Insulation Coordination

Backflash and the Backflashover Rate

When lightning hits the tower or shield wire — not the phase conductor — the tower voltage rises until the insulation flashes over backwards toward the phase: a backflash. How the insulation stress V_ins = V_tower − V_phase is built from footing resistance, tower surge, coupling and reflections; the condition V_ins ≥ CFO_NS; the critical current I_c; and the backflashover rate BFR = 0.6 N_L P(I ≥ I_c).

Reading time ≈ 40 min

Section 1

What a Backflash Is

This article is Part One of a five-part backflashover series. It introduces the physical mechanism and the basic BFR equation before later parts develop the impulse footing resistance, the CIGRE method, a sensitivity analysis and the line-design implications.

Overhead lines carry shield wires (ground wires) to intercept lightning so that most strokes no longer hit the phase conductors directly. Instead they terminate on the tower top, the shield wire, or a point along the span. A large current then flows down the tower into the footing and earth, and outward along the shield wires to adjacent towers.

That current drives the tower and shield wires to a high transient voltage. The phase conductor is not struck, but the tower voltage can rise so far that the insulation between tower and phase conductor breaks down. This flashover — from the tower/ground side toward the phase conductor — is a backflash (backflashover).

Why “back”-flash?

In the laboratory the impulse is applied to the conductor while the tower is earthed, so flashover runs conductor → tower. In a real tower stroke the highest voltage is on the tower/shield-wire side, so the apparent flashover direction reverses to tower → conductor — the opposite of the test, hence “backflash”.

Backflashover vs shielding failure

Do not confuse the two. In a shielding failure the lightning terminates directly on a phase conductor — the shield wire failed to intercept it. In a backflashover the lightning terminates on the tower or shield wire, and the insulation flashes over from the tower side toward the phase conductor.

Section 2

The Voltage Components and the Flashover Condition

The stress on the line insulation during a tower stroke is not one simple source — it is the sum of several components: the tower surge voltage, the footing-resistance voltage, the shield-wire voltage, the induced phase-conductor voltage (coupling), the power-frequency voltage, and travelling-wave reflections from adjacent towers. The insulation sees the difference between the tower side and the phase side:

\[ V_{\text{ins}} = V_{\text{tower side}} - V_{\text{phase conductor}} \qquad\text{backflash when}\quad V_{\text{ins}} \ge \text{CFO}_{\text{NS}} \]

Table 1 — Notation for the insulation voltage and the backflashover condition.

Symbol	Meaning
\(V_{\text{ins}}\)	Voltage across the line insulation (tower-to-phase)
\(\text{CFO}_{\text{NS}}\)	Non-standard critical flashover voltage — strength for the actual backflash waveform, not the standard \(1.2/50\,\mu\text{s}\) laboratory impulse CFO

The waveform here is not the standard \(1.2/50\,\mu\text{s}\) impulse, so the strength is the non-standard CFO, \(\text{CFO}_{\text{NS}}\) — not the standard-impulse CFO.

Section 3

Notation

Table 2 — Symbols used in the backflashover analysis.

Symbol	Meaning
\(I\) / \(I_c\)	Lightning stroke current crest / critical current for backflashover
\(t_f\)	Time to crest (front time) of the stroke current
\(C\)	Coupling factor between shield wire and phase conductor
\(Z_T\) / \(Z_g\)	Tower / shield-wire surge impedance
\(T_T\) / \(T_{TA}\)	Tower travel time to footing / to the crossarm (point A)
\(T_s\)	One-way travel time along one span
\(R_0\) / \(R_i\)	Measured (low-current) / impulse (high-current) footing resistance
\(I_i\)	Current through the struck-tower footing
\(\tau\)	Approximate time constant of the voltage tail
\(N_L\) / \(N_g\)	Strokes terminating on the line/shield wire / ground flash density
\(\text{BFR}\)	Backflashover rate

Section 4

The Coupling Factor

As the shield wire rises in voltage, the phase conductor is pulled up with it by electromagnetic coupling. If the shield-wire voltage is \(V_{gw}\), the induced phase voltage is \(V_{\text{phase}} = C\,V_{gw}\), so both sides of the insulation rise together and the stress falls:

\[ V_{\text{phase}} = C\,V_{gw} \qquad V_{\text{ins}} \approx V_{\text{tower}} - C\,V_{gw} \approx (1 - C)\,V_{\text{tower}} \]

Higher coupling → lower stress

In the backflashover case coupling is beneficial: the shield wire raises the phase-conductor voltage in the same direction as the tower-side voltage, so the net insulation stress \(V_{\text{ins}} = V_{\text{tower}} - C\,V_g\) falls and \(C\uparrow \Rightarrow V_{\text{ins}}\downarrow\). This is why measures that raise coupling — two shield wires, or an underbuilt ground wire — reduce the backflashover rate.

Section 5

The Footing-Resistance Component

A major part of the tower voltage comes from current flowing through the tower footing resistance:

\[ V_F = I_i\,R_i \qquad V_{\text{ins},F} \approx (1 - C)\,V_F = (1 - C)\,I_i\,R_i \]

This component is decisive: a high tower footing resistance strongly increases backflashover risk, and lowering it is usually the single most effective mitigation.

Section 6

Measured vs Impulse Footing Resistance

Footing resistance is normally measured at low current (\(R_0\)). Under a lightning stroke the current is very high, the soil field around the electrode can exceed the breakdown level, and soil ionisation effectively enlarges the electrode and lowers the resistance the impulse sees:

\[ R_i \le R_0 \]

So the struck tower should use the impulse value \(R_i\), not the measured \(R_0\). Adjacent towers carry much smaller current, so their footing stays closer to \(R_0\).

Watch the measured value

The measured low-current resistance \(R_0\) is not always the value seen during a lightning stroke. Using \(R_0\) directly for the struck tower can overestimate the tower voltage and the BFR — the impulse resistance \(R_i < R_0\) is treated in detail in Part Two.

Section 7

The Tower Surge Component and Front Time

The tower is not a simple lumped wire to a fast surge — it has surge impedance and travel time, and its voltage depends on current steepness. For a linear front:

\[ \frac{dI}{dt} \approx \frac{I}{t_f} \qquad t_f \downarrow \;\Rightarrow\; \frac{dI}{dt} \uparrow \;\Rightarrow\; V_{\text{tower}} \uparrow \]

So for the same current crest \(I\), a shorter front time gives a higher tower voltage — which is why \(t_f\) is one of the key variables in backflashover analysis.

Section 8

Adjacent-Tower Reflections

The struck tower is tied to adjacent towers by the shield wires. Travelling waves run out along the shield wires, reflect from the adjacent footings, and some return to the struck tower. If they arrive at or before the current crest, they reduce the struck-tower crest voltage — adjacent towers provide extra current paths and beneficial reflections. This is captured by a correction factor (e.g. \(K_{TT}\)):

\[ V_{\text{corrected}} = K\,V_{\text{uncorrected}}, \qquad K < 1 \]

Section 9

The Voltage Tail

After the front and crest, the tail is approximated conservatively by a single exponential decay:

\[ e(t) = V_F\,e^{-(t - t_0)/\tau} \]

Table 3 — Notation for the exponential voltage-tail approximation.

Symbol	Meaning
\(t_0\)	Reference time where the tail approximation begins
\(\tau\)	Tail time constant — larger \(\tau\) means a slower voltage decay

A slow-decaying tail can still matter for flashover, especially if the non-standard CFO is sensitive to wave duration.

Section 10

The Critical Current I_c

The critical current \(I_c\) is the minimum stroke crest that brings the insulation voltage up to the non-standard CFO:

\[ V_{\text{ins}}(I_c) = \text{CFO}_{\text{NS}} \qquad I \ge I_c \Rightarrow \text{backflash}, \quad I < I_c \Rightarrow \text{no backflash} \]

\(I_c\) depends on the tower surge impedance, footing resistance, coupling factor, front time, adjacent-tower reflections, the non-standard CFO, the power-frequency voltage, the number of phases and corona. Raising \(I_c\) is the goal of good design.

Section 11

Probability and the First BFR Estimate

Lightning current is random, so once \(I_c\) is known the flashover probability is simply the probability the stroke exceeds it — high \(I_c\) means few strokes exceed it, low \(I_c\) means many do. The first estimate of the backflashover rate is the number of strokes times that probability:

\[ P_{\text{flashover}} = P(I \ge I_c) \qquad \text{BFR} = N_L\,P(I \ge I_c) \]

Table 4 — Notation for the first backflashover-rate estimate.

Symbol	Meaning
\(N_L\)	Number of strokes terminating on the line / shield-wire system — usually per 100 km-year, not the ground flash density \(N_g\)
\(P(I \ge I_c)\)	Probability a stroke crest exceeds the critical current

\(\text{BFR}\) is normally quoted in flashovers per 100 km-year: number of strokes × probability each one flashes over.

BFR is a flashover rate, not an outage rate

A flashover is not always an outage. The outage rate may be lower, depending on arc self-extinction, the insulation type, protection operation and successful reclosing — the flashover-versus-outage distinction is developed in the line-design part.

Section 12

Strokes to the Line

The number of strokes a line collects grows with ground flash density, tower height, shield-wire separation and length. A common line-exposure form is:

\[ N_L \propto N_g\,\bigl(28\,h^{0.6} + S_g\bigr) \]

Table 5 — Notation for the line-exposure stroke-collection formula.

Symbol	Meaning
\(h\)	Tower height (m)
\(S_g\)	Horizontal distance between shield wires (m)
\(N_g\)	Ground flash density

The engineering message: \(h \uparrow \Rightarrow N_L \uparrow\) — taller lines collect more strokes.

Section 13

Strokes Within the Span — and the 0.6 Factor

The simple estimate assumes a stroke to the tower, but lightning can hit anywhere along the span. A span stroke raises the voltage at the stroke point, along the shield wire, at the adjacent towers and across both the span air gap and the tower insulator string. The span voltage may even be higher than at the tower — but the span insulation is much stronger, because the shield-wire-to-phase spacing in mid-span is far larger than the tower insulator clearance.

For a typical 500 kV line the minimum tower strike distance might be ~3.35 m while the span spacing is several times larger, so span flashover is possible but usually less probable than tower backflashover. Two further points reduce span flashover:

Front time: a slower front lowers span flashover — e.g. ~16% of relevant strokes for \(t_f = 2\,\mu\text{s}\), falling to ~2% for \(t_f = 4\,\mu\text{s}\).
Predischarge: at high overvoltage, predischarge currents between shield wire and phase conductor induce phase voltage and cut the span stress — inhibiting span flashover.

The 0.6 correction

A span stroke produces a tower voltage no higher than a direct tower stroke (\(V_{\text{tower,span}} \le V_{\text{tower,tower}}\)). So treating all shield-wire strokes as tower strokes is conservative; the tower-stroke BFR is scaled by about 0.6: \(\;\text{BFR} = 0.6\,N_L\,P(I \ge I_c)\). The 0.6 is a practical span-location correction — it does not mean only 60% of strokes hit the tower; it accounts for the fact that many strokes terminate along the shield-wire span and produce a lower tower voltage than a direct tower stroke.

Section 14

Power-Frequency Voltage

The phases already carry power-frequency voltage when the stroke arrives, so the total stress is the surge plus the instantaneous power-frequency voltage:

\[ V_{\text{total}} = V_{\text{surge}} + V_{\text{power-frequency}} \]

Depending on polarity and phase angle this can add to or subtract from the surge. Across three phases the instantaneous values differ, so at the stroke instant one phase is more vulnerable — three phases plus a random stroke instant raise the BFR versus a single-phase assumption.

Section 15

Non-Standard CFO, Front-Time Statistics and Corona

Non-standard CFO. The backflash waveform is not \(1.2/50\,\mu\text{s}\) — it can be very steep, short, long-tailed and full of reflections — so the standard CFO cannot be used directly; the condition is \(V_{\text{ins}} \ge \text{CFO}_{\text{NS}}\).

Front time is probabilistic and correlated with current: it should be treated as a conditional distribution \(f(t_f \mid I)\). Because the tower voltage depends on \(I/t_f\), a complete BFR uses the joint probability of \(I\) and \(t_f\), not the crest alone.

Corona — a front-only effect

Corona raises the shield-wire capacitance and lowers \(Z_g\) on the front; since \(C \approx Z_m/Z_g\), a lower \(Z_g\) raises the coupling factor and lowers \(V_{\text{ins}} \approx (1-C)V_{\text{tower}}\) — so corona appears to reduce BFR. But it acts mainly on the front, not the tail, so it must not be modelled as a uniform reduction of \(Z_g\) over the whole waveform or as a uniform reduction of the whole backflash risk.

Section 16

Reducing the Backflashover Rate

The same handful of quantities set the backflashover rate, so seeing what makes it worse shows directly how to make it better. The three key relationships, each with its physical chain:

Key relationships

Higher footing resistance

\(\displaystyle R_i \uparrow \;\Rightarrow\; V_{\text{tower}} \uparrow \;\Rightarrow\; I_c \downarrow \;\Rightarrow\; \text{BFR} \uparrow\)

Lower coupling

\(\displaystyle C \downarrow \;\Rightarrow\; V_{\text{phase}} \downarrow \;\Rightarrow\; V_{\text{ins}} \uparrow \;\Rightarrow\; \text{BFR} \uparrow\)

Lower insulation strength

\(\displaystyle \text{CFO}_{\text{NS}} \downarrow \;\Rightarrow\; I_c \downarrow \;\Rightarrow\; \text{BFR} \uparrow\)

Therefore, to reduce BFR

Reverse each relationship: \(R_i \downarrow \Rightarrow \text{BFR} \downarrow\), \(\;C \uparrow \Rightarrow \text{BFR} \downarrow\), \(\;\text{CFO}_{\text{NS}} \uparrow \Rightarrow \text{BFR} \downarrow\). Every lever reduces to one aim: increase the critical current \(I_c\), because a higher \(I_c\) means fewer strokes exceed it — so \(\text{BFR} = 0.6\,N_L\,P(I \ge I_c)\) falls. Each measure below works by raising \(I_c\) (or lowering the stress):

Table 6 — Practical mitigation measures.

Measure	Mechanism
Reduce tower footing resistance	\(R_i \downarrow \Rightarrow V_F \downarrow \Rightarrow I_c \uparrow\) — usually the most effective measure
Improve shield-wire / phase coupling	\(C \uparrow \Rightarrow V_{\text{ins}} \downarrow\)
Increase insulation strength	\(\text{CFO}_{\text{NS}} \uparrow \Rightarrow I_c \uparrow\) (longer insulators)
Optimise tower / shield-wire geometry	Shielding, coupling, span flashover, voltage distribution
Line surge arresters	Limit the voltage across the insulation where justified
Account for ground flash density	High \(N_g\) regions have higher BFR for the same design

Section 17

Workflow, Key Messages and Memory Map

Backflashover workflow

Find the line exposure \(N_L\) from \(N_g\), tower height \(h\), shield-wire separation \(S_g\) and length.
Compute the tower/shield-wire surge response — tower surge voltage, footing voltage, adjacent-tower reflections, coupling.
Form the insulation voltage \(V_{\text{ins}} = V_{\text{tower side}} - V_{\text{phase}}\) (with coupling and power-frequency voltage).
Convert the standard CFO to \(\text{CFO}_{\text{NS}}\) for the actual waveform.
Find the critical current \(I_c\) from \(V_{\text{ins}}(I_c) = \text{CFO}_{\text{NS}}\), then \(P(I \ge I_c)\).
First estimate \(\text{BFR} = N_L\,P(I \ge I_c)\); with the span adjustment \(\text{BFR} = 0.6\,N_L\,P(I \ge I_c)\).
Refine with span strokes, power-frequency voltage, three phases, impulse footing, \(f(t_f\mid I)\), corona — usually by computer/EMT statistical simulation.

Key messages

Backflash is a stroke to the tower or shield wire that raises the tower voltage and stresses the insulation — not a direct strike to the phase.
The condition is \(V_{\text{ins}} \ge \text{CFO}_{\text{NS}}\); the critical current \(I_c\) is the crest that reaches it.
First estimate \(\text{BFR} = N_L\,P(I \ge I_c)\); adjusted for span location, \(\text{BFR} = 0.6\,N_L\,P(I \ge I_c)\).
The biggest levers are footing resistance, coupling factor, tower surge impedance, current crest and front time, non-standard CFO, adjacent-tower reflections, power-frequency voltage, span location and corona.
Most effective mitigation: lower the footing resistance, raise insulation strength, improve coupling, and add line arresters where justified.

Equation Summary

Insulation stress

\(\displaystyle V_{\text{ins}} = V_{\text{tower}} - V_{\text{phase}}\)

Backflash condition

\(\displaystyle V_{\text{ins}} \ge \text{CFO}_{\text{NS}}\)

Coupling

\(\displaystyle V_{\text{ins}} \approx (1 - C)\,V_{\text{tower}}\)

Footing component

\(\displaystyle V_F = I_i\,R_i\)

Tower front

\(\displaystyle \frac{dI}{dt} \approx \frac{I}{t_f}\)

Critical current

\(\displaystyle V_{\text{ins}}(I_c) = \text{CFO}_{\text{NS}}\)

Line exposure

\(\displaystyle N_L \propto N_g\,(28\,h^{0.6} + S_g)\)

Backflashover rate

\(\displaystyle \text{BFR} = 0.6\,N_L\,P(I \ge I_c)\)

Part One Reading now