperature coefficient at 0 °C, and it is the one given in IEC 60076-1 and IEEE C57.12.90.
The temperature to enter is that of the winding, not of the oil or of the room. On a transformer that has been de-energised long enough — several hours off load is the usual requirement — the mean oil temperature is accepted as a good estimate. If the unit has just come off service the measurement is worthless: the winding is hotter than the oil and the correction falls short.
Phase imbalance
The three phases of a healthy winding give very similar resistances. The calculator takes the mean and finds the phase furthest from it, as a percentage.
- Below 2%: normal.
- Between 2% and 5%: repeat the measurement. The commonest cause is not a defect but a winding that is not yet thermally stable, or a test current that has not saturated the core for long enough.
- Above 5%: something is wrong. In order of frequency: a dirty or worn tap-changer contact, a loose connection at the bushings or on the link board, a poor joint between sections and — less often than feared — shorted turns.
On transformers with a tap changer it pays to measure every position: a failing contact can give correct resistances on the nominal tap and nonsense on two or three specific ones.
Worked example
20 MVA transformer, copper winding. With the oil at 31 °C the readings are 412.5 mΩ, 419.1 mΩ and 414.0 mΩ.
- Factor to 75 °C = (75 + 234.5) / (31 + 234.5) = 309.5 / 265.5 = 1.1657
- Corrected phases: 480.8 mΩ, 488.6 mΩ, 482.6 mΩ
- Mean: 484.0 mΩ. Maximum deviation: (488.6 − 484.0)/484.0 = 0.95%
Within the normal range. If the factory report gave 478 mΩ at 75 °C, the difference against the measured mean would be 1.3%: consistent with the overall uncertainty.
What this calculator does not do
It cannot correct for an unstabilised winding, which is the commonest source of deviation and the one that produces most false alarms. It does not replace comparison against the factory test report or the machine’s history. And it says nothing about a tap changer in motion: an OLTC’s dynamic signature is read from its current trace, not from three numbers.
What measures it
The measurement is made with a winding ohmmeter able to inject enough DC and to wait out the winding inductance before the reading settles. On circuit breakers and busbars the same quantity is measured with contact resistance micro-ohmmeters.
Frequently asked questions
- Why is winding resistance corrected to 75 °C?
- Because copper resistance rises by about 0.4% per degree. The factory figure in the transformer’s test report is referred to an agreed temperature — 75 °C is usual for power transformers — and a field measurement can only be compared against it once it has been brought to that same temperature.
- What phase imbalance is acceptable?
- The most widespread field criterion is that the deviation between phases should not exceed 2%. Between 2% and 5% it is worth repeating the measurement with the winding thermally stable before condemning anything, because an internal thermal gradient produces apparent imbalance. Above 5% the cause has to be found.
- Does this correction work for aluminium?
- Yes, with a different constant: 234.5 for copper and 225 for aluminium. The calculator asks because using the copper value on an aluminium winding introduces an error of around 1% in the correction.