Transients and insulation
Corona: disruptive critical and visual inception voltage (Peek)
- where
- Peek air density factor (1 at 76 cm Hg, 25 °C)
- atmospheric pressure (kPa); 0.750062 converts to cm Hg
- air temperature (°C)
- disruptive critical voltage, phase to neutral (kV rms)
- breakdown strength of air (kV/cm rms)
- surface irregularity factor
- conductor radius (mm); r/10 is in cm
- phase spacing or GMD (m)
- visual corona inception voltage, phase to neutral (kV rms)
- visual surface factor
Explain this equation
Gives Peek’s disruptive critical voltage, where ionisation starts at the conductor surface, and the higher visual corona voltage, where glow appears. Use them to check a conductor choice for corona loss and radio interference at the operating voltage.
δ is the air density relative to 76 cm Hg and 25 °C; thinner or warmer air breaks down sooner. g0 is the breakdown gradient of air, about 21.1 kV/cm rms. m0 and mv allow for surface roughness and stranding. r/10 converts mm to cm, and ln(D/r) relates surface gradient to voltage for parallel round conductors.
The surface gradient on a round conductor is V/(r ln(D/r)), so setting it equal to the air strength gives V_d. The visual voltage includes Peek’s term 1 + 0.3/√(δr): thin wires need a higher gradient because the ionising zone must extend a finite distance from the surface.
Sense check: a 9.45 mm radius stranded conductor at 3 m spacing with m0 = 0.85 has V_d of about 170 kV line-to-line, above 132 kV operation in fair weather. Larger radius raises V_d almost in proportion.
Watch out: V_d is phase to neutral; compare it with V/√3, not line voltage. Rain greatly lowers corona onset.
Peek’s empirical voltages at which corona starts on smooth-weather overhead conductors: the disruptive critical voltage (onset of ionisation) and the higher visual corona voltage.
Enter your values to see the result.
Good to know
δ is Peek’s air density factor 3.92b/(273 + t) with b in cm Hg (δ = 1 at 76 cm Hg, 25 °C). m0: 1 for polished wire, about 0.93–0.98 for weathered single wire, 0.80–0.87 for stranded conductor. mv: 1 polished, 0.98–0.93 rough, about 0.72 for local and 0.82 for general visual corona on stranded conductors. g0 = 30 kV/cm peak ≈ 21.1–21.2 kV/cm rms. Corona loss becomes significant once the operating phase voltage exceeds Vd.
Common mistake
Using line-to-line voltage directly against the phase-to-neutral Vd, or using diameter instead of radius in cm.
Limits
Peek’s empirical formulae for parallel round conductors in fair weather at power frequency; for three-phase use the GMD. Rain, fog and altitude reduce inception markedly. Bundled conductors and modern surface-gradient methods (e.g. Markt–Mengele, EPRI/CIGRE) are not covered.
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.