Capacitive Switching

Switching Unloaded Transmission Lines

Energising and de-energising unloaded transmission lines — how the line’s shunt capacitance sets the charging current and the Ferranti rise, how the first-pole recovery voltage follows the C₁/C₀ ratio, how shunt reactors change both current and recovery voltage, and how energisation surges and delayed current zeros are controlled with pre-insertion resistors and controlled closing. Follows IEEE Std C37.012-2022, with APS engineering interpretation.

Reading time ≈ 19 min

Section 1

Unloaded Lines as a Capacitive Duty

An unloaded transmission line behaves mainly as a capacitive element. When the line is open-ended, its shunt capacitance — between phases and to earth — draws a charging current. On opening, the breaker interrupts this charging current and a recovery voltage appears across the contacts; on closing, the line is energised by a travelling-wave surge that can create temporary overvoltages, especially if a trapped charge is present. Compared with cables, overhead lines usually have lower capacitance per kilometre, but their length, distributed parameters and travelling-wave reflections make the energisation and overvoltage behaviour just as important.

This note follows IEEE Std C37.012-2022. This page develops the unloaded-line duty introduced in the general application overview, focusing on the line charging current, the Ferranti voltage rise, the recovery voltage after de-energising, shunt compensation, energisation surges and delayed-current-zero behaviour. The cable analogue is covered in unloaded cable switching.

Before energising, a line may or may not carry a trapped charge from a previous opening, and the switching duty after a load rejection needs separate thought because the line voltage can already be elevated.

Lumped or distributed?

For charging-current purposes a line is represented by its capacitance. For short and medium lengths — below about 200 km — the total shunt capacitance can be treated as a lumped value. For longer lines the series inductance and shunt capacitance are distributed along the route, so the travelling-wave behaviour and the voltage rise must be represented with a distributed-line model. The charging current itself is governed mainly by the phase-to-phase capacitance.

Typical per-phase capacitance depends on the conductor arrangement, rising with bundle size because a fatter effective conductor sits closer to its neighbours.

Table 1 — Typical per-phase line capacitance by conductor arrangement.

Line Configuration	Capacitance per Phase
Single conductor	about 9.1 nF/km
Four-conductor bundle	about 14 nF/km

Section 2

Charging Current and the Ferranti Effect

The line charging current is the capacitive current needed to energise the line’s insulation and electric field at power frequency; it is the current the breaker interrupts when an unloaded line is opened, even though no load is connected at the remote end. Its magnitude is a function of system voltage, line length and line configuration, and it is the quantity that decides the required rating. Because the line’s inductance and capacitance are distributed, the power-frequency voltage at the open (receiving) end is higher than at the breaker (sending) end — the Ferranti effect. The rise follows the phase constant of the line:

\[ \frac{U_{\text{receiving}}}{U_{\text{sending}}} = \frac{1}{\cos(\beta\ell)}, \qquad \beta = \omega\sqrt{L'C'} \]

\(\beta\): phase constant of the line (rad/km)
\(\ell\): line length (km)
\(L',C'\): series inductance and shunt capacitance per unit length
\(\omega\): angular power frequency, \(2\pi f_{s}\)

Physically, the Ferranti rise occurs because the line capacitance supplies reactive power along the line, and its interaction with the line inductance lifts the open-end voltage; the effect grows with line length and voltage level. For a 500 kV line the reported voltage rise is about 24% at 500 km and about 4% at 200 km. The small rise below 200 km is why the Ferranti effect can be neglected for shorter lines but must be carried for long ones — it raises both the charging current and, after de-energising, the trapped-charge voltage. It also matters because the line may already be above nominal voltage before switching, so the recovery voltage and the energisation overvoltage should not be assessed from the nominal voltage alone.

A first estimate of the charging current per kilometre against system voltage can be read from the application curves in the standard. If that estimate exceeds about 90% of the preferred line-current rating, a more accurate calculation using the actual line geometry is warranted rather than relying on the generic curve.

Worked example — linear capacitive reactance at 245 kV

Take a 245 kV, 60 Hz system with a charging current of 0.5 A/km. The linear (per-kilometre) capacitive reactance is \(X_{C}' = U/(\sqrt{3}\,I) = 245{,}000/(\sqrt{3}\times0.5)\approx\mathbf{0.283\ M\Omega\!\cdot\!km}\). At 50 Hz the same line gives \(X_{C}'=(60/50)\times0.283\approx0.34\ \text{M}\Omega\!\cdot\!\text{km}\). For a finite length the line reactance is the linear value divided by the length: over 100 km, \(X_{C}=0.283/100\approx\mathbf{2.83\ k\Omega}\).

\[ X_{C}' = \frac{U}{\sqrt{3}\,I} \qquad\qquad X_{C} = \frac{X_{C}'}{\ell} \]

\(X_{C}'\): linear capacitive reactance of the line (MΩ·km)
\(X_{C}\): capacitive reactance of a line of length \(\ell\) (Ω)
\(U\): line-to-line system voltage (kV)
\(I\): charging current per unit length (A/km)
\(\ell\): line length (km)

Section 3

Recovery Voltage — Uncompensated Lines

After interruption the line-side terminal does not immediately lose its charge: the source-side terminal keeps following the system voltage while the line side stays influenced by its trapped charge and capacitance, so the voltage across the open contacts is the recovery voltage, and the first pole to clear normally sees the most severe duty. A three-phase line has capacitance both between phases and to earth, and the peak recovery voltage across the first pole to clear depends on the ratio of positive- to zero-sequence capacitance, C₁/C₀. The two sequence capacitances describe how strongly the phases interact: when C₁=C₀ each phase has only capacitance to earth and the phases are independent; as C₁/C₀ rises the inter-phase coupling grows and couples more voltage onto the first pole to clear. In short, the C₁/C₀ ratio expresses how the positive- and zero-sequence capacitances shape the first-pole-to-clear voltage; it is a line-geometry and earthing-related factor, not an arbitrary safety margin.

Table 2 — First-pole-to-clear recovery-voltage peak versus capacitance ratio.

Condition	C₁/C₀	First-Pole Recovery Peak
Capacitance to earth only (single-phase-like)	1.0	2.0 pu
Typical transmission line, later poles clear at next current zero	about 2.0	about 2.2 pu
High ratio or non-effectively-earthed neutral	large	up to 2.5 pu
Typical line, delayed clearing of later poles	about 2.0	2.42 pu
Delayed clearing, worst case	large	up to 3.0 pu

With modern devices the second and third poles interrupt at the next available current zero, and a typical line at C₁/C₀ ≈ 2.0 sees about 2.2 pu on the first pole. If those later poles are delayed — through an excessive pole spread or a mis-set point-on-wave controller — the first-pole peak climbs to 2.42 pu at the same ratio, and up to 3.0 pu in the worst case. This is a direct reason to control pole scatter on line breakers.

Section 4

Restrike Probability and Long-Line Cases

When the in-service recovery voltage — its shape and peak — departs from the test voltage, the restrike probability shifts with it. Two situations are worth singling out.

High C₁/C₀. For transmission lines a ratio near 2.0 is assumed. A ratio above 2.0 couples higher voltage onto the first pole to clear and raises the restrike probability; because breaker designs respond to both current magnitude and recovery-voltage waveshape, the manufacturer should be consulted in that case.
Ferranti allowance. The Ferranti rise increases the trapped-charge voltage after de-energising. Shunt compensation usually holds the residual rise below 10%, so where the Ferranti effect is to be carried, the recovery voltage is taken as increased by about 0.1 pu.

Uncompensated lines longer than about 300 km, even of simple design, are a special case not necessarily bounded by the standard capacitive-switching test requirements: the peak recovery voltage on interruption can exceed the tested values, and additional testing to the elevated levels of the specific application may be justified. Occasional single-end switching of a very long line — common while a system is still being built out and intermediate substations are bypassed — falls into this category.

Section 5

Shunt-Compensated Lines: Charging Current

Long lines are routinely fitted with shunt reactors to absorb part of the line’s charging reactive power. This reduces the net charging current and helps control the Ferranti voltage rise. It also changes the natural response of the line, however, so it can affect the recovery voltage and the current-zero behaviour (Sections 6 and 9) and must be included in the switching assessment. The degree of compensation is set by the ratio of the line’s capacitive reactance to the reactor’s inductive reactance:

\[ k_{l} = \frac{X_{C,\text{line}}}{X_{L,\text{reactor}}} \qquad\qquad I_{lc} = I_{c}'\,(1 - k_{l}) \]

\(k_{l}\): compensation factor
\(X_{C,\text{line}}\): capacitive reactance of the line
\(X_{L,\text{reactor}}\): inductive reactance of the compensating reactor
\(I_{lc}\): charging current of the compensated line (A rms)
\(I_{c}'\): charging current of the uncompensated line (A rms)

The compensation factor \(k_{l}\) indicates how much of the line’s charging reactive power the shunt reactor absorbs: a higher factor means a smaller net capacitive current, though not necessarily a simpler switching duty. When \(X_{L,\text{reactor}}>X_{C,\text{line}}\) the reactor under-absorbs and the line is undercompensated (\(k_{l}<1\)); when \(X_{L,\text{reactor}}<X_{C,\text{line}}\) it is overcompensated (\(k_{l}>1\)). A line compensated at 60% (\(k_{l}=0.60\)) draws \(I_{lc}=I_{c}'(1-0.60)=0.40\,I_{c}'\) — 40% of the uncompensated charging current. One consequence follows directly: if the breaker rating is chosen for the compensated current, the line cannot be switched with its reactors disconnected. The Ferranti rise and the reactor location shift the current slightly from this simple estimate.

Section 6

Shunt-Compensated Lines: Recovery Voltage

Compensation also changes the shape of the recovery voltage, and generally for the better. On an uncompensated line the line-side voltage after interruption is a trapped dc charge; on a compensated line the reactor and the line capacitance form a resonant circuit, so the line-side voltage oscillates at the natural frequency of that loop:

\[ f_{1} = f_{s}\sqrt{\frac{X_{C,\text{line}}}{X_{L,\text{reactor}}}} = f_{s}\sqrt{k_{l}} = \frac{1}{2\pi\sqrt{LC}} \]

\(f_{1}\): resonance frequency of the compensated line (Hz)
\(f_{s}\): system frequency (Hz)
\(k_{l}\): compensation factor
\(L\): inductance of the reactor (H)
\(C\): total capacitance of the line (F)

Key idea

Because compensation is normally less than unity, \(f_{1}<f_{s}\): the line-side voltage swings back down instead of holding a full trapped charge, so the recovery voltage across the breaker is lower and the restrike probability at a given current is reduced. A compensated line can therefore become effectively restrike-free, or let the breaker interrupt higher charging currents than it could on a bare line. Because such applications markedly alter the recovery voltage, the manufacturer should be consulted.

Section 7

Energising: the Switching Surge

When the breaker closes, the source voltage launches a travelling wave down the line, exactly as when energising a cable. The wave travels to the open far end, reflects, and adds to the incoming wave, so the receiving-end voltage can reach roughly twice the incoming amplitude — higher than the sending-end voltage. The surge grows further under two aggravating conditions.

Table 3 — Energisation overvoltage by closing condition.

Closing Condition	Approximate Line-End Overvoltage
Closing an uncharged line, wave reflected at the open end	up to about 2× the network voltage
Closing onto a trapped charge of opposite polarity (auto-reclose)	theoretically up to about 3× the network voltage
Non-simultaneous pole closing on a three-phase line	a further rise from waves induced on the other phases

If the line was opened earlier it may still carry a trapped charge, and reclosing onto that charge can be far more severe than energising a fully discharged line — especially when the source voltage and the trapped line voltage are of opposite polarity at the instant of closing. This is the classic three-times auto-reclose hazard: a line left with a trapped charge is re-energised when the network is at the opposite polarity, and the reflected wave stacks on the residual voltage. Non-simultaneous poles make it worse still, because a wave on one phase induces waves on the others that can push a second phase higher.

Inrush magnitude and shape

Because a line is a distributed capacitance, its energising inrush is limited by the line surge impedance — typically 300 Ω to 450 Ω — not by a lumped inductance. The inrush is therefore modest: a 138 kV line draws only a few hundred amperes, well below a capacitor-bank inrush. It also takes the form of a square wave whose period is set by the line’s travel time and hence its length, rather than an oscillation at a single natural frequency.

Section 8

Limiting the Energisation Overvoltage

The most effective control on line-energisation overvoltage is a pre-insertion resistor (PIR) — a resistor switched in series with the line a set time before the main contacts close. Closing then happens in two stages:

The resistor is inserted first, so the imposed wave is reduced by the voltage division between the resistor and the line surge impedance.
The main contacts close and short out the resistor; this launches a fresh wave, but of reduced amplitude. The resistor contacts are reset (opened) before the main contacts part again.

The optimum resistance is of the same order as the line surge impedance, and the optimum insertion time is found by simulation — typically an EMTP®-type study — with values of 6 ms to 8 ms being common. Surge arresters (per IEEE Std C62.22) are also used successfully to clamp energisation transients, and controlled (point-on-wave) closing — closing each pole near a favourable point on the voltage wave to reduce the initial voltage difference across the contacts, and hence the energisation surge — is a third route. Whatever the method, surge arresters limit the peak overvoltage only at their installation point; they do not remove the need to check the breaker duty, the remote-end voltage, the trapped-charge condition, and the energy the arresters themselves must absorb.

Section 9

The Delayed-Current-Zero Phenomenon

A delayed current zero occurs when the current is offset so strongly that it does not cross zero when expected. The concern is not the current magnitude but the missing or delayed zero crossing, because an ac circuit breaker relies on a current zero to interrupt: if it must interrupt before a natural zero arrives, the duty becomes much more severe.

When a line or cable is energised together with its shunt reactor already connected, a subtler problem appears. The total current through the breaker is the sum of the line’s capacitive current, which leads the voltage by 90°, and the reactor’s inductive current, which lags by 90° — the two are almost 180° apart and largely cancel in the steady state. The reactor current, however, cannot change instantaneously, so making the circuit injects a dc offset into the reactor branch. That offset is largest when the pole makes at a voltage zero, reaching up to 2.0 pu of the inductive compensation current, and it decays with a time constant set by the reactor’s X/R ratio.

If the reactor compensates 50% or more of the charging current, the offset inductive component outweighs the capacitive component and the combined current may not cross zero for several cycles — a delayed (or missing) current zero. Because an ac breaker needs a current zero shortly after its contacts part to interrupt, a rapid open-after-close in this condition can leave it unable to clear, with the risk of breaker damage or a wider system problem. The triggering sequences are exactly the fast ones:

tripping an unfaulted line immediately after energising it;
tripping all three poles after a reclose onto a single- or two-phase fault.

Worked check — an 80 km, 345 kV line with its reactor

Consider an 80 km overhead line drawing 43.3 Mvar of charging at 345 kV, energised together with a 25 Mvar shunt reactor. The compensation factor is \(k_{l}=25/43.3\approx0.58\) — above the 50% threshold, so delayed current zeros are credible. On energising at a voltage zero the line contributes a fast, quickly-damped high-frequency current settling to the steady charging current, while the reactor current carries a slowly-decaying dc offset; the net current can stay one-signed well beyond the breaker’s interrupting window.

Section 10

Mitigating Delayed Current Zeros

The mitigation methods aim to do one of a few things: reduce the dc offset, reduce the surge magnitude, create a more favourable closing instant, or ensure the breaker is not asked to interrupt before a natural current zero is available. The simplest defences are procedural: impose a tripping delay so the dc offset decays before the line breaker opens, or disconnect the shunt reactor before opening the line breaker. Where the switching itself must be controlled, two device-level measures apply.

Pre-insertion resistors

A PIR lowers the effective X/R of the reactor branch during insertion and drives its dc component to zero more quickly — ideally within the close-open time of the breaker, so a current zero is available when needed. Under worst-case assumptions the maximum compensation factor that avoids missing zeros can be estimated as:

\[ k_{l} = 1 - 0.5\,e^{-\frac{R_{PIR}}{L}\cdot\frac{t_{ins}}{1000}} \]

\(k_{l}\): maximum compensation factor without risk of missing zero crossings
\(t_{ins}\): electrical insertion time (ms)
\(L\): inductance of the reactor (H)
\(R_{PIR}\): resistance of the pre-insertion resistor (Ω)

The form is intuitive: with no resistor (\(R_{PIR}\to0\)) the safe limit falls to \(k_{l}=0.5\), the familiar 50% threshold; a larger resistor or a longer insertion time pushes the exponential toward zero and allows compensation approaching unity. The estimate is conservative — it neglects the oscillation in the capacitive current at making, which itself creates extra zero crossings, and the breaker’s own dc chopping capability of a few tens of amperes.

Controlled closing

Point-on-wave closing avoids making near a voltage zero, and must be applied to reclosing operations as well as the first close. On a highly compensated line there is a conflict: closing near a voltage peak minimises the switching surge but making near a voltage zero is what would avoid delayed zeros, and the two cannot both be satisfied. The usual compromise is an intermediate making angle of about 40 electrical degrees, trading a modest switching surge against an acceptable delayed-zero risk. Because the interaction of reactor decay, making angle and breaker timing is intricate, delayed-zero problems are normally resolved by detailed EMT studies of the specific configuration.

Section 11

Common Mistakes

The recurring errors in line-switching applications come from treating an unloaded line as a small-current duty and overlooking the Ferranti rise, the recovery voltage and the reactor interaction that actually govern it.

Common mistakes to avoid

Ignoring the Ferranti effect on lines beyond 200 km, so the charging current and the trapped-charge recovery voltage are both underestimated.
Assuming 2.0 pu recovery voltage for every line, when a typical C₁/C₀ ≈ 2.0 gives 2.2 pu — and delayed later-pole clearing raises the first pole to 2.42 pu or beyond.
Treating an uncompensated line above 300 km as a standard case, when its elevated recovery voltage may fall outside the tested capability.
Rating the breaker on the compensated charging current and then trying to switch the line with its reactors out of service.
Re-energising a line onto a trapped charge without a PIR, controlled closing or arresters, and meeting the 3× auto-reclose overvoltage.
Opening a line breaker rapidly after energising a >50%-compensated line/reactor combination, and being caught by delayed current zeros.

Section 12

Key Points

Application checklist

Represent the unloaded line by its capacitance — lumped below 200 km, distributed above — and base the charging current on the phase-to-phase capacitance (about 9.1–14 nF/km per phase).
Check the line charging current against 90% of the preferred rating — but do not stop there: for unloaded lines the main concerns are the recovery voltage, the Ferranti rise (about 24% at 500 km / 500 kV), energisation overvoltage, trapped charge, shunt compensation and delayed current zeros.
Take the first-pole recovery voltage from C₁/C₀: about 2.2 pu at the typical ratio of 2.0, up to 2.5 pu for high ratios or non-effectively-earthed neutrals, and 2.42–3.0 pu if later poles are delayed.
Add about 0.1 pu for the Ferranti effect where it is carried, and treat uncompensated lines beyond 300 km as a special case that may need testing to elevated values.
Include shunt reactors in the switching assessment: with the compensation factor \(k_{l}=X_{C,\text{line}}/X_{L,\text{reactor}}\) the charging current falls to \((1-k_{l})\) of the uncompensated value and the Ferranti rise is reduced, but the line-side recovery voltage now oscillates at \(f_{s}\sqrt{k_{l}}<f_{s}\) (lowering restrike probability) and the current-zero behaviour changes.
Limit energisation overvoltage — up to 2× on reflection, 3× onto trapped charge — with pre-insertion resistors (R ≈ surge impedance, 6–8 ms), surge arresters, or controlled closing.
Guard against delayed current zeros when a >50%-compensated line/reactor is switched together: avoid rapid open-after-close, or apply a tripping delay, reactor disconnection, a PIR, or controlled closing at about 40° — confirmed by an EMT study.

Section 13

References and Further Reading

The standards and technical brochures behind this guide.

IEEE Std C37.012-2022, IEEE Guide for the Application of Capacitive Current Switching for AC High-Voltage Circuit Breakers Above 1000 V. New York, NY, USA: IEEE, 2022.
IEEE Std C37.09-2018, IEEE Standard Test Procedures for AC High-Voltage Circuit Breakers with Rated Maximum Voltage Above 1000 V. New York, NY, USA: IEEE, 2018.
IEEE Std C62.22-2009, IEEE Guide for the Application of Metal-Oxide Surge Arresters for Alternating-Current Systems. New York, NY, USA: IEEE, 2009.
CIGRE, Shunt Capacitor Switching in Distribution and Transmission Systems, Technical Brochure 817. Paris, France: CIGRE, 2020.
J. C. Das, Transients in Electrical Systems: Analysis, Recognition, and Mitigation. New York, NY, USA: McGraw-Hill, 2010.

Part 4 Reading now

Switching Unloaded Transmission Lines

Line charging current and the Ferranti effect, the C₁/C₀ recovery voltage, shunt compensation, energisation surges and the delayed-current-zero phenomenon.

Series progress 4 of 8

Part 5

Voltage Factors and Application Considerations

The single-phase test voltage factors, plus switching through transformers, hidden-circuit inrush and outrush, load and reclosing, and behaviour by breaker type.