Insulation Coordination

Line Arresters: Application, Energy Duty and Failure Probability

A line arrester sits across the line insulation and is exposed to lightning far more directly than a station arrester — so the deciding question is whether it can survive the energy and current duty. Part One explains why most line applications use heavy-duty distribution-class arresters, why energy capability is probabilistic rather than a hard limit, how shielded and unshielded lines differ, and how a realistic arrester failure rate (\(\approx 0.55\%\), not \(14\%\)) is built statistically from stroke current, tail duration and stroke location.

Reading time ≈ 30 min

Section 1

What a Line Arrester Has to Survive

This page is about surge arresters installed directly on overhead lines — line arresters — whose purpose is to reduce or eliminate lightning flashovers on transmission and distribution lines. A line arrester is normally installed across the line insulation, between the phase conductor and the tower / earth structure.

The central application question

Can the arrester survive the lightning energy and current duty on the line?

This differs from station arrester application. In a substation, the arrester is normally protected by the line insulation and station layout. On a line, the arrester may be exposed much more directly to lightning — so its energy duty, not just its protective level, is the deciding factor.

This is Part One of a self-study series on line arresters.

What this page teaches

why line arresters are a more direct lightning duty than station arresters;
why most line applications use heavy-duty distribution-class arresters;
why arrester energy capability is probabilistic, not a hard limit;
how shielded and unshielded lines differ in arrester duty;
how the number of towers, span length and stroke tail change the energy;
why tower strokes and shielding failures behave differently;
how a statistical failure rate is built for an unshielded line;
why treating rated energy as a hard limit grossly overestimates failures.

The thesis of this series

Line arrester design is both an insulation-performance problem and a reliability-probability problem — the arrester must clamp the voltage and survive a statistically uncertain energy duty.

Section 2

Why Line Arresters Became Practical

Older line-protection devices such as protector tubes had poor reliability and were discontinued. Line arresters became attractive with the metal oxide arrester block — higher energy capability, non-ceramic housings, better mechanical performance and improved failure safety all made line application practical.

An early application was on a \(138\ \text{kV}\) American Electric Power tower that suffered an unusually high number of flashovers — on a mountain, in rock formations, where supplemental grounding was difficult. Station-class arresters were installed there and on adjacent towers, and the application succeeded. This led to wider use on difficult locations:

Table 1 — Difficult line locations where installing line arresters is most beneficial.

Where Line Arresters Help Most
Towers with poor grounding
River-crossing towers
Towers on rocky ground
Line sections with a high flashover rate
One circuit of a double-circuit line, to avoid double-circuit outages

Section 3

Shielded versus Unshielded Lines

The most important distinction is whether the line has overhead ground wires. On shielded lines the ground wires intercept many strokes, so the arrester mainly sees backflashover-related events, shielding failures and coupled travelling waves — a generally manageable duty. On unshielded lines the phase conductors are directly exposed, and large stroke currents can impinge directly on the arrester.

The hostile case

Unshielded lines impose a much higher arrester energy risk — the stroke current is not limited by the shielding-failure mechanism. Early field experience nonetheless suggested failure rates below about \(1\%/\text{year}\) were achievable.

On a shielded line a direct phase stroke occurs only as a shielding failure, whose maximum current is limited by the shielding geometry — typically in the \(5\)–\(10\ \text{kA}\) range. On an unshielded line the phase conductor can receive much larger strokes, so the arrester energy may exceed rated capability and the probability of that must be calculated (developed later on this page).

Section 4

Which Arrester, and the Main Concern

In most cases — even for transmission lines — line applications use heavy-duty distribution-class arresters, not always a station-class unit. Selection depends on voltage level, energy duty, mechanical requirements, installation practicality, cost, housing safety and expected lightning exposure.

The application concerns are arrester energy discharge, arrester current magnitude, probability of failure, mechanical and public safety, housing type, the number of arresters installed, and shielded-versus-unshielded exposure. The single most important electrical concern is simple:

The governing check

The energy discharged by the arrester must be compared with the arrester energy capability.

Section 5

Energy Capability Is Probabilistic

Energy capability is not a fixed cliff-edge value — it is probabilistic. A Weibull cumulative distribution approximates the probability of arrester failure. The manufacturer's rated energy is taken to represent zero probability of failure, located about \(4\) standard deviations below the mean — so higher energies can sometimes be survived, but with increasing failure probability:

\[ W_e \uparrow \;\Rightarrow\; P_{FA} \uparrow \]

Table 2 — Notation for the probabilistic arrester energy capability quantities.

Symbol	Meaning
\(W_e\)	Energy capability for a selected probability of failure
\(W_v\)	Rated energy capability from the manufacturer
\(P_{FA}\)	Probability of arrester failure

This lets the engineer estimate a failure rate realistically, instead of simply declaring failure the moment rated energy is exceeded.

Section 6

The Example Arrester and Its Capability Curve

The 115 kV line study uses a \(76\ \text{kV}\) MCOV heavy-duty distribution-class arrester with a rated energy capability of \(167\ \text{kJ}\). The energy survivable at each failure probability is:

Table 3 — Energy the example arrester survives at each failure probability.

Probability of Failure	Energy Capability
\(0\%\)	\(167\ \text{kJ}\) (rated)
\(1\%\)	\(274\ \text{kJ}\)
\(5\%\)	\(316\ \text{kJ}\)
\(50\%\)	\(418\ \text{kJ}\)

Do not treat rated energy as a hard physical failure limit

The \(167\ \text{kJ}\) rating is a conservative zero-failure-probability reference, not the energy at which the arrester physically fails. Higher energies are often survived — failure assessment must consider the probability of failure at higher energy levels (the curve above), not a single hard threshold.

A heavy-duty distribution arrester can also discharge a \(100\ \text{kA}\), \(4/10\ \mu\text{s}\) current impulse. Current capability is likely probabilistic too, but at the time of the source it could only be stated as \(100\ \text{kA}\) at zero failure probability.

Two duties, not one

Both energy and current duty must be considered for line arresters.

Section 7

Housing Safety

Line arresters are installed outdoors, often near public or accessible areas. If an arrester fails, ejected parts must not create a hazard — which is why line arresters generally use non-ceramic housings.

A real application criterion

Non-ceramic housings are preferred because they reduce the risk of dangerous fragmented porcelain during failure — a major practical criterion, not an afterthought.

Section 8

The Studied 115 kV Line

Table 4 — Key electrical parameters of the studied 115 kV line.

Quantity	Value
Ground-wire surge impedance	\(339\ \Omega\)
Phase-conductor surge impedance	\(366\ \Omega\)
Span length	\(230\ \text{m}\)
Measured footing resistance \(R_0\)	\(55\ \Omega\)
Soil resistivity / \(\rho/R_0\)	\(1000\ \Omega\cdot\text{m}\) / \(18.2\ \text{m}\)
Arrester MCOV	\(76\ \text{kV}\)

The mutual surge impedances between ground wires and phase conductors give a different coupling factor for each phase. These factors describe how tower / ground-wire voltage couples onto the phases, and they matter for both backflashover and arrester energy distribution:

Table 5 — Ground-wire-to-phase coupling factors for each conductor.

Phase	Coupling Factor
A	\(0.331\)
B	\(0.386\)
C	\(0.331\)

Section 9

Shielding Failure: the Number of Arrester Towers

The first shielded case is a shielding-failure stroke to phase A, with a current equal to the maximum shielding-failure current \(I = 12.3\ \text{kA}\), applied at the centre tower of an 11-tower ATP model with arresters on each phase. The footing resistance stays at \(55\ \Omega\) (the footing current is less than half the critical grounding current).

The energy in the struck-tower arrester depends strongly on how many towers have arresters:

More arrester towers, less struck-tower energy

Adding arresters on adjacent towers reduces the energy in the struck-tower arrester — the energy is shared among more arresters and the current tail becomes shorter. With only one tower fitted, the energy is maximum.

Sharing is not equal It is tempting to assume energy splits equally (e.g. one fifth each across five towers), but the actual sharing is not equal — the struck tower normally carries the highest duty. Do not assume equal energy sharing between line arresters.

Section 10

Shielding Failure: Span Length and Stroke Tail

For shielding failure, shorter spans are beneficial. With 11 arrester towers and a stroke tail \(t_T = 100\ \mu\text{s}\):

Table 6 — How span length affects shielding-failure arrester energy.

Span Length	Arrester Energy
\(100\ \text{m}\)	\(36\ \text{kJ}\)
\(230\ \text{m}\)	\(51\ \text{kJ}\)
\(400\ \text{m}\)	\(62\ \text{kJ}\)

So a longer span increases the arrester energy. The stroke tail \(t_T\) (the current time to half value) has an even stronger effect, for 230 m spans and 11 arrester towers:

Table 7 — How stroke tail duration affects shielding-failure arrester energy.

Stroke tail \(t_T\)	Arrester Energy
\(100\ \mu\text{s}\)	\(\approx 51\ \text{kJ}\)
\(200\ \mu\text{s}\)	\(\approx 81\ \text{kJ}\)
\(300\ \mu\text{s}\)	\(\approx 111\ \text{kJ}\)

Longer = more energy

Longer span length and especially a longer stroke tail increase the arrester energy — more current duration simply means more energy.

Section 11

Shielding Failure: Reflections and Phase Interaction

For the \(12.3\ \text{kA}\) shielding-failure stroke the time to crest is \(0.78\ \mu\text{s}\). Because reflections from adjacent towers arrive before the current crest, the crest current through the struck arrester is reduced to about \(8.4\)–\(8.9\ \text{kA}\) — a reminder that line reflections can reduce the arrester current, not only increase it.

A stroke to phase A couples voltage onto phases B and C, but the ground-wire voltage is greater than the coupled voltages, so the B and C arrester currents may be of opposite polarity to the struck-phase current. The source calls this interesting but unimportant:

Essentially a single-phase event

Shielding failure is essentially a single-phase event — arresters on the other phases do not significantly affect the energy discharged by the struck-phase arrester.

Section 12

Shielding Failure: the Acceptability Check

For the 11-tower, 230 m span case the first stroke gives about \(51\ \text{kJ}\) and each subsequent stroke about \(32\ \text{kJ}\). Assuming two subsequent strokes:

\[ W_{\text{total}} = 51 + 2(32) = 115\ \text{kJ} \]

Acceptable for shielding failure

Since \(115\ \text{kJ} < 167\ \text{kJ}\) (the rated energy), the application is acceptable from a shielding-failure standpoint.

Section 13

Strokes to the Tower

The next case is a \(100\ \text{kA}\) stroke to the tower, with 230 m spans and \(t_T = 100\ \mu\text{s}\). Here the footing resistance matters, because the stroke current flows through the tower and footing system (the impulse footing resistance is adjusted using the footing current). This case behaves differently from shielding failure:

Adjacent arresters can raise the energy

For tower strokes, adding arresters on adjacent towers can increase the struck-tower energy — currents through the adjacent arresters have opposite polarity and flow back toward the struck-tower arrester. Adding adjacent arresters does not always reduce energy for tower-stroke cases.

For a tower stroke the energy divides among the three phase arresters: phases A and C discharge equal energies, while the phase B arrester carries only about \(50\)–\(65\%\) of that (its coupling factor differs). From an energy viewpoint, that is a reason to fit arresters on all three phases.

Section 14

Stroke Location and Footing Resistance

Strokes can terminate anywhere along the span. For a stroke to midspan, the energy in adjacent arresters is much lower — about \(25\%\) of the stroke-to-tower value:

Tower strokes are the more severe case

Tower strokes are more severe for arrester energy than midspan strokes in this configuration.

Unlike shielding failure, tower-stroke energy depends on footing resistance. For 11 arrester towers, a \(100\ \text{kA}\) stroke and \(t_T = 100\ \mu\text{s}\), the energy reaches about \(52\ \text{kJ}\) at \(R_0 = 120\ \Omega\), with arrester currents staying moderate (below about \(10\ \text{kA}\)).

Section 15

The Shielded-Line Conclusion

Table 8 — Key findings summarising arrester duty on the shielded line.

Finding for the shielded 115 kV line
Shielding failure generally produces more arrester energy than stroke-to-tower events
Stroke-to-tower arrester energy is usually below about \(50\ \text{kJ}\)
Arrester current is moderate, around \(10\ \text{kA}\) or less
Shielding failure is limited by the maximum shielding-failure current
Total shielding-failure energy stays below rated energy in the studied case

Shielded lines are generally acceptable

Line arresters on shielded overhead lines are generally acceptable from energy and current viewpoints, for the studied configuration.

Section 16

The Unshielded Line

Removing the ground wires exposes the phase conductors directly. A \(12.3\ \text{kA}\) stroke to the phase conductor at the tower gives curves similar to the shielding-failure case (with somewhat lower energies for this particular current). But the \(12.3\ \text{kA}\) case is not the real problem:

No shielding-failure current limit

On an unshielded line the stroke current is not limited by the shielding-failure mechanism — large direct strokes can hit the phase conductor, so the arrester energy may exceed rated capability and its probability must be calculated.

Section 17

The Failure-Probability Method

For unshielded lines the method builds curves of stroke tail \(t_T\) versus current \(I\) for different arrester failure probabilities (\(0\%, 1\%, 5\%, 50\%\), corresponding to \(167, 274, 316, 418\ \text{kJ}\)), for strokes to the phase conductor at the tower and at midspan. The probability of exceeding a given energy is found by integrating over both stroke current magnitude and stroke tail duration:

Two variables, not one

Failure risk depends on both current magnitude and stroke duration — a large current with a short tail may be less severe than a lower current with a very long tail.

For the zero-failure-probability energy of \(167\ \text{kJ}\), the probability of exceeding it is:

Table 9 — Probability of exceeding rated energy for tower and midspan strokes.

Stroke Location	Probability of exceeding \(167\ \text{kJ}\)
Stroke at tower	\(0.201\)
Stroke to midspan	\(0.219\)

Using rated energy as a hard limit:

\[ P_{\text{exceed}} = \frac{0.201 + 0.219}{2} = 0.210 \]

which would imply a failure rate of about \(14\%\) per 100 km-year — but that is overly severe because it ignores the probabilistic capability above rated energy.

Section 18

The Interval-Probability Calculation

The realistic method divides the energy range into intervals and, for each interval:

find the probability of exceeding the lower energy;
find the probability of exceeding the upper energy;
subtract to get the probability within the interval;
multiply by the average failure probability in that interval;
sum all interval contributions.

Table 10 — Interval-summed failure probability for tower and midspan strokes.

Stroke Location	Summed Probability of Arrester Failure
Stroke at tower	\(0.08442\) (\(\approx 8.442\%\))
Stroke to midspan	\(0.07796\) (\(\approx 7.796\%\))

Assuming half the strokes hit the tower and half hit midspan, the average failure probability per direct stroke is:

\[ P_{\text{failure,avg}} = \frac{0.08442 + 0.07796}{2} = 0.08119 \quad (\approx 8.119\%) \]

Section 19

From Probability to a Failure Rate

For the unshielded 115 kV line there are \(87.7\) flashes per 100 km-year (ground flash density \(N_g = 6\ \text{flashes/km}^2\text{-year}\)). The 100 km line has \(435\) towers with three arresters each. The chain to a per-arrester failure rate is:

\(87.7\) flashes / 100 km-yr

\(\times\,P_{\text{avg}} = 0.0812\)

\(7.12\) failures / 100 km-yr

\(\div\,1305\) arresters

\(\approx 0.55\%\) per arrester

\[ N_{\text{failures}} = 0.08119 \times 87.7 = 7.12, \qquad \lambda = \frac{7.12}{435 \times 3} = \frac{7.12}{1305} \approx 0.55\% \]

Table 11 — Failure rate from hard-limit versus probabilistic capability methods.

Method	Estimated Failure Rate
Rated energy as a hard limit	\(\approx 14\%\)
Probabilistic energy capability	\(\approx 0.55\%\)

Use probabilistic capability

Treating rated energy as an absolute failure threshold overestimates the failure rate by more than an order of magnitude (\(14\%\) vs \(0.55\%\)). The \(0.55\%\) figure agrees reasonably with field experience. Line arrester failure assessment should use probabilistic energy capability.

Section 20

Subsequent Strokes and the Application Workflow

The analysis should also include subsequent strokes in the same way — a flash usually contains a first stroke plus subsequent strokes, and the cumulative energy increases the arrester duty. A complete assessment must consider multi-stroke flash energy. The full application workflow:

Line type: shielded / unshielded

Tower geometry & span

Grounding & footing resistance

Candidate MCOV & class

Model SF / direct stroke

Arrester current & energy

Include first & subsequent strokes

Compare with probabilistic capability

Estimate failure rate

Check housing safety & mechanical

Confirm line arrester application

Section 21

Shielded vs Unshielded, Misconceptions and Final Message

Table 12 — Comparison of arrester duty on shielded versus unshielded lines.

Item	Shielded Line	Unshielded Line
Phase stroke exposure	Limited by shielding failure	Direct phase strokes possible
Stroke current	Limited by shielding geometry	Not limited the same way
Arrester energy	Generally manageable	Probabilistic failure assessment required
Main concern	Shielding failure and tower strokes	Direct-stroke energy
Failure-rate method	Often an energy check is sufficient	Statistical energy / failure-rate calculation

Table 13 — Common line-arrester misconceptions corrected against proper engineering interpretation.

Misconception	Correct Interpretation
“Line arresters behave like station arresters”	They can be exposed much more directly, especially on unshielded lines
“Adding arresters always reduces the struck-tower energy”	True for shielding failure, but not always for tower strokes
“Shielding failure is always the most severe event”	On unshielded lines, direct phase strokes can be far worse
“Rated energy is a strict failure limit”	It is a zero-failure-probability level, not the physical threshold
“Only first strokes matter”	Subsequent strokes add cumulative energy and must be considered
“Ceramic housings are fine anywhere”	Non-ceramic housings reduce hazard from ejected fragments at failure

Equation Summary

Average Failure Probability

\(\displaystyle P_{\text{avg}} = \frac{P_{\text{tower}} + P_{\text{midspan}}}{2}\)

Averages the failure probability between tower and midspan strokes.

Expected Number of Failures

\(\displaystyle N_{\text{fail}} = P_{\text{avg}}\,N_{\text{flashes}}\)

Failures per 100 km-year from the average probability and the flash count.

Failure Rate per Arrester

\(\displaystyle \lambda = \frac{N_{\text{fail}}}{N_{\text{arr}}}\)

Spreads the expected failures across all installed arresters.

Arrester Energy

\(\displaystyle W_A = \int v_A(t)\,i_A(t)\,dt\)

Energy is the integral of arrester voltage times current over time.

Arrester Energy Estimate

\(\displaystyle W_A \approx E_A\,I_A\,T\)

A quick estimate from discharge voltage, current and duration.

Flashover Criterion

\(\displaystyle E_{\text{ins}} < \text{CFO}\)

Insulation is safe while its voltage stays below the CFO.

Memory map. Identify shielded vs unshielded → for shielded lines an energy check usually suffices (SF \(< 167\ \text{kJ}\)) → for unshielded lines build \(t_T\)–\(I\) failure curves → integrate over current and tail → interval-sum the failure probability → multiply by flash rate → divide by installed arresters → \(\approx 0.55\%\) per arrester, not \(14\%\).

Final engineering message

Line arresters effectively reduce lightning flashovers. On shielded lines the energy and current are usually manageable because the ground wires limit direct phase exposure; on unshielded lines, direct strokes impose much higher, more uncertain duty. So arrester energy must be assessed statistically, especially on unshielded lines — rated energy is not a hard physical failure boundary, and a realistic failure rate must account for stroke current, tail duration, location, the probability of failure at each energy, the number of installed arresters, the flash density and subsequent strokes. In short: line arrester design is both an insulation-performance problem and a reliability-probability problem.

Part One Reading now

Application, Energy Duty and Failure Probability

Why line arresters are a direct lightning duty, heavy-duty distribution-class selection, probabilistic energy capability, shielded versus unshielded duty, and a statistical arrester failure-rate calculation.

Series progress 1 of 3

Part Two

Arrester Current, Energy and Intermediate-Tower Protection

Estimating arrester current and energy with travelling-wave and inductance analysis, why arrester current is not the stroke current, energy sharing across towers, and whether every-second-tower arresters protect the intermediate tower.