Power transformer test calculator to IEC 60076-1
For power transformers: load loss and impedance at 75 °C, voltage drop, no-load, Table 1 tolerances, V/Hz overfluxing, tappings, zero-sequence impedance, vector group and cold measurement.
Routine tests on power transformers to IEC 60076-1
Nine calculations from a power transformer test report: losses and impedance at reference temperature, voltage drop, no-load, tolerances, overfluxing, tappings, zero-sequence impedance, vector group and cold-resistance temperature. Pick a tab.
This calculator is for power transformers (IEC 60076-1). It does not apply to motors or other rotating machines, which are covered by IEC 60034-1.
Result
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 together, in nine tabs, the calculations that come up when preparing or reviewing the routine test report of a power transformer to IEC 60076-1:2011. It is not a tool for motors or instrument transformers: everything here comes from the power transformer standard, and where a calculation relies on another part of the IEC 60076 series, that is stated.
To correct winding resistance to reference temperature and check phase imbalance, use the winding resistance calculator.
1. Load loss and impedance at reference temperature
Reference temperature (11.1). For liquid-immersed transformers with an average winding temperature rise up to 65 K (ON or OF) or 70 K (OD), it is 75 °C. If the purchaser requests it, or for other rises, it is the rated average winding rise plus 20 °C, or plus the yearly average cooling medium temperature, whichever is higher. For dry-type units it is set by IEC 60076-11.
Correction (11.4 and Annex E). The loss measured at test current I is brought to rated current by multiplying by (Ir/I)². The standard requires the test current to be at least 50 % of rated. The loss is then split in two:
- Ohmic loss: I²R with the cold resistances R1 (measured at θ₁) brought to the test temperature θ₂: R2 = R1·(235 + θ₂)/(235 + θ₁).
- Additional losses: Pa2 = P2 − ΣI²R₂.
At reference temperature the ohmic part rises and the additional part falls:
Pr = ΣI²R₁·(235 + θr)/(235 + θ₁) + Pa2·(235 + θ₂)/(235 + θr)
with 225 instead of 235 for aluminium. On three-phase units, with resistance measured between line terminals and line current, each winding’s I²R loss is 1.5·I²·R, whether star or delta.
Impedance (3.7.1). The impedance is treated as a reactance in series with a resistance. The reactance is taken as constant, and only the resistive part, derived from the losses, is corrected: ur = Pr/Sr, ux = √(uk² − ur²) at test temperature, and uk(θr) = √(ux² + ur(θr)²). The reference impedance is Zref = U²/Sr.
Worked example
A 40 MVA, 132/20 kV, YNd11 transformer with copper windings. Rated currents are 174.95 A on HV and 1154.7 A on LV. Cold, at 20 °C, the readings are 1.2 Ω between HV terminals and 25 mΩ between LV terminals.
- ΣI²R₁ = 1.5·174.95²·1.2 + 1.5·1154.7²·0.025 = 105.10 kW at 20 °C
- Short-circuit test at 100 A (57 % of rated) and 22 °C: 50 kW measured → P2 = 50·(174.95/100)² = 153.05 kW
- ΣI²R₂ = 105.10·257/255 = 105.92 kW → Pa2 = 47.12 kW
- At 75 °C: ΣI²R = 105.10·310/255 = 127.76 kW; Pa = 47.12·257/310 = 39.07 kW → Pr = 166.83 kW
- With 7.0 kV short-circuit voltage at 100 A: uk = 9.278 % at 22 °C; ur(75 °C) = 0.417 %; ux = 9.270 % → uk(75 °C) = 9.279 %
2. Voltage drop
IEC 60076-1 defines voltage drop or rise in 3.7.2. The working formula is from IEC 60076-8, with load n as a fraction of rated:
- u′ = n·(ur·cos φ + ux·sin φ)
- u″ = n·(ux·cos φ − ur·sin φ)
- u = u′ + u″²/200 + u″⁴/(8·10⁶), in % of no-load voltage
With a capacitive load the sine is negative and the result can be negative: the voltage rises. With ur = 0.42 %, ux = 9.27 %, full load and cos φ = 0.8 lagging, the drop is 6.2 %.
3. No-load loss and current
The test voltage is set with a mean-value voltmeter (U′) while an RMS voltmeter (U) is read alongside. If they agree within 3 %, the waveform is acceptable. The measured loss is corrected as follows (11.5):
P0 = Pm·(1 + d), with d = (U′ − U)/U′, usually negative.
No-load losses are not temperature-corrected. The no-load current is the mean of the three phases.
4. Tolerances (Table 1)
| Quantity | Tolerance |
|---|---|
| Total losses | +10 % |
| Each component (no-load, load) | +15 %, provided the total tolerance is not exceeded |
| No-load ratio, principal tapping, first pair | the lower of ±0.5 % and ±1/10 of the actual impedance in % |
| Ratio on other tappings and pairs | ±0.5 % of the design value |
| Impedance, two windings, principal tapping | ±7.5 % if ≥ 10 %; ±10 % if < 10 % |
| Impedance, two windings, other tapping | ±10 % if ≥ 10 %; ±15 % if < 10 % |
| Impedance, auto-connected or second pair | ±10 % |
| No-load current | +30 % of the design value |
An example of the ratio rule: with an actual impedance of 4 %, the ratio tolerance on the principal tapping is not ±0.5 % but ±0.4 %.
5. V/Hz overfluxing
A transformer must run continuously with voltage/frequency up to 5 % above rated at full load, and up to 10 % at no load. For a load K = I/Ir between 0 and 1 (5.4.3):
(U/Ur)·(fr/f)·100 ≤ 110 − 5K²
A 132 kV transformer at 80 % load and 49.8 Hz can take up to 140.4 kV.
6. Tappings
The tapping factor is the tapping voltage of the tapped winding divided by its rated voltage. The range is written +a %, −b %. With constant flux voltage variation (CFVV), the untapped winding voltage stays the same and the tapped winding voltage is proportional to the factor. With variable flux (VFVV) it is the other way round (6.2). The tapping ratio is the rated ratio multiplied by the factor if the tappings are on HV, or divided by it if they are on LV. The calculator gives the full table with tapping currents, assuming full-power tappings, and compares a measured ratio with the design ratio (±0.5 %).
7. Zero-sequence impedance
It is measured at rated frequency between the joined line terminals of a star or zigzag winding and its neutral (11.6). In ohms per phase:
Z0 = 3U/I
On a star-star transformer without a delta winding, the applied voltage must not exceed the service phase-to-neutral voltage. On Yd units it is measured from the star side only.
8. Vector group
The capital letter is the HV connection (Y, D, Z, with N if the neutral is brought out), the lower-case letter is the LV connection, and the number is the clock number: the LV lag behind HV in steps of 30°. Dyn11 is delta on HV, star with neutral on LV and 330° lag, which is 30° lead. Yy, Dd, Dz and Zz only take even clock numbers; Yd, Dy, Yz and Zy take odd ones. For paralleling, the calculator says whether the same clock number is enough, whether terminals must be reassigned, or whether two phases must be swapped (Dyn1 with Dyn11).
9. Cold-measurement temperature
On liquid-immersed units, after at least 3 h without excitation, the winding temperature is the mean of the top and bottom liquid temperatures. For the temperature-rise test, that difference must not exceed 5 K (11.2.3). On dry-type units, the cooling medium must not have changed by more than 3 °C in 3 h, and the winding sensors must be within 2 °C of it (11.2.2).
What this calculator does not do
It does not apply to motors, generators or instrument transformers. It does not cover dielectric tests (IEC 60076-3), temperature rise (IEC 60076-2), short-circuit withstand (IEC 60076-5) or sound level (IEC 60076-10). It does not allocate losses and impedances among the windings of a three-winding transformer: that is done per IEC 60076-8. And it does not replace the manufacturer’s test report: the result is indicative and must be validated by a competent engineer.
What it is measured with
Winding resistance and turns ratio are measured with transformer test equipment: winding ohmmeters, turns ratio testers (TTR) and combined instruments that take both measurements with a single connection.
Frequently asked questions
- How is transformer load loss corrected to 75 °C?
- As in Annex E of IEC 60076-1. First the measured loss is scaled by the square of rated current over test current. Then the ohmic I²R part, calculated from the cold resistances brought to the test temperature, is separated from the additional losses. The I²R part is taken to 75 °C by multiplying by (235 + 75)/(235 + θ), and the additional losses by dividing by the same factor, because they fall as temperature rises. For aluminium the constant is 225.
- What tolerances does IEC 60076-1 allow on losses, ratio and impedance?
- Table 1: total losses +10 %, and each component +15 % provided the total tolerance is not exceeded. Voltage ratio on the principal tapping: the lower of ±0.5 % and ±1/10 of the actual impedance. Short-circuit impedance on the principal tapping of a two-winding transformer: ±7.5 % if 10 % or more, ±10 % if below 10 %. No-load current: +30 % of the design value.
- Can this calculator be used for motors?
- No. It is built for power transformers to IEC 60076-1. Motors and other rotating machines have their own standard, IEC 60034-1, with different tests, tolerances and temperature-rise method.