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Geometric mean radius of conductor

The formula for round conductors was taken from the book 'Electric Power Generation, Transmission, and Distribution' by Leonard L. Grigsby (2006), chapter 14.1.2.3.

The formula for shaped conductors was taken from the paper 'Series impedance of distribution cables with sector-shaped conductors' by Andrew J. Urquhart (2015)

Symbol
$GMR_c$
Unit
m
Formulae
$K_{GMR} r_{z1}$round conductors
$e^{-\left(\frac{1}{4}\right)} \sqrt{\frac{A_c}{\pi}} \frac{1}{1000}$sector-shaped conductors
Related
$A_c$
Cross-sectional area of conductor [mm$^2$]
$K_{GMR}$
Geometric mean radius factor
$\pi$
Archimedes' constant $\pi$
$r_{z1}$
Radius of conductor [m]
Used in
$GMR_{cc}$
Geometric mean radius of conductor bundle [mm]
$L_a$
Self inductance of conductor [H/m]
$L_i$
Inductance of conductor i [H/m]
$L_m$
Inductance (mean) [H/m]
$X_1$
Positive sequence reactance [$\Omega$/m]
$X_a$
Self reactance of conductor [$\Omega$/m]