Section 1
Switching-Surge Coordination Moves Into the Substation
The previous notes handled switching overvoltages on transmission lines — phase-ground and phase-phase. This note carries the same probabilistic stress–strength idea into the substation, where the goal is to estimate phase-ground and phase-phase BSLs for apparatus, the matching air clearances, the effect of arresters, and the separate requirements of transformers and bushings. This first part focuses mainly on phase-ground switching-surge coordination inside the substation; phase-phase coordination is treated separately in the companion phase-phase note.
The main concern is self-restoring insulation — air clearances, bus support insulators, disconnect switches and the external insulation of bushings — which recovers after a flashover and can be treated statistically. But the note also covers non-self-restoring insulation, chiefly transformer internal insulation and internal bushing insulation, which does not recover and must be treated deterministically.
Section 2
Why a Station Is Not Just a Short Line
Flashover still occurs when stress exceeds strength — but seven features separate a substation from a line, and each one bends the simplified line method:
Table 1 — Seven differences between line and substation insulation coordination.
| # | Difference | Transmission Line | Substation |
|---|
| 1 | Must coordinate with the line | Stands alone | \(V_{3,\text{stn}} \ge V_{3,\text{line}}\) |
| 2 | Parallel insulations \(n\) | 100–1000 | 5–10 |
| 3 | Voltage profile \(\gamma = E_S/E_R\) | \(< 1\) | \(= 1.0\) |
| 4 | Insulation strengths | Roughly equal | Unequal — weak-link controls |
| 5 | Factors \(K_f, K_G, K_E\) | Many-tower form | Modified for small \(n\) |
| 6 | Strength specified as | CFO, \(V_3\) | BSL |
| 7 | Design SSFOR target | 1/100 | Sometimes 1/1000 |
The headline consequences
Because \(n\) is small (5–10 critical points in a breaker-and-a-half bay), the multi-tower steep-strength assumption no longer holds, so the strength scatter cannot be ignored. Because station distances are short relative to the impulse front, every insulation effectively sees the same SOV (\(\gamma = 1.0\)). And because apparatus strengths differ, the weakest item controls.
Section 3
The Station Must Not Weaken the Line
The substation sits at the line end, so the line-end switching surge arrives at the station essentially unattenuated — the station insulation is the insulation at the line end. Unless arresters guard the line entrance, the station strength must therefore meet the line switching-impulse design strength:
\[ V_{3,\text{station}} \ge V_{3,\text{line}} \]
If the station is weaker, it becomes the weak point of the whole system — the substation would become the preferred flashover location instead of the line, and a flashover inside a station is far more serious than one on a line tower. Note the comparison is on a switching-impulse basis only: the line may carry higher insulation for lightning or pollution reasons, but that does not change this rule.
Section 4
Line-Entrance Arresters Change the Rule
If arresters are installed on the line side of the breaker, they cap the surge reaching the station and effectively isolate it from the line SOV. Station insulation can then be selected from the arrester protective level instead of from \(V_{3,\text{line}}\):
Table 2 — How line-entrance arrester presence and location change the station duty.
| Case | Effect on the Station Duty |
|---|
| No line-entrance arrester | Station sees the incoming switching surge more directly — \(V_{3,\text{station}} \ge V_{3,\text{line}}\) |
| Arrester close to the protected equipment | Switching-surge stress limited effectively; station selected from the arrester protective level |
| Arrester separated from the equipment | Residual voltage, lead effects, travelling-wave reflections and separation distance must be considered |
This is why line-entrance arresters can substantially reduce the required station BSLs and clearances — the quantitative effect is worked through in Section 13.
Section 5
Station SSFOR and the Weak-Link Rule
In a substation the number of exposed insulation gaps is far smaller than on a line, so the station flashover risk is controlled by the weakest relevant insulation path rather than by thousands of repeated line spans. With several different apparatus strengths, the station SSFOR sums the no-flashover probabilities \(q_i\) of each insulation point:
\[ \text{SSFOR} = \tfrac{1}{2}\int f(V)\,\Bigl[\,1 - \prod_{i=1}^{n} q_i(V)\,\Bigr]\,dV \]
- \(f(V)\)
- SOV probability density
- \(q_i(V)\)
- probability insulation \(i\) does not flash over
- \(\tfrac{1}{2}\)
- positive-polarity switching-surge factor
A practical, conservative simplification sets every strength equal to the lowest — the weak-link form:
\[ \text{SSFOR} = \tfrac{1}{2}\int f(V)\,\bigl[\,1 - q^{\,n}(V)\,\bigr]\,dV \]
One weak item dominates
For \(n = 5\): reducing all strengths by 10% raises SSFOR by ~500%; reducing just one by 10% still raises it by ~250%. Identifying the weakest component is the heart of station coordination.
Section 6
Linking CFO, V₃ and BSL
CFO, V₃ and BSL
CFO (critical flashover voltage) is the voltage at which self-restoring insulation has a 50% probability of flashover under the specified impulse shape. \(V_3\) is the statistical withstand point three standard deviations below the CFO — a low-flashover-probability strength point used in the probabilistic method. BSL (Basic Switching-impulse insulation Level) is the standard withstand level, about \(1.28\sigma\) below CFO. The coefficients \(0.79\) and \(0.91\) below follow from the assumed Gaussian strength distribution and scatter \(\sigma_f/\text{CFO} = 0.07\) — they are not universal physical constants.
Station apparatus is rated by its BSL, so the method must translate between BSL, CFO and \(V_3\). Taking the station scatter \(\sigma_f/\text{CFO} = 0.07\):
\[ V_3 = \text{CFO}\Bigl(1 - 3\,\tfrac{\sigma_f}{\text{CFO}}\Bigr) = 0.79\,\text{CFO} \]
\[ \text{BSL} = \text{CFO}\,(1 - 1.28\times 0.07) = 0.91\,\text{CFO} \]
So \(\text{CFO} = \text{BSL}/0.91\), and because \(V_3\) sits at the \(-3\sigma\) tail while BSL sits at \(-1.28\sigma\):
\[ V_3 < \text{BSL} < \text{CFO} \qquad V_3 \approx \frac{0.79}{0.91}\,\text{BSL} = 0.868\,\text{BSL} \]
For example, a BSL of 950 kV corresponds to \(V_3 \approx 825\) kV. These three relationships are the workhorse of every station calculation that follows.
Section 7
Station Clearances and Gap Factors
A clearance is sized from its CFO through the Gallet form, with a station gap factor \(k_g\):
\[ \text{CFO}_S = k_g\,\frac{3400}{1 + 8/S} \]
- \(S\)
- strike distance (m), standard atmosphere
- \(k_g\)
- gap factor
Across the common station geometries — conductor-to-structure, conductor-to-rod, conductor-to-plane, rod–rod, post insulators, disconnect-switch gaps — the lowest important value is about \(k_g = 1.3\) — a representative practical value for conductor-to-structure station gaps, used as a conservative default; other electrode configurations may need different gap factors (see Part Three). Post insulators are a special case, taking \(k_g = 1.18\), with their BSL and BIL estimated from height \(S\):
\[ \text{CFO}_S = 1.18\,\frac{3400}{1 + 8/S}, \quad \text{BSL}_S \approx 0.91\,\text{CFO}_S, \quad \text{BIL}_S \approx 450\,S \]
Section 8
Apparatus BSLs and the Weak Points
Different apparatus carry different standard insulation levels, which is exactly why the weak-link concept matters:
- Transformers have specified BSLs at 230 kV and above.
- Most other apparatus have BSLs mainly from 345 kV upward.
- Circuit breakers have a higher BSL in the open position than the closed position.
- Disconnect switches and bus support insulators may have no direct ANSI BSL — estimate them from post-insulator relationships (Section 7).
The breaker open-gap is usually well-insulated; the weak points are typically the bus support insulators, disconnect switches and the bare air clearances.
Section 9
Choosing the Station SSFOR Target
A transmission line is commonly designed to \(\text{SSFOR} = 1/100\) (one flashover per 100 breaker operations). Because a station flashover is more serious, some utilities adopt a target one decade lower, \(1/1000\) — though in practice \(1/100\) is still frequently used. The choice depends on system importance and the consequence of failure; critical EHV GIS/AIS stations on major lines justify the lower target.
The SSFOR is then evaluated through the same reduced-variate forms as the line case, but with station-modified factors (small \(n\)):
\[ \text{SSFOR} = \tfrac{1}{2}\bigl[\,1 - F(Z_e)\,\bigr]\ \text{(Gaussian)} \qquad \text{SSFOR} = \tfrac{1}{2}\bigl[\,1 - F(y_e)\,\bigr]\ \text{(extreme value)} \]
Section 10
Example 1 — Estimating the SSFOR
A 500 kV station, all apparatus at BSL = 850 kV, Gaussian SOV with \(E_2 = 808\) kV, \(\sigma_0/E_2 = 0.10\), \(n = 10\), \(\sigma_f/\text{CFO} = 0.07\). Convert BSL to the tail value, then form the ratio:
\[ \text{CFO} = \frac{850}{0.91} = 934\ \text{kV}, \quad V_3 = 0.79\times 934 = 738\ \text{kV} \]
\[ \frac{V_3}{E_2} = \frac{738}{808} = 0.9134 \;\Rightarrow\; \text{SSFOR} = \frac{0.91}{100} \quad(\text{computer: } 0.86/100) \]
Now place the same station at 1500 m altitude (relative air density \(\delta = 0.840\)) with a standard \(\text{BSL}_S = 950\) kV, so \(\text{CFO}_S = 950/0.91 = 1044\) kV. After applying the altitude correction:
\[ \text{SSFOR} = \frac{0.49}{100} \quad(\text{computer: } 0.50/100) \]
The lesson: altitude reduces external strength, so a higher standard BSL is needed to achieve the same actual-site performance. Altitude correction applies to external self-restoring air insulation; it should not be applied in the same way to internal (oil/SF6/solid) non-self-restoring apparatus insulation.
Section 11
Example 2 — Required BSL and Clearance
Reverse the problem: given \(\text{SSFOR} = 1/100\), find the BSL and clearance. At sea level \(K_f = 0.91\), \(K_G = 1.0\), so \(V_3/E_2 = 0.91\):
\[ V_3 = 0.91\times 808 = 735, \quad \text{CFO} = \frac{735}{0.79} = 931, \quad \text{BSL} = 0.91\times 931 = 847\ \text{kV} \]
The next standard BSL is 895 kV (\(\text{BIL} = 1175\) kV); the breaker BSL of 1300 kV is ample; the clearance with \(k_g = 1.3\) is \(S = 2.13\) m. But the station must also coordinate with the line, which needs \(V_{3,\text{line}} = 783 > 735\) kV. Re-designing to \(V_3 = 783\) kV:
\[ \text{CFO} = \frac{783}{0.79} = 991, \quad \text{BSL} = 0.91\times 991 = 902\ \text{kV} \;\Rightarrow\; \text{BIL} = 1300\ \text{kV}, \;\; S = 2.31\ \text{m} \]
At 1500 m the actual-site targets are unchanged (\(\text{CFO}_A = 991\), \(V_{3A} = 783\), \(\text{BSL}_A = 902\)), but the standard BSL must be raised. Iterating gives \(\text{BSL}_S \approx 981\) kV, so the next standard is 1032 kV (\(\text{BIL} = 1425\) kV) and \(S = 2.69\) m (computer 2.68 m).
Table 3 — How line coordination and altitude drive the selected BIL (Example 2).
| Case | Required BSL | Selected BIL | Clearance |
|---|
| Sea level, line ignored | 847 kV | 1175 kV | 2.13 m |
| Sea level, line coordinated | 902 kV | 1300 kV | 2.31 m |
| 1500 m, line coordinated | 981 kV | 1425 kV | 2.69 m |
Section 12
Why Real 500 kV Stations Use Higher BIL
Switching-surge analysis above lands around 1175–1425 kV BIL — yet, with one exception (BPA), real 500 kV stations often use 1800 kV BIL. The reason is that lightning insulation coordination frequently demands a higher level than switching surge. Switching-surge design may permit a lower BIL, but the lightning requirement can govern the final selection. When a higher BSL is selected for lightning or standardisation, the air clearance should still be checked against the required switching duty, not blindly against the standard BSL chosen for another reason (see Part Three).
Section 13
How Arresters Reshape the SOV Distribution
An arrester discharge characteristic is approximated by a line, and the station voltage adds the surge-impedance drop:
\[ E_A = E_0 + R_A I_A, \qquad E = E_A + I_A Z \;\Rightarrow\; E_A = K_A E + (1 - K_A)E_0, \quad K_A = \frac{R_A}{R_A + Z} \]
- \(E_0,\ R_A\)
- arrester intercept voltage and dynamic resistance
- \(Z\)
- line surge impedance
Above the arrester operating point a Gaussian SOV stays Gaussian but is compressed: \(\mu_A = K_A\mu_0 + (1-K_A)E_0\), \(\sigma_A = K_A\sigma_0\). Since \(K_A\) is small, the spread of the high-voltage tail shrinks dramatically — the reason arresters are so effective at cutting SSFOR.
Worked example. A 318 kV MCOV arrester (switching discharge 823 kV), \(Z = 350\,\Omega\), original \(E_2 = 808\), \(\mu_0 = 642\), \(\sigma_0 = 80.8\) kV:
\[ K_A = 0.2441, \quad \sigma_A = 19.72\ \text{kV}, \quad \mu_A = 696.4\ \text{kV} \]
\[ E_{2A} = 737\ \text{kV}, \quad \frac{\sigma_A}{E_{2A}} = 0.0268 \;\Rightarrow\; \frac{V_3}{E_2} = 0.9555 \]
\[ V_3 = 704, \quad \text{CFO} = 891, \quad \text{BSL} = 811\ \text{kV} \;\Rightarrow\; \text{BIL} = 1050\ \text{kV}, \;\; S = 2.00\ \text{m} \]
Table 4 — Required BSL, selected BIL and clearance across conditions.
| Condition | Required BSL | Selected BIL | Clearance |
|---|
| Sea level, line ignored | 844 kV | 1175 kV | 2.12 m |
| Sea level, line coordinated | 902 kV | 1300 kV | 2.31 m |
| Sea level, with arresters | 804–811 kV | 1050 kV | 2.00 m |
| 1500 m, line coordinated | 981 kV | 1425 kV | 2.68 m |
| 1500 m, with arresters | 881 kV | 1175 kV | 2.33 m |
Arresters vs closing resistors
Closing resistors reduce SOVs along the entire line, so they help both line and station. Line-entrance arresters reduce SOVs mainly near the station and over a limited stretch — excellent station protection, but less effective than resistors along the whole line. If closing resistors are omitted (e.g. \(E_2 = 2.8\) pu \(= 1257\) kV), the required BSL at 1500 m climbs to ~1400 kV, exceeding the standard breaker BSL — so line-entrance arresters become required.
Section 15
Phase-Ground Station Design Workflow
The end-to-end sequence for phase-ground substation switching-surge coordination:
Design workflow
- From the line-end study, obtain the SOV distribution \(E_2,\ \sigma_0/E_2\) — or the arrester-modified \(E_{2A},\ \sigma_A/E_{2A}\).
- Set the station target SSFOR (typically 1/100, or 1/1000 for critical stations).
- Find the station \(V_3\) via \(V_3/E_2 = K_f K_G\) (or \(K_f K_E\)) with small-\(n\) factors.
- Coordinate with the line: enforce \(V_{3,\text{station}} \ge V_{3,\text{line}}\), else raise strength or add line-entrance arresters.
- Convert with \(V_3 = 0.79\,\text{CFO}\) and \(\text{BSL} = 0.91\,\text{CFO}\), then select the next standard BIL/BSL.
- Size clearances from \(\text{CFO}_S = k_g\,\tfrac{3400}{1+8/S}\) with \(k_g = 1.3\); apply altitude correction.
- Check transformer (\(\text{BSL} \ge 1.15\,E_{SI}\)) and external bushing (altitude-corrected) separately.
Section 16
Key Lessons and Memory Map
Key lessons
- A station is not a short line: few insulation points, unequal strengths, no voltage profile (\(\gamma = 1.0\)), and higher failure consequence.
- Station strength must meet the line switching-impulse strength — \(V_{3,\text{station}} \ge V_{3,\text{line}}\) — unless line-entrance arresters isolate it.
- The weakest apparatus dominates: at \(n = 5\), one item 10% low raises SSFOR ~250%.
- For station apparatus (\(\sigma/\text{CFO} = 7\%\)): \(V_3 = 0.79\,\text{CFO}\), \(\text{BSL} = 0.91\,\text{CFO}\); practical \(k_g = 1.3\).
- Altitude raises required standard BSL and clearance; line-entrance arresters lower them.
- Transformer internal insulation is non-self-restoring — coordinate deterministically with \(\text{BSL} \ge 1.15\,E_{SI}\).
Equation Summary
Strength relationship
\(\displaystyle V_3 = 0.79\,\text{CFO}\)
Switching impulse level
\(\displaystyle \text{BSL} = 0.91\,\text{CFO}\)
V₃ vs BSL
\(\displaystyle V_3 \approx 0.868\,\text{BSL}\)
Station clearance (CFO)
\(\displaystyle \text{CFO}_S = k_g\,\frac{3400}{1+8/S}\)
Station coordination
\(\displaystyle V_{3,\text{stn}} \ge V_{3,\text{line}}\)
Transformer deterministic margin
\(\displaystyle \text{BSL} \ge 1.15\,E_{SI}\)
Altitude (external air)
\(\displaystyle \text{BSL}_S = \frac{\text{BSL}_A}{\delta^{\,m}}\)
