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TOPIC-03 · Engineering guide

Steady-State Cable Thermal Current Estimate

The estimate is the current whose I²R heat matches the entered temperature rise across one thermal resistance. For the base fixture, resistance at the maximum temperature is 0.0128 Ω/m and the current is sqrt(60 / (0.0128 × 0.5)).

Formula, variables and conditions

R(Tmax) = R_Ω/km × (1 + α × (Tmax − Tref)) / 1000
I = sqrt( (Tmax − Tambient) / (R(Tmax) × thermalResistance) )
Derating against a reference ambient is I(Tambient) / I(Treference).

Variables and units

  • R_Ω/km: AC resistance at the reference conductor temperature, in ohms per kilometre.
  • α: temperature coefficient per kelvin.
  • Tmax, Tref, Tambient, Treference: temperatures in °C. Ambient values must be below Tmax.
  • thermalResistance: kelvin-metres per watt, one lumped path, greater than 0.

Conditions

  • One conductor, continuous constant current, steady ambient, conductor heat only.
  • The resistance factor must stay positive.
  • Sources SRC-025, SRC-026 and SRC-027 are stored as review-required. Their pages are scope or context links. No IEC table is reproduced and the status is not promoted to verified.

Worked example

Base fixture from the BACKLOG-013 unit test.

Resistance
10 Ω/km at 20 °C
α / thermal resistance
0.004 /K and 0.5 K·m/W
Temperatures
Tmax 90 °C, ambient 30 °C, reference ambient 20 °C
R at 90 °C
0.0128 Ω/m
Current at 30 °C
sqrt(60 / (0.0128 × 0.5)) A
Reference current and ratio
sqrt(70 / (0.0128 × 0.5)) A, derating sqrt(60 / 70)

Hotter ambient lowers the current. The unit test also locks a second illustrative point at 542.304878105656 A when resistance is 0.2 Ω/km, α is 0.00393 /K and thermal resistance is 0.8 K·m/W, with the same 90/30/20 °C temperatures. Neither number is a catalogue rating.

Boundaries and common mistakes

Boundaries

  • Standards compliance, cable construction, installation method and protection are marked not-evaluated.
  • The warning on the calculation record says this is not a safe, approved or guaranteed conductor rating.
  • Voltage drop is a separate model. A thermal-current result does not imply a voltage-drop pass.

Common mistakes

  • Forgetting to convert Ω/km to Ω/m. The divisor is 1000.
  • Using the reference-temperature resistance inside the square root without the α correction.
  • Publishing the result as an IEC 60287 ampacity. The stored IEC links were not used as copied tables.

Sources