Lightning Phenomena and Overvoltages

A power system spends its life at a steady operating voltage, but it must be built to survive brief excursions far above it. These overvoltages are measured in per unit of the normal peak phase-to-earth voltage, so that a \(3~\mathrm{p.u.}\) surge means three times that crest whatever the system voltage. They sort naturally into three families by how long they last and how they are shaped — and, helpfully, the time scale and the origin go together.

Temporary overvoltages are sustained, lightly damped power-frequency rises — a few cycles to seconds — from events such as load rejection, earth faults or resonance; they are modest in size (often \(1.3\)–\(1.5~\mathrm{p.u.}\)) but long enough to matter for arrester ratings. Switching overvoltages are slow-front transients of a few hundred microseconds, born inside the system when breakers operate; on long EHV lines they dominate the insulation design and are the subject of Chapter 23. Lightning overvoltages are the fast-front extreme — a steep spike over in tens of microseconds — caused by the external strike of a flash, and they govern the insulation of lower and medium transmission voltages. This chapter is devoted to that last, fiercest source.

Lightning begins in the cumulonimbus cloud, where violent updraughts carry water and ice through the freezing level. Collisions between rising ice crystals and falling soft hail (graupel) transfer charge, and the updraught then sorts the charge by particle size, leaving the cloud with a broadly negative base, a positive top, and often a small positive pocket near the base. The negative base induces positive charge on the ground beneath, and the field between them builds until the air can no longer hold it.

The discharge unfolds in stages. A faint stepped leader works downward from the cloud base in a jagged series of jumps, each a few tens of metres, carving an ionised channel and lowering negative charge toward the earth. As it nears the ground the intensified field launches upward connecting streamers from tall, grounded objects. When one meets the leader — the moment of attachment — a conducting bridge is completed from cloud to ground, and the stored charge pours down it. This is the return stroke: a brilliant wave of current racing up the channel that carries the bulk of the flash's energy and is what the eye sees as the flash. A single flash often contains several strokes, later ones travelling down a re-used channel via a fast dart leader. About nine in ten cloud-to-ground flashes are negative and downward, and it is the return-stroke current that threatens a power line.

For the power engineer the crucial abstraction is that a lightning return stroke behaves essentially as a current source: it injects a fixed quantity of charge almost regardless of what it strikes, and whatever it strikes develops whatever voltage that current demands. The peak current varies widely from flash to flash and is described statistically — the median first-stroke peak is about \(30~\mathrm{kA}\), a small fraction of flashes exceed \(100~\mathrm{kA}\), and the distribution of peaks is taken as roughly log-normal. Three features of the current matter for insulation:

To test and rate insulation against lightning, the messy natural surge is replaced by a standard, repeatable waveform: the \(1.2/50~\mu\mathrm{s}\) lightning impulse voltage. It rises swiftly to a crest and then decays more slowly, and two numbers define it. The front time \(T_1 = 1.2~\mu\mathrm{s}\) is a virtual rise time, defined as \(1.67\) times the interval the wave takes to climb from \(30\%\) to \(90\%\) of its peak (a construction that sidesteps the ill-defined toe of the curve). The tail time \(T_2 = 50~\mu\mathrm{s}\) is the time from the virtual origin to the point where the wave has fallen back to half its peak.

The companion standard lightning current impulse is the \(8/20~\mu\mathrm{s}\) wave, used to rate the current-handling duty of surge arresters and to test earthing. Both waveforms are specified with tolerances (about \(\pm30\%\) on the front and \(\pm20\%\) on the tail for the voltage impulse) so that laboratories worldwide reproduce the same stress. The whole apparatus of impulse generators from the earlier high-voltage-generation chapter exists to manufacture exactly these shapes on demand.

Now join the current source to the line. A conductor in free space has a surge impedance \(Z\) — the ratio of voltage to current for a travelling wave, typically \(300\)–\(500~\Omega\) for an overhead line. When lightning strikes the conductor directly, the injected current \(I\) cannot go anywhere but along the line, splitting into two waves that travel in opposite directions. Each direction carries half the current, so the voltage that appears at the strike point is

The numbers are alarming. Even a modest \(30~\mathrm{kA}\) stroke into a \(400~\Omega\) line raises the conductor by \(\tfrac12(400)(30{,}000)=6~\mathrm{MV}\) — vastly beyond any line's insulation. A direct stroke to a phase conductor is therefore almost always destructive, and the practical art of lightning protection is mostly about preventing such strikes from reaching the phase conductors at all, and about draining the inevitable surges harmlessly to earth. These launched waves do not stay put; they race along the line as travelling waves, reflecting and refracting at every junction — the subject taken up in detail in Chapter 23.

Because a direct hit to a phase conductor is intolerable, transmission lines are shielded by one or more earthed ground wires (shield wires) strung above the phase conductors and bonded to every tower. Their job is to intercept the descending leader so the stroke terminates on the shield wire and tower rather than on the live conductor. How well they do this is captured by the shielding angle \(\alpha\) — the angle between the vertical through the shield wire and the line to the conductor it protects. A smaller angle gives better coverage; the modern electrogeometric model refines this by recognising that the leader is "caught" by whichever earthed or live part it first comes within a striking distance of, a distance that grows with the stroke current.

Shielding creates a subtler danger of its own. When the stroke lands on the shield wire or tower, its current must flow down the steel to earth through the tower footing resistance \(R_f\). That current drives the tower top to a high potential — roughly \(I R_f\) plus an inductive \(L\,\mathrm{d}i/\mathrm{d}t\) term — and if this exceeds the insulation's withstand, the tower flashes back onto the phase conductor it was meant to protect. This back-flashover is the dominant lightning fault mechanism on shielded lines, and the chief defence against it is a low footing resistance: good earthing, counterpoise wires and ground rods that let the surge current bleed away without lifting the tower to a flashover potential. Lightning protection thus rests on two pillars — shield wires to keep strokes off the phases, and low footing resistance to keep the shielded strokes from flashing back.

A line need not be struck at all to feel lightning. When a flash hits the ground or another object near a line, its rapidly collapsing electromagnetic field couples a surge onto the conductors by induction. These induced overvoltages are far smaller than a direct hit — usually a few hundred kilovolts at most — because they scale with the field at a distance rather than with the full stroke current. On high-voltage transmission lines, whose insulation easily withstands a few hundred kilovolts, they are usually unimportant. But on distribution lines at \(11\)–\(33~\mathrm{kV}\), where the insulation level is low and direct strikes are comparatively rare, induced surges from nearby ground flashes become the main lightning threat, and the number of nearby strokes — set by the local flash density — drives the outage rate.

How often a line is threatened depends on how lightning-prone its territory is. The traditional measure is the keraunic level \(T_d\), the number of thunderstorm-days per year, but the modern and more useful quantity is the ground-flash density \(N_g\) — the number of cloud-to-ground flashes per square kilometre per year, now measured directly by lightning-location networks. A common empirical bridge between them is

A line is a wide target: it collects not only the flashes that fall on it directly but those within a lateral attractive width that grows with conductor height. The expected number of strokes to a span, and hence the expected number of back-flashovers and outages, follows from \(N_g\), the line height and the footing resistance. This risk figure is the starting point for the protection and insulation-coordination design of Chapter 24: knowing how many strokes will come, and how big they are likely to be, tells the engineer how much shielding, how low a footing resistance and how many arresters the line must have to meet its target reliability.

For each item, first identify what it tests — the overvoltage classification, the flash mechanism, the current-source idea, the standard impulse, the surge voltage, shielding and back-flashover, or risk — then apply it. Difficulty rises down the list.