Section 1
Why Shielding-Failure Surges Must Be Studied
A shielding failure is lightning bypassing the shield wire and terminating directly on a phase conductor. In line design, attention focuses on shielding failures that flash the line over. But for substation incoming-surge studies, even shielding failures that do not flash over the line matter — a direct stroke to the conductor still launches a travelling surge toward the station.
So the quantity that counts here is the total shielding-failure rate \(\text{SFR}\), not only the shielding-failure flashover rate \(\text{SFFOR}\).
This is Part Two of the incoming-surge and open-breaker protection series. It explains how shielding failures launch travelling surges toward the station, even when the line insulation does not flash over — the companion to the backflashover-originated incoming surge of Part One. Parts One and Three are linked in the series navigation below.
What this page teaches
- why the total \(\text{SFR}\) matters, not only \(\text{SFFOR}\);
- why a shielding failure launches a surge even without line flashover;
- why the struck-point voltage is \(V_s = Z_c I/2\);
- why shielding-failure surges have a finite front steepness;
- why the surge tail is longer than a backflash surge tail;
- why corona mainly reduces steepness, not crest, over short distances;
- how \(\text{SFR}\) and MTBS are used to select the design surge;
- how the equivalent station circuit is applied.
Table 1 — How the total shielding-failure rate differs from the flashover rate.
| Term | Meaning | Used for |
|---|
| \(\text{SFR}\) | Total shielding-failure rate | Incoming-surge selection |
| \(\text{SFFOR}\) | Shielding-failure flashover rate | Line outage / flashover assessment |
Every shielding failure can launch a surge
For incoming-surge studies, a shielding failure does not need to flash over the line insulation to matter. A direct stroke to the phase conductor still launches a travelling surge toward the station — so it is counted by \(\text{SFR}\), not \(\text{SFFOR}\). This is the most important teaching point on the page.
Section 2
Voltage at the Struck Point
The current is injected directly into the conductor, so the struck-point voltage is half the surge-impedance product (the current splits and travels both ways — one part away from the station, one toward it):
\[ V_s = \frac{Z_c\,I}{2} \]
Table 2 — Notation for the struck-point surge voltage equation.
| Symbol | Meaning |
|---|
| \(V_s\) | Surge voltage at the struck point |
| \(Z_c\) | Phase-conductor surge impedance |
| \(I\) | Shielding-failure stroke current |
Why the factor \(1/2\)?
The injected lightning current divides at the struck point into two equal travelling waves — one moving toward the station and one moving away from it. Each carries half the current, so the conductor sees \(Z_c\,(I/2)\), giving \(V_s = Z_c I/2\).
With a minimum shielding-failure current of \(I_{\min} = 3\) kA and a maximum \(I_m\), the surge magnitude is naturally bounded:
\[ V_l = \frac{Z_c\,I_{\min}}{2}, \qquad V_u = \frac{Z_c\,I_m}{2} \]
Table 3 — Notation for the minimum and maximum shielding-failure surge voltages.
| Symbol | Meaning |
|---|
| \(V_s\) | Surge voltage at the struck point |
| \(V_l\) / \(V_u\) | Minimum / maximum shielding-failure surge voltage |
| \(Z_c\) | Phase-conductor surge impedance |
| \(I_{\min}\) / \(I_m\) | Minimum (\(\approx 3\) kA) / maximum shielding-failure current |
The upper voltage \(V_u\) is limited by the maximum shielding-failure current \(I_m\) — unlike the backflashover case, where the stroke current is not bounded the same way and very high currents remain possible.
Section 3
Distribution of the Shielding-Failure Current
The shielding-failure current distribution is approximately linear except near the maximum, and for engineering work it can be treated as roughly uniform. So very high currents close to \(I_m\) are relatively unlikely:
The maximum sets the limit, but is rare
The maximum shielding-failure current \(I_m\) defines the upper bound of the surge, but surges close to that limit are uncommon.
Section 4
Backflash versus Shielding-Failure Surges
Table 4 — Comparison of backflashover and shielding-failure surge characteristics.
| Item | Backflashover Surge | Shielding-Failure Surge |
|---|
| Stroke termination | Tower or shield wire | Phase conductor |
| Initial voltage source | Flashover from tower to phase | Direct conductor stroke |
| Initial front steepness | Almost infinite at flashover | Finite, from the stroke-current steepness |
| Crest limitation | Line insulation may chop the surge | Limited by the shielding-failure current |
| Rate used | BFR | SFR |
| Typical severity | Often controlling | Usually less severe, but must be checked |
The key difference
Backflash surges start with a very steep front; shielding-failure surges have a finite initial steepness set by the lightning-current waveshape.
Section 5
Waveshape at the Struck Point
The voltage follows the current waveshape, so the voltage steepness scales with the current steepness:
\[ S_v = \frac{Z_c}{2}\,S_i \]
Table 5 — Notation for the voltage-steepness relation at the struck point.
| Symbol | Meaning |
|---|
| \(S_v\) | Voltage steepness |
| \(S_i\) | Current steepness |
The median current steepness is typically \(8\) to \(14\) kA/μs for shielding-failure currents of about \(3\) to \(10\) kA, and the steepness distribution can be taken as roughly independent of crest current. The tail is long — a median time-to-half near \(77.5\) μs (average \(\approx 92\) μs), giving a tail time constant of about:
Table 6 — Crest, front steepness and tail of the struck-point waveshape.
| Quantity | Description |
|---|
| Crest voltage | Between \(V_l\) and \(V_u\) |
| Front steepness | \(S_v = (Z_c/2)\,S_i\) from the lightning-current steepness |
| Tail time constant | ≈ 133 μs (longer than the backflashover tail) |
The shielding-failure surge follows the lightning-current waveshape, so its tail is normally much longer than a backflashover chopped surge. For practical estimation the mean time-to-half may be represented by a tail time constant of about \(133\) μs:
Table 7 — How backflashover and shielding-failure surge tails differ.
| Surge Type | Typical Tail Behaviour |
|---|
| Backflashover incoming surge | Shorter, chopped / flashover-controlled |
| Shielding-failure incoming surge | Longer, current-waveshape controlled |
Section 6
Corona During Travel to the Station
Corona reduces the front steepness as the surge travels. Because the surge starts with a finite steepness, the station steepness is lower than the backflash case:
\[ S = \frac{S_0}{1 + \dfrac{S_0\,d}{K_c}}, \qquad S_0 = \frac{S}{1 - \dfrac{S\,d}{K_c}} \]
Table 8 — Notation for the corona steepness-reduction equations.
| Symbol | Meaning |
|---|
| \(S\) | Steepness at the station |
| \(S_0\) | Steepness at the struck point |
| \(d\) | Travel distance (km) |
| \(K_c\) | Corona constant |
For an infinitely steep surge this reduces toward \(S \approx K_c/d\) (the backflash limit), but a finite \(S_0\) gives a lower station steepness. Crest: because the tail is long, corona barely reduces the crest over short distances, so:
\[ V_{\text{station}} \approx V_{\text{struck point}} \qquad (\text{short distances}) \]
This is unlike the backflash case, where corona and chopping can strongly reduce the crest. Soil-resistivity attenuation is usually minor over the short distances of interest.
Section 7
Selecting the Surge for a Given MTBS
The incoming surge is selected for a target MTBS, with design rate \(N_D = 1/\text{MTBS}\). The number of shielding-failure surges meeting a given crest and steepness is, conceptually:
\[ N_s = \text{SFR} \times \text{distance} \times P(V_s) \times P(S_0) \]
and the design surge is the crest/steepness combination for which \(N_s = N_D\). The first design distance comes from the same form as backflashover, with SFR in place of BFR:
\[ d_m = \frac{100}{\text{SFR} \times \text{MTBS}} \]
Table 9 — Notation for the minimum design-distance calculation.
| Symbol | Meaning |
|---|
| \(d_m\) | Minimum design distance (km), rounded to the next tower |
| SFR | Shielding-failure rate (per 100 km-year) |
Section 8
Minimum-Crest Case and a Worked Example
The simplest first estimate takes the crest as the minimum shielding-failure voltage (every surge equals or exceeds it, so \(P(V_l) = 1\)), then chooses the steepness so the surge count equals \(N_D\):
\[ V_l = \frac{3\ \text{kA} \times Z_c}{2}, \qquad P(V_l) = 1 \]
Table 10 — Input parameters for the worked design-surge example.
| Quantity | Value |
|---|
| SFR / MTBS / \(N_D\) | 0.534 per 100 km-year / 400 years / 0.0025 surges/year |
| \(I_m\) / critical current | 21.13 kA / 5.43 kA |
| SFFOR | 0.476 per 100 km-year |
| \(Z_c\) / CFO / \(K_c\) | 477 Ω / 1296 kV / 700 |
| \(V_u\) / \(V_l\) | 3742 kV / 716 kV |
\[ d_m = \frac{100}{0.534 \times 400} \approx 0.468\ \text{km} \;\to\; d = 0.6\ \text{km}, \qquad S \approx 796\ \text{kV/}\mu\text{s}, \quad V \approx 716\ \text{kV} \]
This is the minimum crest-voltage case for the required MTBS.
Section 9
Higher Crest-Voltage Cases
Including more (farther) towers lowers the station steepness but allows a higher required crest — so the shielding-failure surge is a family of design surges, with the shielding-failure current distribution adding a further statistical layer:
Table 11 — How close and distant strokes trade steepness against crest voltage.
| Case | Steepness | Crest Voltage |
|---|
| Close stroke | Higher steepness | Lower crest possible |
| Distant stroke | Lower steepness | Higher crest possible |
Section 10
Adjacent-Tower Flashover Chops the Surge
A high shielding-failure surge may exceed the line insulation at an adjacent tower and be chopped before reaching the station, leaving a lower crest, a shorter time above CFO and reduced severity. In the source example a \(\sim 2413\) kV surge is reduced to \(\sim 1492\) kV after adjacent-tower flashover — about 62% of the original. The maximum incoming surge is limited by the line insulation:
\[ V_{\text{incoming,max}} \approx (1.35 \text{ to } 1.45)\,\text{CFO} \]
Line insulation limits the surge
The line insulation can limit the shielding-failure surge voltage before it reaches the station — though the limit (\(\approx 1.35\)–\(1.45\,\text{CFO}\)) is higher than the typical backflash limit.
Section 11
The Usual Practical Case
The example used to develop the method is not typical. In many real lines \(\text{SFFOR} \approx 0\), so few shielding-failure flashovers occur. Shielding-failure incoming surges may still exist, but they are usually lower in steepness and crest and less severe than backflash surges — so backflashover normally remains the controlling mechanism. Shielding failure should still be checked, especially for high-voltage lines or marginal shielding.
Section 12
Power-Frequency Voltage in Shielding-Failure Surges
For shielding-failure incoming-surge calculations the power-frequency voltage is not included — the average power-frequency voltage is taken as zero for shielding failure:
\[ V_{PF} \approx 0 \qquad (\text{shielding-failure incoming surge}) \]
This differs from backflashover, where the power-frequency voltage affects the flashover condition.
Section 13
A Simplified Quick Estimate
For screening studies, the most sensitive parameter for station equipment is often the steepness, so a backflash-based quick estimate is used: find the distance, round to the next tower, and take the corona-controlled steepness:
\[ d_m = \frac{100}{\text{BFR} \times \text{MTBS}} \;\to\; \text{next tower}, \qquad S = \frac{K_c}{d_m} \]
The crest is commonly taken as \(0.85\) to \(1.0\,\text{CFO}\) (historically a conservative \(1.2\,\text{CFO}\)), with a tail constant near \(20\) μs and the BFR opposite-polarity power-frequency voltage:
Table 12 — Recommended values for the simplified quick-estimate surge.
| Quantity | Quick-Estimate Value |
|---|
| Crest \(E\) | \(0.85\)–\(1.0\,\text{CFO}\) (conservative \(1.2\,\text{CFO}\)) |
| Tail time constant \(\tau\) | ≈ 20 μs (range 10–35 μs for \(R_0 \approx 20\,\Omega\)) |
| Power-frequency \(V_{PF}\) | \(0.70\,V_{LN}\), with \(V_{LN} = \sqrt{2}\,V_{LL}/\sqrt{3}\) |
| Voltage to ground | \(E - V_{PF}\) (sign per polarity) |
Section 14
Applying the Surge: the Station Equivalent Circuit
The surge is applied through an equivalent circuit: a surge source, a source impedance \(Z_i\), a line section of impedance \(Z\) and length \(d_m\), then the station equipment and arresters. It represents both the first surge and reflections from the struck point (which can raise arrester current, raise terminal voltage and shift the crest timing):
Surge source \(V_s\)
Source impedance \(Z_i\)
Line section length \(d_m\)
Station equipment & arresters
\[ Z_i = R_i \parallel Z_c \parallel \frac{Z_g}{2} \approx R_i, \qquad Z \approx Z_c \]
Table 13 — Notation for the station equivalent-circuit source impedance.
| Symbol | Meaning |
|---|
| \(Z_i\) | Source impedance seen by the returning surge |
| \(R_i\) | Impulse footing resistance |
| \(Z_c\) | Phase-conductor surge impedance |
| \(Z_g\) | Ground-wire surge impedance |
In many practical cases \(Z_i \approx R_i\), because the footing resistance is much smaller than the conductor and ground-wire surge impedances. The reduced circuit neglects the remote struck-point reflection and is valid only until reflections return:
\[ t_{\text{valid}} = 2T_d = \frac{2\,d_m}{v}, \qquad d_m = 900\ \text{m},\ v \approx 300\ \text{m/}\mu\text{s} \;\Rightarrow\; 2T_d = 6\ \mu\text{s} \]
Table 14 — When to choose the reduced or full station circuit model.
| Use the reduced circuit when… | Use the full circuit when… |
|---|
| only the early crest matters; the peak occurs before reflections return; arrester current is not reflection-sensitive; it matches the full circuit | the crest occurs after \(2T_d\); arrester energy matters; open-breaker stress over longer time; reflections govern severity; GIS / critical coordination |
The power-frequency voltage is applied separately (e.g. added to the arrester discharge voltage); the station voltage to ground is \(V_{\text{station}} = V_{\text{surge}} - V_{PF}\), the sign set by the polarity relationship.
Section 15
The Quick-Estimate Workflow
Select MTBS
\(d_m\), round to next tower
\(S = K_c/d_m\)
\(E = 0.85\text{–}1.0\,\text{CFO}\)
\(\tau \approx 20\ \mu\text{s}\)
Apply surge to station model
Check equipment voltage & arrester duty
This suits screening; detailed studies should use full travelling-wave modelling.
Section 16
Summary, Misconceptions and Memory Map
Table 15 — Which incoming-surge aspect each mechanism usually governs.
| Mechanism | Usually controls… |
|---|
| Backflashover | The high-steepness incoming surge |
| Shielding failure | Direct conductor surge; limited by \(I_m\) and line CFO |
| Quick estimate | Usually the backflash BFR + corona-controlled steepness |
Backflashover usually controls the steepness, but shielding failure can still matter if shielding is weak, \(I_m\) is high, \(Z_c\) is high, the station is crest-sensitive, or the line CFO is high enough to allow large unchopped surges.
Table 16 — Common shielding-failure misconceptions corrected against sound practice.
| Misconception | Correct Interpretation |
|---|
| “Only shielding failures that flash the line over matter” | Even non-flashover shielding failures launch a surge toward the station |
| “Shielding-failure surges have infinite steepness” | They follow the current waveshape — finite initial steepness |
| “Corona always greatly reduces the crest” | For long-tail SF surges over short distances, it mainly reduces steepness |
| “The highest crest is always most severe” | For open breakers, front steepness may matter more than crest |
| “The reduced circuit is always sufficient” | It is valid only before struck-point reflections return (\(2T_d\)) |
Equation Summary
Struck-point voltage
\(\displaystyle V_s = \frac{Z_c I}{2}\)
Min / max surge
\(\displaystyle V_l = \frac{Z_c I_{\min}}{2},\; V_u = \frac{Z_c I_m}{2}\)
Voltage steepness
\(\displaystyle S_v = \frac{Z_c}{2}S_i\)
Corona steepness
\(\displaystyle S = \frac{S_0}{1 + S_0 d/K_c}\)
Infinite-front limit
\(\displaystyle S \approx \frac{K_c}{d}\)
Design distance
\(\displaystyle d_m = \frac{100}{\text{SFR}\times\text{MTBS}}\)
Source impedance
\(\displaystyle Z_i = R_i \parallel Z_c \parallel \frac{Z_g}{2}\)
Reduced-circuit validity
\(\displaystyle t_{\text{valid}} \approx \frac{2 d_m}{v}\)
Memory map. Shielding failure strikes the conductor → \(V_s = Z_c I/2\) → finite-front surge travels to the station → corona reduces steepness → crest stays similar over short distances → select the surge using SFR and MTBS → check whether an adjacent tower chops the wave → apply via the full or reduced circuit → check breaker, arrester and equipment stresses.
Final engineering message
A shielding failure need not flash the line over to matter: the direct stroke launches \(V_s = Z_c I/2\) toward the station, with a finite front and a long tail. Corona mainly cuts the steepness, while the crest can stay roughly unchanged over short distances. Select the surge statistically from SFR and MTBS and apply it through a travelling-wave circuit. The bottom line: backflashover usually controls the steepness, but shielding failure must still be checked for crest voltage and open-breaker stress.
