Section 1
Which Assumptions Really Matter?
This article is Part Four of the backflashover series. Parts One to Three introduced the backflashover mechanism, the impulse footing resistance and the CIGRE calculation method. This page examines which assumptions have the largest influence on the calculated BFR.
Once the CIGRE backflashover method is in place, the next question is not how to compute the rate but which of its many uncertain inputs actually move the answer. A backflashover calculation carries a long list of approximate quantities:
\[ \text{CFO}_{\text{NS}},\; R_i,\; t_f,\; C,\; Z_g,\; Z_T,\; N_g,\; K_{PF} \]
A sensitivity analysis changes each in turn and watches the calculated BFR respond. The source examines the accuracy of the \(\text{CFO}_{\text{NS}}\) regression, the validity of the simplified method, corona, \(R_0 \to R_i\), one versus two shield wires, an underbuilt ground wire, counterpoises, medium-voltage and distribution performance, and the CIGRE–IEEE comparison. The aim is engineering judgement: not merely to calculate BFR, but to know which design changes are effective.
Which parameters move BFR most?
In rough priority order: footing resistance (\(R_0 \to R_i\)), tower height \(h\), coupling \(C\) and the shield-wire arrangement — the dominant design-side levers; then the modelling assumptions \(t_f\) and the tower component, \(\text{CFO}_{\text{NS}}\) and corona (important especially for high towers); and the exposure term \(N_g\). The detail of each follows below.
Section 2
The Test Lines and Base Case
Representative high-voltage geometries are used — 230 kV double-circuit and single-circuit, 500 kV single-circuit, different tower heights, one or two shield wires, with or without an underbuilt ground wire. The main high-voltage cases share a fixed exposure so that the changes in BFR are caused by the line, not the lightning:
Table 1 — Base-case assumptions for the high-voltage sensitivity studies.
| Quantity | Value |
|---|
| Span length | 300 m |
| CFO | 1200 kV |
| Ground flash density \(N_g\) | 4 flashes/km²-year |
With exposure held constant, any change in BFR is attributable to tower geometry, grounding, corona, coupling and the modelling method — exactly the levers a designer can pull.
Section 3
Is the CFONS Regression Trustworthy?
The backflash waveform is not a standard \(1.2/50\,\mu\text{s}\) impulse, so the strength is the non-standard \(\text{CFO}_{\text{NS}}\). The CIGRE method replaces a full Leader Progression Model (LPM) simulation with a regression equation. If that shortcut is inaccurate, every BFR built on it is suspect — so the test is direct:
\[ \text{full LPM} \quad\overset{?}{\approx}\quad \text{CFO}_{\text{NS}}\ \text{regression equation} \]
The comparison used a 230 kV double-circuit line with two shield wires at tower heights of 35 m and 70 m. The result: the regression gives excellent agreement with the direct LPM for the studied cases and within the parameter range used to develop it. In the 70 m case the curves are almost identical, parting only slightly at low footing resistances of about \(5\,\Omega\) to \(15\,\Omega\). This is what makes the CIGRE method practical without a leader-progression run for every case — but outside that range, a direct LPM or a more detailed insulation-strength assessment should be considered.
Section 4
When the Simplified Method Holds — and When It Fails
The simplified method neglects the tower component of voltage, keeping mainly the footing-resistance and coupling terms so that front time \(t_f\) is no longer a major variable:
\[ V_{\text{ins}} \approx (1 - C)\,I_i R_i + K_{PF}\,V_{LN} \]
For lower towers (\(h \approx 35\) m) the tower surge is not dominant, so the simplified result tracks the full CIGRE method closely. For high towers (\(h \approx 70\) m) the travel time \(T_T\) and the tower surge \(\Delta V_T\) both grow, so neglecting them understates the insulation stress and yields a BFR that is too low. The practical method-selection rule:
Table 2 — When the simplified method suffices and when the full CIGRE method is needed.
| Tower Height | Recommended Approach | Reason |
|---|
| \(h < 50\,\text{m}\) | Simplified method may be acceptable | Tower component is usually less dominant |
| \(h \ge 50\,\text{m}\) | Full CIGRE method should be used | Tower surge component becomes more important |
The 50 m value should be treated as a practical rule of thumb, not a strict physical boundary. For tall towers, steep current fronts, long spans or high-reliability studies, the full CIGRE method is preferred.
Section 5
The Effect of Corona
Corona on the shield wire lowers its effective surge impedance \(Z_g\), which raises the coupling factor \(C\). Since the insulation voltage is the tower voltage minus the coupled phase voltage, more coupling means less stress:
\[ Z_g \downarrow \;\Rightarrow\; C \uparrow \;\Rightarrow\; V_{\text{ins}} \approx V_T - C V_g \;\downarrow \]
For the 230 kV double-circuit line with two ground wires, the corona effect is small for lower towers but more noticeable near 70 m, where the larger tower voltage makes front-shape effects matter more. Neglecting corona is conservative — it gives a slightly higher BFR:
\[ \text{neglect corona} \;\Rightarrow\; \text{BFR slightly higher (conservative)} \]
The balanced view: corona increases coupling on the wave front and tends to reduce the crest stress, but it acts mainly on the front and not the whole tail of the wave — so its effect on BFR is often limited. Neglecting it is generally conservative for ordinary towers, while it becomes more relevant for high towers or where the tower component is significant (consistent with the CIGRE method treatment).
Section 6
R0 versus Ri — the Dominant Effect
This is one of the most important sensitivities of all. The measured low-current footing resistance is \(R_0\); under high lightning current the soil ionises and the effective impulse resistance \(R_i\) falls below it. The footing voltage scales directly with whichever value is used:
\[ V_F = I_i R \qquad R_i < R_0 \;\Rightarrow\; V_F \downarrow \;\Rightarrow\; I_c \uparrow \;\Rightarrow\; \text{BFR} \downarrow \]
- \(R_0\)
- measured low-current footing resistance
- \(R_i\)
- high-current (impulse) footing resistance after soil ionisation
- \(I_i\)
- current into the footing
One of the strongest sensitivities
The reduction from the measured low-current resistance \(R_0\) to the high-current impulse resistance \(R_i\) is one of the strongest sensitivities in the whole BFR calculation: \(R_i < R_0\), and \(R_i \downarrow \Rightarrow V_F \downarrow \Rightarrow I_c \uparrow \Rightarrow \text{BFR} \downarrow\). It must not be used to justify poor grounding, though — a high measured \(R_0\) still indicates a weak tower footing system.
Assuming \(R_i = R_0\) ignores ionisation and pushes the tower voltage — and hence the BFR — much too high. For a representative case with \(R_0/\rho = 20\), the impulse resistance is roughly \(R_i \approx 0.5\,R_0\): the lightning current sees only about half the measured value. The ratio \(R_0/\rho\) (equivalently \(\rho/R_0\)) is a compact way of linking soil resistivity and measured footing resistance in the impulse-resistance model — it sets how strongly soil ionisation reduces the effective resistance during a high-current stroke. The practical tension is clear: using \(R_0\) directly may badly overestimate BFR, but using \(R_i\) demands a justified impulse-resistance model.
Section 7
Span Length
Increasing the span raises the BFR. For the studied case, going from 300 m to 600 m increased the BFR by about 60%. The reason is travel time: beneficial reflections from the adjacent towers take longer to return for longer spans:
\[ \text{longer span} \;\Rightarrow\; T_s \uparrow \;\Rightarrow\; \text{relief arrives later} \;\Rightarrow\; \text{BFR} \uparrow \]
This makes span length a real consideration in tower spotting and line design, not just a mechanical or cost parameter.
Section 8
One Shield Wire versus Two
The number of shield wires changes several parameters at once. Two wires in parallel lower \(Z_g\), which raises coupling and lowers the insulation stress; one wire does the opposite:
\[ \text{two wires:}\quad Z_g \downarrow,\; C \uparrow,\; V_{\text{ins}} \downarrow \qquad\qquad \text{one wire:}\quad Z_g \uparrow,\; C \downarrow,\; V_{\text{ins}} \uparrow \]
For the 230 kV double-circuit line, using one shield wire instead of two approximately doubles the BFR:
\[ \text{one shield wire} \;\Rightarrow\; \text{BFR} \approx 2 \times (\text{two shield wires}) \]
The mechanism is physical: two shield wires lower the effective ground-wire surge impedance \(Z_g\), raise coupling \(C\) to the phases, and give a better surge-current path to the adjacent towers — so \(Z_g \downarrow, C \uparrow \Rightarrow V_{\text{ins}} \downarrow \Rightarrow I_c \uparrow \Rightarrow \text{BFR} \downarrow\). One shield wire can still be justified where lightning density is low, economics dominate, the voltage is lower or the required reliability is modest — but technically, two wires give clearly better performance.
Section 9
The Underbuilt Ground Wire
An underbuilt ground wire is a grounded conductor strung below the phase conductors. Because it is not above them it does not intercept strokes, so it barely helps shielding-failure performance. Its job is different: it increases coupling to the phases, especially the lower ones. Since the insulation stress is the tower voltage minus the coupled phase voltage:
\[ V_{\text{ins}} = V_{\text{tower}} - V_{\text{phase}}, \qquad V_{\text{phase}} = C V_g \;\Rightarrow\; C \uparrow \Rightarrow V_{\text{ins}} \downarrow \]
For a 230 kV double-circuit line, adding the underbuilt wire makes the coupling factors both larger and more uniform across phases:
Table 3 — Coupling factors with and without an underbuilt ground wire.
| Configuration | \(C_A\) | \(C_B\) | \(C_C\) |
|---|
| Without underbuilt wire | 0.350 | 0.248 | 0.183 |
| With underbuilt wire | 0.441 | 0.347 | 0.307 |
The result is a dramatic BFR reduction. Yet utilities do not fit them everywhere, because a grounded conductor below the phases must be coordinated with conductor sag, temperature, ice and wind loading, electrical clearance and mechanical safety. Technically very effective, but the sag and clearance coordination limits its use.
Section 10
The Counterpoise
A counterpoise is a buried horizontal conductor connected to the tower base. It lowers the footing resistance and therefore the BFR:
\[ R_i \downarrow \;\Rightarrow\; \text{BFR} \downarrow \]
The caveat is the model. Treated like a concentrated footing electrode, a counterpoise shows a large BFR reduction in the sensitivity study — but that lumped approximation is imperfect. Its high-current impulse behaviour is harder to model than concentrated grounds because, during the early part of the surge, a counterpoise behaves as a travelling-wave element rather than a simple lumped resistance (developed in Part Two). The benefit is real; the detailed impulse modelling remains uncertain.
Section 11
Backflashover of 34.5 kV Lines
Backflashover is not a transmission-only problem. A 34.5 kV line has weaker insulation but usually lower structures and shorter spans. With \(N_g = 4\) flashes/km²-year and footing resistance \(R_0 = 20\)–\(40\,\Omega\), the reported performance is about 3–8 flashovers per 100 km-year. Because BFR scales linearly with exposure:
\[ \text{BFR} \propto N_g \qquad N_g: 4 \to 10 \;\Rightarrow\; \times \tfrac{10}{4} = 2.5 \;\Rightarrow\; 3\text{–}8 \to 7.5\text{–}20 \]
Conversely, if good grounding can drive \(R_0\) down to about 10 \(\Omega\), the BFR may fall to roughly 1.5 flashovers per 100 km-year. The message holds even at medium voltage: good grounding is critical.
Section 12
Distribution-Line Performance
Distribution insulation is so weak that almost any direct stroke to a phase conductor flashes over. With \(Z = 500\,\Omega\) and \(\text{CFO} = 300\) kV, the threshold current is tiny:
\[ I = \frac{2\,\text{CFO}}{Z} = \frac{2 \times 300}{500} \approx 1.2\ \text{kA} \]
A 1.2 kA stroke is very common, so direct strokes to distribution phase conductors almost always flash over. A ground wire helps: for a studied 12 kV line with a shield wire, \(N_L \approx 42.3\) strokes per 100 km-year, and at \(R_0 = 20\)–\(40\,\Omega\) the BFR is 6–7.5 — only 14–18% of strokes to the ground wire flash over, far better than the unshielded case. This relatively low BFR comes from the line's geometry:
\[ \text{short span} \;\Rightarrow\; V_{\text{ins}} \downarrow \qquad \text{low height} \;\Rightarrow\; N_L \downarrow \]
But the decisive point is different from transmission: backflashover from shield-wire strokes is only part of the problem, because most distribution flashovers are caused by induced voltages from nearby strokes, not by direct strokes to the line. So distribution lightning performance — arrester application and insulation coordination — must consider induced-voltage performance as well, whereas shielded HV lines are dominated by backflashover and shielding failure. Transmission-line BFR logic should not be applied too broadly to distribution.
Section 13
CIGRE versus IEEE
Both methods estimate BFR, and with identical parameters their voltage across the insulation agrees to within about 0.4–4.4%. The differences are therefore not in the basic calculation but in the assumptions:
Table 4 — Where the CIGRE and IEEE assumptions diverge.
| Assumption | CIGRE | IEEE (as Described) |
|---|
| High-current footing resistance | Reduces \(R_0 \to R_i\) by ionisation | No high-current reduction |
| Corona | Neglected (conservative) | Applied to the whole wave shape |
| Front time \(t_f\) | Tied to stroke-current magnitude | Fixed \(t_f = 2\,\mu\text{s}\) |
| Non-standard CFO | LPM-derived \(\text{CFO}_{\text{NS}}\) | Time-lag curve, two time instants |
| Power-frequency voltage | Equivalent factor \(K_{PF}V_{LN}\) | Many AC angles (e.g. every 10°) |
| Span / tower velocities | Per the CIGRE model | \(0.90c\) span, \(0.85c\) tower |
The IEEE stroke-current probability uses the simple closed form:
\[ P(I > I_c) = \frac{1}{1 + \left(\dfrac{I_c}{31}\right)^{2.6}} \]
This approximation overestimates probability above about 70 kA (so it can overstate BFR when \(I_c\) is high) and underestimates it below about 10 kA (affecting shielding-failure work). On power-frequency voltage the IEEE approach — sweeping many AC angles — is the more accurate, at the price of needing a computer; CIGRE's single \(K_{PF}V_{LN}\) is the simpler equivalent. (The source has an apparent OCR slip stating IEEE “does reduce” footing resistance in one bullet; the surrounding text makes clear the intended meaning is that IEEE does not include the CIGRE high-current reduction.)
For low-height lines the two methods often agree well — an “inexact science” in which the differing assumptions happen to offset one another. For high towers (e.g. a 230 kV double-circuit at \(h = 70\) m) IEEE can predict a much higher BFR, driven mainly by footing-resistance treatment, the fixed front time, the current-probability model and corona.
Section 14
Ranking the Mitigation Measures
Pulling the sensitivities together gives a practical order of preference for reducing BFR:
Table 5 — Practical ranking of BFR-reduction measures.
| Measure | Why It Works / Caveat |
|---|
| Reduce tower footing resistance | Most effective and practical — directly cuts tower voltage rise |
| Use two shield wires (not one) | Lowers \(Z_g\), raises coupling — very effective where feasible |
| Add an underbuilt ground wire | Strong coupling gain to lower phases, but sag/clearance is hard |
| Install counterpoises | Effective in high-resistivity soil; impulse modelling uncertain |
| Install line surge arresters | Directly limit insulator voltage; cost and maintenance matter |
| Increase insulation strength (CFO) | Raises \(\text{CFO}_{\text{NS}}\); mechanical and cost limits apply |
Section 15
What Matters Most
BFR is not governed by any single parameter, but the sensitivity study makes the hierarchy clear. The influential set is:
\[ R_i,\; h,\; C,\; Z_g,\; t_f,\; N_g,\; \text{shield-wire arrangement} \]
and above all, \(R_i\) and tower height \(h\) are dominant. The supporting conclusions:
- the simplified method is for hand checks below \(\approx 50\) m only — above that, use full CIGRE;
- corona is usually not dominant but grows in importance with tower height;
- soil ionisation (\(R_0 \to R_i \approx 0.5\,R_0\)) must not be ignored;
- two shield wires beat one; an underbuilt wire is even stronger but constrained by sag/clearance;
- MV lines can perform well with good grounding, while distribution lines are limited by induced voltages.
\[ \text{BFR} = 0.6\,N_L\,P(I \ge I_c) \qquad I_c \uparrow \;\Rightarrow\; P(I \ge I_c) \downarrow \]
Why the effects are so large: because the lightning-current exceedance probability \(P(I \ge I_c)\) is nonlinear, a moderate increase in \(I_c\) can produce a large reduction in BFR — which is exactly why grounding and coupling improvements pay off so strongly.
Do not average footing resistance blindly
Because BFR rises disproportionately with \(R_0\), a small number of high-resistance towers can dominate the line BFR. Do not design from the line average alone — the worst towers matter most. This is developed in the line-design part.
Section 16
Summary and Memory Map
Equation Summary
Adjusted BFR
\(\displaystyle \text{BFR} = 0.6\,N_L\,P(I \ge I_c)\)
Critical-current condition
\(\displaystyle V_{\text{ins}}(I_c) = \text{CFO}_{\text{NS}}\)
Insulation voltage
\(\displaystyle V_{\text{ins}} = V_{\text{tower}} - V_{\text{phase}}\)
Coupling effect
\(\displaystyle V_{\text{phase}} = C V_g,\quad C\uparrow \Rightarrow V_{\text{ins}}\downarrow\)
Footing voltage
\(\displaystyle V_F = I_i R_i\)
Impulse-resistance effect
\(\displaystyle R_i < R_0,\; R_i\downarrow \Rightarrow I_c\uparrow \Rightarrow \text{BFR}\downarrow\)
IEEE current probability
\(\displaystyle P(I > I_c) = \frac{1}{1 + (I_c/31)^{2.6}}\)
Exposure scaling
\(\displaystyle \text{BFR} \propto N_g\)
The memory map for the whole topic: what controls \(I_c\) — \(R_i, C, h, Z_g, Z_T, t_f, \text{CFO}_{\text{NS}}\); what controls exposure — \(N_g, h, S_g\) and line length; combined through \(\text{BFR} = 0.6\,N_L\,P(I \ge I_c)\); reduced by raising \(I_c\) or lowering \(N_L\).
Key messages
- BFR is not controlled by one parameter — but the most influential and practical levers are \(R_i\), tower height \(h\), coupling \(C\) and the shield-wire arrangement.
- The \(\text{CFO}_{\text{NS}}\) regression closely matches the full Leader Progression Model, so the CIGRE method is practical without a leader-progression run per case.
- The simplified (no-tower) method is for hand checks below \(\approx 50\) m; above that the tower component is too large to neglect.
- Soil ionisation matters: \(R_i \approx 0.5\,R_0\) for typical concentrated grounds, and ignoring it badly overestimates BFR.
- Two shield wires roughly halve BFR versus one; an underbuilt ground wire is even more effective but limited by sag and clearance.
- CIGRE and IEEE agree for low lines but diverge on tall towers, mainly through footing resistance, front time, current probability and corona.
- The objective is unchanged: \(I_c \uparrow \Rightarrow P(I \ge I_c) \downarrow \Rightarrow \text{BFR} \downarrow\) — improve grounding and coupling, choose the right shield wires, and watch tower height.
Engineering priorities
- First, reduce the number of high-risk towers — improve footing resistance, or apply line surge arresters where grounding is ineffective or uneconomic.
- Second, improve coupling through the shield-wire arrangement (two wires, or an underbuilt ground wire) where feasible.
- Third, use the full CIGRE method whenever tower height, front time or the tower surge component makes the simplified method unreliable.
