APPENDIX B:  CABLE DATA

B.1  Introduction

The cable-constants feature in the Line Database requires you to input various physical parameters such as resistivity, permittivity and permeability.  This appendix shows you how to derive these parameters from information typically provided by the cable manufacturer.  It also gives you the typical values for various materials in case the information is not available.

B.2  Resistivity

The resistivity of the core, the sheath, the armor and the pipe should be computed directly from the dc resistance given by the manufacturer whenever possible.  The equation is:

                     = 211.68 R A                            (1)

where

                        is the equivalent resistivity in microOhm-cm.

                     R    is the conductor's dc resistance in Ohms per 1000 ft.

                     A    is the conductor's cross-sectional area in in2.  The value 'A' should be computed using the physical parameters you entered into the dialog box, with the assumption that the conducting element in question is solid.  Specifically,  A = (ro2 - ri2 ) where ro and ri are outer and inner radii.

You may find the following conversion factors useful for applying this formula to other units of measurement:

                     1 mile           = 5280 ft.

                     1 foot = 30.48 cm.

                     1 in2   = 1.27324 x 106 circular mils.

                     1 in2   = 6.4516 cm2.

In the absence of resistivity data from the manufacturer, the typical values of resistivity in table 1 can be used.  The resistivity values in the second column of table 1 are for 20C.  The resistivity at operating temperatures other than 20C is given by this equation:

                     t = ( 1 + ( T - 20 ) )                        (2)

where

                     t   is the resistivity at temperature T.

                        is the resistivity at 20C

                        is the temperature coefficient

                     T    is the operating temperature in degree Centigrade.

Table 1.  Typical values of resistivity and temperature coefficient of metals

B.3  Relative Permittivity of Insulation

The relative permittivity of the insulating elements is rarely given by the manufacturer.  Table 2 shows the typical values for materials that are commonly used for insulation.

Table 2.  Typical values of relative permittivity for various insulating materials.

B.4  Relative Permeability

The relative permeability of the conductor and sheath is equal to 1.0 because they are typically made of non-magnetic metal such as cooper, aluminum or stainless steel.

The pipe, which is typically made of steel, has a much higher permeability.  The pipe's relative permeability can vary between 40 and 1400, depending on the pipe current.  The permeability curve for steel pipes can be found in the following references:

J. H. Neher, "The phase sequence impedance of pipe-type cables," IEEE Trans. on Power Apparatus and Systems,  Vol. PAS-83, No. 8, pp. 795-804, August 1964.

R.C. Dugan, R.G. Rocamora, G. W. Brown,  "Surge propagation in three-phase pipe-type cables, Part II - Duplication of field tests including the effects of neutral wires and pipe saturation,"  IEEE Trans. on Power Apparatus and Systems, Vol. PAS-96, No. 3, pp. 826-833, May/June, 1977.

P.L. Ostermann, Underground Transmission Systems Reference Book, 1992 Edition, pp. 409-413, EPRI Distribution Center (Report TR-101670), 1992.

The permeability's dependence on the zero-sequence current causes the pipe's zero-sequence impedance to vary as a function of the current flow.  The Line Database gives a single zero-sequence impedance for the permeability values you enter.  You may wish to use a range of permeability values in multiple runs to see how the cable's impedances vary as function of the current.