Insulation Coordination
With the calculation in hand, the real task is interpretation: how the backflashover method drives line design. This closing note works through multiphase and double-circuit flashovers, differential insulation, tower surge impedance, alternate flashover paths, the difference between a flashover and an outage, the uneven distribution of footing resistance and the “rogue towers” that dominate it, design targets, line surge arresters, how the predictions compare with field data, and the historical background behind the CIGRE and IEEE methods.
Section 1
This article is Part Five and the closing article of the backflashover series. The previous pages developed the BFR equation, the impulse footing resistance, the CIGRE calculation method and the sensitivity analysis. This page explains how those results are used in real line design.
The earlier notes built the backflashover calculation step by step, ending in the familiar rate:
The remaining question is one of interpretation: how is this method actually used to design a line? The overall design workflow is:
This closing note works through that workflow: multiphase flashovers, DC lines, double-circuit rates and differential insulation, tower surge impedance, alternate flashover paths, flashover versus outage, the distribution of footing resistance, design targets, rogue towers, surge arresters, comparison with field data, and the historical background that produced the CIGRE and IEEE methods.
Section 2
The simplified CIGRE approach folds the three-phase AC voltage into the strength by subtracting \(K_{PF}V_{LN}\) from the non-standard CFO, using \(K_{PF} = 0.70\) (horizontal) or \(0.40\) (vertical) with the lowest coupling factor. This gives a good estimate of the total line BFR — but it does not mean only the lowest-coupling phase flashes over.
The lowest-coupling phase is most exposed because less voltage is induced onto it:
But the AC voltage depends on the instant of the stroke, so a better-coupled phase can still flash if the power-frequency voltage adds unfavourably:
For a typical horizontal line the two outer phases share most of the risk while the better-coupled middle phase keeps a non-zero share — roughly 43% / 43% / 14%. The message: the lowest-coupling phase is dominant, but not exclusive.
Section 3
The total rate is the sum of the flashover types:
The basic critical current is the minimum for the first flashover. Once a phase flashes to the tower it is effectively grounded for the surge — it acts like an extra ground wire, raising \(Z_g\)-equivalent coupling to the remaining phases. So each successive flashover needs a higher current:
For single-circuit lines the three-phase component is usually under 1% of total BFR, so often \(\text{BFR}_{\text{total}} \approx \text{BFR}_{1\phi} + \text{BFR}_{2\phi}\).
Section 4
A DC line has no sinusoidal phase voltage, so the AC equivalent term is replaced by the crest pole-to-ground DC voltage:
The calculation logic is the same; only the power-frequency phase-angle effect disappears.
Section 5
On a double-circuit tower a stroke may flash one phase, several phases of one circuit, or phases of both circuits. A double-circuit flashover is the most damaging to reliability because it can trip both circuits on the same structure, so it is worth separating from the total:
On a vertical double-circuit tower the lower phases are usually most vulnerable: the lower phase of one circuit flashes first, becomes a grounded conductor, and the next likely flashover is the lower phase of the other circuit. After each flashover, \(Z_g\) and \(C_A, C_B, C_C\) must be recomputed, then the same equations reused. For a 230 kV double-circuit line (\(\text{CFO} = 1200\) kV, \(R_0 = 30\,\Omega\), \(\rho = 600\,\Omega\)·m):
So about 20% of total backflashovers involve both circuits. For a double-circuit line the total BFR is not enough on its own: a lower total BFR with a high double-circuit component may still be unacceptable for system reliability, because losing both circuits at once is far more damaging than a single-circuit trip.
Section 6
Differential insulation gives one circuit more strength than the other so that one circuit is far less likely to flash, cutting double-circuit outages. The example compares three options:
| Case | BFRtotal | BFRdc | Double-Circuit % |
|---|---|---|---|
| Both circuits 1200 kV | 3.00 | 0.60 | 20% |
| 1400 kV + 1200 kV | 3.00 | 0.18 | 6% |
| Both circuits 1400 kV | 1.19 | 0.18 | 15% |
Differential insulation slashes the double-circuit percentage (20% → 6%), but raising both circuits improves the total BFR, the double-circuit BFR and overall reliability together. The two options side by side:
| Design Option | Main Effect | Engineering Interpretation |
|---|---|---|
| Differential insulation | Reduces the percentage of double-circuit flashovers | Useful where one circuit can be intentionally made stronger |
| Both circuits strengthened | Reduces total BFR and double-circuit BFR | Usually preferred where tower geometry and clearances allow |
Differential insulation can reduce the proportion of double-circuit events, but strengthening both circuits usually gives better total lightning performance — so it is not automatically preferred; where tower geometry and clearances permit, raising both circuits is the more effective choice.
Section 7
Hanging a lower-voltage circuit below an HV circuit on the same tower cuts two ways. If lightning flashes the lower circuit first, that circuit becomes a grounded conductor and improves coupling to the HV circuit above — so HV performance improves. But the lower-voltage circuit now sits on a taller-than-necessary structure, which collects more strokes, and it has weaker insulation:
The trade-off is clear: good for the HV circuit, worse for the lower-voltage circuits.
Section 8
Tower surge impedance is the transient voltage-to-current ratio for waves travelling on the tower — a fast-front parameter, not the DC resistance:
| Structure | \(Z_T\) |
|---|---|
| Two-shield-wire lattice tower | ≈ 150–200 Ω (\(\approx 0.5\,Z_g\)) |
| Single downlead on wood pole | ≈ 550–600 Ω |
For many ordinary heights the tower component is not the dominant term — footing resistance usually matters more — so the approximation \(Z_T \approx 0.5\,Z_g\) is acceptable for ordinary two-shield-wire towers. The tower component grows in importance for high towers, steep fronts and delayed shield-wire reflections, and for cases where the simplified method is being used near its limit (the sensitivity analysis sets that at about 50 m) — there it should be treated carefully rather than approximated.
Section 9
The CFO used must be the lowest of all possible flashover paths:
On steel lattice towers the competing paths are the insulator string and the air gap from conductor/hardware to steel — use the lower. For vertical or I-string towers the string usually controls, and a practical positive-polarity gradient of \(560\) kV/m can be applied to both strike distance and string length. Wood-pole lines are more complex: porcelain, wood crossarm, wood-plus-porcelain in series, pole-to-conductor and crossarm paths must all be checked. The wood–porcelain rules:
| Wood Length vs Insulator | Approximate CFO |
|---|---|
| Wood ≈ 2× insulator | \(\text{CFO}_{\text{ins}} + 100\,\text{kV/m} \times L_{\text{wood}}\) |
| Wood > 2× insulator (wood controls) | \(300\,\text{kV/m} \times L_{\text{wood}}\) |
| Wood < 2× insulator | \(\text{CFO}_{\text{ins}} + 40\,\text{kV/m} \times L_{\text{wood}}\) |
Wind can swing a vertical string toward the tower, reducing strike distance \(S\) and hence CFO, which raises BFR — but the effect is usually minor and often neglected.
Section 10
BFR is a flashover rate. An outage occurs only if the flashover develops into a sustained power-frequency arc and protection operates, so the outage rate is the BFR scaled by the conditional outage probability:
On wood-pole lines the arc voltage across wood can limit current and self-extinguish, the chance depending on the power-frequency gradient across the wood:
For a 34.5 kV line with a 4 ft wood crossarm, \(G \approx 16\) kV/m and the outage probability is about \(p \approx 0.46\), so:
Even air or porcelain insulation yields a typical outage-to-flashover ratio of about \(0.85\) — this is an engineering approximation, not a universal constant (and often left out as minor). One caution: repeated flashovers along wet wood crossarms expel splinters and weaken the crossarm. Replacing a wood crossarm with steel improves mechanical durability but removes the wood's insulation contribution — a mechanical improvement can worsen lightning performance. Extra insulators may not fully recover the lost CFO, so lightning performance should be rechecked after such a modification.
Section 11
Towers do not share one footing resistance — some are low, a few are very high. Because BFR rises disproportionately with resistance, an average value is misleading. In one example, the 25% of the line with \(R_0 > 100\,\Omega\) produced 61% of the total BFR. The correct approach weights resistance groups:
Average footing resistance is misleading because BFR is nonlinear with \(R_0\): in the example, the 25% of the line with \(R_0 > 100\,\Omega\) produced ~61% of the total BFR. Prefer a tower-by-tower or grouped-resistance calculation, \(\text{BFR}_{\text{total}} = \sum_i f_i\,\text{BFR}(R_{0,i})\), over a single line average.
So tower-by-tower resistance records are valuable, and the priority is the worst towers, not the average — which is exactly why rogue towers matter.
Section 12
A rogue tower contributes disproportionately to the line BFR — typically high lightning exposure and high footing resistance at the same place. Hilltop towers are the classic case: they collect more strokes and often sit on rocky or dry soil:
A rogue tower should be treated as a targeted mitigation problem, not hidden inside the line average. Because a few of them can dominate the line, treating them directly beats improving the average. Recommended actions:
Treat the worst towers first.
A small number of high-resistance or highly exposed towers can dominate the total line BFR. Targeted grounding improvement or line arresters at these locations may be more effective than uniform minor improvements along the whole route.
Section 13
Lightning design starts from a target rate and asks what insulation, grounding and shielding meet it. It helps to separate the levers the designer controls from the conditions that are simply inputs:
| Category | Examples |
|---|---|
| Controllable design levers | Insulation length, footing resistance, shield-wire arrangement, underbuilt ground wire, surge arresters, double-circuit insulation arrangement |
| Input conditions | Ground flash density, route, terrain, tower height, span length, soil profile, reliability requirement |
The design target should normally be based on total lightning tripout performance, not BFR alone. The final tripout rate depends on shielding-failure flashovers, backflashovers, the outage-to-flashover ratio and the successful-reclose probability:
This is a conceptual expression, not a strict universal formula. There is no universal target: the right value depends on voltage level, system importance, reliability needs, economics and reclose success. Higher voltages demand better performance — if 500 kV is a utility's highest voltage, a goal near \(0.6\) flashovers per 100 km-year is typical, with 230 kV at \(1.2\). But if 230 kV is the highest voltage in another system, its target may itself be \(0.6\) — the target follows the line's role in the system.
Section 14
A line arrester clamps the insulation voltage instead of letting it reach the CFO:
Arrester duty depends strongly on whether the line is shielded:
| Case | Arrester Duty |
|---|---|
| Shielded line, stroke to shield wire | Most current flows through tower / footing; arrester duty usually manageable |
| Shielding failure to phase conductor | Energy governed by the shielding-failure current (\(\approx 5\)–\(15\) kA) and subsequent strokes |
| Unshielded line | Exposed to direct phase strokes of all magnitudes — application is more severe and must be checked |
| Distribution line | Highly effective against induced overvoltages; energy usually within capability |
On double-circuit lines, arresters on the three phases of one circuit can largely eliminate double-circuit flashovers — used extensively in Japan, including at 500 kV.
Strong candidates are where: footing resistance cannot be reduced (rock or terrain); the tower is a river crossing or special tall structure; the line supplies a critical load; a double-circuit outage must be prevented; distribution-line induced-overvoltage performance is unacceptable; or counterpoise installation is impractical or uneconomic. Where soil allows effective counterpoise installation, grounding improvement may be more economical; where grounding improvement is limited, arresters are often the practical solution.
Use grounding where practical; use arresters where grounding is ineffective or uneconomic.
Section 15
CIGRE-method predictions generally match field performance to within 20–30%. That level of agreement is reasonable because field BFR depends on uncertain inputs — ground flash density, stroke-current distribution, soil moisture, footing-resistance variation, tower geometry, insulation condition and outage reporting. One 115 kV line measured \(4.2\) versus a calculated \(3.8\) flashovers per 100 km-year.
The methods have a long lineage. Early work used measured tower currents (AIEE distribution, median \(\approx 15\) kA) and fixed fronts of \(2\,\mu\text{s}\), later \(4\,\mu\text{s}\) because \(2\,\mu\text{s}\) over-predicted midspan flashovers. Field theory and the loop-voltage method described the shield-wire / tower / phase system, and travelling-wave theory was shown to approximate it if the tower is represented by a surge impedance \(Z_T\) — the origin of that parameter. Predischarge currents helped explain why midspan flashovers are rarer than simple calculations suggest. Reduced-scale nanosecond models plus Monte Carlo methods then let BFR be estimated statistically over random current, front time, location and AC angle. Newer measurements found higher median currents (\(25\), \(30\), \(31\) kA), raising calculated BFR — some studies by over 200% — and forcing the methods to be reformulated. In 1982 Anderson published a revised method using updated current distributions and a constant \(2\,\mu\text{s}\) front, which (with modifications) became the IEEE method. CIGRE and IEEE thus answer the same need: to estimate lightning backflashover rates with simplified but realistic engineering assumptions.
Section 16
The chapter's conclusions in brief: span flashovers are usually negligible against tower flashovers; the \(0.6\) factor corrects tower-stroke BFR for span strokes; soil ionisation makes \(R_i < R_0\) a dominant effect; AC voltage and phases reduce to \(K_{PF}V_{LN}\) with the lowest coupling factor; the LPM regression gives an accurate \(\text{CFO}_{\text{NS}}\); a single equivalent (median) front time replaces the distribution; corona is conservative to neglect; the simplified method suits hand calculation below \(\approx 50\) m; two ground wires (and especially an underbuilt wire) cut BFR; MV and distribution lines need induced voltages considered; and CIGRE and IEEE agree for low towers but diverge for tall ones.
Memory map. Backflashover design → \(\text{BFR} = 0.6\,N_L\,P(I \ge I_c)\), where \(N_L\) is exposure (\(N_g, h, S_g\), route) and \(I_c\) is the line's withstand. \(I_c\) rises when \(R_i\downarrow, \text{CFO}\uparrow, C\uparrow, Z_g\downarrow\), so BFR falls. If grounding is not enough, use line arresters — and remember that a few poor towers can dominate the line, so the goal is to raise \(I_c\) and treat the high-risk towers until:
The line design is acceptable when the calculated or expected backflashover performance meets the selected design target — while also considering shielding failures, the outage-to-flashover ratio and reclosing performance.
Five-Part Technical Series
A five-part study of transmission-line backflashover — the backflashover rate, the impulse resistance of ground electrodes, the CIGRE calculation method, a sensitivity analysis, and line design with engineering conclusions.
Interpreting BFR in design — multiphase and double-circuit flashovers, differential insulation, tower surge impedance, flashover vs outage, rogue towers and line surge arresters.
