Section 1
The Two Questions This Part Answers
Earlier parts covered arrester ratings, MCOV, TOV capability, switching-surge energy, protective characteristics and arrester models. This part moves to the next practical question: when a lightning surge reaches the arrester, how much current flows through it, and what voltage appears across it?
Why both quantities matter
The arrester current sets the energy duty; the arrester voltage sets the equipment insulation stress. Transformer reflections, struck-point reflections and station layout can all change the current — so it must be estimated from the circuit, not assumed.
This is Part Four of the metal oxide surge arrester series. It builds on the ratings and models of the earlier parts to estimate the lightning impulse discharge current and the resulting arrester voltage.
What this page teaches
- how MCOV ratings are set from the maximum line-to-ground voltage;
- the basic end-of-line arrester-current equation and surge doubling;
- why opposite-polarity power-frequency voltage increases the duty;
- why more connected lines reduce the arrester current;
- how transformer / open-end reflections increase the current;
- how struck-point reflections add further current;
- why the two reflection effects are taken separately (not multiplied);
- why a large current change gives only a small arrester-voltage change.
Section 2
Typical MCOV Ratings
Typical MCOV ratings exist for HV, EHV and distribution systems. They are selected from the maximum continuous line-to-ground voltage:
\[ V_{\text{LG,max}} = \frac{V_{\text{LL,max}}}{\sqrt{3}}, \qquad \text{MCOV} \ge V_{\text{LG,max}} \]
The actual selection also depends on the grounding method, the maximum system voltage, the expected TOV, distribution feeder voltage variation, and whether the system is effectively grounded.
The selection principle
MCOV is selected from the maximum continuous line-to-ground voltage — not only the nominal voltage.
Section 3
What Drives the Lightning Discharge Current
When a lightning surge reaches an arrester, the arrester conducts and limits the voltage — but the current is not fixed. It depends on the incoming surge crest and steepness, the arrester characteristic, the line surge impedance, the number of connected lines, the transformer distance and capacitance, reflections from the stroke termination point, and the power-frequency voltage polarity. The key quantities are:
Table 1 — Notation for the quantities driving arrester discharge current.
| Symbol | Meaning |
|---|
| \(I_A\) | Arrester discharge current |
| \(E_d\) | Arrester discharge voltage |
| \(E\) | Incoming surge crest voltage |
| \(Z\) | Line surge impedance |
| \(V_{PF}\) | Opposite-polarity power-frequency voltage |
Section 4
Arrester at the End of a Line
The simplest case is a surge of crest \(E\), steepness \(S\) and line surge impedance \(Z\) reaching an arrester at the end of a line. At the open end the travelling surge voltage tends to double — but the power-frequency voltage does not double. The source voltage seen by the arrester is therefore taken as \(2E\), and the arrester current is driven by the difference between that and the arrester voltage:
\[ I_A = \frac{2E - E_d}{Z}, \qquad I_A = \frac{2E - (E_A + V_{PF})}{Z} \]
Table 2 — Symbols used in the end-of-line arrester-current equation.
| Symbol | Meaning |
|---|
| \(E_A\) | Arrester discharge voltage |
| \(E_d\) | Effective arrester voltage in the circuit |
| \(V_{PF}\) | Opposite-polarity power-frequency contribution |
| \(Z\) | Phase-conductor surge impedance |
The incoming surge may ride on an opposite-polarity power-frequency voltage. If the power-frequency voltage is \(-100\ \text{kV}\), then \(+100\ \text{kV}\) is effectively added to the crest arrester voltage in the calculation — raising the current.
Sign convention for \(V_{PF}\)
Throughout this page, \(V_{PF}\) is the opposite-polarity contribution — a positive quantity that adds to the arrester-side voltage and so reduces the net driving voltage. That is why it appears as \(-(E_A + V_{PF})\) in the end-of-line current and as \(-V_{PF}\) in the combined estimate of the next section. The instantaneous power-frequency voltage of opposite polarity is taken at its worst (crest) value.
Power-frequency voltage adds duty
Opposite-polarity power-frequency voltage increases the arrester discharge duty — the current is driven by the difference between the doubled surge voltage and the arrester voltage.
Section 5
Linear Approximation and the Combined Estimate
Over a limited current range the arrester characteristic can be approximated by a straight line between two known V–I data points (a local approximation only, not a full model):
\[ E_d = E_0 + R_A\,I_A \]
Table 3 — Notation for the local straight-line arrester characteristic.
| Symbol | Meaning |
|---|
| \(E_0\) | Intercept voltage of the local straight-line approximation |
| \(R_A\) | Apparent arrester resistance over the range |
Combining this with the end-of-line relation gives a direct estimate of the current (with the power-frequency term applied by polarity convention), after which the discharge voltage follows:
\[ I_A = \frac{2E - E_0 - V_{PF}}{Z + R_A}, \qquad E_d = E_0 + R_A\,I_A \]
Section 6
Including Power-Frequency Voltage in EMTP® / ATP
When using EMTP®, ATP or a similar transient program, the power-frequency voltage should be added to each value of arrester voltage in the V–I characteristic — i.e. the V–I points are shifted by \(V_{PF}\). After solving the circuit, the actual arrester discharge voltage is recovered by subtracting the power-frequency contribution.
Modelling instruction
Include power-frequency voltage by shifting the arrester voltage characteristic by \(V_{PF}\), then subtract it back out after the solution.
Section 7
The Effect of the Number of Connected Lines
In an \(n\)-line station a surge arrives on one line while the other \(n-1\) lines remain connected. Those lines provide extra parallel surge-impedance paths, so part of the surge is transmitted into them and less current flows through the arrester:
\[ n \uparrow \;\Rightarrow\; I_A \downarrow \]
Table 4 — How the number of connected lines changes arrester current.
| Station Condition | Effect on Arrester Current |
|---|
| One line connected | Highest arrester current |
| Several lines connected | Part of the surge travels into the other lines |
| More connected lines | Lower current through the arrester |
More lines help the arrester
A multi-line station shares the surge across parallel paths, reducing arrester current — though surge distribution through the station can still stress equipment, so insulation coordination is still required.
Section 9
Example — Open End, No Transformer Capacitance
Table 5 — Input parameters for the open-end reflection worked example.
| Quantity | Value |
|---|
| Arrester voltage (held constant) | \(620\ \text{kV}\) |
| Incoming surge crest | \(1560\ \text{kV}\) |
| Time to crest / tail | \(0.5\ \mu\text{s}\) / infinite |
| Line surge impedance | \(450\ \Omega\) |
| Arrester-to-open-end distance | \(100\ \text{m}\) |
\[ I_{\text{initial}} = 4.18\ \text{kA}, \qquad I_{\text{crest}} = 6.93\ \text{kA} \]
The open-end reflection clearly increases the arrester current. Note, however, that a \(100\ \text{m}\) arrester-to-transformer distance is unrealistic for proper protection — much shorter distances are normally required, because longer separation increases travelling-wave effects and allows higher equipment terminal voltage.
Keep arresters close
Arresters should be located close to the equipment they protect.
Section 11
Reflections from the Struck Point
A second reflection effect comes from the origin of the surge — the struck point (a tower, shield wire, or flashover point). When the surge reaches the station, part reflects back toward the struck point, reflects again toward the station, and so on. For a backflashover the struck-point impedance includes half the ground-wire surge impedance, the phase-conductor surge impedance and the impulse footing resistance, summarised by equivalent impedances \(Z_s\) and \(R_e\) (the impedance seen by the reflected surge). The returning wave is governed by a reflection coefficient denoted \(-p\):
A reflecting source
The struck point can behave like a reflecting source that increases the arrester current through repeated reflections.
The arrester current is then the initial current plus a series of increments from successive reflections:
\[ I_A = I_{A1} + \Delta I_{A1} + \Delta I_{A2} + \dots \]
An infinite rectangular surge is useful analytically but unrealistic: repeated reflections would cause a large buildup, and for \(n = 1\) almost all the stroke current could discharge through the arrester (all of it if the arrester voltage were zero — a short circuit). A more realistic surge has a near-zero time to crest and an exponential tail with time constant \(T \approx 10\)–\(20\ \mu\text{s}\), which limits how many late reflections contribute. The number of contributing reflections is \(N = 0, 1, 2, \dots\), found by maximising the approximate current expression and taking the nearest integer:
Only early reflections count
Only reflections that arrive before the relevant crest time significantly increase the current.
Section 12
ATP Example — Struck-Point Reflections
Table 7 — Input parameters for the ATP struck-point reflection example.
| Quantity | Value |
|---|
| Incoming surge crest / time to crest | \(1560\ \text{kV}\) / zero |
| Tail time constant | \(14\ \mu\text{s}\) |
| Surge impedance | \(450\ \Omega\) |
| Struck point to arrester / travel time \(T_s\) | \(600\ \text{m}\) / \(2\ \mu\text{s}\) |
| Arrester discharge voltage / model | \(620\ \text{kV}\) / constant voltage |
Table 8 — Estimated crest current for one and two connected lines.
| Station Lines | Estimated Crest Current |
|---|
| \(n = 1\) | \(8.28\ \text{kA}\) |
| \(n = 2\) | \(6.59\ \text{kA}\) |
The maximum reflection number was \(N = 2\), and the ATP results were only about \(4\)–\(5\%\) higher — so the approximate method is useful for quick estimates.
Section 13
Combining the Two Reflection Effects
Three travelling-wave effects shape the arrester current — two raise it and one lowers it:
Table 9 — The three travelling-wave effects that raise or lower arrester current.
| Source | What Happens | Effect |
|---|
| Transformer / open end behind arrester | Surge passes the arrester and reflects back from the transformer / open end | Increases arrester current |
| Struck point on the line | Surge reflects between the station and the stroke origin | Can build up additional arrester current |
| Multiple connected lines | Surge energy splits into the other lines | Reduces arrester current |
The two current-increasing effects raise a natural question: should they be multiplied? ATP simulations say no. Two cases illustrate it:
Table 10 — Comparing separate and combined reflection currents at two struck-point distances.
| Case | Transformer Cap Alone | Struck-Point Alone | Combined Circuit |
|---|
| Struck point \(600\ \text{m}\) | \(8.66\ \text{kA}\) | increases later | \(8.75\ \text{kA}\) |
| Struck point \(150\ \text{m}\) | \(8.66\ \text{kA}\) | \(16.2\ \text{kA}\) | \(17.8\ \text{kA}\) |
In neither case is the combined current the product of the separate effects. At \(600\ \text{m}\) the first struck-point reflection returns after about \(4\ \mu\text{s}\) — after the transformer-voltage crest — so it barely changes that crest. At \(150\ \text{m}\) the reflection returns in about \(1\ \mu\text{s}\), early enough to matter; yet the transformer voltage rose only from \(769\ \text{kV}\) to \(771\ \text{kV}\) (about \(1\%\)), because the arrester V–I curve is very flat.
Take the larger, do not multiply
The transformer/open-end and struck-point effects should be evaluated separately, and the larger current used:
\[ I_{A,\text{crest}} = \max\!\big(I_{A,\text{transformer reflection}},\ I_{A,\text{struck-point reflection}}\big) \]
Late reflections: current, not voltage
Late struck-point reflections may increase the arrester current but not the transformer-voltage crest — a large current increase can produce only a small arrester-voltage increase.
Section 14
The Timing Criterion for Transformer Voltage
For the transformer voltage, the timing of its crest decides whether struck-point reflections matter. The comparison is between the transformer-voltage crest time and twice the travel time to the struck point:
\[ t_T \le 2T_s \quad\text{or}\quad t_T > 2T_s \]
Table 11 — Notation for the transformer-voltage timing criterion.
| Symbol | Meaning |
|---|
| \(t_T\) | Time to crest of the transformer voltage |
| \(T_s\) | Travel time between arrester and struck point |
Table 12 — When struck-point reflections need to be considered for transformer voltage.
| Condition | Consequence |
|---|
| \(t_T \le 2T_s\) | Struck-point reflections arrive too late — transformer/open-end equations are sufficient |
| \(t_T > 2T_s\) | Struck-point reflections may contribute and should be considered |
Section 15
Example 5 — A Reflection-Influenced Current
Table 13 — Input parameters for the reflection-influenced current of Example 5.
| Quantity | Value |
|---|
| Incoming surge crest \(E\) / steepness \(S\) | \(1560\ \text{kV}\) / \(1400\ \text{kV/}\mu\text{s}\) |
| Surge impedance \(Z\) / lines \(n\) | \(450\ \Omega\) / \(1\) |
| Struck-point travel time \(T_s\) / tail \(T\) | \(0.5\ \mu\text{s}\) / \(14\ \mu\text{s}\) |
| Power-frequency voltage \(V_{PF}\) | \(156\ \text{kV}\) |
| Transformer voltage crest time \(t_T\) | \(2.1\ \mu\text{s}\) |
Because \(t_T > 2T_s\) (\(2.1 > 1.0\)), struck-point reflections must be considered. The calculation gives \(N = 2\) and:
\[ I_A \approx 12.3\ \text{kA}, \quad E_d \approx 473\ \text{kV} \;\longrightarrow\; I_A \approx 12.4\ \text{kA}, \quad E_d \approx 470\ \text{kV} \]
After updating the straight-line approximation the result barely changes. The current changed noticeably while the voltage changed only slightly — the signature of the flat MO discharge characteristic:
Why current moves more than voltage
\(\Delta I_A\) may be large while \(\Delta E_d\) is small, because the MO V–I curve is very flat in the discharge region — which is exactly why metal oxide arresters give effective voltage limitation.
Section 16
The Shielding-Failure Exception
The same general circuit applies to backflashover surges and to shielding failures with flashover. But there is an important exception for shielding failures without flashover: the phase-conductor stroke launches a travelling surge, but there is no flashover-created discontinuity at the stroke point.
No struck-point reflection
For a shielding failure without flashover, no reflection occurs from the stroke-terminating point — so there is no struck-point reflection increase in arrester current.
Section 17
The Discharge-Current Calculation Workflow
Define surge \(E,\ S,\ T\)
Line impedance \(Z\)
Include \(V_{PF}\)
Arrester V–I data, \(E_0,\ R_A\)
Simple end-of-line current
Effect of \(n\) lines
Transformer / open-end reflection
Struck-point reflection
Take the larger \(I_{A,\text{crest}}\)
Arrester voltage \(E_d\)
Use \(E_d\) for insulation coordination
Section 18
Misconceptions, Equations and Final Message
Table 14 — Common arrester-current misconceptions with their correct engineering interpretations.
| Misconception | Correct Interpretation |
|---|
| “Arrester current is just the surge voltage over \(Z\)” | It depends on doubled surge voltage, arrester voltage, \(V_{PF}\), \(Z\) and reflections |
| “Power-frequency voltage can be ignored” | Opposite-polarity \(V_{PF}\) can increase the current — include it |
| “More lines always worsen arrester duty” | Extra lines usually reduce current via parallel travelling-wave paths |
| “Transformer and struck-point reflections multiply” | Evaluate them separately and use the larger current |
| “Large current rise means large equipment-voltage rise” | The flat V–I curve means a large \(\Delta I_A\) gives a small \(\Delta E_d\) |
| “Shielding failures always build up struck-point current” | Without flashover, there is no struck-point reflection effect |
Equation Summary
Maximum line-to-ground voltage
\(\displaystyle V_{\text{LG,max}} = \frac{V_{\text{LL,max}}}{\sqrt{3}}\)
Basic end-of-line current
\(\displaystyle I_A = \frac{2E - E_d}{Z}\)
Local arrester characteristic
\(\displaystyle E_d = E_0 + R_A I_A\)
Combined estimate with \(V_{PF}\)
\(\displaystyle I_A = \frac{2E - E_0 - V_{PF}}{Z + R_A}\)
Total reflected current
\(\displaystyle I_A = I_{A1} + \Delta I_{A1} + \Delta I_{A2} + \dots\)
Crest current rule
\(\displaystyle I_{A,\text{crest}} = \max\!\big(I_{\text{tx}},\ I_{\text{sp}}\big)\)
Transformer-voltage timing
\(\displaystyle t_T \lessgtr 2T_s\)
Memory map. The lightning discharge current is driven by \(E\), \(Z\), \(E_d(I_A)\), \(V_{PF}\) and \(n\), then modified by transformer and struck-point reflections. Estimate the simple end-of-line current → reduce it for \(n\) lines → check the transformer/open-end reflection → check the struck-point reflection → take the larger (do not multiply) → read off \(E_d\) for insulation coordination.
Final engineering message
The arrester discharge current is not set by the incoming surge magnitude alone — it is controlled by \(E\), \(Z\), \(E_d(I_A)\), \(V_{PF}\), \(n\), and the transformer and struck-point reflections. The key practical rule is to evaluate the transformer and struck-point reflection effects separately and use the larger arrester current. Because metal oxide arresters have a flat discharge characteristic, a large current increase causes only a small voltage increase — which is why accurate arrester modelling and correct travelling-wave representation matter in critical lightning insulation-coordination studies.
