The voltage that will show up along a 1 kilometer (1 KM) sheath with 1000 amps (1000 A) running continuously is known as the steady state voltage gradient, and it depends on the dimensions and configuration of the cable in the trench.
There are two fundamental trench configurations:
Flat Configuration: The flat configuration in which all cables are laid so that they are in the same plane and at the same distance from one another.
Trefoil Configuration: the trefoil, which is made up of three cables spaced equally apart so that their cross-section forms an equilateral triangle.
The voltage gradient can be computed using pertinent formulas and techniques taken from IEEE 575, “Guide for Bonding Sheaths & Shields of Single-Conductor Power Cables Rated 5 to 500 kV,” if the cable manufacturer does not supply it for the configuration being used:
E = k(S/d)n
Where
E – Sheath Voltage Gradient (V/km/kA)
K – Constant
S – Center-to-Center distance between cables (m)
d – Diameter of Sheath in meters
For Trefoil & Center Conductor of Flat Layout
For Outer Conductors of Flat Layout
The voltage at the open end of a section during a fault occurrence can be computed using the voltage gradient for 1 km at 1000 A.
This voltage level is significant because the SVL voltage rating (Uc) must be adjusted just higher to prevent arrester conduct during a fault condition.
If the arrester acts in this way, it would take more energy than distribution type arresters. Transient study will determine the SVL’s Uc and energy rating if a lower Uc is needed later in the sizing procedure.
If the margin of protection is sufficient, the SVL’s Uc rating will exceed the voltage at the open point (Eopen):
Uc >= Eopen = Voltage Gradient X Segment Length X Highest Predicted Fault Current.
Where
voltage gradient is V/km/1000A,
length is km, and
fault current is kA.
Ex: If a system has a voltage gradient of 200V/km/kA and a 2-km line with 17.5 kA potential, the lowest SVL Uc rating is 7000 V. The SVL’s minimum Uc could be half that of the 2 km line and might be 3500 V if the line were 1 km long.