## Derating Factors - cables grouped in air

Part 2-2 of the IEC 60287 "Calculation of current rating" standard, gives various approaches to obtaining reduction (derating) factors for cables in free air and protected from solar radiation. These are principally designed for multicore cables or single core cables in trefoil but can be extended to other arrangements.

### Symbols

D_{e} |
external diameter of multicore cable or one single core in trefoil | mm | ||

e | clearance between adjacent cables in a group (between surfaces) | mm | ||

F_{g} |
group reduction factor | |||

h | heat dissipation coefficient, calculation of thermal resistance | W.m^{-2}.K^{-5/4} |
||

h_{g} |
heat dissipation coefficient of the hottest cable or circuit in a group | W.m^{-2}.K^{-5/4} |
||

h_{i} |
heat dissipation coefficient of isolated cable or circuit | W.m^{-2}.K^{-5/4} |
||

I_{g} |
rating of the hottest cable in a group | A | ||

I_{t} |
rating of one cable or circuit assumed isolated | A | ||

k_{1} |
surface temperature rise factor | |||

T_{4g} |
external thermal resistance of the hottest cable in a group | K.m.w^{-1} |
||

T_{4i} |
external thermal resistance of one cable assumed to be isolated when carrying I_{t} |
K.m.w^{-1} |
||

W |
power loss from isolated cable or circuit in trefoil, carrying I_{t} |
W.m^{-1} |
||

Θ_{c} |
conductor temperature used for calculating I_{t} |
°C | ||

Θ_{a} |
ambient temperature used for calculating I_{t} |
°C |

### Reduction factors for cables with existing ratings

Where the sustained current for an isolated cable or circuit is known, the rating of the cable installed within a group of similar cables is given by:

${I}_{g}={F}_{g}{I}_{t}$

The reduction (derating) factor *F _{g}* for the group is calculated from:

${F}_{g}=\sqrt{\frac{1}{1-{k}_{1}+{k}_{1}\left({\displaystyle \raisebox{1ex}{${T}_{4g}$}\!\left/ \!\raisebox{-1ex}{${T}_{4i}$}\right.}\right)}}$

where the surface temperature rise *k _{1}* is provided by:

${k}_{1}=\frac{W{T}_{4i}}{{\theta}_{c}-{\theta}_{a}}$

and the term (*T _{4g}*/

*T*) is derived iteratively from the ratio (

_{4i}*hi*/

*h*) by:

_{g}${\left(\raisebox{1ex}{${T}_{4g}$}\!\left/ \!\raisebox{-1ex}{${T}_{4i}$}\right.\right)}_{n+1}=\left(\raisebox{1ex}{${h}_{i}$}\!\left/ \!\raisebox{-1ex}{${h}_{g}$}\right.\right){\frac{1-{k}_{1}}{\left({\displaystyle \raisebox{1ex}{${T}_{4g}$}\!\left/ \!\raisebox{-1ex}{${T}_{4i}$}\right.}\right)}+{k}_{1}}^{0.25}$

starting with ${\left(\raisebox{1ex}{${T}_{4g}$}\!\left/ \!\raisebox{-1ex}{${T}_{4i}$}\right.\right)}_{n+1}=\left(\raisebox{1ex}{${h}_{i}$}\!\left/ \!\raisebox{-1ex}{${h}_{g}$}\right.\right)$

with values for (*h _{i}*/

*h*) are given in the data section below.

_{g}### Reduction factor for IEC 60287 calculated ratings

When using IEC 60287 itself to calculate the sustained current ratings of cables, part 2-2.1 gives methods for the calculation of thermal resistance. To apply group derating for cables, the heat emission coefficient *h* is substituted by the group heat emission coefficient *h _{g}*, with

*h*being given by:

_{g}${h}_{g}=\frac{h}{\left({\displaystyle \raisebox{1ex}{${h}_{i}$}\!\left/ \!\raisebox{-1ex}{${h}_{g}$}\right.}\right)}$

and values for (*h _{i}*/

*h*) as provided in the data section below.

_{g}### Clearance values to avid a reduction in rating

Data for calculating reduction coefficients (below) give the necessary conditions which need to be achieved to avoid the need to apply any group derating.

### Data for calculating reduction coefficients

Image reproduced from IEC 60287-2-2, Table 1

Where cables are arranged in both the horizontal and vertical planes, the sustained current capacity shall be derived using values of *h _{i}*/

*h*for the vertical plane.

_{g}