Capacitive Switching

Voltage Factors and Application Considerations for Capacitive Switching

The test voltage factors that make a single-phase capacitive-switching test represent three-phase service — the \(k_{c}\) = 1.0 to 1.7 table and its earthing and fault dependence — together with the practical application questions: switching through a transformer, the “hidden” inrush and outrush currents that reach other breakers in a multi-bank station, combined load and reclosing duties, and how oil, vacuum, SF₆ and air-blast breakers each respond. Follows IEEE Std C37.012-2022, with APS engineering interpretation.

Reading time ≈ 18 min

Section 1

Test Voltage Factors and Why They Matter

Capacitive-switching type tests may be run three-phase or single-phase. At the highest rated voltages — 362, 420, 550 and 800 kV — a full three-phase laboratory test may not be practical, because no laboratory can supply the full three-phase power, so a single-phase or per-interrupter (unit) test is used instead. When that is done, the applied test voltage must represent the recovery voltage the breaker would see in actual three-phase service, and that is the purpose of the single-phase voltage factor \(k_{c}\). The voltage factor is not a generic safety margin; it is the factor that makes a single-phase test reproduce the recovery-voltage severity of the real three-phase application.

This page connects the application duties described in the earlier pages — capacitor banks, cables and lines — to the voltage-factor and test-duty rules used when a single-phase test represents three-phase service. The general application overview introduces \(k_{c}\) as part of the breaker-selection process; this page explains how \(k_{c}\) is selected for specific applications, and why the same breaker can see different recovery-voltage duties depending on earthing, neutral connection, circuit configuration and fault condition. It follows IEEE Std C37.012-2022.

What the voltage factor sets

Per IEEE Std C37.09-2018, the test voltage measured at the breaker just before interruption must be at least the product of the rated phase-to-earth voltage and the voltage factor:

\[ U_{\text{test}} \;\ge\; \frac{U_{r}}{\sqrt{3}}\,k_{c} \]

\(U_{\text{test}}\): test voltage at the breaker before interruption
\(U_{r}\): rated (line-to-line) voltage
\(k_{c}\): single-phase test voltage factor (1.0 to 1.7)

A three-phase test naturally includes the phase relationships of the service condition; a single-phase test does not, so the missing three-phase behaviour must be represented by choosing the correct test voltage — the voltage factor \(k_{c}\) is the bridge between the single-phase laboratory test and the three-phase service duty. Two things drive the value of \(k_{c}\): the earthing arrangement of the network, and the presence of single- or two-phase faults. Both change how much of the phase-to-phase voltage couples onto the first pole to clear, and therefore the recovery voltage the single-phase test must reproduce.

Section 2

The Single-Phase Voltage Factors

Four values of \(k_{c}\) cover the recognised applications. They rise from unity — a solidly earthed system where the phases barely interact — to 1.7, where an unearthed system carries an earth fault and the healthy phase sees the full phase-to-phase voltage. The value of \(k_{c}\) increases whenever the first pole to clear is exposed to a higher recovery voltage — for example through non-effective earthing, isolated neutrals, double-circuit coupling, or faulted conditions.

Table 1 — Single-phase test voltage factors \(k_{c}\) and their applications.

\(k_{c}\)	Application
1.0	Solidly earthed-neutral systems with no significant mutual influence between adjacent phases — typically capacitor banks with effectively earthed neutral, and screened cables.
1.2	Belted cables and line-charging-current switching in effectively earthed systems, at rated voltages of 72.5 kV and above.
1.4	Non-effectively earthed systems including screened cables; unearthed-neutral capacitor banks; belted cables and line-charging switching in non-effectively earthed systems at 72.5 kV and below; line-charging switching at 362 kV and above in effectively earthed systems; breaking with single or two phase-to-earth faults in effectively earthed systems; and line-charging switching with delayed clearing of the second and third poles.
1.7	Breaking in non-effectively earthed systems in the presence of single or two phase-to-earth faults — the healthy phase sees the phase-to-phase voltage.

The earthing terms in the table have a direct physical meaning. In an effectively earthed system the neutral is held close to earth potential during normal operation and many fault conditions, so the recovery-voltage duty is usually less severe. In a non-effectively earthed or unearthed system the neutral can shift, raising the voltage across the first pole to clear. The capacitor-bank neutral connection matters for the same reason: it controls how the bank’s phase voltages shift after the first pole opens, which directly affects the voltage across the remaining breaker contacts.

Three qualifications matter in practice. The line-charging factors of 1.2 and 1.4 assume single-circuit construction. The 1.4 value is a compromise valid where the second and third poles interrupt 90° after the first. And where the pole-to-pole non-simultaneity of a breaker exceeds one-sixth of a cycle, the standard recommends either raising the factor or testing three-phase — such breakers fall outside its scope.

Where the 1.4 factor comes from

On an ungrounded capacitive load the first pole to clear would, on its own, drive the recovery voltage toward 3× the source-voltage peak. But the second and third poles interrupt 90° later, and at that instant the slope changes discontinuously and the first-pole peak settles at about 2.5× — a recovery voltage of roughly 2.8 pu whose half is the 1.4 factor. Reproducing that with a single-phase test is a balancing act: the first pole rises initially as though the factor were 1.5, then follows a 1 − cosine as if it were 1.25. A test factor of 1.25 fails to cover the initial rise, and 1.5 overstresses the breaker, so 1.4 is chosen as the value that adequately envelopes the real recovery voltage without being punitive.

Section 3

Multiple Circuits and Relocation

The tabulated factors are chosen to cover all known conductor arrangements of a single-circuit line. A double- or multiple-circuit line can be more onerous, because the switched circuit is never fully isolated from the rest of the system: the adjacent energised circuit couples (picks up) voltage onto it, adding a power-frequency residual of up to 0.2 pu depending on the conductor geometry. That coupling raises the line-side trapped voltage after interruption and changes the shape of the transient recovery voltage across the first pole to clear.

Two responses are available. The existing factor can be replaced by the next higher tabulated value — 1.4 in place of 1.2 — to envelope the more severe waveshape, or additional testing can be specified if even that does not cover the combined effect. In practice some utilities specify \(k_{c}=1.3\) rather than 1.2 for their double-circuit lines. Whenever a breaker is relocated to a part of the system where the earthing, fault exposure or circuit arrangement differs from its original duty, the voltage factor should be reviewed against the new application, not assumed to carry over.

Section 4

Switching Through an Interposed Transformer

A breaker sometimes switches a capacitor, line or cable through a transformer rather than directly, and it then does not necessarily see the same duty as a breaker connected straight to the load: the transformer impedance, winding connection and neutral earthing can change both the inrush path and the recovery-voltage duty. The current it interrupts is the far-side capacitive current scaled by the turns ratio:

\[ I_{CB} = N\,I_{\text{cap}} \]

\(I_{CB}\): current through the switching device
\(I_{\text{cap}}\): capacitive current on the far side of the transformer
\(N\): transformer turns ratio (breaker side to load side)

Energising a capacitive load through a transformer is generally milder than switching the same current directly: the transformer inductance lowers both the magnitude and the frequency of the inrush, the capacitance rings against that inductance, and the resulting saturation softens the transient recovery voltage and lowers the restrike probability. If a restrike does occur, the added inductance limits the inrush. There is a caveat — some configurations, such as a delta winding feeding a capacitive load, can support resonant overvoltages excited by switching, which should be checked by an EMT study (for example an EMTP®-type simulation).

When \(N>1\), switching through the transformer increases the current the breaker sees. De-energising an unloaded line or cable with a low-voltage breaker on the far side of a step-up transformer can present effective charging currents of 750 A to 1000 A, and the breaker’s capacitive rating must cover that raised value. Importantly, the higher current does not raise the recovery voltage, so it is not itself a concern for interruption — only the rating check is.

Section 5

“Hidden” Circuits: Inrush and Outrush on Other Breakers

A hidden capacitive circuit is a capacitance that is not obvious from the immediate breaker bay but is still electrically connected in a way that affects the switching duty; it can raise the inrush on closing or the outrush during fault clearing, even where the local equipment looks simple. In a station with banks of capacitors, the transient currents do not stay within the breaker assigned to capacitor switching. Two transient families circulate: the inrush when banks are energised, and the discharge (outrush) current when banks dump into a fault. Where many parallel banks are installed, these can reach large peaks at high frequency and affect breakers that were never intended for the duty:

a breaker may carry a transient inrush current exceeding its rating — while closed, or when closing into an effectively earthed fault;
the magnitude and rate of change of the current may flash over the secondaries of linear couplers or bushing current transformers (as used in dead-tank breakers) or the associated control wiring.

The following three cases — a bus-tie exposed to inrush, a line breaker exposed to total outrush, and a tie breaker left with a capacitive duty during fault clearing — are where non-assigned breakers get caught.

Section 6

Exposure to Inrush and Total Discharge (Outrush) Current

A bus-tie breaker sitting between two bus sections, each carrying capacitor banks, is exposed to the inrush when either side’s banks are energised. The peak rarely exceeds the breaker’s capability, but the rate of change can drive overvoltages on the secondaries of nearby linear couplers or current transformers, which appropriately sized metal-oxide varistors (MOVs) can clamp. With a linear coupler the induced secondary voltage is proportional to both the frequency and the amplitude of the transient current and must stay within the transducer standard’s limits.

More onerous is the total discharge current. Any breaker connected to a bus with several parallel banks behind it can, during a fault, carry the combined discharge of all those banks. For \(n\) banks of roughly equal capacitance, each separated from the fault by roughly equal inductance, the crest discharge current is:

\[ \hat{\imath}_{d} \;=\; u_{r}\,n\,\sqrt{\dfrac{2\,C}{3\,(L + n\,L_{\text{bus}})}} \]

\(\hat{\imath}_{d}\): crest value of the discharge current (A)
\(u_{r}\): source (line-to-line) voltage (V rms)
\(n\): number of banks of approximately equal capacitance
\(C\): per-phase capacitance of each bank (F)
\(L\): per-phase inductance between each breaker and its bank (H)
\(L_{\text{bus}}\): common per-phase inductance between the breakers and the bus (H)

The worst case — the highest discharge current — is a bolted three-phase fault with ungrounded banks, or a three-phase-to-earth or line-to-earth fault with effectively earthed banks. For class C₀ breakers (oil breakers should be treated as C₀) both the crest and the rate of change should be checked with the manufacturer. For class C₁/C₂ breakers, provided the peak stays within the close-and-latch rating, such a discharge is permissible up to twice in the breaker’s life without extra maintenance; the ringing frequency is generally not a concern but is worth confirming. Because the outrush can far exceed the inrush magnitudes and frequencies in IEEE Std C37.04 — it is not limited by the single-bank inrush impedance — its effect on linear couplers and CTs must also be assessed, with MOVs available to limit induced voltages and transient earth-rise on those circuits.

Note — induced voltage on CT and linear-coupler secondaries

The practical concern is that a high-frequency transient current induces a high voltage in the secondary circuit, which can stress the relays, meters and insulation connected to the CT or linear-coupler circuit — so surge suppression and secondary-circuit protection may be needed. The secondary voltage a bushing CT or linear coupler develops from the discharge current is proportional to both the transient frequency and the current, \(V_{cts} = \dfrac{I}{N}\,Z_{b}\,\dfrac{f_{t}}{f}\), where \(I\) is the primary discharge current, \(N\) the CT ratio, \(Z_{b}\) the burden (Ω), \(f_{t}\) the transient frequency and \(f\) the supply frequency. A 20 kA discharge at 2000 Hz through a 1000/5 CT with a 0.5 Ω burden therefore develops about 1.67 kV across the secondary — enough to stress every relay and instrument on that CT, which is why surge suppressors are fitted across the terminals.

Section 7

Capacitive Duty During Fault Clearing

A fault-clearing sequence can leave a breaker with a capacitive switching duty it was never rated for. A bus-tie or bus-section breaker can, in effect, become the capacitor-switching breaker if the clearing sequence leaves capacitor banks connected on both sides of the tie. The classic case is a bus-section tie breaker with capacitors on both sides: if it is the last to clear a bus fault that leaves banks energised, it must interrupt those banks in parallel — in the standard example, two banks on the section being de-energised in parallel with two on the source side. The tie breaker must therefore be equipped and rated for that parallel-bank switching, which was not obvious from the normal operating arrangement. Where possible, the cleaner solution is to coordinate the clearing sequence so the tie breaker always clears first, avoiding the capacitive duty altogether. This section gives only the application-level warning; the detailed treatment of capacitive switching under fault conditions is covered in the next page of the series.

Section 8

Combined Load, Reclosing and Resistor Limits

Switching a mixed load and capacitive current

When load current and capacitive current are switched together, the duty is no longer a pure capacitive-current duty: the power factor, the total current, the capacitive component and any source-side capacitance all influence the risk of restriking. The breaker has the capability provided the total current stays within its rated continuous current and either the power factor is at least 0.8 leading or the capacitive component does not exceed the rated capacitive switching current. Outside those bounds the performance is undefined by the standards and the manufacturer should be consulted: below 0.8 leading the voltage can be sufficiently out of phase with the current to cause unacceptable restriking, and a capacitor bank on the source side makes it worse.

Reclosing onto a charged bank

After a capacitor bank is disconnected it can remain charged for some time. If the breaker recloses before that trapped voltage has bled away, the source voltage and the trapped bank voltage can oppose each other, so reclosing can produce up to twice the normal inrush: a bank interrupted near a current zero holds close to peak voltage, and reclosing against that trapped charge draws a high inrush. Two remedies apply — isolate the bank from other loads after tripping and before reclosing (using the regular capacitor-switching device), which is especially advisable where other banks share the bus; or increase the reclosing dead time so the bank’s discharge resistors (or a magnetic voltage transformer) bleed the residual voltage down. Manufacturer discharge curves should be consulted; a typical discharge time constant is about 40 s.

Pre-insertion resistor thermal capability

A pre-insertion resistor is not selected for its resistance value alone: its energy and thermal duty must also be checked for the expected switching sequence, including reclosing. For capacitor-bank breakers fitted with pre-insertion resistors, the resistor’s thermal capability sets the minimum interval between switching operations. The resistance is matched to the bank size, and the resistors should have a thermal rating consistent with the rated duty cycle. Field tests that exceed the resistor’s thermal capacity, or that use a specially designed breaker, warrant consulting the manufacturer on the permissible frequency of operations.

Section 9

Behaviour by Circuit-Breaker Type

Capacitive switching stresses each interrupting technology differently, on both opening (restrikes) and closing (pre-strikes / inrush). In brief: oil breakers are the most sensitive to restrike and to inrush-energy (shock-wave) effects; air-blast breakers have their own transient behaviour and historical application limits; SF₆ breakers generally perform well but still need the correct duty selection; and vacuum breakers recover dielectric strength very fast but can produce pre-strikes on closing. In every case the manufacturer data and tested ratings remain essential. The behaviour below is drawn from laboratory and field experience.

Table 2 — Capacitive-switching behaviour of the main circuit-breaker types.

Type	On Opening (Restrikes)	On Closing (Pre-strikes / Inrush)
Oil	Long arcing times; restrike probability rises with current as gas bubbles cut the oil’s dielectric strength. High arc impedance damps the restrike and usually prevents multiple restrikes; older contraction types could escalate to evolving faults. Special care when line-charging current exceeds the rating.	Very sensitive to high-frequency pre-strikes: the shock wave in the (incompressible) oil can shatter the chamber insulator or crack contacts. Needs a severe inrush-frequency reduction or a special design. Bulk oil applied at up to 20 kA·kHz for decades without issue; minimum-oil about 1 kA·kHz.
Vacuum	Gap strength recovers very fast, so restrike probability is low; the peculiarity is a delayed restrike after the first recovery-voltage peak. Usually clears the high-frequency restrike current; rare voltage escalation. Class C₂ plus surge arresters recommended for critical capacitors. NSDDs occur but are generally harmless.	Short pre-strike (~2 ms); shock waves are not a problem. High-frequency discharge with contact bounce can micro-weld the contacts, mainly for back-to-back peaks above 10 kA; a later low-current opening can degrade the surface, but a higher-current opening can restore it.
SF₆	Interruption limited by the recovery voltage, so frequency and earthing conditions govern capability; current amplitude above C37.04 is not a concern. Low ability to clear the high-frequency restrike current (lower still for self-blast), so voltage-escalation risk is low, but a restrike may track or puncture the nozzle/sleeve insulation.	Short pre-strike; SF₆ is compressible so the shock wave does no damage unless \(di/dt\) is unrealistically high. Successful inrush tests up to 100 kA_peak in the 25 kHz range have been reported.
Air-blast	Higher restrike probability than SF₆; can interrupt the high-frequency discharge current, so a higher chance of multiple restrikes and voltage escalation. Restrike effects similar to SF₆.	As for SF₆ — short pre-strike in a compressible medium, shock wave not damaging unless \(di/dt\) is unrealistically high.

Applying the type test to a field duty

Three practical rules follow from the restrike physics (CIGRE TB 817). A capacitive breaking current up to about 50% above the tested value can be applied with the same expected performance, provided the inrush-current integral stays below the tested value. Counter-intuitively, a higher capacitive breaking current tends to lower a vacuum interrupter’s restrike probability — the cathode spots of the breaking arc smooth the contact surface and remove the field-emission sites that trigger restrikes, and longer arcing times help for the same reason. For SF₆, contact and nozzle erosion instead accumulates with operations and eventually raises the restrike probability (first restrikes are reported anywhere from a few hundred to a few thousand operations depending on design); point-on-wave closing sharply reduces that erosion and can defer the first restrike to several thousand operations.

Section 10

Common Mistakes

The recurring errors here come from treating \(k_{c}\) as a fixed safety factor rather than an application-specific one, and from overlooking the circuits and duties that are not obvious from the breaker bay.

Common mistakes to avoid

Applying a single-circuit voltage factor to a double- or multiple-circuit line and missing the up-to-0.2 pu coupling from the parallel circuit (some utilities use \(k_{c}=1.3\) for double circuits).
Relocating a breaker to a different earthing or fault environment without re-checking the voltage factor.
Sizing a breaker on the far-side current when switching through a transformer — forgetting the \(\times N\) current on the breaker side, which can reach 750–1000 A.
Rating only the assigned capacitor breaker, and overlooking the inrush and total outrush that reach bus-tie and line breakers in a multi-bank station.
Checking only peak current on a class C₀ (or oil) breaker exposed to bank discharge, and not the \(di/dt\), or ignoring the induced voltages on linear couplers and CTs.
Reclosing onto a charged bank without isolating it or extending the dead time past the ~40 s discharge time constant.
Applying an oil breaker to capacitor-bank switching without reducing the inrush frequency below its shock-wave limit (~20 kA·kHz bulk, ~1 kA·kHz minimum-oil).

Section 11

Key Points

Application checklist

Select \(k_{c}\) from the actual application, not the breaker rating alone: earthing, neutral connection, double-circuit coupling, transformer connection and fault condition can all change the recovery-voltage duty. The values run 1.0 (solidly earthed), 1.2/1.4 (cables and line charging) and 1.7 (earth faults on unearthed systems), applied as \(U_{\text{test}}\ge (U_{r}/\sqrt{3})\,k_{c}\).
Add margin for double/multiple circuits (up to 0.2 pu coupling; \(k_{c}=1.3\) is common) and re-check the factor whenever a breaker is relocated.
When switching through a transformer, size the breaker for the \(\times N\) current; energising through the transformer softens the transient but watch for resonance with delta windings.
Check for hidden capacitive circuits: a breaker can be affected by capacitor banks, cables or filters that sit outside its bay but stay electrically connected during switching. In multi-bank stations, assess the inrush and the total outrush on bus-tie and line breakers, not just the assigned capacitor breaker; use \(\hat{\imath}_{d}=u_{r}n\sqrt{2C/[3(L+nL_{\text{bus}})]}\) for the discharge crest.
Protect linear-coupler and CT secondaries against inrush/outrush \(di/dt\) with MOVs, and coordinate fault clearing so a bus-tie is not left with an unrated parallel-bank duty.
For mixed load-plus-capacitive switching, stay within rated continuous current and either 0.8 leading power factor or the rated capacitive current; isolate or delay reclosing onto a charged bank (~40 s discharge time constant).
Match the breaker technology to the inrush stress: oil is shock-wave limited (~20 / ~1 kA·kHz), vacuum can micro-weld above ~10 kA, SF₆ handles ~100 kA_peak at 25 kHz, air-blast has the highest restrike probability.

Section 12

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 C37.04-2018, IEEE Standard for Ratings and Requirements for AC High-Voltage Circuit Breakers with Rated Maximum Voltage Above 1000 V. New York, NY, USA: IEEE, 2018.
IEEE Std C37.010-2016, IEEE Application Guide for AC High-Voltage Circuit Breakers Above 1000 V. New York, NY, USA: IEEE, 2016.
IEEE Std 1036-2010, IEEE Guide for the Application of Shunt Power Capacitors. New York, NY, USA: IEEE, 2011.
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 5 Reading now

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.

Series progress 5 of 8

Part 6

Capacitive Switching Under Fault Conditions

How a fault raises both the current and the recovery voltage: fault voltage factors, faulted-line and faulted-bank cases, and the application alternatives.