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Positive sequence impedance

Definition according to Cigré guide 531 chapter 4.2.4.3

Definition for three-core cables with armour was specifically for submarine armoured three-core cables, with individual separate metal screens.

For cables, the negative sequence impedance is equal to the positive sequence impedance.

Symbol
$Z_d$
Unit
$\Omega$/m
Formulae
$Z_a-Z_x-\frac{\left(Z_m-Z_x\right)^2}{Z_s-Z_x}$single-core cables, solid bonding
$Z_a-Z_x$single-core cables, single-point bonding
$Z_a-Z_x$single-core cables, cross-bonding
$Z_a-Z_x-\frac{\left(Z_m-Z_x\right)^2}{Z_s-Z_x}+R_c \lambda_2$three-core cables, with armour
$R_{cDC} \left(1+y_p+y_s+\lambda_1+\lambda_2+\lambda_3\right)+j X_d$pipe-type cables
Related
$\lambda_1$
Loss factor of shield (screen and sheath)
$\lambda_2$
Loss factor of armour
$\lambda_3$
Loss factor of steel pipes for pipe-type cables
$R_c$
Electrical resistance of conductor [$\Omega$/m]
$R_{cDC}$
Electrical DC resistance of conductor [$\Omega$/m]
$X_d$
Reactance steel pipe [$\Omega$/m]
$y_p$
Proximity effect factor of conductors
$y_s$
Skin effect factor of conductor
$Z_1$
Positive sequence impedance [$\Omega$/m]
$Z_a$
Self impedance of phase conductor with earth return [$\Omega$/m]
$Z_m$
Mutual impedance between phase conductor and metal screen with earth return [$\Omega$/m]
$Z_s$
Self impedance of metal screen with earth return [$\Omega$/m]
$Z_x$
Equivalent mutual impedance between cables with earth return [$\Omega$/m]
Used in
$I_{k0}$
Phase-to-ground fault current [A]
$I_{k1}$
Phase-to-neutral fault current [A]