Section 1
Why the Incoming Surge Matters
When lightning strikes an overhead line, the resulting surge can travel toward the substation — the incoming surge. It sets the voltage stress on circuit breakers, disconnectors, busbar supports, transformers, surge arresters, line entrances, open breaker gaps and the rest of the station insulation. To coordinate the insulation, the designer must estimate the surge's magnitude, front steepness and tail time constant.
These are not fixed numbers. They depend on the lightning event, the line and the station arrangement — so the incoming surge is statistical, not a single deterministic waveform.
This is Part One of the incoming-surge and open-breaker protection series. It explains how the design incoming surge is selected from MTBF/MTBS, the line BFR, the distance from the station, corona steepness and nearby tower performance. Parts Two and Three (linked in the series navigation below) cover the shielding-failure incoming surge and subsequent strokes / open-breaker protection.
What this page teaches
- why the incoming surge is statistical, not a fixed waveform;
- how MTBF and MTBS are related;
- why a multi-line station needs special MTBS treatment;
- how \(d_m\) is selected from BFR and MTBS;
- why the nearest statistically relevant tower gives the steepest surge;
- why crest voltage and steepness must both be checked;
- how improving the first few towers reduces incoming-surge severity;
- why an open breaker can see roughly double the incoming surge.
Section 2
What Controls the Incoming Surge
Table 1 — Physical factors that shape the incoming lightning surge severity.
| Parameter | Effect on the Incoming Surge |
|---|
| Stroke location | Distance between the flashover point and the station |
| Stroke current | Magnitude of the lightning current |
| Initiating event | Backflashover or shielding failure |
| Line insulation | CFO and flashover behaviour of the adjacent towers |
| Corona | Reduces front steepness and crest magnitude |
| Surge impedances \(Z_g, Z_c\) | Control the travelling-wave behaviour |
| Tower footing resistance | Affects backflashover current and voltage |
| BFR / SFR | Determine how often surges are produced |
| MTBS / MTBF target | Determines the design severity of the surge |
Section 3
MTBF and MTBS
Station insulation is designed for a target mean time between failures (MTBF) — e.g. \(\text{MTBF} = 100\) years means roughly one insulation failure per 100 years. The incoming surge is then selected using a mean time between surges (MTBS) — the time in which a surge of equal or greater severity is equalled or exceeded:
\[ N_D = \frac{1}{\text{MTBS}} \]
Table 2 — Notation for the design surge rate and its mean time between surges.
| Symbol | Meaning |
|---|
| \(N_D\) | Design number of incoming surges per year |
| MTBS | Mean time between surges of equal or greater severity |
For example, \(\text{MTBS} = 400\) years gives \(N_D = 1/400 = 0.0025\) surges/year. The three quantities side by side:
Table 3 — Comparison of MTBF, MTBS and design surge rate and their uses.
| Term | Meaning | Used for |
|---|
| \(\text{MTBF}\) | Mean time between insulation failures | Station / equipment reliability target |
| \(\text{MTBS}\) | Mean time between incoming surges of equal or greater severity | Design incoming-surge selection |
| \(N_D = 1/\text{MTBS}\) | Design surge rate | Annual exceedance rate |
For a single-line station, \(\text{MTBS}\) may be close to \(\text{MTBF}\). For a multi-line station, each line collects surges, so transformer-bus equipment may require a higher per-line \(\text{MTBS}\) (next section).
Section 4
Multi-Line Stations: MTBS Is Not Always MTBF
For a single-line station it may be reasonable to set \(\text{MTBS} = \text{MTBF}\). But in a multi-line station each incoming line collects lightning surges, so equipment on the transformer bus is exposed to surges from all \(n\) lines:
\[ \text{MTBS}_{\text{per line}} = n \times \text{MTBF}_{\text{station}} \]
So a three-line station with \(\text{MTBF} = 100\) years checks the transformer bus at \(\text{MTBS} = 3 \times 100 = 300\) years per line. Equipment on a specific line bay (its breaker, disconnector, bus supports) is stressed mainly by the surge entering from that same line, so for those items \(\text{MTBS}_{\text{line bay}} \approx \text{MTBF}\).
For complex station arrangements this rule is only a starting point — preliminary station simulations may be required to identify which incoming line produces the controlling equipment voltage.
Topology and operating probability both matter
The number of lines in service changes (\(n\), \(n-1\), \(n-2\) during contingencies). If a contingency exists only for a small fraction of thunderstorm time, its probability reduces its contribution — so MTBS selection must consider both the station topology and the probability of each operating condition.
Table 4 — Typical mean-time-between-failure targets by substation type and practice.
| Station Type / Practice | Typical MTBF Range |
|---|
| Air-insulated substations | 50–100 years |
| IEC guide examples | 400–500 years |
| Gas-insulated substations | 300–1000 years |
GIS stations justify a higher MTBF because failure consequences and repair times are more severe.
Section 5
Shielding Failure versus Backflashover
A shielding failure is lightning bypassing the shield wire and striking a phase conductor directly; the surge magnitude is limited by the conductor surge impedance and the maximum shielding-failure current:
\[ V \approx \frac{Z_c\,I}{2} \]
Table 5 — Notation for the shielding-failure surge voltage estimate.
| Symbol | Meaning |
|---|
| \(Z_c\) | Phase-conductor surge impedance |
| \(I\) | Stroke current |
A backflashover is lightning striking the tower or shield wire and raising the tower voltage until it flashes to the phase. Its maximum surge is usually more severe — it is not limited the same way, the BFR is usually larger than the SFR, and high lightning currents give high tower voltages:
Backflashover usually controls
In many practical cases the backflashover-originated incoming surge is the controlling design case.
Section 6
Review of the Backflashover Voltage
In the simplified CIGRE approach, the tower/ground-wire voltage and the coupled phase voltage are:
\[ V_B = I\,R_e, \qquad V_C = C\,V_B, \qquad V_I = (1 - C)\,V_B + V_{PF}, \qquad \text{backflash when } V_I \ge \text{CFO}_{\text{NS}} \]
Table 6 — Notation for the backflashover tower and phase voltage equations.
| Symbol | Meaning |
|---|
| \(V_B\) | Tower / ground-wire voltage component |
| \(V_C\) | Coupled voltage on the phase conductor |
| \(C\) | Coupling factor |
| \(R_e\) | Equivalent resistance seen by the surge |
| \(V_{PF}\) | Power-frequency contribution at the stroke instant |
The power-frequency term is \(V_{PF} = K_{PF}V_{LN}\), with \(K_{PF} \approx 0.70\) (horizontal) or \(0.40\) (vertical). It reduces the critical lightning current because the AC voltage can add to the surge stress.
Section 7
Equivalent Resistance and Impulse Footing Resistance
The surge sees the footing impulse resistance in parallel with the ground-wire travelling-wave path:
\[ R_e = \frac{R_i\,Z_g}{R_i + Z_g} \qquad\begin{cases} R_i \ll Z_g \Rightarrow R_e \approx R_i \\[4pt] R_i \gg Z_g \Rightarrow R_e \approx Z_g \end{cases} \]
Table 7 — Notation for the equivalent footing and ground-wire resistance.
| Symbol | Meaning |
|---|
| \(R_i\) | Impulse footing resistance |
| \(Z_g\) | Ground-wire surge impedance |
The impulse resistance falls with current through soil ionisation (Weck form):
\[ R_i = \frac{R_0}{\sqrt{1 + I/I_g}}, \qquad I_g = \frac{E_0\,\rho}{2\pi R_0^2}, \qquad E_0 \approx 400\ \text{kV/m} \]
so \(I \uparrow \Rightarrow R_i \downarrow\), because the ionised zone enlarges the effective electrode.
Section 8
Critical Current, Time to Flashover, and the Launched Surge
Only backflashovers above the critical current \(I_c\) launch a travelling surge toward the station, and the rate of such events is the BFR:
\[ \text{BFR} = 0.6\,N_L\,P(I > I_c) \]
At \(I = I_c\) flashover just occurs and the time to breakdown is long; as the current rises the voltage builds faster and flashover occurs earlier (\(I \uparrow \Rightarrow t_B \downarrow\)). At flashover the insulation path becomes a conducting arc, the voltage collapses, and a travelling surge is launched onto the conductor — like a closing switch dividing between the tower side \(R_e\) and the conductor side \(Z_c/2\). As the wave passes successive towers the ground-wire voltage is drained, so the coupled component vanishes — the surge reaching the station is not the same as the voltage at the struck tower; it is shaped by propagation, coupling removal, tower reflections and corona.
Section 9
Corona and the Front Steepness
Corona is decisive for the incoming surge: as the wave travels it pushes back the wavefront, reduces the steepness and lowers the crest. The steepness at the station is approximately inversely proportional to distance:
\[ S = \frac{K_c}{d} \qquad\Rightarrow\qquad d \uparrow \;\Rightarrow\; S \downarrow \]
Table 8 — Notation for the corona-controlled front-steepness relation.
| Symbol | Meaning |
|---|
| \(S\) | Surge steepness at the station |
| \(K_c\) | Corona constant (km·kV/μs) |
| \(d\) | Distance the surge has travelled (km) |
Table 9 — Corona constant values for different conductor bundle arrangements.
| Conductor Arrangement | \(K_c\) (km·kV/μs) |
|---|
| Single conductor | 700 |
| Two-conductor bundle | 1000 |
| Three- or four-conductor bundle | 1700 |
| Six- or eight-conductor bundle | 2500 |
For a single conductor (\(K_c = 700\)) at \(d = 0.6\) km: \(S = 700/0.6 \approx 1167\) kV/μs. Doubling the distance to \(1.2\) km halves the steepness to \(\approx 583\) kV/μs.
Why steepness is set by the nearest flashover
Because \(S = K_c/d\), the steepness is largest for the smallest travel distance. A flashover at the closest statistically relevant tower therefore produces the steepest incoming surge — and steepness is what drives the terminal voltages on open breaker gaps and transformer entrances. This is why \(d_m\) (next section) matters so much.
Section 10
The Minimum Design Distance and the Nearest Towers
For the selected MTBS, the minimum distance \(d_m\) is the closest flashover point whose backflashover rate is statistically consistent with the design surge rate:
\[ d_m = \frac{100}{\text{BFR} \times \text{MTBS}} \]
Table 10 — Notation for the minimum design-distance calculation.
| Symbol | Meaning |
|---|
| \(d_m\) | Minimum line distance contributing the design surge (km) |
| BFR | Backflashover rate (flashovers per 100 km-year) |
| MTBS | Mean time between surges of equal or greater severity (years) |
Example: \(\text{BFR} = 0.5\), \(\text{MTBS} = 400\) → \(d_m = 100/(0.5 \times 400) = 0.5\) km. A worse line shifts the design flashover closer and steepens the surge:
Round outward, not inward
\(d_m\) is rounded out to the next whole tower, never in — a closer tower would imply a steeper surge than the MTBS justifies. For a \(0.2\) km span, \(d_m = 0.5\) km rounds to the tower at \(0.6\) km, and the design steepness is evaluated at that rounded distance.
\[ \text{BFR} \uparrow \;\Rightarrow\; d_m \downarrow \;\Rightarrow\; S = \frac{K_c}{d} \uparrow \]
The first towers are critical
Because \(S = K_c/d\), the nearest possible flashover gives the highest steepness — so the first few towers near the station control the steepest incoming surges that stress open breaker gaps, transformer terminals, bus insulation and line-entrance equipment.
Section 11
Crest Voltage versus Steepness
The closest tower gives the highest steepness, but it does not always give the highest crest. More distant towers can give a larger crest because the statistical current required to meet the same MTBS can be larger there:
\[ \text{nearest tower} \Rightarrow \text{maximum steepness}, \qquad \text{more distant towers} \Rightarrow \text{possibly higher crest} \]
Table 11 — How steepness and crest differ between the nearest and more distant flashover towers.
| Property | Nearest Relevant Tower | More Distant Tower |
|---|
| Travel distance \(d\) | Smallest | Larger |
| Steepness \(S = K_c/d\) | Highest | Lower (corona-attenuated) |
| Crest voltage | Lower | Possibly higher (larger statistical current) |
| Governs | Terminal voltages, open-gap stress | Peak-magnitude-sensitive insulation |
Selecting the design surge
If only one surge is chosen, normally take the nearest-tower surge with maximum steepness (steepness governs equipment terminal voltages) — but verify that a more distant, higher-crest surge is not more severe for the equipment being studied.
Section 12
A 230 kV Worked Example
Table 12 — Input parameters for the 230 kV incoming-surge worked example.
| Quantity | Value |
|---|
| BFR / \(N_L\) | 2.0 FO / 61.5 flashes per 100 km-year |
| \(Z_c\) / \(Z_g\) | 350 Ω / 350 Ω |
| \(R_0\) / \(\rho\) / \(I_g\) | 20 Ω / 400 Ω·m / 63.7 kA |
| CFO / coupling \(C\) / \(V_{PF}\) | 1040 kV / 0.20 / 75 kV |
| Span / desired MTBS | 300 m / 100 years |
\[ d_m = 0.5\ \text{km} \;\to\; d = 0.6\ \text{km}, \qquad S = \frac{700}{0.6} = 1167\ \text{kV/}\mu\text{s} \]
Table 13 — Computed incoming-surge results for the 230 kV worked example.
| Incoming Surge (Nearest Design Tower) | Value |
|---|
| Steepness | 1167 kV/μs |
| Crest voltage | 685 kV (66% of line CFO) |
| Tail time constant | 26.9 μs |
| Riding on power-frequency | −75 kV (opposite polarity) |
| Net voltage to ground | 685 − 75 = 610 kV |
For more distant flashovers the steepness falls; even at the fourth tower the crest may still be below the line CFO while the steepness has already dropped a lot — which is exactly why both \(S\) and the crest must be considered, not just one.
Section 13
Flashover at Adjacent Towers Chops the Wave
If a very large surge travels along the line it may flash over at an adjacent tower before reaching the station, chopping the wave. The chopped wave continues with a reduced crest, a modified front and extra corona attenuation — so the line insulation acts as a natural limiter. The maximum surge at the station entrance is typically limited to about 1.25 to 1.35 times the positive-polarity CFO of the line insulation:
\[ V_{\text{station,max}} \approx (1.25 \text{ to } 1.35)\,\text{CFO}_{\text{line}} \]
Why \(1.25\text{ to }1.35\,\text{CFO}\)?
A surge cannot exceed the line insulation’s flashover voltage by much before some tower flashes over and chops it. Under the steep, short fronts of an incoming surge the insulation withstands slightly more than its standard CFO — the volt–time curve rises for short times — so the largest surge that can survive to the station is roughly \(1.25\) to \(1.35\) times the line CFO, not exactly the CFO. This factor is a practical ceiling, not a design target.
Self-limiting
Adjacent-tower flashover can reduce the severity of the surge entering the station.
Section 14
Open Breaker Protection
An open breaker is especially exposed: one side sees the incoming surge while the other stays at a different voltage, and the surge reflects at the open point. At an open end the voltage approximately doubles, so a surge of crest \(V_s\) can drive the open-end voltage toward:
\[ V_{\text{open end}} \approx 2\,V_s \qquad (\text{before losses and arrester action}) \]
This doubling is why both the steepness and the crest of the incoming surge matter so much for open breaker protection.
Doubling is a first approximation
The factor of \(2\) is the ideal lossless open-end reflection. The actual open-gap voltage depends on the station layout, line and bus reflections, traversal times, corona losses and any nearby arrester action, so it can be somewhat below \(2V_s\) in practice. Use \(V_{\text{open end}} \approx 2V_s\) for screening, then confirm with a travelling-wave / EMTP® station model for the final design.
Section 15
Ameliorating Measures
The main lever is to reduce the BFR near the station — reduce tower footing resistance, improve counterpoises, raise tower insulation where practical, install line surge arresters near the station, and improve shielding — concentrating on the first few towers (within about 1 km / 0.5 mile), because those towers control the steepest incoming surges. Pushing \(d_m\) farther out lowers the steepness:
\[ d_m \uparrow \;\Rightarrow\; S = \frac{K_c}{d_m} \downarrow \qquad (\text{e.g. } 1167 \to 583\ \text{kV/}\mu\text{s}, \text{ a } 2{:}1 \text{ reduction}) \]
Improve first towers (footing, counterpoise, arresters)
BFR near station \(\downarrow\)
Design distance \(d_m \uparrow\)
Steepness \(S = K_c/d_m \downarrow\)
Equipment stress \(\downarrow\)
Targeted grounding can halve the steepness
Improving the grounding of just the first few towers can roughly halve the incoming-surge steepness. It is rarely economical to improve a whole line to protect one station entrance — treat the nearby towers first, especially where station margins are limited, open-breaker protection is critical, arrester placement is constrained, the line BFR is high, or footing resistance near the station is poor.
Section 16
The Insulation-Coordination Workflow
Select station MTBF
MTBS per line / location
Line BFR & SFR
Distance \(d_m\)
Steepness \(S = K_c/d\)
Crest & tail; apply to station model
Check withstand; improve grounding / arresters if needed
Treat this as a probabilistic insulation-coordination process, not a single fixed waveform.
Section 17
Summary, Misconceptions and Memory Map
Table 14 — Common incoming-surge misconceptions corrected against sound engineering practice.
| Misconception | Correct Interpretation |
|---|
| “A 100-year station MTBF means every line uses a 100-year surge” | Transformer-bus equipment sees all lines; per-line MTBS may be \(n \times\) MTBF |
| “The nearest flashover gives the highest crest” | It gives the highest steepness; distant flashovers may give higher crest |
| “Corona only reduces voltage magnitude” | It mainly reduces front steepness, and also the crest |
| “The whole line must be improved” | Improving the first few towers near the station is highly effective |
| “Backflashover and shielding failure give the same surge” | Backflashover surges are usually more severe (higher BFR, unlimited current) |
Equation Summary
Design surge rate
\(\displaystyle N_D = \frac{1}{\text{MTBS}}\)
Minimum design distance
\(\displaystyle d_m = \frac{100}{\text{BFR}\times\text{MTBS}}\)
Corona-controlled steepness
\(\displaystyle S = \frac{K_c}{d}\)
Equivalent resistance
\(\displaystyle R_e = \frac{R_i Z_g}{R_i + Z_g}\)
Impulse resistance
\(\displaystyle R_i = \frac{R_0}{\sqrt{1 + I/I_g}}\)
Ionisation current
\(\displaystyle I_g = \frac{E_0\,\rho}{2\pi R_0^2}\)
Backflashover rate
\(\displaystyle \text{BFR} = 0.6\,N_L\,P(I > I_c)\)
Power-frequency term
\(\displaystyle V_{PF} = K_{PF}V_{LN}\)
Memory map. Select MTBF → convert to per-line MTBS → \(N_D = 1/\text{MTBS}\) → use BFR to find \(d_m\) → \(S = K_c/d_m\) → the nearest design tower gives the highest steepness → compute crest and tail → apply the surge to the station → check breaker, bus, transformer and arrester stresses → improve nearby footing / arresters if required.
Final engineering message
The incoming surge is a statistically selected travelling surge whose magnitude, steepness and tail depend on BFR/SFR, MTBS/MTBF, distance, corona, line insulation and footing resistance. The steepest design surge usually comes from the closest statistically relevant flashover, so the first few towers are critical — and the most effective mitigation is often to reduce the BFR near the station with better footing resistance and/or line arresters, lowering the incoming-surge steepness and protecting open breakers and station equipment.
