This equation somewhat underestimates the equivalent diameter of sector-shaped conductors that are not solid.
An alternative approach for multi-core cables with sector-shaped conductors would be to set the equivalent diameter equal to the nominal diameter of a round conductor with the same cross-sectional area. This would still only be an approximation, since the exact degree of compaction of sector-shaped conductors can vary and depends on manufacture. Also, nominal diameters are not available for all cross-sectional areas of conductors and we extrapolated the missing values.
For sector-shaped conductors, CIGRE TB 880 Case study 10 recommends to use the smallest typical conductor diameter as given in IEC 60228 or analogue American standard for AWG/kcmil conductors.
$2\sqrt{\frac{A_c}{\pi}}$ | round conductors |
$2\sqrt{\frac{A_c}{\pi}}+t_i$ | sector-shaped conductors |
$\operatorname{min}\left(d_c\right)$ | sector-shaped conductors CIGRE TB 880 Case study 10 |