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IEC 60287-1-1 / -2-111 min read

Worked Example: First-Principles Thermal Rating of a 132 kV Single-Core Cable

Instead of looking up a table value, this calculator solves the IEC 60287 thermal circuit directly — the same method behind CIGRE's own published verification cases.

Scenario

System voltage132 kV
ConductorCopper, 30.3 mm diameter, R₀ = 0.0283 Ω/km at 20°C
InsulationXLPE, 15.5 mm thick, max conductor temp 90°C
SheathAluminium, solid bonded
InstallationBuried in duct, 1000 mm depth, soil resistivity 1.0 K·m/W
Ambient (soil)20°C
Reference caseCIGRE Technical Brochure 880, Case #0-1

Step-by-step calculation

Step 1: Build the cable's thermal-resistance network

IEC 60287 models heat flow from conductor to ambient as a series of thermal resistances: T1 (conductor to sheath, through the insulation), T3 (sheath to any armour/serving) and T4 (cable surface to ambient, through the soil).

Thermal resistanceValue
T1 — conductor to sheath0.420 K·m/W
T3 — sheath to surface (duct-corrected)0.087 K·m/W
T4 — surface to ambient (soil)1.595 K·m/W

Step 2: Account for sheath circulating-current loss (solid bonding)

With both sheath ends solidly bonded, circulating currents flow in the sheath and add loss on top of the conductor's own I²R loss — captured by the sheath loss factor lambda1.

Step 3: Solve the rating equation iteratively

The conductor's own resistance rises with its temperature, which is exactly what the rating current is trying to find — so IEC 60287's rating equation is solved iteratively: guess a temperature, compute current, recompute temperature, repeat until it converges.

Step 4: Read off the rating current and sheath temperature

QuantityResult
Conductor temperature90.0°C (at the stated maximum)
Sheath temperature78.7°C
Continuous current rating821.8 A

Result summary

CheckRequirementActualStatus
Conductor temperature at rated current= 90°C (design maximum)90.0°C✓ PASS
Continuous current ratingn/a (this is the computed result)821.8 A✓ PASS
This 132 kV single-core cable, buried in duct under the stated soil conditions, has a continuous current rating of 821.8 A — found by solving the full IEC 60287 thermal circuit rather than reading a generic table, and matching CIGRE TB880's own published verification case for this exact configuration.

Key insight: Unlike LV/MV cable tables (which pre-compute ratings for a fixed set of standard configurations), MV/HV single-core cable ratings are genuinely project-specific — burial depth, soil resistivity, bonding method and sheath material all change the answer meaningfully, which is why IEC 60287 solves the thermal circuit from first principles rather than publishing one universal table the way IEC 60364-5-52 does for LV cables.

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Frequently asked questions

Why does solid bonding matter so much?

Solid bonding (both sheath ends earthed) allows circulating current to flow in the sheath whenever the conductor carries current, adding real I²R loss (captured here as lambda1 = 0.294, roughly 29% extra heat on top of the conductor's own loss). Single-point bonding eliminates this circulating current at the cost of needing sheath voltage limiters and different fault-current withstand considerations — the choice is a real engineering trade-off, not just a wiring preference.

Why does the rating change so much with burial depth and soil resistivity?

T4 (surface-to-ambient thermal resistance) is the dominant term in this example (1.595 K·m/W, more than 3x T1 and T3 combined) precisely because soil is a much worse heat conductor than the cable's own insulation — deeper burial or drier/higher-resistivity soil both increase T4 and directly reduce the current the cable can carry before exceeding 90°C.

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