Insulation resistance calculator: temperature correction, PI and DAR

What this calculator does

It takes megohmmeter readings and machine data and applies the IEEE Std 43-2000 recommended practice for windings of rotating machines rated 750 W (1 hp) or more: synchronous machines, induction machines, DC machines and synchronous condensers. It returns:

• the 1-minute resistance corrected to 40 °C (and, if selected, to 20 °C for comparison with older records);
• the polarization index and its minimum for the thermal class of the insulation;
• the DAR and the 5 min / 1 min ratio as indicative figures;
• the minimum resistance for the winding type and the test connection;
• the overall verdict of the standard — fit or not for service or for an overvoltage test — taking the machine rating into account;
• the test voltage recommended by the standard and the minimum grounding time after the test;
• warnings when the measurement is made under conditions in which the standard cautions that the result may be misleading: winding below the dew point, temperature far from 40 °C, hot winding, test voltage outside the recommended range, or an abnormally high PI on old insulation.

The calculation runs in your browser; no reading is sent to any server.

The four currents in an insulation test

When a DC voltage is applied to the winding, the total current measured by the megohmmeter is the sum of four:

• Geometric capacitive current. Large at first and gone within seconds; by the 1-minute reading it no longer counts.
• Absorption current (polarization). It decays over time following a power law and, in clean, dry insulation, dominates from 30 seconds through the first few minutes.
• Conduction current. Constant. Practically zero in well-cured modern epoxy-mica or polyester insulation unless it is saturated with moisture; higher in older asphaltic mica or shellac insulation.
• Surface leakage current. Constant. It is caused by moisture, dust, oil or carbon on the surface of the end windings.

A clean, dry winding lets the absorption current die away, and the measured resistance climbs with time. A dirty or wet one is dominated by the constant currents and the reading barely moves. This is the basis of the polarization index.

The temperature correction

Insulation resistance varies inversely and exponentially with temperature. IEEE 43-2000 recommends correcting all readings to a common base of 40 °C:

R(40 °C) = Kt × R(T)

If the actual behavior of the insulation is unknown, the standard allows Kt to be approximated by assuming the resistance halves for every 10 °C:

Kt = 0.5^((40 − T) / 10)

T is the winding temperature, not the air temperature. The standard itself warns of three limitations, which the calculator turns into warnings:

• It is an approximation. The 10 °C rule comes from tests carried out in the 1950s; later measurements have found halving intervals between 5 and 20 °C. That is why the interval is an editable input. When the test is made far from 40 °C, the error multiplies; the correct approach is to obtain the winding’s own curve by measuring at several temperatures above the dew point and extrapolating on a semi-logarithmic scale.
• It is not valid below the dew point. If the winding is colder than the dew point of the air, moisture condenses on its surface and the correction introduces an unacceptable error for trend analysis. Machines coming out of service should be tested before they cool below the dew point.
• There is no humidity correction. There is no reliable method for converting a reading taken at one humidity to the value that would be obtained at another.

The 20 °C option is kept because many transformer and cable records are referred to that temperature, but the minimums in the standard are always compared with the 40 °C value.

Polarization index

PI = R(10 min) / R(1 min)

It does not need temperature correction, because the machine temperature hardly changes in ten minutes. The exception is a hot winding: if it cools during the test, the resistance rises and the PI comes out artificially high. That is why, if the winding is above 40 °C — and particularly if it gives a low PI above 60 °C — the standard recommends repeating the measurement at 40 °C or below, always above the dew point.

Two cases in which PI does not decide:

• Field windings with exposed copper, such as those on many turbine generator rotors: the very large area of uninsulated copper has no absorption current and the resistance barely changes between 1 and 10 minutes. PI is not applicable. If the field winding is encapsulated in insulation, it is applicable, with the minimum for its thermal class.
• 1-minute resistance above 5000 MΩ at 40 °C. The total current is in the sub-microampere range, and small variations in the supply voltage, humidity or connections weigh more than the insulation. The standard allows PI to be disregarded.

Conversely, a very high PI (above 8) on an old winding of varnished cambric, shellac or asphaltic mica may indicate thermally aged, dry and brittle insulation. If this is confirmed by touch, the standard advises against cleaning or testing it: it may fail at any moment when returned to service.

DAR and other short variants

In modern insulation the absorption current dies away within two or three minutes, so shorter ratios are used that shorten both the test and the subsequent grounding time:

• DAR = R(1 min) / R(30 s)
• R(5 min) / R(1 min)

Annex A of IEEE 43-2000 describes them, but makes clear that there is no agreement on which intervals to use and no agreed acceptance criterion like the one for the classic PI. The calculator shows them; the DAR thresholds (1.25 and 1.6) are the usual industry values and are labeled as such. Their real value lies in trending the same machine from test to test.

Minimum 1-minute resistance

The 1-minute resistance of the whole winding, corrected to 40 °C, is compared with:

kV is the rated terminal-to-terminal voltage of the machine, in kV rms. If one phase is tested with the other two grounded, the minimum is roughly doubled; if the other two phases are connected to the guard, tripled. Some special designs or materials allow lower values: for these, comparison with their own history prevails.

Fit or not fit: the combined criterion

• Up to 10 000 kVA: it is enough for the PI or the 1-minute resistance at 40 °C to exceed its minimum.
• Above 10 000 kVA: both must exceed it.

If PI is not applicable or not meaningful, the decision is made on the resistance alone. A result below the minimums does not mean the machine cannot run, but the standard does not recommend it and calls for the cause to be investigated using the winding history, visual inspection and other tests. If the cause is dirt or moisture, cleaning and drying usually restore it, and PI indicates when drying can be considered complete. If the cause is serious deterioration of or damage to the insulation, neither service nor an overvoltage test is recommended.

Test voltage and grounding

The rated voltage is the line-to-line voltage for three-phase AC machines, the line-to-ground voltage for single-phase machines and the rated DC voltage for DC machines and field windings. Too high a test voltage can overstress the insulation, especially on small low-voltage machines or with a wet winding. The standard prefers negative polarity, because of electroendosmosis in old wet windings.

Before measuring, the winding must be fully discharged. Afterwards, it must remain grounded for at least four times as long as the voltage was applied: 4 minutes after a 1-minute reading and 40 minutes after a 10-minute PI. Until then, the test is not over.

Worked examples

6.6 kV, 3500 kVA motor, form-wound coils from 1998, class F, whole-winding test. With the winding at 25 °C and the dew point at 12 °C, the readings are 2.4 GΩ at 1 minute and 6.0 GΩ at 10 minutes.

• Kt = 0.5^((40 − 25)/10) = 0.5^1.5 = 0.354
• R(40 °C) = 2400 MΩ × 0.354 = 848.5 MΩ, above the 100 MΩ minimum
• PI = 6000 / 2400 = 2.5, above the class F minimum of 2.0
• Recommended test voltage: 2500 – 5000 V. Grounding afterwards: 40 minutes.
• Fit. The uncorrected reading, 2.4 GΩ, would have looked almost three times better than it really is.

The same machine, testing one phase with the other two grounded, gives 1.1 GΩ at 1 minute and 1.9 GΩ at 10 minutes at 25 °C. R(40 °C) = 389 MΩ against a minimum of 2 × 100 = 200 MΩ: it passes. The PI is 1.7, below 2.0. Since the machine does not exceed 10 000 kVA, one of the two criteria is enough and the result is fit, but the low PI deserves monitoring. On a turbine generator above 10 000 kVA, the same PI would make it not fit.

What this calculator does not do

It does not replace the judgment of whoever performs the test. Insulation resistance is not directly related to dielectric strength: unless there is a concentrated defect, it does not indicate at what voltage the winding will fail. A single measurement does not distinguish between localized and widespread contamination; very large, slow-speed machines or machines with commutators can give low values without being in poor condition, and for these the trend in the records is what counts. The DC test does not detect internal voids caused by poor impregnation, thermal deterioration or thermal cycling in form-wound coils — that is what AC tests, power factor, tan δ and partial discharge testing are for — nor problems that only appear with the machine running, such as loose coils or end-winding vibration.

In directly water-cooled windings, the circuit must be drained and dried before measuring, unless the manufacturer specifies another procedure; if it is not drained, the water conductivity must be very low, and the winding manufacturer’s manual gives the permissible value.

What measures it

The measurement is made with an insulation resistance tester able to hold the test voltage steady throughout the ten minutes of the PI — supply variations translate directly into variations in the reading — and to record the curve at the usual intervals (15 s, 30 s, 45 s, 1 min, 1.5 min, 2 min… 10 min). For AC diagnostics, partial discharge detectors cover what the DC test cannot see.