Insulation Resistance Degradation Calculator
Estimate insulation resistance degradation over time using the Arrhenius thermal aging model and calculate the Polarization Index (PI) and Dielectric Absorption Ratio (DAR).
Formulas Used
1. Arrhenius Acceleration Factor (AF):
AF = exp[ (Eₐ / k) × (1/T_ref − 1/T) ]
- Eₐ = Activation energy (eV)
- k = Boltzmann constant = 8.617 × 10⁻⁵ eV/K
- T, T_ref = Temperatures in Kelvin (°C + 273.15)
2. Degraded Resistance after time t:
R(t) = R₀ × exp[ −(t / 8760) × ln(AF) ]
- R₀ = Initial insulation resistance (MΩ)
- t = Aging time (hours); 8760 h = 1 year normalization
- When AF > 1 (T > T_ref), resistance degrades faster
3. Polarization Index (PI):
PI = R(10 min) / R(1 min)
4. Dielectric Absorption Ratio (DAR):
DAR = R(1 min) / R(30 s)
Assumptions & References
- The Arrhenius model assumes a single dominant thermal degradation mechanism with constant activation energy.
- Degradation model uses annual normalization (8760 h/year); suitable for steady-state thermal aging estimates.
- Typical activation energies: XLPE ~0.7–1.0 eV, EPR ~0.8–1.1 eV, PVC ~0.5–0.8 eV, varnished windings ~0.9–1.2 eV.
- PI and DAR measurements must be taken at the same temperature for valid comparison (IEEE 43 recommends correcting to 40°C).
- Minimum acceptable insulation resistance per IEEE 43-2013: R_min (MΩ) = kV_rated + 1 for rotating machines.
- IEEE Std 43-2013: Recommended Practice for Testing Insulation Resistance of Electric Machinery.
- IEC 60085: Thermal evaluation and designation of electrical insulation.
- IEEE Std 930-2004: Guide for Statistical Analysis of Electrical Insulation Breakdown Data.
- Results are estimates only. Field measurements, temperature correction, and professional assessment are required for maintenance decisions.