Winding resistance changes with temperature because the resistance of copper and aluminium conductors is temperature-dependent. To compare a site measurement with a factory baseline, the measured value must be corrected to the reference temperature used by the factory report, usually through a formula that uses a material constant specific to the conductor.
Temperature correction makes the comparison valid, but it cannot repair a measurement that was taken with poor connections, the wrong current or an incorrect temperature reading: correction is the last step of a valid measurement, not a substitute for one.
Why Winding Resistance Must Be Corrected to a Reference Temperature
A copper winding measured at 20 °C and the same winding measured at 70 °C give different resistance values even though the winding is identical, because the resistivity of the conductor rises with temperature. Over the range of winding temperatures seen in service, the difference is large enough to hide a real change or to create a false one. Factory reports state results at a reference temperature so that every unit is judged on the same basis, and a site measurement must be brought to that same reference before it is compared.
The reference temperature is usually defined by the governing standard or the transformer specification. Common practice for liquid-immersed transformers uses a reference such as 75 °C, while dry-type transformers may use a different reference, and the correct value is the one used in the report you are comparing against. When the factory report and the site procedure use different references, convert both to a common temperature instead of comparing unlike values.
Choosing the Reference Temperature and Material Constant
The correction formula uses a constant related to the conductor material. Common practice uses 234.5 for copper and 225 for aluminium, but the exact constant and reference temperature should be taken from the standard or manufacturer document that governs your comparison rather than assumed. Some specifications define a slightly different constant for alloys or for specific conductor grades, and using the wrong constant introduces an error that grows as the temperature difference grows.
Record the choices with the calculation: the measured resistance, the measured winding temperature, the reference temperature and the material constant. A corrected value without its inputs cannot be checked later, and the whole purpose of the correction is to produce a defensible comparison.
Applying the Correction Formula Correctly
The standard correction takes the measured resistance and scales it by the ratio of temperature terms. In words, the corrected resistance equals the measured resistance multiplied by the sum of the reference temperature and the material constant, divided by the sum of the measured temperature and the material constant. The measured temperature must be the winding temperature at the moment of measurement, not the ambient temperature, because the winding can be substantially warmer than the air around it after load or after other tests.
Worked examples remove the ambiguity. If a copper winding measures 1.200 Ω at 30 °C and the reference is 75 °C with a constant of 234.5, the corrected value is 1.200 × (75 + 234.5) / (30 + 234.5) = 1.200 × 309.5 / 264.5, which gives approximately 1.404 Ω. The same measurement corrected to a 20 °C reference gives 1.200 × (20 + 234.5) / (30 + 234.5), approximately 1.155 Ω. Presenting the arithmetic in the record makes the result reproducible and protects it from transcription errors.
What Correction Cannot Fix: Setup and Connection Errors
Temperature correction assumes the measurement itself is valid. A resistance reading taken through a poor connection includes the connection resistance, and no temperature formula can remove it. A reading taken before the current has stabilized includes the inductance transient of the winding and is not the true DC resistance. A winding temperature that was measured on the tank surface rather than estimated from the winding condition can be wrong by several degrees, which moves the corrected value by more than the tolerance of the comparison.
The correction also assumes the winding is at a uniform temperature, which is not always true after a transformer has been loaded or after other tests have heated part of the winding. When the temperature distribution is uncertain, the honest approach is to let the winding cool until the temperature is stable, record the uncertainty, or repeat the measurement rather than applying a formula to a temperature that was never known.
Comparing Corrected Values with Factory Baselines
Once the site value is corrected to the reference temperature, the comparison with the factory baseline becomes meaningful: the same winding, the same reference temperature, and only the transformer condition and the measurement uncertainty between the two values. Compare phase by phase and tap position by tap position, because a change in one phase or one tap position is more significant than a uniform shift across the whole unit. A uniform shift can be caused by a systematic difference in temperature estimation, while a single-phase change points to a condition in that winding or its connections.
The acceptable difference between site and factory values is defined by the governing specification, not by a universal rule. Report the corrected values and the comparison basis, and let the specification decide whether the difference is within tolerance. When the difference is outside tolerance, the next step is to verify the measurement conditions before concluding that the winding has changed.
A Worked Temperature-Correction Example
| Input | Value |
|---|---|
| Measured resistance | 1.200 Ω at 30 °C winding temperature |
| Material constant | 234.5 (copper, per the governing document) |
| Reference temperature | 75 °C |
| Calculation | 1.200 × (75 + 234.5) / (30 + 234.5) |
| Corrected result | ≈ 1.404 Ω at 75 °C |
| Comparison | Against factory baseline of the same phase at 75 °C |
Use the same template for every winding and every tap position so that the arithmetic is consistent and reviewable. The example is illustrative: the constant, reference and acceptable difference must come from the document that governs your transformer.
Practical temperature measurement is where corrections most often go wrong. The winding temperature is not the same as the top-oil temperature, the tank temperature or the ambient temperature, and on a transformer that has been recently loaded or tested, the winding can be significantly warmer than all of them. When the transformer has been de-energized and allowed to cool, the winding temperature approaches the average of the cooling medium, and many procedures estimate the winding temperature from the top-oil or the average oil temperature under those stabilized conditions. Record how the temperature was obtained, because a value estimated from oil temperature and a value measured by an embedded sensor are not the same evidence. If the cooling history is unknown, the honest options are to wait for stabilization, to repeat the measurement later, or to state the temperature uncertainty in the record rather than pretending the correction is exact.
After correction, compare the phases with each other as well as with the factory baseline. A uniform difference across all three phases can indicate a systematic temperature estimation error, while a difference concentrated in one phase points to that winding or its connections. The phase comparison is also the fastest check of the correction itself: if two phases measured at different temperatures correct to values that disagree with the factory pattern, revisit the temperature inputs before suspecting the transformer.
Frequently Asked Questions
What reference temperature should I use?
Use the reference temperature defined by the governing standard or the factory report you are comparing against. Common practice for liquid-immersed transformers uses 75 °C, but the correct reference is the one used in the document that governs your comparison, not a universal value.
Why is the material constant different for copper and aluminium?
The constant represents the temperature behaviour of the conductor material. Common practice uses approximately 234.5 for copper and 225 for aluminium, but the exact value should be taken from the governing standard or manufacturer document, because the correction error grows as the temperature difference grows.
When is temperature correction not needed?
Correction is unnecessary when both measurements were taken at the same winding temperature, or when the comparison is between phases measured within minutes of each other at the same temperature. It is required whenever a result is compared with a baseline recorded at a different temperature.
For the instruments used in these measurements, see the winding test equipment range, and for the wider test programme read What Tests Are Required for a Power Transformer.