Insulation Coordination

Station Lightning Coordination: Comparing the Severity-Index Methods

Part Seven of the series. The three severity-index methods — the Leader Progression Model and the Destructive Effect method with and without a threshold V₀ — are put to the test on a linear-front exponential-tail surge and an oscillatory surge. This self-study shows how severity rises with tail duration, why the V₀=0 form fails for long or oscillatory waves (errors over 30%), the practical 75% time-duration rule, the flat-time-lag treatment of GIS, and how to apply a margin through the severity index.

Reading time ≈ 35 min · Part Seven of the series

Section 1

Putting the Severity-Index Methods to the Test

Part Six introduced three severity-index methods for nonstandard waveshapes — the Leader Progression Model (LPM), the Destructive Effect method with \(V_0 \neq 0\), and the Destructive Effect method with \(V_0 = 0\). This part compares them on two representative surge waveshapes and draws the practical rules.

It answers: when is the simplified \(V_0 = 0\) method acceptable; why it becomes inaccurate for long-duration surges; how long the waveform should be tracked in the calculation; why GIS is treated differently; and how a margin can be applied to the severity index.

From Part Six to Part Seven

Part Six introduced the Severity Index and the main methods used to evaluate nonstandard surge waveshapes. Part Seven compares these methods and explains which one is suitable for different types of surge waveform.

What Part Seven covers

the two test waveshapes — linear-front exponential-tail and oscillatory;
how the severity index rises with tail duration;
why LPM is the accurate reference and DE (\(V_0\neq0\)) tracks it well;
why DE (\(V_0=0\)) fails for long / oscillatory surges;
the 75% time-duration rule;
the flat-GIS treatment and the \(SI\)-based margin.

Section 2

The Comparison and Its Reference Values

The aim of the comparison

The purpose is not only to compare numerical values, but to understand the behaviour and limitations of each method. The key question is: which method gives reliable results for short-duration, long-duration and oscillatory surge voltages?

The three methods are compared using two waveshapes that represent practical nonstandard surges across self-restoring station insulation. The reference values are \(E_c = 2000\ \text{kV}\) (the applied nonstandard crest) and \(CFO = 1800\ \text{kV}\) (the standard-wave critical flashover voltage):

\[ \frac{E_c}{CFO} = \frac{2000}{1800} = 1.111 \]

On crest alone, the surge appears to exceed the insulation CFO — but the severity-index methods account for waveshape and duration, so the actual severity may be lower or higher depending on the waveform.

What the reference values tell us

With a surge crest of \(2000\ \text{kV}\) and a standard-wave CFO of \(1800\ \text{kV}\), a simple crest comparison would suggest the surge exceeds the insulation strength. The Severity Index methods show whether the actual nonstandard waveform is more or less severe than that simple comparison suggests.

Why these two waveshapes

The linear-front exponential-tail wave is useful because it represents a fast surge that decays with a defined tail time constant. The oscillatory wave is useful because station surge voltages often contain reflections and oscillations caused by bus sections, arresters, transformer capacitance and open points.

Section 3

The Linear-Front, Exponential-Tail Surge

The first waveshape has a linear rising front to crest \(E_c\), then an exponential tail — a fast voltage rise followed by a controlled decay with a defined time constant. The tail duration is important: a longer tail gives more time for leader development, so for the same crest, a longer-tail surge can be more severe.

Section 4

The Oscillatory Surge

The second waveshape is oscillatory — arising from travelling-wave reflections, arrester interaction, transformer and bus capacitance/inductance, and open-ended connections. It may have a high initial crest followed by decaying oscillations, and its severity depends not only on the first crest but on how long the oscillations stay high enough to contribute to breakdown development.

Same crest, different severity

Both comparison waves can share the same crest voltage but differ in severity. A short-duration wave may not give the leader enough time to develop, while a longer-tail or oscillatory wave can continue to support breakdown after the first crest.

Section 5

Linear-Front Results — Air-Porcelain Insulation

Reading \(E_{\max}\) in the tables

\(E_{\max}\) is the maximum crest voltage of the same nonstandard waveshape that the insulation can withstand. A lower \(E_{\max}\) means the waveform is more severe; a higher \(SI\) also means the waveform is more severe.

For air-porcelain insulation, the LPM severity index rises as the tail time constant increases — the same \(2000\ \text{kV}\) crest becomes progressively more severe:

Table 1 — LPM results vs tail time constant (air-porcelain, \(E_c = 2000\) kV).

Tail Time Constant	\(SI\)	\(E_{\max}\) (kV)	Verdict
20 µs	0.9862	2028	small margin
50 µs	1.0764	1858	exceeds limit
100 µs	1.1161	1792	clearly over limit

The trend is clear: longer tail ⇒ higher \(SI\) ⇒ lower \(E_{\max}\). At 20 µs the surge is just below the limit; by 100 µs it is clearly above it.

Why the trend goes this way

As the tail time constant increases, the voltage stays high for longer, which gives more time for leader development. So the Severity Index increases and the permissible crest \(E_{\max}\) decreases.

Section 6

Linear-Front Results — Apparatus Insulation

Apparatus insulation shows the same behaviour — longer duration is more severe for the same crest — but the numbers differ because its time-lag characteristic differs. Apparatus has \(V_{2\mu\text{s}} = 1.29\,CFO\) and \(V_{3\mu\text{s}} = 1.15\,CFO\), whereas air-porcelain has \(1.67\,CFO\) and \(1.38\,CFO\). So the same nonstandard surge has different severity depending on the insulation type.

Section 7

Why Oscillatory Waves Are Special

An oscillatory surge may not decay quickly to zero — in the comparison it decays only to about 50% of its original value, remaining at a significant fraction of crest for several cycles. This is exactly the situation that breaks the \(V_0 = 0\) DE method, which lets all voltage — even relatively low values — contribute to the destructive effect. For oscillatory surges that do not decay quickly, the \(V_0 = 0\) method becomes invalid.

Section 8

LPM as the Reference Method

LPM is the reference

The Leader Progression Model is treated as the reference method because it follows the physical breakdown process more directly — it calculates whether the leader has enough time to bridge the air gap before the voltage decays.

The Leader Progression Model is directly based on the physical breakdown process — it follows the leader developing across the gap — so its results are taken as the most accurate reference. The DE methods are then judged by how closely they match LPM.

Section 9

The DE Methods on the Oscillatory Surge

Why DE with \(V_0 \neq 0\) tracks LPM

The DE method with \(V_0 \neq 0\) agrees well with LPM because it ignores the low-voltage part of the waveform below the threshold \(V_0\). That is physically reasonable, since low voltage does not significantly contribute to leader development.

The DE method with \(V_0 \neq 0\) compares reasonably well with LPM, because \(V_0\) stops low-voltage portions from contributing unrealistically — only voltage above the threshold counts, which is physically reasonable since a voltage below a certain level does not produce leader development. It therefore stays useful for shorter, longer and oscillatory surges, provided the constants are properly calibrated.

The DE method with \(V_0 = 0\) is not even shown for the oscillatory comparison, because it gives invalid results when the voltage decays slowly or stays at a significant fraction of crest — treating all the voltage area as destructive overestimates the severity.

Why \(V_0 = 0\) fails for long surges

With \(V_0 = 0\), every part of the waveform contributes to the destructive effect, including the low-voltage tail. For long-duration waves this artificially raises the calculated destructive effect, so the method predicts a much lower \(E_{\max}\) and becomes overly conservative.

Why it is not even shown for the oscillatory surge

The oscillatory surge decays only to about 50% of its original value. With \(V_0 = 0\) the continuing oscillations would keep contributing to the destructive effect even when they may not be physically significant, so the \(V_0 = 0\) method is not valid for this case.

Section 10

Main Findings from the Comparison

Table 2 — How the DE methods compare with LPM.

Method	Short-Duration Surges	Long-Duration Surges
DE with \(V_0 \neq 0\)	\(E_{\max}\) within −0.3% to +6% of LPM	best agreement — a useful simplified alternative
DE with \(V_0 = 0\)	within about 4% of LPM	\(E_{\max}\) up to 30% low (over-severe) at \(100\ \mu\text{s}\)

The \(V_0 = 0\) error arises because removing \(V_0\) lets the time-lag curve fall below the standard CFO — not physically suitable for long-duration voltage. The DE method with \(V_0 \neq 0\) is a good engineering substitute for LPM, best for longer-duration surges.

What “30% lower \(E_{\max}\)” means in practice

If \(E_{\max}\) is calculated 30% lower than the LPM value, the method is predicting that the insulation can withstand much less voltage than it actually can — which may lead to an unnecessarily high BIL or an overly conservative clearance requirement.

Table 3 — Choosing a severity-index method.

Method	Accuracy	Suitable Use	Main Limitation
LPM	highest	detailed evaluation of nonstandard waveshapes	requires numerical calculation
DE with \(V_0 \neq 0\)	good approximation	practical engineering evaluation	requires calibrated constants
DE with \(V_0 = 0\)	approximate	short-duration surges, screening, initial \(SI\)	can be very conservative for long / oscillatory waves
Direct crest comparison	simple	GIS or preliminary check	ignores waveshape duration

Section 11

The Practical Conclusion

When to use which method

The DE method with \(V_0 = 0\) should be used only for short-duration surges, preliminary estimates, obtaining an initial \(SI\), or simple approximate screening. For accurate or long-duration waveform evaluation, use either the LPM or the DE method with \(V_0 \neq 0\).

Section 12

The Appeal of the \(V_0 = 0\) Form — a Direct Equation

The trade-off of the \(V_0 = 0\) form

The advantage of the \(V_0 = 0\) form is that it gives a direct Severity Index equation without iteration, which is useful for quick screening. But that simplicity is gained by removing the voltage threshold — which is exactly why it becomes unreliable for long-duration waves.

The \(V_0 = 0\) method is attractive because it can give a direct, non-iterative equation for the severity index. At the flashover threshold \(DE = DE_B\), the maximum permissible crest \(E_{\max}\) follows directly, and the severity index separates cleanly into a waveshape term and a crest-magnitude term:

\[ SI = (\text{waveshape severity factor}) \left(\frac{E_c}{CFO}\right) \]

The \(E_c/CFO\) term compares crest magnitude; the waveshape factor compares how severe the nonstandard shape is versus the standard reference — usefully separating crest magnitude from waveshape duration. For \(SI = 0.8\), reaching the critical \(SI = 1.0\) means either the crest could rise to \(E_{\max} = E_c/0.8\), or the required CFO could fall to \(CFO_{\min} = 0.8\,CFO\) — the index directly shows the stress-to-strength margin.

Two parts of the index

The simplified \(SI\) can be read as the product of two effects: a waveshape-severity term and a crest-ratio term \(E_c/CFO\) — separating the effect of waveform shape from the effect of voltage magnitude. If \(SI = 0.8\), the surge uses about 80% of the severity limit; to reach the critical \(SI = 1.0\) the crest could rise by \(1/0.8\), or the required CFO could fall to \(0.8\,CFO\).

Section 13

How Long to Track the Waveform — the 75% Rule

Why a practical cut-off works — the 75% rule

In theory the full waveform should be included, but once the voltage has fallen well below crest its contribution to leader development becomes much smaller. As a practical rule, compute the Severity Index until the voltage has decreased to at least 75% of its crest — this captures the most important high-voltage part without excessive computation.

Ideally the waveform would be considered from the start to \(t = \infty\) to capture its full destructive effect — but that can need excessive computation for long-tail or oscillatory surges. In practice, accuracy within about 5% is achieved by continuing until the voltage falls to about 80% of crest; as a general rule, continue until it has decreased to at least 75% of crest:

\[ \text{compute } SI \text{ until } e(t) \le 0.75\,E_c \]

This works because the most severe part of the waveform is near the crest, where leader progression is strongest; once the voltage decays significantly its contribution becomes small. The rule must still be applied carefully for unusual long-duration or slowly decaying waveforms, which may need further checks.

When the 75% rule needs a longer window

For slowly decaying oscillatory waves the 75% rule must be applied carefully. If later oscillations stay high, or the voltage repeatedly returns near crest, a longer calculation window may be required.

Section 14

Gas-Insulated Stations Are Treated Differently

Connecting to Part Five

As explained in Part Five, GIS insulation has an almost flat time-lag characteristic, so its strength does not increase significantly for short-duration waves. GIS surge evaluation is therefore normally a direct crest comparison with BIL, \(SI = E_c/\text{BIL}\) — nonstandard waveshape duration has little influence on GIS strength compared with external air insulation.

For GIS, the time-lag curve is essentially flat (with perhaps a small turn-up at submicrosecond times), so GIS strength is not strongly affected by the nonstandard waveshape the way air gaps are. The severity index is therefore a direct crest comparison:

\[ SI = \frac{E_c}{CFO} = \frac{E_c}{\text{BIL}} \]

So ordinary GIS coordination needs no detailed LPM or DE waveform evaluation — because the flat time-lag curve means waveshape duration has little effect within the range considered.

Section 15

Applying a Margin Through the Severity Index

A margin expressed through \(SI\)

A margin can be applied by requiring the Severity Index to be below 1.0. For example, for a 10% margin the acceptance criterion can be set to \(SI \le 0.90\).

The severity index is based on gap-breakdown mechanisms and gives a consistent evaluation — but it has not yet been used extensively everywhere, so some safety may still be wanted. Rather than adding a voltage margin directly, a margin can be applied to the index itself:

\[ SI \le 1.00 \;\text{(no explicit margin)} \qquad SI \le 0.90 \;\text{(}\approx 10\%\text{ margin)} \]

Requiring \(SI \le 0.90\) means the surge stress should not exceed 90% of the calculated severity limit — analogous to a safety margin, but applied to the severity index rather than the crest voltage.

A note on acceptance

Severity-index methods give a consistent, physically based approach, but they may not be used in every utility standard or project specification. Where a project standard requires a direct BIL comparison, the SI method can still be used as supporting engineering justification.

Section 16

Altitude Still Applies

Altitude must still be considered. At higher altitude the CFO or BIL of external insulation decreases with the lower air density, so \(CFO_{\text{altitude}} < CFO_{\text{sea level}}\) and \(BIL_{\text{altitude}} < BIL_{\text{sea level}}\). The altitude correction should be applied to the insulation strength before evaluating the severity index — and if a standard BIL is being selected, the selected value must compensate for the reduction.

Section 17

Engineering Lessons

The key lessons

LPM is the reference method — physics-based, the most accurate of the three.
DE with \(V_0 \neq 0\) is a useful approximation — good agreement with LPM for engineering use.
DE with \(V_0 = 0\) is for short surges only — errors over 30% for long / oscillatory waves.
Duration matters — a longer tail gives more time for leader development and raises severity.
GIS is different — flat time-lag, so compare the crest directly with BIL.
Apply margins through \(SI\) — e.g. \(SI \le 0.90\) for ~10% margin.

Section 18

Summary of Key Equations

Equation Summary

Severity index (crest)

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

Severity index (CFO)

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

Max permissible crest

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

Minimum required CFO

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

Crest ratio (reference)

\( \dfrac{E_c}{CFO} = \dfrac{2000}{1800} = 1.111 \)

DE (\(V_0=0\)) split

\( SI = (\text{shape})\dfrac{E_c}{CFO} \)

GIS severity index

\( SI = \dfrac{E_c}{\text{BIL}} \)

Time-duration rule

\( e(t) \le 0.75\,E_c \)

No-margin criterion

\( SI \le 1.00 \)

~10% margin criterion

\( SI \le 0.90 \)

Section 19

Reader Should Remember

This part compares the severity-index methods for nonstandard waveshapes on self-restoring insulation. The Leader Progression Model is the most physically based and is the accurate reference. The Destructive Effect method with \(V_0 \neq 0\) agrees reasonably well with LPM and is suitable for engineering use. The Destructive Effect method with \(V_0 = 0\) is simple and useful for short-duration surges, but can be seriously over-conservative for long-duration surges — errors above 30% when the tail is long.

The calculation need not run to infinity: continue until the voltage falls to at least 75% of crest. For GIS, the flat time-lag curve means waveshape effects are unimportant, so the crest is compared directly with BIL. And a margin can be applied by requiring the index below unity — e.g. \(SI \le 0.90\) for about 10%.

The single most important message

For self-restoring insulation, the severity index gives a consistent way to compare nonstandard surge waveshapes with standard insulation strength — but the method chosen must match the waveform duration and the insulation type.

Reader should remember

LPM is the most physically based method and is suitable as the reference. DE with \(V_0 \neq 0\) gives a good practical approximation. DE with \(V_0 = 0\) is simple but should only be used for short-duration surges or initial screening. Long-duration and oscillatory waves require caution, because low-voltage tails and repeated oscillations can distort the calculated severity. GIS is treated differently because its time-lag curve is almost flat.

This is Part Seven of the station lightning insulation coordination series, comparing the severity-index methods and setting the duration, GIS and margin rules. Later parts continue the series.

Section 20

Key Symbols

Table 4 — Key symbols used on this page.

Symbol	Meaning
SI	Severity Index
LPM / DE	Leader Progression Model / Destructive Effect method
\(V_0\)	Voltage below which no flashover is assumed in the DE method
\(E_c,\ E_{\max}\)	Crest of the applied nonstandard surge; maximum permissible crest of that shape
CFO / \(CFO_{\min}\) / \(CFO_{NS}\)	Standard-wave CFO; minimum standard CFO required; CFO for the nonstandard wave
BIL	Basic Lightning Impulse Level
\(E_A,\ E_t\)	Arrester voltage; equipment voltage to ground
\(T_f\)	Time to crest of the waveform
\(e(t)\)	Applied surge voltage as a function of time

Part Seven Reading now

Comparing the Severity-Index Methods

Comparing the methods on linear-front and oscillatory surges, the 75% duration rule, the GIS treatment and severity-index margins.

Series progress 7 of 8

Part Eight

Summary, Rules & Conclusions

The whole series drawn together — the key voltage and coordination equations, and the ten main conclusions and final engineering lessons.