IEC 60287 — Cable Current Rating from the Thermal Model

IEC 60287 calculates the continuous current rating of a cable from first principles: the losses that heat the conductor, and the thermal resistances between the conductor and the surrounding medium. Where IEC 60364-5-52 reads a rating out of a table for a reference installation, IEC 60287 computes it for the installation you actually have.

IEC 60287-1-1:2006+AMD1:2014 · IEC 60287-2-1:2015 · IEC 60287-3-1:2017

What is IEC 60287?

IEC 60287 is the IEC series for calculating the current rating of cables at 100 % load factor. Part 1-1 gives the rating equations and the losses; Part 2-1 gives the thermal resistances; Part 3-1 covers reference operating conditions and the selection of cable type.

The physics is a steady-state heat balance: the conductor sits at its permitted temperature, the losses generate heat, and the heat must escape through the insulation, the sheath, the serving and the medium around the cable. The rating is the current at which that balance holds exactly.

When is IEC 60287 used rather than a table?

  • a trench as built — several circuits at real spacings and depths, not the two-cable reference arrangement of a table;
  • soil thermal resistivity that differs from the 2,5 K·m/W the buried tables assume, or a route where the soil changes;
  • duct banks and pipes, where the air gap and the duct wall add thermal resistance;
  • medium-voltage cables where dielectric loss and sheath loss matter, which the low-voltage tables ignore because at 1 kV they are negligible;
  • any case where an engineer has to justify a rating rather than cite a table row.

Clause 523.3 of IEC 60364-5-52 explicitly allows the current to be “determined by calculation” — and this is that calculation.

The rating equation (clause 1.4)

The permissible current follows from the temperature-rise expression of IEC 60287-1-1 clause 1.4.1.1, which balances the conductor temperature rise above ambient against the losses and the thermal resistances in their path.

Δθ = (I²R + ½Wd) · T1 + [I²R(1 + λ1) + Wd] · n · T2 + [I²R(1 + λ1 + λ2) + Wd] · n · (T3 + T4) IEC 60287-1-1, 1.4.1.1

Δθ conductor temperature rise above ambient (K) · I current in one conductor (A) · R a.c. resistance per unit length at maximum operating temperature · Wd dielectric loss per unit length · λ1, λ2 loss factors of sheath/screen and armour · n number of load-carrying conductors · T1…T4 thermal resistances of insulation, bedding, serving and the external medium.

Solving that for I gives the rating. Note where each loss enters: the dielectric loss appears with a factor of one half against T1, because it is generated throughout the insulation rather than at the conductor. Clause 1.4 also carries the instruction for partially dried-out soil: calculate both cases and use the lower rating.

The losses (clauses 2.1 to 2.4)

Loss calculations of IEC 60287-1-1 and the tables that support them.
QuantityClauseWhat it accounts for
A.C. resistance of the conductor R2.1 The d.c. resistance at operating temperature, raised by the skin effect (ys) and the proximity effect (yp). Table 1 holds the resistivities and temperature coefficients of the metals; Table 2 holds the experimental coefficients ks and kp.
Dielectric loss Wd2.2 Loss in the insulation, a.c. cables only, from the capacitance, the operating voltage and tan δ. Table 3 gives relative permittivity and loss factors for HV and MV insulations.
Sheath and screen loss factor λ12.3 Circulating and eddy-current losses in the metallic sheath or screen — strongly dependent on whether single-core cables are bonded at both ends and on the formation.
Armour loss factor λ22.4 Loss in armour, reinforcement and steel pipes, which is why a steel-wire-armoured single-core cable behaves quite differently from an unarmoured one.
Solar radiationTable 4 Absorption coefficient of the cable surface, for cables in direct sunlight.

Thermal resistances T1 to T4 (Part 2-1)

T1, T2 and T3 belong to the cable; T4 belongs to the installation. T4 is where the trench, the spacing, the depth, the soil and the neighbouring circuits enter the calculation — and it is usually the dominant term for a buried cable.

Thermal resistances of IEC 60287-2-1:2015, clause 4.
ResistanceClauseBetween
T14.1.2one conductor and the sheath
T24.1.3sheath and armour
T34.1.4the outer covering (serving)
T4 — free air4.2.1cable surface and ambient air
T4 — single buried cable4.2.2cable surface and the ground surface
T4 — groups of buried cables, not touching4.2.3with mutual heating between circuits
T4 — groups of buried cables, touching, equally loaded4.2.4
T4 — buried pipes, troughs, ducts4.2.5 to 4.2.7including the air space inside a duct

Part 2-1 clause 5 additionally gives the digital forms of quantities the older editions presented as graphs — the geometric factor G for belted cables among them — which is what makes the whole calculation programmable rather than a chart-reading exercise.

Input data the calculation needs

  • Cable construction: conductor material and cross-section, insulation type and thickness, screen or sheath material and dimensions, armour, oversheath — from the cable datasheet;
  • Permitted conductor temperature for the insulation, and the ambient temperature of the medium (air or ground) at the installation;
  • Installation geometry: laying depth, spacing between circuits, formation of single-core cables, duct dimensions and material;
  • Soil thermal resistivity, and whether partial drying-out has to be considered;
  • System data: voltage and frequency for the dielectric and sheath losses, and the bonding arrangement of the screens.

Construction dimensions are manufacturer data. A rating calculated on assumed dimensions is an estimate, and a tool should say which numbers came from a datasheet and which from a default — the ampacity calculator here prints both.

Calculation workflow

  1. Fix the permitted conductor temperature and the ambient temperature; Δθ is their difference.
  2. Compute the a.c. resistance R at that temperature, with skin and proximity effects (2.1).
  3. Compute the dielectric loss Wd (2.2) — negligible at low voltage, not at MV and above.
  4. Compute the loss factors λ1 and λ2 for the sheath and armour (2.3, 2.4), respecting the bonding arrangement.
  5. Compute T1, T2, T3 from the construction and T4 from the installation (Part 2-1, clause 4), including mutual heating for a group.
  6. Solve the clause 1.4 expression for I.
  7. For a buried route with possible drying-out, repeat for the dry condition and take the lower rating (clause 1.4).
  8. Check the result against the fault duty separately — a continuous rating says nothing about short-circuit withstand, which is IEC 60949 and the currents from IEC 60909.

IECCalc calculators for IEC 60287

Open the cable ampacity calculator →