Corona and Breakdown in Non-Uniform Fields

In a uniform gap the field is the same everywhere, so the criterion for breakdown is met at every point simultaneously and the whole gap goes at once. Non-uniform geometries — a transmission conductor above ground, a point facing a plane, a sharp protrusion on an otherwise smooth electrode — behave quite differently. As Chapter 2 showed, the field crowds wherever the radius of curvature is small, reaching a peak \(E_{\max}\) at the sharp electrode that may be many times the average \(E_{\text{mean}} = V/d\). The ratio is the field-enhancement factor, and its reciprocal the utilization factor:

The consequence is decisive. When the voltage is raised, the breakdown criterion is reached at the sharp electrode long before the average field is anywhere near the breakdown value. The gas there ionizes and glows — but the avalanche, advancing into the gap, soon runs into a region where the field has fallen below what it needs, and it stalls. The result is not a spark across the gap but a localized, persistent discharge clinging to the stressed electrode. That is corona.

Corona is a self-sustained discharge confined to the high-field region around a sharp or thin electrode, where the gas is fully ionized, while the remainder of the gap stays an insulator. It announces itself unmistakably: a faint bluish-violet luminous sheath, a hissing or crackling sound, and the sharp smell of ozone. Electrically it draws a small current and dissipates power, yet it does not bridge the gap — it is breakdown arrested partway.

Corona is self-limiting precisely because the field falls away from the electrode. The ions it creates form a space-charge cloud that pushes back on the field at the electrode surface, throttling the discharge; the corona settles into a steady or pulsing equilibrium rather than running away. Raise the voltage further, however, and the ionized region extends deeper into the gap, the space charge reorganises, and eventually a streamer (Chapter 6) escapes the corona envelope and crosses to the far electrode — at which point the partial discharge becomes a full spark-over. Corona is thus both a nuisance in its own right and the herald of breakdown in any non-uniform gap.

The voltage at which corona just begins is its inception (or critical disruptive) voltage. From his classic experiments on parallel conductors, F. W. Peek gave an empirical law that remains the engineer's working tool. Corona starts when the surface gradient reaches a critical disruptive value \(g_0\) — about \(30~\mathrm{kV/cm}\) peak, or \(21.1~\mathrm{kV/cm}\) rms, for air at standard density. For two parallel conductors of radius \(r\) spaced \(d\) apart, the disruptive critical voltage to neutral is:

Two correction factors carry the real-world departures from the ideal. The surface-irregularity factor \(m\) accounts for the conductor not being a perfect smooth cylinder: \(m=1\) for a polished wire, around \(0.85\) for a weathered stranded conductor, lower still for dirty or damaged surfaces. The air-density factor \(\delta\) corrects \(g_0\) for pressure and temperature away from standard, since a thinner atmosphere ionizes more easily:

Corona becomes visible at a somewhat higher voltage than it begins, because a glow bright enough to see needs a little more ionization. Peek captured this with the visual critical voltage, which adds a curvature term and uses a slightly smaller irregularity factor \(m_v\):

Non-uniform gaps behave differently depending on the sign of the stressed electrode — a subtlety that has no counterpart in a uniform gap and that matters enormously for insulation design. Consider a point–plane gap with the point at high voltage.

Positive point. Corona ignites at a relatively high voltage, but once breakdown does set in it crosses the gap at a lower voltage than the negative case. The reason is space charge: electrons created near the positive point are swept instantly into it, leaving a slow positive-ion cloud just ahead of the tip. That cloud effectively extends the anode into the gap, pushing the high field outward toward the cathode and helping a streamer march across. The positive point is therefore the dangerous polarity — it sparks over first.

Negative point. Corona begins at a lower voltage (the well-ordered Trichel pulses of the next section appear early), but full breakdown needs a higher voltage. Here the positive ions are drawn back into the negative point while electrons drift away into a region of falling field and attach; the resulting space charge weakens the field ahead of the tip and chokes the streamer's advance.

This is why high-voltage apparatus is tested, and insulation coordinated, against the polarity that breaks down first — usually positive for rod–plane geometries under switching surges. The lesson recurs throughout Parts 6 and 7 of this course.

Corona is not one discharge but a family, and which member appears depends on polarity and voltage. With a negative point, the discharge organises into a remarkably regular train of current pulses — the Trichel pulses — at frequencies from kilohertz up to megahertz. Each pulse is one small burst of ionization that is promptly snuffed out by the negative-ion space charge it creates; once that charge drifts clear, the next pulse fires, and the rhythm repeats. Raising the voltage quickens the pulses until, near breakdown, the discharge passes into a steady negative glow.

With a positive point, corona instead takes the form of intermittent burst pulses and outward-reaching streamers that flicker into the gap, with no comparably tidy periodicity; as the voltage climbs these streamers lengthen until one bridges the gap. On a power conductor under AC, both polarities occur each cycle, and the corona breathes in step with the voltage — generating activity twice per cycle and stamping its signature on the current, the radio spectrum, and the audible hum.

On a transmission line corona is rarely a safety threat, but it is a chronic and expensive nuisance with four distinct costs.

Power loss. Every corona discharge dissipates energy, drawn continuously from the line — a real \(I^2R\)-like loss that, on a long EHV line in foul weather, can run to tens of kilowatts per kilometre per phase and noticeably dent transmission efficiency.

Radio and television interference (RI/TVI). The fast current pulses of corona radiate across a broad band of radio frequencies, polluting reception for kilometres around the line. Limiting RI is often the binding constraint on conductor surface gradient, stricter even than the loss limit.

Audible noise. The crackle and hum — especially the characteristic 100/120 Hz tone and broadband hiss in wet weather — is an environmental factor in line routing near habitation.

Chemical action. Corona converts atmospheric oxygen to ozone and produces nitrogen oxides; in moist air these form corrosive nitric acid that attacks fittings, and the ozone itself degrades nearby organic insulation.

Once the line voltage exceeds the disruptive critical voltage, corona loss sets in and grows steeply. Peek's empirical formula gives the fair-weather loss per phase per kilometre:

with \(f\) the frequency in Hz, \(r\) and \(d\) in cm, and the phase voltage \(V_{ph}\) and disruptive voltage \(V_d\) in kV to neutral. Two features guide design. First, the loss is zero until \(V_{ph}\) exceeds \(V_d\), then climbs as the square of the excess — so keeping the operating gradient just below the threshold is hugely rewarding. Second, foul weather (rain, snow, fog) collapses \(V_d\) and can multiply the loss many-fold, which is why lines are rated for both fair- and foul-weather corona.

The engineer's levers all trace back to the surface gradient: increase the conductor radius, bundle the sub-conductors, polish or grade the surface to raise \(m\), and keep \(V_d\) comfortably above the operating voltage. These same measures, taken to suppress corona, also tame the radio interference and audible noise — so corona control quietly shapes the whole mechanical design of an EHV line.

For each item, first name the idea it tests — field enhancement, corona inception, Peek's law, the polarity effect, the forms of corona, or corona loss — then work it through. Difficulty rises down the list.