Station Lightning Coordination, Part Six

Section 1

Comparing a Nonstandard Surge with a Standard BIL

Equipment insulation strength is defined by standard test waves — chiefly the \(1.2/50\ \mu\text{s}\) lightning impulse. But the surge voltages that actually appear inside a station are usually not standard waves, so this part explains how to evaluate a nonstandard waveshape for self-restoring insulation.

Station surges may be spike-like behind an arrester, oscillatory ahead of one, chopped or distorted by reflections, strongly shaped by arrester operation and station layout — very different from a laboratory test wave. The question is: how should a nonstandard waveshape be compared with BIL or CFO?

From Part Five to Part Six

Part Five discussed GIS and the guide-method comparisons. Part Six returns to a more general problem: how should a nonstandard surge waveshape be compared with a standard BIL or CFO? This matters because the surge voltage calculated in EMTP® often does not look like the standard \(1.2/50\ \mu\text{s}\) test wave.

The practical difficulty

BIL is defined using a standard laboratory waveshape, but actual station surge voltages may be spike-like, oscillatory or strongly distorted by reflections and arrester action. So the same crest voltage can have a different insulation severity depending on its duration and waveshape.

Self-restoring insulation only

The methods on this page apply only to self-restoring insulation — air gaps, external porcelain, bus supports, disconnectors and circuit breakers. They should not be used for transformer internal insulation or internal bushing insulation.

What Part Six covers

why a simple crest comparison with BIL is not enough;
the severity index \(SI\) and how to read it;
the gap-breakdown process behind the models;
the Leader Progression Model (LPM);
the Destructive Effect (DE) method;
why these apply only to self-restoring insulation.

Section 2

The Standard Test Basis of Insulation Strength

The BIL is verified by applying a standard \(1.2/50\ \mu\text{s}\) impulse (front \(\approx 1.2\ \mu\text{s}\), time to half-value \(\approx 50\ \mu\text{s}\)); the equipment must withstand the specified crest. Some equipment is also tested with chopped waves — a standard impulse suddenly chopped after a short time:

Table 1 — Chopped-wave test levels.

Equipment	Chopped-Wave Strength	Chop Time
Circuit breaker	\(1.15 \times \text{BIL}\)	3 µs
Circuit breaker	\(1.29 \times \text{BIL}\)	2 µs
Bushing	\(1.15 \times \text{BIL}\)	3 µs
Transformer	\(1.10 \times \text{BIL}\)	3 µs

The key point: standard tests define strength using standard waveshapes, but real station surges are nonstandard.

Section 3

Real Surge Waveshapes in Stations

Behind an arrester, a surge may have a sharp initial spike, a rapid reduction, then decay toward the arrester discharge voltage — because the arrester clamps after the surge arrives and reflections modify the shape. Ahead of an arrester, the surge may be oscillatory, with damped oscillations, equipment reflections and arrester interaction. Across line insulation, a stroke to a tower can give a fast, irregular wave shaped by footing resistance, coupling, backflashover and travelling waves. In every case the waveform is not a standard \(1.2/50\ \mu\text{s}\) wave, so a general evaluation method is needed.

Section 4

Why a Simple Crest Comparison Is Not Enough

Why crest comparison is subjective

A simple crest comparison is subjective because the engineer must decide whether the calculated surge looks more like a full wave, a chopped wave or another waveform — and different engineers may judge the same waveform differently.

The easy method is to compare the nonstandard crest with BIL or a chopped-wave level. But it is subjective: the engineer must decide whether the waveform is more like a full wave, a 2 µs or 3 µs chopped wave, or an oscillatory wave.

Two equal crests can differ in severity

Two waveforms with the same crest can have different severity, because their duration and time behaviour differ. A more consistent, objective method is needed.

Section 5

Severity-Index Methods — and Their Limit

To evaluate nonstandard waveshapes objectively, two severity-index methods are used — the Leader Progression Model (LPM) and the Destructive Effect (DE) method. Both compute a Severity Index (\(SI\)) that measures how severe the applied surge is relative to the insulation strength, and both are based on the physical gap-breakdown process.

Self-restoring insulation only

These methods apply only to self-restoring insulation — air gaps, external clearances, line insulation, bus supports, disconnectors, breakers and air-porcelain insulation. They must not be used for transformer internal insulation, internal bushing insulation or oil-paper (non-self-restoring) insulation, which still need subjective comparison with transformer test levels.

Section 6

Reminder — Transformer Internal Insulation

Why the transformer is mentioned here

The transformer discussion is included only to explain why subjective comparison is still used for non-self-restoring insulation. The severity-index methods described on this page should not be applied to transformer internal insulation.

For transformer internal insulation, the crest is compared with the chopped-wave strength \(1.10\,\text{BIL}\), reduced by a safety factor — \(\frac{1.10}{1.15}\,\text{BIL} = 0.96\,\text{BIL}\) for a 15% factor, or \(\frac{1.10}{1.20}\,\text{BIL} = 0.92\,\text{BIL}\) for 20%. This long-standing criterion needs caution: if the transformer oscillations are not rapidly attenuated, the waveform is closer to a full wave and the crest should be compared with \(\text{BIL}\), not \(1.10\,\text{BIL}\). This reinforces why self-restoring and non-self-restoring insulation are treated separately.

Table 2 — Where the severity-index methods apply.

Insulation	Examples	SI Methods?	Reason
Self-restoring	air gaps, bus supports, disconnectors, circuit breakers	Yes	breakdown is related to air-gap leader development
Non-self-restoring	transformer internal, internal bushing, oil-paper insulation	No	different failure mechanism; damage may be permanent
GIS	GIS bus and gas-insulated components	Direct crest comparison	the time-lag curve is nearly flat

Section 7

The Severity Index — Definition and Meaning

A short spike versus a longer surge

A short spike of \(1000\ \text{kV}\) may be less severe than a \(1000\ \text{kV}\) voltage that stays high for a longer time, because air-insulation breakdown needs time to develop. The Severity Index is used to include this time-dependent effect.

For a nonstandard surge of crest \(E_c\) applied across insulation of standard-wave strength CFO, the severity index is:

\[ SI = \frac{E_c}{E_{\max}} = \frac{CFO_{\min}}{CFO} \qquad (E_{\max} = CFO_{NS}) \]

\(E_c\): crest of the applied nonstandard surge
\(E_{\max}\): maximum crest of that same waveshape the insulation can withstand (\(= CFO_{NS}\))
\(CFO_{\min}\): minimum standard-wave CFO required for the applied surge
\(CFO\): standard-wave critical flashover voltage of the insulation

Reading the severity index

\(SI = 1.00\): stress equals strength (at the limit). \(SI < 1.00\): stress below strength (margin exists). \(SI > 1.00\): stress exceeds strength (insulation insufficient). \(SI\) is far more informative than a pass/fail crest check.

Section 8

A Severity-Index Example

Reading \(E_{\max}\) and \(CFO_{\min}\)

\(E_{\max}\) is not the maximum voltage found in the simulation — it is the maximum crest of the same nonstandard waveshape that the insulation could just withstand for the given standard CFO. \(CFO_{\min}\) is the minimum standard-wave CFO that would be required to withstand the applied nonstandard surge; it converts the nonstandard surge into an equivalent standard insulation requirement.

With \(E_c = 2000\ \text{kV}\), \(CFO = 1800\ \text{kV}\) and \(SI = 0.80\):

\[ E_{\max} = \frac{E_c}{SI} = \frac{2000}{0.80} = 2500\ \text{kV} \qquad CFO_{\min} = SI \times CFO = 0.80 \times 1800 = 1440\ \text{kV} \]

So the insulation could withstand the same waveshape up to \(2500\ \text{kV}\), and the applied surge needs only \(1440\ \text{kV}\) of standard-wave CFO — \(SI = 0.80\) means about 20% margin. Conversely, \(SI = 1.20\) means the required CFO or BIL must be increased by about 20%.

Why the index is below 1 here

Although the applied crest (\(2000\ \text{kV}\)) is higher than the standard CFO (\(1800\ \text{kV}\)), the waveform is not as severe as a standard wave of the same crest, so the Severity Index is below 1.0. This is exactly why waveform duration matters.

Section 9

Using the Severity Index to Select BIL or CFO

BIL versus CFO

BIL is a specified withstand level used for equipment rating. CFO is the statistical critical flashover voltage, usually associated with self-restoring insulation. For self-restoring insulation the Severity Index is often expressed using CFO, while for apparatus it may be related back to BIL.

The severity index translates a nonstandard waveshape into an equivalent standard insulation requirement. If the insulation CFO is known, the minimum required CFO is \(CFO_{\min} = SI \cdot CFO\); using BIL instead, \(BIL_{\min} = SI \cdot BIL\). The maximum permitted surge in per-unit of BIL is \(E_{\max}/\text{BIL} = E_c/(SI\cdot\text{BIL})\). In short, \(SI\) is the bridge between the real waveform and the standard insulation level.

Section 10

The Breakdown Process Behind the Models

Both methods are based on gap breakdown. Across a gap of spacing \(d\), a leader begins to progress once the voltage gradient exceeds a threshold \(E_0\). As the leader advances, the unbridged gap shrinks, the field across the remaining gap rises, the leader accelerates, and it finally bridges the gap — flashover. This is a time-dependent process, so the waveform duration matters, not only the crest.

Why waveshape matters

A very short spike may have a high crest but not last long enough for the leader to bridge the gap; a lower but longer-lasting voltage can be more severe because it gives more time for leader development. Crest voltage alone is not sufficient — the severity-index methods include the time behaviour.

Section 11

The Leader Progression Model (LPM)

Why breakdown takes time

Air-gap breakdown does not occur the instant the voltage reaches crest. A leader must start, extend across the gap and finally bridge the remaining distance. A high voltage that lasts only a very short time may not allow enough time for this process to complete.

The LPM directly represents leader movement, computing the leader velocity at each time step from the voltage across the remaining gap:

\[ v = k\left(\frac{e(t)}{x} - E_0\right) \qquad \left(\text{progresses only if } \frac{e(t)}{x} > E_0\right) \]

\(v\): leader velocity
\(k\): model constant
\(e(t)\): applied voltage versus time
\(x\): remaining unbridged gap length
\(E_0\): gradient at which leader progression starts

The calculation steps each time interval: compute \(e(t)\), the remaining gap \(x\), the velocity \(v\), the leader extension, then subtract it from \(x\) — repeating until the gap is bridged (\(x = 0\)) or the voltage decays.

Reading \(x\) and \(E_0\)

\(x\) is the part of the gap not yet bridged by the leader; as the leader progresses, \(x\) shrinks, so for the same applied voltage a smaller \(x\) gives a higher field across the remaining gap and the leader accelerates. \(E_0\) is the threshold gradient below which the leader does not continue — if the gradient across the unbridged gap is too low, the breakdown process stops.

Section 12

Finding the Severity Index with LPM

Why LPM is more physical — and why it needs a computer

The LPM is more physically meaningful because it follows the leader-development process directly, checking whether the leader can bridge the gap before the applied voltage decays. Because the remaining gap, voltage and leader velocity change at every time step, it is normally implemented numerically rather than by a simple hand calculation.

Method 1 — vary the crest. Fix the insulation CFO and apply the nonstandard surge; raise the crest if no flashover, lower it if flashover occurs, until flashover just occurs — that crest is \(E_{\max}\), and \(SI = E_c/E_{\max}\).

Method 2 — vary the CFO. Keep \(E_c\) fixed and vary the CFO until the minimum standard CFO that prevents flashover is found — that is \(CFO_{\min}\), and \(SI = CFO_{\min}/CFO\). Both routes give the same severity index.

Section 13

The Destructive Effect (DE) Method

Why the DE method exists

The DE method is a simplified way of representing the accumulated breakdown effect of a waveform. Instead of tracking leader movement step by step, it integrates the damaging part of the voltage waveform.

Reading \(V_0\) — and why \(V_0 = 0\) is conservative

\(V_0\) is the voltage below which the waveform is assumed not to contribute to flashover, so low-voltage portions of a long wave are not counted as strongly as the high-voltage portions near crest. When \(V_0 = 0\), every part of the waveform contributes — even low-voltage parts — which can make the method overly conservative for long-duration or slowly decaying waves.

Rather than tracking the leader directly, the DE method computes a destructive-effect integral — flashover occurs if the surge's destructive effect exceeds a base value:

\[ DE = \int \left(e(t) - V_0\right)^{k_d}\,dt \qquad \text{(over the part where } e(t) > V_0) \]

\(e(t)\): applied voltage
\(V_0\): voltage below which no flashover can occur
\(k_d\): DE method exponent

\[ DE \ge DE_B \;\Rightarrow\; \text{flashover} \qquad (DE = DE_B \text{ at the threshold}) \]

Section 14

The Equal-Area Form and \(V_0 = 0\)

If \(k_d = 1\), the DE method becomes an equal-area criterion: the destructive effect is proportional to the area of the voltage above the threshold \(V_0\). Taking \(V_0 = 0\) simplifies it further — the iterative process may not be needed — but it can overestimate severity for long-duration surges, because even low voltages then contribute to the destructive effect. This \(V_0 = 0\) version is adequate for short-duration surges but conservative for long-duration waves.

Section 15

Calibrating the Constants from Test Data

The constants are not arbitrary

The constants in the LPM and DE methods are calibrated so that the model reproduces known standard test results — the full-wave CFO and the 2 µs and 3 µs chopped-wave strengths.

The model constants come from standard test waves — the full-wave CFO and the 2 µs and 3 µs chopped waves — for two insulation categories: air / air-porcelain, and apparatus. The chopped-wave (time-lag) points differ between them:

Table 3 — Chopped-wave (time-lag) points by insulation category.

Insulation	2 µs chopped	3 µs chopped
Air / air-porcelain	\(1.67\,CFO\)	\(1.38\,CFO\)
Apparatus (breakers, bushings)	\(1.29\,CFO\)	\(1.15\,CFO\)

Air-porcelain withstands much higher crests for very short durations (a steeper time-lag curve); the apparatus curve is flatter. The standard \(1.2/50\ \mu\text{s}\) impulse is approximated as a double exponential \(e(t) = A\left(e^{-\alpha t} - e^{-\beta t}\right)\), with crest normalised to 1.0, and used to derive the model constants.

Reading the time-lag ratios

Air-porcelain and apparatus insulation have different time-lag curves, so they do not respond the same way to short-duration overvoltages — which is why different calibration constants are needed. The ratios show how much higher the withstand may be for very short chopped waves than for the standard full-wave CFO: air-porcelain (\(1.67\,CFO\), \(1.38\,CFO\)) has a stronger time-lag effect than apparatus (\(1.29\,CFO\), \(1.15\,CFO\)).

Section 16

LPM Constants and the Breakdown Gradient

The LPM constants \(k\) and \(E_0\) are fixed from the time-lag points and the breakdown gradient \(CFO_g\), which depends on gap configuration and polarity: positive polarity \(540\) to \(650\ \text{kV/m}\); negative polarity \(540\) to \(750\ \text{kV/m}\) (the higher for a rod-plane gap). Although negative polarity usually predominates, a conservative \(CFO_g = 560\ \text{kV/m}\) is used. The resulting constants are:

Table 4 — LPM constants for \(CFO_g = 560\) kV/m.

Insulation	\(k\)	\(E_0\) (kV/m)
Air-porcelain	\(7.785 \times 10^{-6}\)	535.0
Apparatus	\(1.831 \times 10^{-6}\)	551.3

These constants reproduce time-lag curves consistent with the selected chopped-wave and full-wave points.

Section 17

DE Method Constants

With \(V_0 \neq 0\), the DE method has three constants — \(DE_B\), \(k_d\), \(V_0\) — needing three voltage points (full-wave CFO, 2 µs and 3 µs chopped), chosen so the destructive effect is equal at all three flashover points. With \(V_0 = 0\), only two constants are needed, so the 2 µs and 3 µs points suffice — but, as noted, even low-voltage portions of a long surge then contribute, making this version conservative for long-duration waves.

Section 18

LPM versus DE

DE versus LPM, in one line

The LPM models the physical leader movement; the DE method converts the waveform into an accumulated severity integral. Both aim to estimate the same Severity Index, but the LPM is more directly connected to the physical breakdown process.

Table 5 — The two severity-index methods compared.

Aspect	Leader Progression Model	Destructive Effect Method
Basis	Physical leader development across the gap	Integral measure of severity
Models	Inception, velocity, remaining gap, bridging	Area of voltage above a threshold
Complexity	More physical; usually needs a computer	Simpler; easier for hand calculation
Caution	—	Sensitive to \(V_0\), \(k_d\); \(V_0 = 0\) conservative for long waves

Both produce \(SI\), giving a consistent alternative to subjective crest comparison.

Which method to use

In practice, the LPM should be preferred when an accurate evaluation is needed. DE with \(V_0 \neq 0\) is a practical approximation, and DE with \(V_0 = 0\) should be treated as a simplified screening approach, mainly for short-duration surges.

Section 19

Practical Interpretation for Coordination

For self-restoring insulation, the severity-index approach answers questions such as: is the surge at the breaker more severe than its BIL? Can a bus support withstand a spike-like surge? Is the air clearance adequate for an oscillatory wave? What BIL would a nonstandard surge require? Instead of asking only "is \(E_c < \text{BIL}\)?", it asks "is \(SI < 1\)?" — which is more meaningful because it accounts for waveform duration and breakdown development.

Section 20

The Key Practical Warning

Self-restoring insulation only — never transformers

Severity-index methods are not universal. Apply them only to self-restoring insulation, never to transformer internal or internal bushing insulation. For those non-self-restoring insulations, the evaluation stays with comparison to chopped-wave strength, full-wave BIL, switching-impulse strength, engineering judgement and a safety factor.

Section 21

Engineering Lessons

The key lessons

Crest voltage alone is not enough — two surges with the same crest can differ in severity by their duration.
BIL is a standard-wave strength — it must be interpreted carefully for nonstandard station waves.
The severity index gives an equivalent measure — \(SI = 0.8\) means ~20% margin; \(SI = 1.2\) means ~20% more strength needed.
LPM is more physical — it follows leader development but is more computational.
DE is simpler but needs caution — the \(V_0 = 0\) version is conservative for long waves.
Self-restoring insulation only — transformers stay on the test-comparison approach.

Section 22

Summary of Key Equations

Equation Summary

Severity index (crest)

\( SI = \dfrac{E_c}{E_{\max}} \)

Severity index (CFO)

\( SI = \dfrac{CFO_{\min}}{CFO} \)

Max nonstandard crest

\( E_{\max} = \dfrac{E_c}{SI} \)

Required standard CFO

\( CFO_{\min} = SI \cdot CFO \)

Leader progression

\( v = k\!\left(\dfrac{e(t)}{x} - E_0\right) \)

Destructive effect

\( DE = \displaystyle\int (e(t)-V_0)^{k_d}\,dt \)

DE flashover condition

\( DE \ge DE_B \)

Air-porcelain time-lag

\( 1.67\,CFO,\; 1.38\,CFO \)

Apparatus time-lag

\( 1.29\,CFO,\; 1.15\,CFO \)

Standard impulse model

\( e(t) = A(e^{-\alpha t} - e^{-\beta t}) \)

Section 23

Reader Should Remember

Station surge voltages are often nonstandard — spike-like, oscillatory or distorted by reflections and arrester action — while BIL is defined on a standard \(1.2/50\ \mu\text{s}\) wave. A simple crest comparison is easy but subjective. The severity-index methods give a more consistent answer for self-restoring insulation, with \(SI = E_c/E_{\max} = CFO_{\min}/CFO\): \(SI < 1\) means margin, \(SI = 1\) is the limit, \(SI > 1\) means more strength is required.

The Leader Progression Model follows the physical leader development across a gap; the Destructive Effect method is a simpler integral derived from breakdown behaviour. Both are for self-restoring insulation only — air gaps, bus supports, disconnectors, breakers and line insulation — never transformer internal or internal bushing insulation, which keep the test-comparison approach with a safety factor.

The single most important message

For self-restoring insulation, waveform shape matters. A nonstandard surge should be judged by its severity — through \(SI\), the LPM or the DE method — not by its crest voltage alone.

Reader should remember

Actual station surge voltages are often nonstandard. For self-restoring insulation, the Severity Index gives a consistent way to compare these waveshapes with a standard CFO or BIL. The LPM is the most physically based method; the DE method is a simplified alternative. Neither should be used for transformer internal insulation or internal bushing insulation.

This is Part Six of the station lightning insulation coordination series, covering the evaluation of nonstandard waveshapes for self-restoring insulation. Later parts continue the series.

Section 24

Key Symbols

Table 6 — Key symbols used on this page.

Symbol	Meaning
BIL	Basic Lightning Impulse Level
CFO / \(CFO_{NS}\)	Critical Flashover Voltage for the standard impulse / for a nonstandard waveshape
\(CFO_{\min}\)	Minimum standard-wave CFO required for the applied surge
\(E_c,\ E_{\max}\)	Crest of the applied nonstandard surge; maximum withstandable crest of that shape
SI	Severity Index
LPM / DE	Leader Progression Model / Destructive Effect method
\(DE,\ DE_B\)	Destructive effect; base destructive effect (threshold)
\(e(t),\ v,\ x,\ d\)	Applied voltage vs time; leader velocity; remaining gap; total gap
\(E_0,\ k\)	Leader inception/progression gradient; LPM constant
\(V_0,\ k_d\)	DE threshold voltage; DE exponent
\(CFO_g\)	CFO gradient (kV/m)

Station Lightning Coordination: Nonstandard Waveshapes & the Severity Index