Section 1
Why This Part Matters
Parts One and Two developed the incoming surge from backflashover and from shielding failure, MTBS/MTBF, corona-controlled steepness and how to apply the surge to the station. This closing part completes the topic: why the tower-voltage component can usually be neglected, why subsequent strokes endanger an open breaker, how to estimate the open-breaker MTBF, when line-side arresters or gaps are needed, and how the method compares with IEEE/AIEE/IEC/CIGRE approaches.
This is Part Three (the closing part) of the incoming-surge and open-breaker protection series. It explains why subsequent lightning strokes may become critical after the breaker has opened, even when the first stroke is controlled by the station arresters. Parts One and Two are linked in the series navigation below.
What this page teaches
- why the tower-voltage spike is normally negligible for the incoming surge;
- why first strokes and subsequent strokes create different risks;
- why a breaker can become vulnerable after opening;
- how open-end reflection can approximately double the voltage;
- why chopped-wave withstand is the relevant breaker strength;
- how \(N_s\), \(P_o\) and the open-breaker MTBF are linked;
- why fleet exposure matters across many breakers;
- when line-side arresters or rod gaps should be considered.
First strokes vs subsequent strokes
First strokes usually define the incoming surge, but subsequent strokes may define the open-breaker risk.
Section 2
Why the Tower Component Can Be Neglected
During a backflashover the tower voltage adds a short spike to the conductor voltage, but the spike lasts only a tower round-trip:
\[ t_{\text{tower}} = \frac{2h}{c} \approx 0.15 \text{ to } 0.30\ \mu\text{s} \]
Table 1 — Notation for the tower round-trip travel-time equation.
| Symbol | Meaning |
|---|
| \(h\) | Tower height |
| \(c\) | Velocity of light |
| \(2h/c\) | Round-trip tower travel time |
That is extremely short next to the corona-modified front. Corona delays the front, so the surge crest at the station occurs later than the tower spike:
Table 2 — Compares the brief tower spike with the delayed station front.
| Feature | Tower-Voltage Spike | Corona-Modified Station Front |
|---|
| Duration / arrival | Very short (\(\approx 0.15\)–\(0.30\) μs), at the struck tower | Delayed front, crest arrives later at the station |
| Effect on the incoming surge | Essentially none — passes before the station crest | Governs the crest and steepness seen at the station |
The spike has essentially no effect
The tower-voltage spike sits near the original crest at the struck tower, but the corona-modified crest arrives at the station later — so the tower component can be neglected when estimating the incoming surge.
Section 3
First Stroke versus Subsequent Strokes
The first stroke usually produces the most severe incoming surge, so the incoming-surge calculation is based on it. But a flash contains several strokes, and the typical sequence creates a new hazard:
First stroke
Line flashover
Relay detects fault
Breaker opens \((t_o)\)
Subsequent stroke (breaker open)
Open breaker stressed
Reclose \((t_c)\)
Table 3 — Typical breaker opening, reclosing and vulnerable-window times.
| Event | Typical Time |
|---|
| Breaker opening \(t_o\) | \(\approx 50\) ms |
| Reclosing \(t_c\) | \(\approx 300\) ms |
| Vulnerable window | \(t_o < t < t_c\) |
Table 4 — Contrasts first and subsequent strokes and their differing risks.
| Item | First Stroke | Subsequent Stroke |
|---|
| Typical role | Main incoming-surge severity | Open-breaker risk |
| Current magnitude | Usually higher | Usually lower |
| Tail duration | Longer | Shorter |
| Breaker condition | Usually closed initially | May be open after relay operation |
| Main concern | Station insulation / arrester duty | Open breaker gap stress |
Section 4
Why Subsequent Strokes Threaten Open Breakers
With the breaker closed, station arresters usually protect the equipment. With the breaker open, the line side may be isolated from those arresters, so an incoming surge can stress the open gap. The dangerous window is between opening and reclosing:
\[ t_o = 50\ \text{ms} \;\le\; t \;<\; t_c = 300\ \text{ms} \]
Table 5 — Notation for the breaker opening and reclosing times.
| Symbol | Meaning |
|---|
| \(t_o\) | Breaker opening time |
| \(t_c\) | Breaker reclosing time |
Subsequent strokes have lower current, a shorter time-to-half and a shorter tail (parameters \(M = 12.3\) kA, \(\beta = 0.53\)). Their shorter tail gives a shorter incoming-surge tail:
Table 6 — Compares median tail durations of first and subsequent strokes.
| Stroke Type | Median Time to Half Value |
|---|
| First stroke | 77.5 μs |
| Subsequent stroke | 30.5 μs |
Section 5
The Incoming Surge from Subsequent Strokes
For a chosen station voltage \(V_s\), the method finds the subsequent-stroke current needed at each tower to produce \(V_s\) at the station (corona modifies the wave differently per tower, so each tower needs a different current). The number of surges meeting \(V_s\) is summed over the towers:
\[ N_s = \sum \Big[\,\text{BFR contribution per tower} \times P(I > I_n)\,\Big], \qquad \text{MTBS} = \frac{1}{N_s} \]
Table 7 — Notation for the subsequent-stroke surge-rate calculation.
| Symbol | Meaning |
|---|
| \(N_s\) | Surges per year equal to or exceeding \(V_s\) |
| \(I_n\) | Subsequent-stroke current required at tower \(n\) |
| \(P(I > I_n)\) | Probability the subsequent-stroke current exceeds \(I_n\) |
Section 6
Example: a 580 kV Subsequent-Stroke Surge
Table 8 — Input parameters for the 580 kV subsequent-stroke surge example.
| Quantity | Value |
|---|
| Target \(V_s\) | 580 kV |
| BFR / coupling \(C\) | 3.0 per 100 km-year / 0.30 |
| \(R_0\) / \(\rho\) / \(I_g\) | 30 Ω / 600 Ω·m / 42.44 kA |
| \(Z_g\) / \(Z_c\) / span | 400 Ω / 400 Ω / 300 m |
\[ N_s = 0.000266\ \text{surges/year} \;\Rightarrow\; \text{MTBS} = \frac{1}{0.000266} \approx 3765\ \text{years} \]
The full computer program gives \(\approx 3769\) years — the simplified procedure is very accurate here. The tail time constant for this case is short, about 9 to 11 μs, which makes chopped-wave / short-duration breaker withstand the relevant strength.
Section 7
The Open-Breaker Protection Problem
Station arresters are usually near the transformer; with a line breaker open, the line side may be unprotected by them. An incoming surge then appears directly on the line side, and the open end reflects the wave, so the voltage roughly doubles:
\[ V_{\text{open breaker}} \approx 2\,V_s \qquad\Rightarrow\qquad V_s \le \frac{V_{\text{withstand}}}{2} \]
Doubling is an approximation
At an open terminal the travelling wave is reflected and the local voltage may approach twice the incoming surge voltage. The actual value depends on the breaker grading capacitance, station layout, surge arresters, connected equipment and reflections, so it can be somewhat below \(2V_s\) in practice. Use \(V_{\text{open}} \approx 2V_s\) for screening, then confirm with a travelling-wave / EMTP® model for the final design.
An open breaker is not protected by transformer arresters
When the breaker is open, the line side may be isolated from the station arresters and exposed to the incoming surge — and open-end doubling makes the gap stress severe.
Section 8
Breaker Chopped-Wave Withstand
The relevant strength is the breaker chopped-wave withstand. For a \(9\)–\(11\) μs tail the non-standard CFO is about \(1.23\)–\(1.29\) times the standard CFO, and a \(2\,\mu\text{s}\) chopped-wave test at \(1.29\,\text{BIL}\) is applied, so:
\[ V_{\text{withstand}} \approx 1.29\,\text{BIL}, \qquad V_{s,\text{limit}} = \frac{1.29\,\text{BIL}}{2} \]
Table 9 — Notation for the open-breaker surge-limit calculation.
| Symbol | Meaning |
|---|
| \(V_{s,\text{limit}}\) | Maximum incoming-surge crest before open-end doubling |
| \(\text{BIL}\) | Basic lightning impulse insulation level of the breaker |
| \(1.29\,\text{BIL}\) | Approximate \(2\,\mu\text{s}\) chopped-wave withstand |
| \(2\) | Approximate open-end doubling factor |
For a 230 kV breaker with \(\text{BIL} = 900\) kV:
\[ V_{\text{withstand}} = 1.29 \times 900 \approx 1160\ \text{kV}, \qquad V_{s,\text{limit}} = \frac{1160}{2} = 580\ \text{kV} \]
which is exactly the \(V_s = 580\) kV used in the subsequent-stroke example.
Section 9
Probability the Breaker Is Open, and the Open-Breaker MTBF
A subsequent stroke is only dangerous if it arrives while the breaker is open. With \(t_o = 50\) ms and \(t_c = 300\) ms, the open probability is \(P_o \approx 0.423\) (computer: \(0.417\)). The annual risk and the open-breaker MTBF are then:
\(N_s\) surges/year \(> V_s\)
\(P_o\) breaker open
\(P_T = N_s P_o\)
\(\text{MTBF} = 1/P_T\)
\[ P_T = N_s\,P_o, \qquad \text{MTBF} = \frac{1}{P_T} \]
Table 10 — Notation for the annual open-breaker risk and MTBF.
| Symbol | Meaning |
|---|
| \(N_s\) | Number of subsequent-stroke surges per year exceeding \(V_s\) |
| \(P_o\) | Probability the breaker is open when the surge arrives |
| \(P_T\) | Annual probability of a dangerous open-breaker surge |
| MTBF | Mean time between open-breaker flashover events |
\[ P_T = 2.66\times10^{-4} \times 0.423 \approx 1.125\times10^{-4} \;\Rightarrow\; \text{MTBF} \approx 8887\ \text{years} \]
The computer program gives \(\approx 8832\) years — again confirming the simplified estimate.
Section 10
Why the System Voltage Level Matters
Open-breaker protection becomes more important at lower system voltages, because lower-voltage breakers have a lower BIL and lower chopped-wave withstand, often a higher BFR, and a more severe relative surge exposure. As the voltage falls, \(\text{BIL}\downarrow\) and often \(\text{BFR}\uparrow\) — both lower the open-breaker MTBF:
Where protection is needed
Open-breaker protection may be required at 69 kV and below, while 345 kV and above may not need additional line-side breaker protection — subject to the line and station design.
Section 11
Protection Options and the Fleet Effect
Table 11 — Compares line-side arrester, rod gap and no-protection options.
| Option | Benefit | Limitation | Use When |
|---|
| Line-side surge arrester | Best technical protection; controlled voltage limitation | Higher cost; more equipment, maintenance and space | Critical breakers or low MTBF |
| Rod gap | Low cost; simple hardware; flashover path before the gap fails | Less precise; difficult coordination; risk of needless flashover | Moderate risk and acceptable flashover path |
| No additional protection | No added cost or equipment | Risk accepted; fleet exposure can still matter | Calculated MTBF is acceptable |
A rod gap must be large enough that station arresters protect equipment when the breaker is closed, yet small enough to protect the breaker when open — coordination is not always easy. And a high single-breaker MTBF does not guarantee low fleet risk:
\[ \text{MTBF}_{\text{fleet}} \approx \frac{\text{MTBF}_{\text{single}}}{n} \qquad\Rightarrow\qquad \frac{8832}{100} = 88.3\ \text{years} \]
Fleet exposure matters
With \(n\) similar breakers, the fleet MTBF falls as \(1/n\) — a comfortable single-breaker figure (e.g. 8832 years) can become marginal across 100 breakers (88.3 years).
Section 12
Comparison with IEEE / AIEE / IEC / CIGRE
Earlier IEEE/AIEE work noted that multiple lines both help (extra travelling-wave paths reduce voltage and steepness) and hurt (they collect more surges), so the design surge must be made more severe to hold the station MTBF — broadly \(d_m = 100/(n \times \text{BFR} \times \text{MTBF})\), often applied without fully accounting for contingency line-out conditions. Historical 120 kV and 24 kV studies used distance, CFO and steepness assumptions (e.g. \(\sim 900\) kV crest, \(\sim 450\) kV/μs, \(\sim 17\) μs tail). The Weck / Eriksson / IEC-style methods assume flashover at the crest (surge \(\approx\) non-standard CFO) applied through a resistor to a fixed line length (e.g. 300 m). Different methods can give quite different values:
Table 12 — Compares surge parameters from the present and IEC-style methods.
| Quantity | Present Method | IEC / CIGRE-Style |
|---|
| Steepness | 1167 kV/μs | 1667 kV/μs |
| Crest voltage | 685 kV | 1110 kV |
| Tail time constant | 26.9 μs | 17.5 μs |
The IEEE arrester guide historically used \(E = 1.2\,\text{CFO}\) with a steepness tied to arrester MCOV — but the authors recognised that steepness should follow MTBF and BFR, not the arrester rating, because the incoming surge is a line-and-station statistical phenomenon.
Section 13
Key Design Conclusions
Table 13 — Key design conclusions for incoming-surge and open-breaker protection.
| # | Conclusion |
|---|
| 1 | Select the incoming surge from the station target MTBF, converted to a per-line MTBS by layout and equipment location |
| 2 | Transformer-bus equipment: generally \(\text{MTBS} = n \times \text{MTBF}\) (\(n\) = incoming lines) |
| 3 | Other buses (e.g. line-bay breakers): often \(\text{MTBS} = \text{MTBF}\) |
| 4 | Complex stations need preliminary studies to set the correct MTBS |
| 5 | Backflashover-originated surges are often more important than shielding-failure surges |
| 6 | Describe the surge by crest, front steepness, tail time constant and opposite-polarity power-frequency voltage |
| 7 | Subsequent strokes may endanger open breakers, especially at lower system voltages |
Section 14
The Open-Breaker Workflow and Decision Guide
The breaker-protection decision follows a fixed sequence — from the breaker BIL to the chosen protection:
Breaker \(\text{BIL}\)
Chopped-wave \(1.29\,\text{BIL}\)
Limit \(V_{s,\text{limit}} = \dfrac{1.29\,\text{BIL}}{2}\)
Surge rate \(N_s\)
Open probability \(P_o\)
\(\text{MTBF} = 1/(N_s P_o)\)
Fleet correction \(/\,n\)
Arrester, rod gap, or accept risk
Station MTBF → equipment MTBS
First-stroke surge (breaker closed + arresters)
Subsequent-stroke surge (open breaker)
Probability breaker open \(P_o\)
\(\text{MTBF} = 1/(N_s P_o)\)
Line-side arrester, rod gap, or accept risk
Table 14 — Decision guide linking conditions to recommended protection actions.
| Condition | Recommended Action |
|---|
| Low-voltage system (≈ 69 kV and below) | Consider line-side arrester or gap protection |
| High BFR near the station | Improve nearby tower footing or install line arresters |
| Breaker normally open, disconnect closed | Provide protection |
| Many similar breakers | Consider the fleet MTBF, not only the single-breaker MTBF |
| 345 kV+ with low BFR | Additional protection may not be required (subject to study) |
Section 15
Common Misunderstandings
Table 15 — Corrects common misunderstandings about strokes and open-breaker protection.
| Misconception | Correct Interpretation |
|---|
| “The first stroke is the only important stroke” | It defines the incoming surge, but subsequent strokes can be critical for open breakers |
| “The tower-voltage spike must always be included” | It is very short; corona pushes the station crest past it, so it can often be neglected |
| “An open breaker is protected by transformer arresters” | When open, the line side may be isolated and exposed to incoming surges |
| “A high single-breaker MTBF means no issue” | Fleet exposure matters: many breakers reduce the effective MTBF |
| “Rod gaps are equivalent to arresters” | Gaps are cheaper but less effective and harder to coordinate |
Section 16
Summary and Memory Map
Equation Summary
Tower-spike duration
\(\displaystyle t_{\text{tower}} = \frac{2h}{c}\)
Mean time between surges
\(\displaystyle \text{MTBS} = \frac{1}{N_s}\)
Open-end doubling
\(\displaystyle V_{\text{open}} \approx 2\,V_s\)
Open-breaker surge limit
\(\displaystyle V_{s,\text{limit}} = \frac{1.29\,\text{BIL}}{2}\)
Annual open-breaker risk
\(\displaystyle P_T = N_s P_o\)
Open-breaker MTBF
\(\displaystyle \text{MTBF} = \frac{1}{P_T}\)
Fleet MTBF
\(\displaystyle \text{MTBF}_{\text{fleet}} \approx \frac{\text{MTBF}_{\text{single}}}{n}\)
Multi-line distance
\(\displaystyle d_m = \frac{100}{n\,\text{BFR}\,\text{MTBF}}\)
Memory map. Define station MTBF → convert to the equipment MTBS → compute the first-stroke incoming surge (breaker closed, arresters protect) → compute the subsequent-stroke surge for the open breaker → estimate the probability the breaker is open → \(\text{MTBF} = 1/(N_s P_o)\) → choose a line-side arrester, a rod gap, or accept the risk.
Final engineering message
The incoming surge is normally based on the first stroke, but after it the breaker may open and a subsequent stroke can arrive while the line side is unprotected — and the wave roughly doubles at the open gap. The design check is (subsequent-stroke surge) × 2 ≤ breaker chopped-wave withstand; if it fails with adequate margin, add line-side arresters or rod gaps. In short: backflash controls the incoming surge, but subsequent strokes can control open-breaker protection.
