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.
The impedances of pipetype cable are generally determined using semi-empirical formulae based on laboratory measurements, performed by Neher in 1964. The theoretical approach is very difficult because of the non linear permeability and losses in the steel pipe. The accuracy of these formulae is quite questionable. In his paper, Neher points out a difference between the calculated and measured results within 19 % and 35 % for the zero-sequence resistance and reactance, respectively, on an example. The parameter $X_{sp}$ is unknown. It was determined by Neher from curves, based upon experimental results.
An iterative process has to be performed since these impedances depend on the magnitude of the zero sequence current.
| $Z_a+2Z_x-\left(Z_m-2Z_x\right) \frac{Z_m+2Z_x+\frac{3X_h}{L_{link}}}{Z_s+2Z_x+\frac{3R_h}{L_{link}}}$ | single-core cables, solid bonding |
| $Z_a+2Z_x-3Z_{mt} \frac{Z_{mt}+\frac{X_h}{L_{link}}}{Z_{ct}+\frac{R_h}{L_{link}}}$ | single-core cables, single-point bonding |
| $Z_a+2Z_x-\left(Z_m-2Z_x\right) \frac{Z_m+2Z_x+\frac{3X_h}{L_{link}}}{Z_s+2Z_x+\frac{3R_h}{L_{link}}}$ | single-core cables, cross-bonding |
| $R_{cDC} \left(1+y_s\right)+j X_a+2Z_x-\frac{\left(Z_m+2Z_x\right)^2}{Z_s+2Z_x}$ | three-core cables, with armour |
| $R_{cDC} \left(1+y_s\right)+j X_{cp}+3\left(R_{sp}+j X_{sp}\right)$ | pipe-type cables |
