Insulation Coordination
Why lightning-impulse strength is simpler than switching impulse, the practical CFO gradients (560 and 605 kV/m), cautions on the old data, full-scale tower behaviour, time-lag curves, wood and fibreglass in series, the impulse-tail effect, the flashover mechanism, and the Gaussian-versus-Weibull question.
Section 1
This page explains how the lightning-impulse strength of line and substation insulation is estimated — including CFO gradients, volt-time behaviour and practical insulation materials such as wood and fibreglass.
The earlier notes focused on switching-impulse strength. This one covers lightning-impulse strength. The key point is that switching-impulse strength ≠ lightning-impulse strength — they behave differently.
Lightning impulse strength depends on both the voltage magnitude and the time to flashover — not on crest voltage alone.
| Switching Impulse | Lightning Impulse | |
|---|---|---|
| What matters most | The wavefront (front time) | The tail, more than the front |
| CFO vs distance | Strongly non-linear (Gallet, saturating) | Almost linear with distance |
| Standard deviation | Relatively large (~5–7%) | Small (~1–3%) |
| Treatment | Statistical treatment essential | Often a single deterministic value (CFO/BIL) |
So lightning-impulse insulation strength is simpler to estimate than switching impulse — but it still has important details, which the rest of this note works through.
Section 2
A lightning impulse is a fast transient with the standard waveform \(1.2/50\ \mu\text{s}\) (front ≈ 1.2 µs, time to half-value ≈ 50 µs). Its strength is represented by CFO, BIL, or the time-lag (volt-time) curve.
For self-restoring insulation, CFO is the 50% flashover voltage. But for lightning impulse the scatter is small:
Strictly, lightning flashover is also statistical — a Gaussian curve with mean = CFO and standard deviation \(\sigma\). But because \(\sigma\) is small, engineers usually simplify: below BIL/CFO assume no flashover, above it assume flashover. Not perfectly true, but acceptable here — unlike switching impulse, where the larger \(\sigma\) makes the statistics unavoidable.
And unlike the Gallet equation for switching impulse, the lightning CFO is approximately linear with distance, \(\text{CFO} = \text{gradient}\times S\) (kV/m) — so a simple gradient is usually enough.
Section 3
For tower insulation and practical substation gaps, the recommended lightning-impulse gradients are:
The positive CFO is lower than the negative \((\text{CFO}_{+} < \text{CFO}_{-})\), so positive polarity flashes over at a lower voltage and is the critical design case — which is why design uses 560 kV/m rather than 605 kV/m.
| Insulation Case | Practical CFO Gradient |
|---|---|
| Line insulation | 560 kV/m |
| Substation insulation | 605 kV/m |
These are practical engineering gradients and should be used within the context and assumptions of the source method. Detailed design may still require geometry-specific data, test data or standard-based verification.
These gradients connect to the switching-impulse gap factor: for a tower-like gap with \(k_g \approx 1.2\), the positive lightning CFO gradient is around 538 to 560 kV/m, and 560 kV/m is recommended for practical use.
Section 4
McAuley’s 1938 data gave lightning CFO curves for suspension insulators, apparatus insulators and rod gaps, and equations were derived from them. The guide is emphatic that these old curves must be used carefully, for three reasons:
Section 5
More recent CIGRE data for rod-plane gaps shows positive-polarity CFO is approximately linear, negative becomes linear only above about 2 m, and — importantly — wet and dry conditions give almost the same CFO for pure air gaps. Rain has little effect on air-gap lightning strength; it affects insulators through surface wetting.
For the outside phase (a conductor-crossarm gap): without insulators, polarity has little effect; with insulators, polarity matters and flashovers occur across the insulators, not to the tower side. So for the outside phase the insulator string often controls the lightning flashover — the relevant distance is the insulator length, not the air strike distance.
Section 6
During the 500 kV full-scale switching tests, lightning tests were also run — valuable because they capture real tower geometry, not isolated strings.
As with switching impulse: a short string flashes across the insulators; once the string is long enough, flashover goes through air to the tower, and a saturation point is reached — here at about 24–25 insulators, string length 3.51–3.65 m, tower strike distance ~3.4 m. The ratio is \(IL/S \approx 1.03\) to 1.07, confirming the same practical rule:
In wet conditions (24 insulators) most flashovers returned to the string — rain weakened the insulator path — so one extra insulator restores roughly the dry strength. The minimum CFO from these tower tests was about 1950 kV at ~3.4 m:
Outside phase: the strike distance was larger and all flashovers crossed the insulators, so CFO must be analysed using insulator length. Suggested values: positive dry ~585, positive wet ~562, negative dry ~628 kV/m of insulator length — all supporting the simplified 560/605 kV/m recommendation.
Section 7
For tower insulation and substation clearances, the practical recommended values are:
| Polarity | CFO | Metric | Imperial |
|---|---|---|---|
| Positive (controlling) | \(\text{CFO}_{+} = 560\,S\) | 560 kV/m | 170 kV/ft |
| Negative | \(\text{CFO}_{-} = 605\,S\) | 605 kV/m | 185 kV/ft |
Section 8
In plain terms: a higher voltage can cause flashover faster, while a lower voltage may still cause flashover if it persists long enough. Lightning impulse insulation strength is therefore not defined only by crest voltage — the waveform and the time to breakdown also matter.
A time-lag curve plots flashover voltage against time to flashover. Insulation strength depends on how long the voltage is applied: at very short times a higher voltage is needed; for longer times the required voltage approaches the CFO. The shape depends on field uniformity — a near-uniform gap gives a flatter curve, while a highly non-uniform gap rises sharply at short times (stronger short-time withstand).
A crude curve-fit (valid roughly 2 to 11 µs) is:
For design, use the practical multipliers directly:
| Insulation | At 2 µs | At 3 µs |
|---|---|---|
| Tower insulation | 1.67 × CFO | 1.38 × CFO |
| Apparatus porcelain | 1.32 to 1.48 × CFO | 1.22 to 1.31 × CFO |
So to flash over a tower in 2 µs needs ~67% more than CFO; in 3 µs, ~38% more — important for chopped-wave and fast-front studies. In practice, apparatus is tested at standard chopped-wave levels (e.g. 1.15 × BIL at 3 µs, or 1.29 × BIL at 2 µs for breakers) rather than from detailed time-lag curves.
Volt-time behaviour explains why chopped-wave and full-wave stresses are different: a wave that collapses early (chopped) is survived only at a higher voltage than a full wave, because there is less time for the flashover to complete.
Section 9
Wood-pole construction (wood crossarms with porcelain insulators) matters mainly for distribution and lower-voltage lines. Two facts about wood:
Under a fast impulse the voltage divides capacitively between the two elements:
Because the capacitances differ, voltage is not shared by physical length alone — the insulator usually takes most of the voltage and flashes first; the full voltage then appears across the wood, which flashes only if it exceeds the wood’s own CFO. This leads to a critical wood length:
| Wood Length | Behaviour | Contribution |
|---|---|---|
| ~half critical length | Insulator controls | +40 kV/m (10 kV/ft) |
| At critical length \(L_{cw}\) | Transition | +100 kV/m (30 kV/ft) |
| Above critical length | Wood controls | ~300 kV/m (90 kV/ft) of wood |
(A handy shortcut: the critical length in feet is about the number of standard 5¾ × 10 inch insulators.) For transmission lines, wood is often near or just above critical length and adds only marginally. For lower-voltage lines, wood may far exceed critical length and dominate the strength — which is why wood matters for distribution-line lightning performance.
Section 10
There is less data for fibreglass, but for fibreglass crossarms in series with porcelain insulators, the negative-polarity CFO gradient of fibreglass alone was about 605 kV/m wet and 700 kV/m dry — the wet value matching the recommended air/porcelain negative value of 605 kV/m. So fibreglass behaves approximately like air-porcelain insulation, and the combination can be estimated from the combined length:
Used carefully, wood and fibreglass can add impulse withstand strength — but the contribution is not unlimited. It depends on moisture, contamination, geometry and the critical-length assumptions, and the actual flashover path may not follow the intended series path through the material.
Do not simply add insulation lengths together without checking the valid method and the flashover path. The series strength of wood or fibreglass plus porcelain is less than the arithmetic sum, only applies below the relevant critical length, and degrades with moisture and contamination. Confirm which path actually controls before crediting any added length.
Section 11
Tail effect. For lightning impulse the front time matters little if it is between 0.5 and 5 µs; the tail matters more (the opposite of switching impulse). The standard wave is \(1.2/50\ \mu\text{s}\), but real surges may have shorter tails. A shorter tail raises the CFO, because the voltage does not stay high long enough to complete the flashover. For a 10 µs tail the CFO may be about 17% higher than standard; for the standard 50 µs tail the error is only ~1.6% — relevant for backflashover studies, where tails can be short.
Lightning flashover develops in three stages:
Section 12
A key conclusion: for the same CFO, a switching impulse needs a larger strike distance than a lightning impulse. To reach a 1600 kV CFO needs ~3 m for lightning but ~5 m for switching:
That is precisely why switching-surge design became critical for EHV systems.
Power frequency. For clean, non-contaminated conditions, power-frequency strength usually does not control line or substation design — lightning, switching, and contamination/wet-pollution performance do. Rain effects differ by type: negligible for air gaps, but for insulator strings it can be significant (up to ~30% reduction for vertical I-strings as water runs down the surfaces). For a 3 m gap with \(k_g = 1.2\), the power-frequency CFO is about 19% greater than the positive switching-impulse CFO — so clean-condition power frequency is still less severe than switching impulse.
When comparing impulse strength with power-frequency strength, keep the reference consistent: impulse withstand and CFO values are peak quantities unless otherwise stated, and should not be mixed with rms power-frequency values without explicit conversion.
| Item | Lightning Impulse | Switching Impulse |
|---|---|---|
| Front time | Fast | Slower |
| Main concern | Stroke / backflashover stress | EHV switching overvoltage and long air gaps |
| Important concept | Volt-time / time lag | Critical wave front and gap factor |
| Typical use | BIL / lightning insulation coordination | BSL / switching insulation coordination |
Section 13
The chapter used the Gaussian distribution for insulation strength, but it has a weakness: it extends to \(-\infty\), implying a tiny flashover probability even at zero voltage, which is unphysical. There should be a voltage below which the probability is exactly zero — and the Weibull distribution can represent this with a lower truncation point.
| Gaussian | Weibull (IEC) | |
|---|---|---|
| Low-voltage tail | Extends to \(-\infty\) (unphysical) | Truncated — zero probability below a threshold |
| Truncation | none | \(p = 0\) below \(\text{CFO}-4\sigma\) |
| Reference points | 50% at CFO, 16% at \(\text{CFO}-\sigma\) | Fitted to match Gaussian near and below CFO |
| Use | Simple, widely used | More physically realistic; IEC-recommended |
Near the CFO and below, the two are close, so for normal calculations the difference is small — but Weibull is conceptually better.
Three-Part Technical Series
A focused three-part series on the switching- and lightning-impulse strength of transmission-line and substation insulation — from statistical air-gap behaviour to deterministic clearance design.
The practical lightning-impulse CFO gradients (560/605 kV/m), time-lag curves, wood and fibreglass in series, the impulse-tail effect, the flashover mechanism, and Gaussian vs Weibull statistics.
