Insulation Coordination

Switching Impulse Strength of Transmission-Line Insulation

Why switching impulses can be more severe than lightning for long air gaps, how tower insulation is treated statistically (CFO, σ and the statistical withstand voltage \(V_3\)), the critical wave front, the Gallet equation for strike distance, and the practical corrections for polarity, rain, phase position and altitude.

Reading time ≈ 35 min

Section 1

Why Switching Impulse Strength Became Important

This page explains how the switching-impulse withstand strength of transmission-line insulation is estimated and corrected for practical line-design conditions.

Before 500 kV transmission, engineers mainly worried about lightning impulse strength and power-frequency withstand. Switching impulses were not considered as critical as lightning.

When 500 kV and EHV systems appeared, a surprising discovery was made:

The surprising result

For long air gaps, air insulation can have a lower withstand strength under switching impulses than under lightning impulses.

We might expect lightning — sharper and faster — to always be more severe. But for long air gaps in EHV systems, switching impulses interact with the discharge-development process in air in a way that makes them more dangerous. That is why switching impulse strength is treated first: understanding it is the key to understanding the insulation strength of towers.

This note covers the switching-impulse strength of line/tower insulation. For the underlying definitions of BIL, BSL and CFO for equipment, see the companion note on insulation strength (BIL, BSL, CFO and impulse testing).

What this page teaches

why switching impulses can become more severe than lightning impulses for long air gaps;
what CFO means in a statistical insulation-strength context;
why \(V_3\) is used as a withstand voltage;
why the critical wave front is important;
how strike distance affects switching impulse strength;
why a gap factor is required for real tower geometries;
how polarity, rain, phase position and altitude corrections modify the withstand level.

Key message

Switching impulse strength is not only a voltage value: it depends on the gap geometry, the wave front and the atmospheric conditions.

Table 1 — The core quantities of switching-impulse line-insulation strength.

Item	Meaning	Practical Use
\(\text{CFO}\)	Voltage with 50% flashover probability	Basic statistical strength
\(V_3\)	Statistical withstand voltage	Deterministic design comparison
Critical wave front	Front time producing minimum withstand	Worst-case switching impulse strength
Gap factor	Correction for electrode / tower geometry	Converts a reference gap to real geometry
Atmospheric correction	Correction for density, humidity and altitude	Site-specific withstand strength

Section 2

The Tower Flashover Test and Its Key Parameters

The strength is measured by a laboratory test on a full-scale simulated tower: a grounded tower frame, a conductor bundle, a V-string insulator assembly, and the impulse voltage applied to the conductor. The test asks: at what voltage does the insulation between the live conductor and the grounded tower flash over? This is exactly the real overhead-line problem — conductor (live), tower (grounded), and the air + insulators (the insulation system).

Table 2 — The four main test parameters.

Parameter	Meaning	Effect on Strength
Strike distance \(S\)	Shortest practical flashover distance between live and grounded parts (conductor–tower side, yoke–truss, etc.) — the controlling air clearance.	Larger \(S\) → higher CFO.
Insulator string length \(S_I\)	Physical length of the porcelain string. The tower is controlled by the weaker path — across the string if it is short, through the air gap if it is long enough.	Must be long enough not to be the limiting path.
Switching impulse waveshape	Not just the peak — the wavefront (time to rise to crest, tens to thousands of µs) strongly affects long-gap strength.	A particular front gives minimum strength (see CWF).
Wet or dry condition	Rain wets insulator surfaces and encourages surface discharge.	Wet is normally more severe for outdoor insulation.

Section 3

Tower Insulation Is a Statistical, Multi-Path System

A tower is not one clean rod-plane gap. It is a parallel system of many possible flashover paths: conductor to the right tower side, conductor to the left side, yoke plate to upper truss, partly along the string then to the tower, or a mixed air-and-insulator path. Under identical test conditions, flashover can occur in different locations from shot to shot — proof that the tower is not a single deterministic gap.

This forces a statistical treatment. The old lightning-impulse picture imagined one critical voltage — below it no flashover, above it flashover. Switching-impulse testing showed this is wrong:

Apply 1200 kV → flashover.
Reduce to 1100 kV → flashover may still occur.
Reduce to 1000 kV → withstand may occur.
Increase back to 1100 kV → now withstand may occur.

So at 1100 kV both flashover and withstand are possible — flashover is probabilistic, not deterministic.

The flashover probability curve

Applying many shots at each level gives a percentage of flashovers — e.g. 5% at 1000 kV, 20% at 1100 kV, 50% at 1200 kV, 80% at 1300 kV. Plotted, this is an S-shaped curve: near zero at low voltage, rising rapidly through the middle, approaching 100% at high voltage. This curve is the insulation strength characteristic.

CFO in the statistical sense

CFO = the voltage at which the flashover probability is 50%. Apply an impulse equal to CFO many times and about half the shots flash over, half withstand. CFO is the centre of the statistical curve — not a guaranteed (safe) withstand value.

The curve is approximated by a Gaussian cumulative distribution described by two parameters: the CFO (its centre) and the standard deviation \(\sigma\) (its spread). A large \(\sigma\) means a gradual withstand→flashover transition; a small \(\sigma\) a sharp one. In practice \(\sigma\) is expressed as a fraction of CFO — the coefficient of variation, which engineers simply call “sigma”:

\[ \frac{\sigma}{\text{CFO}} \approx 5\% \quad\Rightarrow\quad \sigma = 0.05 \times \text{CFO} \;\;(=50\ \text{kV if CFO}=1000\ \text{kV}) \]

Section 4

The Statistical Withstand Voltage V₃

Design does not use CFO directly. For line insulation the practical design value is the statistical withstand voltage \(V_3\):

\[ V_3 = \text{CFO} - 3\sigma = \text{CFO}\,(1 - 3\times 0.05) = 0.85\,\text{CFO} \]

\(V_3\): statistical withstand voltage (line insulation)
\(\text{CFO}\): 50% flashover voltage
\(\sigma\): standard deviation \((\approx 5\%\ \text{of CFO})\)

\(V_3\) is not an arbitrary safety margin applied on top of CFO — it is a statistical withstand level read directly from the flashover distribution. In a Gaussian distribution, CFO is the 50% point; \(\text{CFO}-3\sigma\) is placed far below it, giving a very low flashover probability (about 0.1%). It is not zero risk, but it is a practical statistical withstand level for self-restoring line insulation.

The Gaussian model is imperfect — it extends to negative infinity, implying a tiny flashover probability even at negative voltage, which is unphysical. But it is a good engineering approximation down to about four standard deviations below CFO, and \(V_3\) is only three, so the method holds.

Note — \(V_3\) (line) vs the 10% point (equipment)

Don’t confuse the two design points. Transmission-line self-restoring insulation is designed at \(V_3 = \text{CFO}-3\sigma \approx 0.85\,\text{CFO}\) (~0.1% flashover). Equipment BIL/BSL is usually taken at the 10% point, \(\text{CFO}-1.28\sigma \approx 0.94\,\text{CFO}\). Same statistics, different acceptable risk — lines tolerate more flashovers (they self-restore) yet are designed at a lower probability point because a line has enormous numbers of towers and stress events.

Peak vs rms

All CFO and \(V_3\) values on this page are peak impulse quantities unless otherwise stated. They must not be mixed with rms power-frequency quantities without explicit conversion.

Section 5

The Critical Wave Front (CWF)

The CFO of air insulation depends on the wavefront, and the relationship is U-shaped: for very short fronts CFO is higher; as the front lengthens CFO falls to a minimum; for even longer fronts CFO rises again. The front that gives the minimum is the Critical Wave Front (CWF) — the most dangerous wavefront for switching-impulse flashover.

Why the CWF exists

Air-gap flashover is not instantaneous — it needs time for streamer formation, leader development, space-charge effects and field redistribution. If the voltage rises too fast, the discharge cannot fully develop before the voltage decays. If it rises too slowly, the field is never severe enough at the right moment for efficient leader propagation. At an intermediate front, the voltage rise and discharge development are optimally matched — giving the lowest flashover voltage. That front is the CWF.

The practical consequence: the most severe switching impulse is not necessarily the fastest one. If the actual switching surge front is near the CWF, the tower insulation is at its weakest.

Section 6

Polarity, Wet Condition and Long Fronts

Polarity. Positive and negative switching impulses behave differently. For tower insulation, positive polarity is more severe (negative-polarity strength is higher), so design and the equations below focus on positive polarity.

Wet condition. Rain reduces CFO. A practical rule for tower insulation:

\[ \text{CFO}_{wet} = 0.96 \times \text{CFO}_{dry} \]

So rain reduces CFO by about 4% — which is why line insulation design normally assumes thunderstorm / wet conditions.

Long wavefronts. In some EHV systems — especially where EHV lines are switched from the low-voltage side of the transformer — the actual surge front can be much longer than the CWF, typically 1000 to 2000 µs. At these long fronts CFO may be about 13% higher than at the CWF, but the practical increase is taken as 10% because \(\sigma\) also rises with front time:

\[ \text{CFO}_{\text{long-front}} = 1.10 \times \text{CFO}_{\text{CWF}} \]

So long-front switching surges are less severe than critical-front ones. (Because \(V_3 = \text{CFO}-3\sigma\) and \(\sigma\) also increases, \(V_3\) rises a little less than CFO — which is exactly why the 13% CFO gain is reduced to a practical 10%.)

Section 7

Strike Distance and the Gallet Equation

Strike distance is one of the most important design parameters: increasing \(S\) increases CFO. For the switching-impulse CFO of air gaps / tower windows, the Gallet equation is used:

\[ \text{CFO} = k_g \cdot \dfrac{3400}{1 + \dfrac{8}{S}} \]

\(\text{CFO}\): critical flashover voltage (kV)
\(S\): strike distance (metres)
\(k_g\): gap factor (geometry — see next section)

The behaviour: when \(S\) is small, \(8/S\) is large, the denominator is large and CFO is smaller. When \(S\) is large, \(8/S\) shrinks, the denominator approaches 1, and CFO tends toward \(3400\,k_g\) kV. The increase is strongly non-linear — CFO rises much more slowly than strike distance. Note, however, that this apparent “ceiling” of \(3400\,k_g\) is a limitation of the Gallet equation, not real physics: it is valid only up to about 15 m, and for longer gaps the strength keeps rising (a separate rod-plane equation, \(\text{CFO}=1400+55\,S\), is used for \(S\approx 13\) to 30 m).

Section 8

Gap Factor and Tower Geometry

The gap factor \(k_g\) accounts for geometry: gaps of the same distance do not have the same strength. A rod-plane gap, a conductor–tower gap, a conductor–window gap, a bundle–tower geometry, a steel pole and a lattice tower all have different electric-field distributions. The gap factor scales the basic CFO to the real geometry.

Table 3 — Typical gap factors for tower windows.

Geometry	Gap factor \(k_g\)
Lattice tower	about 1.20
Steel pole / narrow tower	up to about 1.25
Window with \(W/S \approx 0.20\) and \(h/S \approx 6\)	about 1.25

The geometry is captured by ratios of the strike distance: \(h/S\) and \(W/S\), where \(h\) = conductor height, \(W\) = tower width, \(S\) = strike distance. Tower height shapes the field environment, tower width sets the side clearance and field distribution, and \(S\) sets the basic insulation length. The tower window is therefore not only a distance problem, but a shape problem.

Warning — do not use rod-plane CFO directly

Do not apply the rod-plane CFO directly to every tower gap. The rod-plane gap is only a reference geometry. The real tower geometry, conductor position, insulator configuration and gap factor must be considered before a CFO is accepted for a specific gap.

Section 9

Insulator String Length

For a fixed strike distance, increasing the insulator string length raises CFO — but only up to a point, because the controlling (weakest) path changes.

Dry: CFO rises with string length until the string equals the strike distance; beyond that there is little benefit. If the string is shorter than the air gap, flashover tends to go across the string; once the string is as long as the gap, the air gap becomes controlling.
Wet: the saturation point shifts — the string must be \(1.05\) to \(1.10\) times the strike distance, because rain degrades the porcelain path more than the pure air path.

Hence the practical rule:

\[ S_I \ge 1.05\,S \qquad \text{(preferably up to } S_I \approx 1.10\,S\text{)} \]

\(S_I\): insulator string length
\(S\): strike distance

The string should be at least 5% longer than the strike distance. If it is too short, the tower strength is limited by the insulator string rather than the air clearance.

Section 10

Phase Position and String Type

Outside vs centre phase. A centre-phase conductor has tower steel on both sides; an outside phase has only one side nearby, so it has fewer flashover paths and a higher CFO:

\[ \text{CFO}_{\text{outside}} = 1.08 \times \text{CFO}_{\text{centre}} \]

So the centre phase is usually the more critical (about 8% lower).

V-strings vs I-strings

A V-string uses two strings in a V, controlling conductor movement and giving a defined window geometry — the main equations are based on V-strings. An I-string is vertical; testing it wet is difficult because water runs down the string, making results highly variable. Importantly, this does not mean I-strings are weaker — only that their CFO is harder to measure consistently in rain. For estimation, \(\text{CFO}_{\text{I-string}} = 1.08 \times \text{CFO}\), with the effective strike distance chosen carefully.

Effective strike distance for I-strings

The effective strike distance is the smallest of three values:

\[ S = \min\!\left(S_H,\; S_V,\; \dfrac{S_I}{1.05}\right) \]

\(S_H\): strike distance to the upper truss
\(S_V\): strike distance to the tower side
\(S_I/1.05\): insulator-string-controlled distance (since \(S_I \ge 1.05\,S\))

If the string is controlling, the effective strike distance is reduced. In practice, the insulator string length is often the controlling factor.

Section 11

Altitude and Atmospheric Correction

Line design usually assumes thunderstorm/wet conditions at the average altitude of the line. At altitude, air density is lower, which reduces external insulation strength. The relative air density is approximated by:

\[ \delta = e^{-A/8.6} \qquad\bigl(\text{or approximately } \delta = 0.997 - 0.106\,A\bigr) \]

\(\delta\): relative air density
\(A\): altitude in km

The exponential form is generally the better one. At higher altitude the same strike distance gives a lower CFO \((\text{CFO}_A < \text{CFO}_S)\), so a line designed using sea-level strength without correction may be optimistic — the CFO must be reduced from standard to actual altitude conditions. This matters most for high-elevation lines.

Section 12

Calculation Workflow and Worked Example

The full workflow for tower switching-impulse strength:

Identify geometry: centre or outside phase; V- or I-string; \(S\), \(h\), \(W\), \(S_I\).
Check the string: \(S_I \ge 1.05\,S\) (else the string may control).
Gap factor: \(k_g \approx 1.20\) (lattice) to \(1.25\) (narrow/steel pole).
Dry centre-phase CFO at CWF from the Gallet equation.
Wet correction: \(\times 0.96\).
Outside phase (if applicable): \(\times 1.08\).
Long front (≥ 1000 µs, if applicable): \(\times 1.10\).
Altitude correction via relative air density.
Statistical withstand: \(V_3 = 0.85\,\text{CFO}\).

Worked example

Centre phase, V-string, positive polarity, critical wavefront, standard atmospheric conditions, \(S = 5\) m, \(k_g = 1.20\). First the dry CFO:

\[ \text{CFO} = 1.20 \cdot \dfrac{3400}{1 + \frac{8}{5}} = 1.20 \cdot \dfrac{3400}{2.6} = 1.20 \times 1307.7 = 1569\ \text{kV} \]

Apply the wet correction, then the statistical withstand:

\[ \text{CFO}_{wet} = 0.96 \times 1569 = 1506\ \text{kV} \qquad V_3 = 0.85 \times 1506 \approx 1280\ \text{kV} \]

Interpretation

The tower has a 50% flashover probability near 1506 kV (wet), but the practical design withstand is only about 1280 kV. This is the whole point of statistical insulation design: CFO must not be used directly as the design withstand — use \(V_3 = \text{CFO}-3\sigma \approx 0.85\,\text{CFO}\).

Section 13

Lessons and the Insulation-Coordination Link

Table 4 — Correction factors for tower switching-impulse CFO.

Factor	Relationship	Effect
Wet condition	\(\text{CFO}_{wet} = 0.96\,\text{CFO}_{dry}\)	−4%
Outside phase	\(\text{CFO}_{\text{outside}} = 1.08\,\text{CFO}_{\text{centre}}\)	+8%
Long wavefront (≥ 1000 µs)	\(\text{CFO} = 1.10\,\text{CFO}_{\text{CWF}}\)	+10% (practical)
Statistical withstand	\(V_3 = \text{CFO}-3\sigma,\ \sigma/\text{CFO}=5\%\)	\(=0.85\,\text{CFO}\)
Insulator string	\(S_I \ge 1.05\,S\)	avoid string-limited strength

Put simply, the actual tower withstand is a function of many variables:

\[ \text{tower withstand} = f\bigl(S,\ k_g,\ \text{CWF},\ \text{polarity},\ \text{rain},\ \text{phase},\ \text{altitude},\ \sigma\bigr) \]

In an insulation-coordination study you: determine the expected switching overvoltage; determine the tower (or equipment) withstand; correct for atmospheric conditions; compare stress vs strength; and ensure an acceptable margin or flashover risk. If the calculated switching overvoltage exceeds \(V_3\), the design may not be acceptable. Remedies include increasing strike distance or string length, controlled switching, closing resistors, surge arresters, reducing the overvoltage by system design, modifying tower geometry or phase arrangement, or changing operating procedure.

The key lessons

Tower insulation is not a single gap — it is a parallel system of air and insulator paths, so it must be treated statistically.
CFO is the 50% flashover voltage, not a guaranteed withstand; design with \(V_3 = \text{CFO}-3\sigma \approx 0.85\,\text{CFO}\).
Switching strength depends strongly on wavefront — there is a critical wave front where CFO is minimum, and positive polarity is more severe.
Strike distance drives CFO via the Gallet equation (with saturation); the string must satisfy \(S_I \ge 1.05\,S\).
Apply corrections for rain (0.96), phase position (1.08), long front (1.10) and altitude; the centre phase and wet conditions are usually the critical case.

Part One Reading now

Switching Impulse Strength of Transmission-Line Insulation

Why switching impulses can exceed lightning for long air gaps, the statistical CFO and withstand voltage V₃, the critical wave front, the Gallet equation, and corrections for polarity, rain, phase and altitude.

Series progress 1 of 3

Part Two

Deterministic Line Design and Gap Factors

The deterministic method (V₃ = E_m), a worked 500 kV example, post-insulator strength, and the general gap-factor approach — Paris–Cortina and Gallet equations for common gap configurations.