Masts and shield wires

The design shields the high-voltage (HV) yard with overhead shield wires and adds lightning masts until the protected levels are inside the envelope of the rolling sphere (IEEE Std 998-2012 §6.6). This topic explains the zone a mast protects, how the design places the wires and the masts, and how it checks the coverage.

Read first: Direct stroke shielding by the rolling sphere

1The zone of a lone mastCopy link to The zone of a lone mast

A sphere of radius $S$ that rests on the ground and touches the tip of a mast leaves a zone around the mast that it cannot reach. The sphere's centre is then at height $S$, at a horizontal distance $\sqrt{S^2-(S-h{)}^2}$ from a mast of height $h$. At a protected height $a$, the sphere's surface lies $\sqrt{S^2-(S-a{)}^2}$ from the centre. The protected radius $r$ at height $a$ is the difference: $r=\sqrt{S^2-(S-h{)}^2}-\sqrt{S^2-(S-a{)}^2}$.

A mast taller than the sphere's radius protects as a mast of height $S$. At or above the mast's tip, the radius is zero.

Figure 1 shows the radius of a lone mast of the design's height for the HV bus's sphere and for the sphere of 20 m of IEC 62305-3 protection level I (LPL I, Table 2). The smaller sphere gives the smaller zone.

2Masts on a square gridCopy link to Masts on a square grid

Four masts of height $h$ at the corners of a square hold the sphere up at its centre, where the sphere reaches lowest. The masts protect height $a$ at the centre when their spacing is at most $\sqrt{2}\sqrt{S^2-(S-h+a{)}^2}$, with $h$ taken no greater than $S$. For masts at least $S$ tall that protect the ground, the spacing is $S\sqrt{2}$. The design places masts by a search, not on a grid. The grid spacing is derived geometry, and it compares the spheres: masts of 25.0 m under the LPL I sphere protect the medium-voltage (MV) areas' height of 5.5 m at a spacing of 27.2 m. Under the HV equipment's sphere of 28.97 m, they protect the equipment's height of 5.9 m at 38.5 m.

3Shield wires over the HV yardCopy link to Shield wires over the HV yard

The design runs one shield wire along each column boundary of the HV yard. A wire runs from a peak on the north gantry to a shield-wire tower of the same height south of the transformer bays, at the north edge of the internal road. The peaks stand 3.0 m above the gantry beam. A switching substation's lower yard has its own wires on its own column boundaries, above its own gantry beam.

The rolling sphere rests on a wire as on a line at the wire's attachment height. The masts and the shield-wire towers have 2 earth electrodes per support, bonded to the earth mat, and the earthing calculation counts them.

4Lightning mastsCopy link to Lightning masts

The masts protect what the wires leave exposed: the row of interconnecting transformers (ICT), the MV outdoor areas, the control building's roof, a gas-insulated switchgear (GIS) hall's roof, and any gaps in the HV yard. Their height is the design's value for the HV level. The design places them area by area, one mast a round. In each round it finds the protected points still outside the envelope and adds the candidate site that protects the most of them.

The candidate sites for the HV bus and equipment lie on the column boundaries, where no equipment stands, at 4.0 m steps. For the other areas they lie on a ring 2.0 m outside the area's edge, at the same steps. No mast stands within 6.0 m of another mast or tower.

No mast stands on a road or the building. The design removes the sites inside the internal road, the transformer road, the roads the user adds, the peripheral road band and the building, each grown by 1.0 m. Where this removes part of an area's ring, the design tries further sites: rings closer to and further from the area, free ground near the transformer row, and the bay boundaries inside an outdoor MV yard.

The search runs up to 200 rounds per area. It stops when the area is covered, or when no site protects a further point, and the report then shows the gap. The masts are numbered by position: LM-1 is the westernmost, and the numbers run west to east, then north to south.

5The coverage checkCopy link to The coverage check

The coverage check rolls the sphere of a protected level over the wires, the towers and the masts. For a plan point $c$, the lowest height of the sphere's centre is $H(c)$, the larger of $S$ and the heights $z+\sqrt{S^2-d^2}$ of the elements within $S$ of it. Here $z$ is the element's height and $d$ its plan distance from $c$. At a protected point $P$, the sphere reaches down to $E(P)$, the least of $H(c)-\sqrt{S^2-|c-P{|}^2}$ over the centres $c$ within $S$ of $P$.

A point $P$ at height $A$ is protected when Eq. (1) holds. The design calculates $H$ on a grid of 1.0 m. It samples the bus and the areas at 2.0 m, and the equipment at the phase positions of the built bays. The least margin of a level is the least of $E(P)-A$ over its points. A margin of zero or more is a pass. A negative margin is a gap, with the verdict Gaps.

6The fixed-angle radiusCopy link to The fixed-angle radius

The report lists the masts with their fixed-angle protected radius at a height of 5.5 m, with an angle of 45°: $r=(h-a)\tan 45^{\circ }$. It is shown for information. The coverage check does not use it.

7What the check leaves outCopy link to What the check leaves out

The coverage check takes a shield wire at its attachment height along the whole span and leaves out its sag. For a wire below the sphere's radius, the protected half-width $\sqrt{2Sh-h^2}$ grows with the wire's height $h$. The attachment height therefore overstates the coverage at mid-span, on the unsafe side. The report and the shielding sheet ask for a check of the mid-span coverage with the stringing sag at detail design.

The design takes the striking distance factor of a shield wire for the masts too. A smaller sphere gives a smaller zone where the mast is lower than the sphere's radius, so the mast coverage shown is the smaller one. The heights of the wires, masts, bushing tops and building roof are the design's values. The control building's own air terminals and down conductors are the building's design to IEC 62305-3.