Explore the corona discharge that forms around a high-voltage transmission-line conductor and the power loss it causes. Adjust the line voltage, conductor radius and phase spacing to see the disruptive critical voltage and the corona loss per kilometre update in real time, and find a conductor design that keeps losses low.
Parameters
Line voltage V_L
kV
Line-to-line voltage of the three-phase line
Conductor radius r
cm
Radius of the sub-conductor (or effective radius)
Phase spacing d
m
Centre-to-centre distance between adjacent phases
Frequency f
Hz
System frequency (50 or 60 Hz)
Air density factor δ
1.0 at standard conditions; falls at altitude, heat or foul weather
Results
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Phase voltage V_ph (kV)
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Critical voltage V_c (kV)
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Over-voltage margin (kV)
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Corona loss (per phase, per km) (kW/km)
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Total corona loss (3-phase, per km) (kW/km)
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Corona verdict
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Conductor cross-section and corona sheath
A cross-section of the transmission-line conductor. Once the phase voltage exceeds the disruptive critical voltage, a bluish-violet corona sheath appears around the conductor and grows thicker and brighter as the over-voltage margin increases.
Disruptive critical voltage V_c and Peek's corona loss P. m: conductor surface-irregularity factor (0.85 for a stranded conductor), δ: air density factor, r: conductor radius, d: phase spacing, f: frequency, V_ph: phase voltage.
The corona loss is zero when the phase voltage stays below the critical voltage. Increasing the conductor radius r lowers the surface electric field, raises the critical voltage and suppresses the corona loss. The total loss for the three-phase line is three times the per-phase value.
What is corona loss?
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I have heard the term "corona loss" in the context of power lines. What exactly is corona here? It's not the same as the Sun's corona, right?
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Same name, different thing. The corona on a power line is a "corona discharge". Push the voltage on a conductor high enough and the electric field right at its surface becomes intense — so intense that it tears electrons out of the surrounding air molecules and ionises them. A thin, glowing sheath of ionised air forms around the conductor. That is corona discharge. On a humid night you can sometimes see it as a faint bluish-violet glow and even hear it as a hiss and crackle.
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It glows and makes noise? So the "loss" means energy escaping as that light and sound?
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Exactly — corona is not free. Ionising the air, generating ozone and nitrogen oxides, producing audible noise and radio/television interference: all of that draws real power out of the line. That power drains away continuously, kilometre after kilometre. That is the corona loss. Try raising the "line voltage" slider on the left. Above a certain voltage you will see the loss suddenly start to climb.
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You're right — at low voltage the loss is zero, then it shoots up past a certain point. What is that "certain voltage"?
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That is the "disruptive critical voltage". Corona only begins once the conductor's surface voltage exceeds this threshold. Below it the corona loss is essentially zero. And the further the operating voltage rises above it, the steeper the loss grows. Peek's formula — a century-old empirical formula, but the one this tool uses — captures the main behaviour: the loss scales with the square of the over-voltage, and the critical voltage itself depends on the conductor radius, the spacing and the air density. In rain, snow or fog the air density factor delta drops, so the critical voltage falls sharply. That is why corona loss in foul weather can be many times the fair-weather value.
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I see. So to reduce corona loss, what do I change? You can't just lower the voltage, can you?
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Right — the transmission voltage is fixed by the grid, so you can't move it. The most effective lever is to increase the conductor radius. A larger radius spreads the same surface charge over more area, so the field is weaker, the critical voltage rises and corona is suppressed. Move the slider on the "Critical voltage vs conductor radius" chart below and you will see the critical voltage rise with radius. But making a single conductor very thick and heavy is impractical. So extra-high-voltage lines use "bundled conductors" — each phase split into two, three or four sub-conductors held apart by spacers. Several of them together behave like one conductor of much larger effective radius. Corona control is a big reason EHV lines look the way they do.
Frequently Asked Questions
This tool uses Peek's empirical formula. Corona occurs only when the phase voltage (line-to-neutral voltage) exceeds the disruptive critical voltage V_c, and the loss per phase per kilometre is P = (242.2/δ)(f+25)√(r/d)(V_ph − V_c)²×10⁻⁵ kW, where δ is the air density factor, f is the frequency, r is the conductor radius, d is the phase spacing and V_ph is the phase voltage. The total loss for the three-phase line is three times this value. Because the loss scales with the square of the over-voltage (V_ph − V_c), it rises steeply as the operating voltage moves above the critical level.
The disruptive critical voltage V_c is the phase voltage at which corona discharge begins at the conductor surface. In Peek's formula it is V_c = 21.1·m·δ·r·ln(d/r) kV, where m is the conductor surface-irregularity factor (about 0.85 for a stranded conductor, which this tool uses), δ is the air density factor, r is the conductor radius and d is the phase spacing. A larger conductor radius r lowers the surface electric field, so it raises V_c and suppresses corona. In foul weather (rain, snow, fog) δ falls, V_c drops, and the corona loss can multiply many times over.
The most effective measure is to increase the effective conductor radius. A larger radius lowers the surface electric field, raises the critical voltage and suppresses corona. Because making a single conductor very thick and heavy is impractical, extra-high-voltage (EHV) lines use bundled conductors instead: each phase is split into two, three or four sub-conductors held apart by spacers, which together behave like one conductor of much larger effective radius. Choosing an adequate phase spacing d and keeping the conductor surface free of scratches and deposits also help.
Corona discharge draws real power out of the line, and that power is consumed in ionising the air, in generating ozone and nitrogen oxides, and in producing audible noise and radio/television interference. Even a few to a few tens of kilowatts per kilometre adds up to a significant figure over a line hundreds of kilometres long. Corona can also be seen as a faint bluish-violet glow on a humid night and heard as a characteristic hiss. It is a central design driver for the conductor size and bundle configuration of EHV lines, and it is managed not only for loss but also for the environmental limits on noise and radio interference.
Real-World Applications
Conductor design for EHV transmission lines: On extra-high-voltage lines at 275 kV, 500 kV or 765 kV, keeping the corona loss, radio interference and audible noise within acceptable limits is the central challenge in selecting the conductor. Splitting each phase into two to four sub-conductors as a bundle is the classic way to increase the effective radius, lower the surface field and raise the disruptive critical voltage. The "Critical voltage vs conductor radius" curve in this tool is a miniature of that design decision.
Estimating annual line losses: On long transmission lines, corona loss adds to the resistive conductor loss (I²R loss) in the yearly energy-loss budget. Because corona loss depends strongly on the weather, the annual average loss is estimated by weighting the time spent in fair, rainy and snowy conditions. The steep increase in loss you see in this tool when the air density factor δ is lowered is exactly the foul-weather behaviour.
Environmental assessment of noise and radio interference: Corona discharge is a source of radio interference (RI) and audible noise (AN). When choosing the route and designing the towers of a transmission line, engineers check, together with the surface-field evaluation, whether corona can be sufficiently suppressed in sections close to residential areas. Keeping the phase voltage well below the critical voltage is the basis for controlling noise and interference.
High-voltage engineering education and sanity checks: An estimate from Peek's formula like this tool provides a first read before running a detailed field analysis (such as the finite-element method). It gives an intuitive feel for how the critical voltage and loss change with conductor radius and spacing, and if a detailed result differs from this estimate by an order of magnitude, it serves as a sanity check pointing to an error in the input or boundary conditions.
Common Misconceptions and Pitfalls
The biggest misconception is "corona loss is negligibly small". It is true that on a well-designed line in fair weather, corona loss is kept small compared with the resistive loss. But in rain, snow or fog the air density factor δ falls, the disruptive critical voltage drops, and corona loss jumps to several times — in bad cases more than ten times — the fair-weather value. Any annual loss estimate must include this foul-weather surge. Lowering δ toward 0.7 in this tool shows the loss climbing rapidly.
Next, the assumption that "Peek's formula gives an exact value". Peek's formula is an empirical formula established a century ago. It compactly captures the main dependencies (the square of the over-voltage, and the dependence on radius, spacing and air density), but it is an approximation. The real corona loss varies with conductor surface scratches, deposits and water droplets, the layout of sub-conductors in a bundle, the terrain and the fine distribution of humidity. The values from this tool are meant to give a sense of design direction; a final loss evaluation needs measured data or detailed analysis.
Finally, the idea that "as long as you stay below the critical voltage there is no problem at all" needs care. The corona loss itself is essentially zero below the critical voltage, but if a small part of the conductor surface has a scratch, a sharp burr, an insect or a water droplet, the field concentrates locally there and partial corona can occur. The disruptive critical voltage assumes the whole conductor is an ideal smooth cylinder, and the real surface irregularity is only roughly accounted for by the surface factor m (0.85 in this tool). On a real line, managing the surface condition is also an important measure.
How to Use
Enter the phase voltage (kV) using the voltage slider or numeric input; typical transmission lines operate 115–765 kV
Set the conductor radius (mm) – ACSR bundles range 4–15 mm; larger conductors increase critical voltage threshold
Specify the air density factor (0.8–1.0) to account for altitude effects; sea level is 1.0, high elevation reduces air's dielectric strength
Input the frequency (Hz), typically 50 or 60 Hz for power systems
Read the critical voltage V_c, over-voltage margin, and corona loss per phase in kW/km; total 3-phase loss appears below
Worked Example
A 345 kV transmission line uses ACSR Drake conductor (radius 7.85 mm) at sea level (air density 1.0) at 60 Hz. The simulator calculates V_c ≈ 187 kV. Phase voltage is 345 ÷ √3 ≈ 199 kV, yielding an over-voltage margin of 12 kV. Corona loss per phase is approximately 8.2 kW/km; total 3-phase loss is 24.6 kW/km across the entire line length, representing real power dissipated as electromagnetic radiation, heat, and ozone formation.
Practical Notes
Corona initiates when phase voltage exceeds critical voltage; higher altitude or wet conditions lower V_c and increase losses dramatically
Bundle conductors (two or four sub-conductors per phase) reduce electric field at the surface and suppress corona onset compared to single-strand designs
Operating margins below 5 kV indicate high audible noise risk and radio interference; utilities typically design for 15–30 kV margins
Frequency shift from 50 to 60 Hz reduces corona loss by ~4 %; cooler seasons and rain increase corona activity significantly