Insulation Resistance Formulas: PI and DAR

Insulation resistance formulas: polarisation index, dielectric absorption ratio, correction to 40 °C, the kV plus 1 MΩ minimum and leakage current.

The formulas

IR is the insulation resistance in megohms from a megohmmeter at a stated test voltage, and t the winding temperature in °C. The resistance roughly halves for every 10 °C rise, so readings must be corrected to a common temperature before they are compared with each other or with earlier results. The kV plus 1 MΩ figure is the usual minimum for a rotating machine winding at 40 °C. The index values that count as acceptable depend on the insulation class and the standard, so use the limits of the one you work to. A single reading is less useful than a trend over the years.

Worked example: polarisation index and DAR

A winding reads 800 MΩ at 1 minute and 2,400 MΩ at 10 minutes, and 600 MΩ at 30 s.

1. PI = 2400 / 800 = 3
2. DAR = 800 / 600 = 1.333 (using 800 MΩ at 60 s)

Worked example: temperature correction

A reading of 500 MΩ at 20 °C.

1. IR40 = 500 × 0.5^((40 − 20) / 10) = 125 MΩ

Worked example: minimum and leakage current

1. An 11 kV winding needs at least 11 + 1 = 12 MΩ at 40 °C
2. At 5,000 V the leakage with 800 MΩ is 5,000 / 800 MΩ = 6.25 µA

Correction of a 500 MΩ reading taken at each temperature

Frequently asked questions

What does the polarisation index show?

It shows how the leakage current falls as the insulation polarises. Dry, clean insulation shows a rising resistance. A low index of about 1 points to moisture or dirt.

Why correct to 40 °C?

The resistance depends strongly on temperature. A common reference temperature makes a reading comparable with the previous ones and with the limit.

Which test voltage should I use?

Use the value in the standard or in the maker’s instructions, which depends on the rated voltage of the equipment. A test voltage that is too high can damage old or wet insulation.

Should I discharge the winding after the test?

Yes. The insulation stores charge, so ground the winding for as long as the test lasted, and follow the safety procedure for the equipment.

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