### Electrical Constants

The following electrical constants are used in the application of power cables.

#### Positive- and negative-sequence resistance

The resistance of a conductor to positive- and negative-sequence currents is affected by the following factors.

*S**k**i**n effect: *This effect is due to unequal distribution of alternating current (AC) flowing in a conductor because of the tendency of the current to flow more on the outside than inside strands of the con- ductor. This results in a higher resistance to AC than direct current (DC). Usually this effect can be neglected in smaller conductors.

*P**ro**ximity effect: *This effect is due to alternating magnetic flux produced by circulating current in a conductor caused by the current flowing in a neighboring conductor. This effect increases the resistance of a conductor. It can become pronounced where cables are installed parallel to metal beams, plates, walls, and the like.

*Sheath currents: *The alternating current (AC) flowing in a sheathed single conductor induces voltage in the sheath. Since the sheath is bonded and grounded at both ends, currents flow longitudinally, causing *I**2**R *losses. One way to account for these losses is to increase the resistance of the conductor.

#### Positive- and negative-sequence reactance The reactance of a single lead-sheath conductor to positive- and negative-

sequence current can be calculated by taking into account the effect of sheath currents. It can be expressed mathematically by the following:

where

*X*1 is the positive-sequence reactance

*X*2 is the negative-sequence reactance

*X*a is the self-reactance of conductor at 1 ft radius

*X*d is the reactance of conductor beyond 1 ft radius

*X*s is the equivalent reactance value due to sheath currents

For three-phase conductors, *X*s can be neglected and the positive and negative reactances are *X*1 = *X*2 = *X*a + *X*d Ω/mile/phase.

#### Zero-sequence resistance and reactance

When zero-sequence currents flow in the three-phase system, the return

path is usually either through the earth ground, sheath, ground wire, or

a combination of these paths. In actual installation, the following combination of paths should be considered:

1. All currents in the ground, none in sheath

2. All currents in the sheath, none in ground

3. All currents in sheath and ground

When low-voltage cables are installed in magnetic ducts, the zero-sequence resistance and reactance are influenced by the magnetic material surrounding the conductor. No methods have been developed yet to accurately calculate the zero-sequence impedance. However, test data are available to give the required zero-sequence impedance data in standard reference handbooks on transmission and distribution of electrical power for various sizes of cables.

#### Shunt capacitance reactance

The positive-, negative-, and zero-sequence shunt capacitive reactances of cable are the same and can be expressed mathematically as follows:

#### Insulation resistance

The insulation resistance of the cable is very difficult to calculate because of varying insulation properties. However, a generalized formula can be expressed in terms of the power factor (PF) of the insulation system. For single-conductor cable,