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Equivalent depth of earth return path

Definition according to Cigre TB 531 chap. 4.2.3.3

The equivalent depth of the earth return path of a 50 Hz system with an electric soil resistivity of 100 $\Omega$.m is about 930 m.

Symbol
$D_E$
Unit
m
Formulas
$\frac{2e^{0.5}}{\gamma_{bessel} m_E}$
Related
$\gamma_{bessel}$
Bessel constant [p.u.]
$m_E$
Parameter m earth return
Used in
$a_m$
Mean distance between the phases [mm]
$E_a$
Induced shield voltage phase a [V/m]
$E_b$
Induced shield voltage phase b [V/m]
$E_c$
Induced shield voltage phase c [V/m]
$GMD$
Geometric mean distance between phases of the same system [m]
$L_m$
Inductance (mean) [H/m]
$X_a$
Self reactance conductor [$\Omega$/m]
$X_{ap}$
Equivalent mutual reactance between conductors [$\Omega$/m]
$X_{ar}$
Self reactance armour [$\Omega$/m]
$X_c$
Mutual reactance between middle and outer cables in flat formation with earth return [$\Omega$/m]
$X_{ij}$
Mutual reactance between conductors i + j [$\Omega$/m]
$X_L$
Mutual reactance between outer cables in flat formation [$\Omega$/m]
$X_s$
Self reactance screen/sheath [$\Omega$/m]
$X_{sw}$
Reactance skywire [$\Omega$/m]
$Z_{ct}$
Self impedance earth continuity conductor [$\Omega$/m]
$Z_{kp}$
Impedance between cable k and p in ground [$\Omega$/m]
$Z_{mt}$
Equivalent mutual impedance between earth continuity conductor and any cable [$\Omega$/m]
$\mathscr{z}_g$
Impedance earth return in ground [$\Omega$/m]