The application estimates conductor ampacity using the Neher‑McGrath method. This approach was introduced in the 1957 paper The Calculation of the Temperature Rise and Load Carrying Capability of Cable Systems by J. H. Neher and M. H. McGrath. It forms the basis of ampacity guidance in NEC 310‑15(C) and the calculation procedures detailed in IEEE Std 835.
Equation
The allowable current I in amperes is obtained from:
I = sqrt( (T_c - (T_a + ΔT_d)) / ( R_dc × (1 + Y_c) × R_ca ) )where R_ca = R_cond + R_ins + R_duct + R_soil.
Variable Definitions
- T_c – maximum conductor temperature rating in °C.
- T_a – ambient temperature of the surrounding medium (earth or air) in °C.
- ΔT_d – dielectric loss temperature rise in °C.
- R_dc – dc resistance of the conductor at temperature
T_c(Ω/m). - Y_c – ac resistance correction factor for skin and proximity effects.
- R_cond – thermal resistance internal to the conductor.
- R_ins – thermal resistance of insulation.
- R_duct – thermal resistance of any raceway or duct.
- R_soil – thermal resistance of the surrounding soil. It is calculated using a cylindrical model:
R_soil = (ρ_m / (2π)) · ln(4·d / D)
where ρ_m = ρ / 100 converts resistivity from °C·cm/W to °C·m/W, d is the burial depth of the conduit in meters and D is the conduit diameter in meters.
These terms follow the notation of NEC 310‑15(C) and Clause 4 of IEEE Std 835.
AC Resistance Correction
The factor Y_c is derived from IEEE Std 835 Table 4. The implementation converts the conductor size to kcmil and linearly interpolates the table so that Y_c varies smoothly with cross‑sectional area.
The dielectric loss temperature rise ΔT_d follows IEEE Std 835 Table 9 with simple interpolation. Typical values are around 5 °C at 5 kV and 10 °C at 15 kV.
Soil Resistivity Ranges
Typical soil resistivity values per IEEE Std 835 Table 1:
- 40 °C·cm/W – very wet clay
- 60 °C·cm/W – moist clay or sand
- 90 °C·cm/W – average native soil
- 120 °C·cm/W – dry sand
- 150 °C·cm/W – dry sand and gravel
Calibration
The resistance constants were tuned so that calculated ampacities match IEEE 835 tables.
The library now exposes a calibrateAmpacityModel function which performs a grid search over reasonable model parameters. The routine compares the calculated ampacity of three common cables against their IEEE 835 free‑air ratings:
- 4/0 AWG Cu THHN (90 °C) – 260 A
- 500 kcmil Cu THHN (90 °C) – 430 A
- 250 kcmil Al THHN (75 °C) – 215 A
calibrateAmpacityModel adjusts the assumed insulation thermal conductivity, default duct resistance and the air thermal resistance until the maximum deviation from these reference values falls below ±10 %. Typical calibrated values are an air resistance near 3.4 °C·m/W and an insulation thermal conductivity of about 0.31 W/m·°C.
The original Neher‑McGrath paper provides additional discussion on how soil conditions influence ampacity.
IEEE 835 Underground Benchmarks
The automated test suite validates underground calculations using published values from IEEE Std 835. A key benchmark is a 500 kcmil Copper conductor with a 90 °C insulation rating installed 36 inches deep in average soil (90 °C·cm/W). IEEE 835 lists an ampacity of roughly 392 A for this configuration. The Neher‑McGrath implementation and the finite‑element solver are calibrated so that the predicted ampacity and resulting conductor temperature are within ±5 % of these values.
References
- NEC 310‑15(C) – National Electrical Code, 2023 edition.
- IEEE Std 835 – IEEE Standard Power Cable Ampacity Tables.
- J. H. Neher and M. H. McGrath, “The Calculation of the Temperature Rise and Load Carrying Capability of Cable Systems,” AIEE Transactions, 1957.