# Parameters of Underground Cables

In traditional paper insulated cables with three conductors contained within a lead or aluminium sheath, the electric field set up has components tangential to the layers of impregnated paper insulation in which direction the dielectric strength is poor. Therefore, at voltages over 11 kV, each conductor is separately screened to ensure only radial stress through the paper. Cables using cross-linked polyethylene (XPLE) insulation are now commonly used and again the electric stresses are arranged to be radial. The capacitance of single-conductor and individually screened three-conductor cables is readily calculated. For three-conductor unscreened cables one must resort to empirical design data. A typical high-voltage XLPE insulated cable is shown in Figure 3.30. The capacitance (C) of single-core cables may be calculated from design data by the use of the formula

where r and R are the inner and outer radii of the dielectric and *e _{r}* is the relative permittivity of the dielectric. This expression also holds for three core cables with each conductor separately screened.

Owing to the symmetry of the cable the positive phase-sequence values of C and L are the same as the negative phase-sequence values (i.e. for reversed phase rotation). The series resistance and inductance are complicated by the magnetic interaction

**Figure 3.30 **150 kV XLPE insulated 3 core cable with fibre optic communications

between the conductor and sheath. The effective resistance of the conductor is the direct current resistance modified by the following factors: the skin effect in the conductor; the eddy currents induced by adjacent conductors (the proximity effect); and the equivalent resistance to account for the I^{2}R losses in the sheath. The determination of these effects is complicated and is left for advanced study.

The parameters of the cable having been determined, the same equivalent circuits are used as for overhead lines, paying due regard to the selection of the correct model for the appropriate length of cable. Owing to the high capacitance of cables the charging current, especially at high voltages, is an important factor in deciding the permissible length to be used.

Table 3.3 gives the charging currents for self-contained low-pressure oil-filled (LPOF) cables.

**Figure 3.31 **Equivalent circuit of a two-winding transformer