Switching of Shunt Capacitor Banks

This document describes the application of alternating-current high-voltage circuit breakers (rated above 1000 V) when switching shunt capacitor banks. It addresses the transient voltages and currents that arise when capacitor banks are energised and de-energised, the way these stresses influence circuit-breaker selection, and the measures available to limit them.

Capacitive-current interruption is generally regarded as a light duty in terms of current magnitude, because the steady-state capacitive currents involved are normally no more than a few hundred amperes. The principal concern is not the magnitude of the current to be interrupted but the probability of restrike on opening and the high-magnitude, high-frequency inrush current on closing. Both phenomena can stress the circuit breaker, the capacitor units, and surrounding plant.

The guidance below follows the structure and methods of IEEE Std C37.012-2022. Where the standard expresses caution or notes that a given case is not fully covered, that qualification is retained here. For any application that approaches or exceeds the rated values of a circuit breaker, the manufacturer should be consulted.

Capacitive currents are encountered when switching shunt capacitor banks, unloaded cables, unloaded transmission lines, and filter banks. This document concentrates on shunt capacitor banks. The growth of reactive-compensation requirements means that it is increasingly common for more than one bank to be connected to the same busbar, which has a strong influence on the inrush current at closing even though it does not change the conditions at interruption.

Two distinct switching events must be considered: de-energising (opening) and energising (closing). They present very different stresses.

• De-energising is easy to interrupt because the current is small and the initial rate-of-rise of recovery voltage is low. The risk is that the recovered voltage across a small contact gap may exceed the gap’s withstand, causing dielectric breakdown — a restrike — with the associated overvoltages.
• Energising produces a high-magnitude, high-frequency inrush current. For a single bank this is limited by the source; for back-to-back arrangements it can be very large and is limited only by the small inductance between banks.

Connecting a capacitive load to a predominantly inductive supply causes a power-frequency voltage rise (a voltage step). Planners use the rms voltage step when sizing banks. Typical acceptable limits are around 5% for distribution, 2.5% for sub-transmission, and 1% to 1.5% for bulk power. For a single bank, the voltage step is inversely proportional to the square of the harmonic order of the natural inrush frequency; for example, a 1% step corresponds to a natural frequency near the 10th harmonic, and a 4% step to the 5th harmonic. These are steady-state planning rules and the actual magnitude is system- and load-dependent.

At a single-phase level, the de-energising circuit reduces to the source inductance in series with the capacitor bank. The capacitive current leads the voltage, so when the current passes through zero the source voltage is at its crest. After interruption:

• The charge on the capacitor bank is trapped, so the load-side voltage remains essentially constant at the source-voltage crest at the instant of current zero.
• The source-side voltage continues to follow the system, so the voltage across the open contacts (the recovery voltage) rises at power frequency and reaches a peak of no less than twice the source-voltage crest, about half a cycle later.

Because the current is small and the initial rate-of-rise of recovery voltage is low, interruption itself is easy. The difficulty is withstanding the high recovery voltage that develops across a contact gap that may still be small.

If the contact gap breaks down near the recovery-voltage peak, the load-side voltage recovers through an oscillation that ideally (without damping) reaches up to three times the source-voltage crest. The breaker may then interrupt the high-frequency transient current again at one of its zeros, leaving an even higher trapped voltage. Successive breakdowns can in theory escalate the voltage on the load with each event.

Practical limits to escalation include circuit damping and the behaviour of the particular interrupter. Nevertheless, the possibility of escalating overvoltages is the principal reason for selecting an appropriate restrike-probability class and, where justified, applying surge arresters.

When interrupting small capacitive currents, some interrupter types chop the current before its natural zero. In a capacitive circuit, chopping leaves the trapped charge below its peak value, which actually reduces the recovery-voltage peak and the stress on the contact gap. The degree of chopping varies with interrupter technology.

No circuit breaker is genuinely restrike-free; demonstrating restrike-free performance would require an unlimited number of test operations. The practical approach is a restrike-probability classification tied to a defined test procedure. Three classes are defined in IEEE Std C37.04.

Class C₂ tests are performed on preconditioned contacts (preconditioning consists of three interruptions at 60% of rated short-circuit current). The C₂ programme involves more tests overall and many more operations near minimum arcing time than C₁.

Selection among the classes depends on the service conditions, the expected number of operations per year, and the consequences of a restrike for both the network and the breaker itself. At distribution voltages below 38 kV, restrike overvoltages are generally a minor network concern; the consequences for the breaker are difficult to assess in service.

Two situations arise at energisation, distinguished by whether other capacitive sources are close enough electrically to contribute significantly to the inrush current.

• Single (isolated) capacitor bank switching — the bank is energised from a bus with no other significant capacitor banks or long cables (> 1000 m) energised. The inrush current is limited by the source inductance and the bank capacitance.
• Back-to-back capacitor bank switching — the bank is energised from a bus that already has other banks and/or long cables energised. The inrush current is limited only by the small inductance between the energised and switched banks and can be very large.

The magnitude and frequency of the inrush current depend on the driving voltage (the point on the voltage wave at closing), the circuit capacitance, the amount and location of inductance, any pre-existing charge on the bank, and any damping introduced by closing resistors or other resistance. Banks are normally assumed discharged before energisation, which is reasonable because discharge resistors fitted to the units typically discharge a bank within a few minutes (a time constant of the order of 40 s).

For a single bank the series RLC circuit (source plus bank) is almost always underdamped, so the inrush is an oscillation. The two quantities of interest for breaker application are the peak inrush current and its natural frequency. Expressed in terms of the system short-circuit current and the bank current, the standard gives the following simplified relationships:

The frequency typically approaches the order of 1 kHz for a single bank. The single-bank inrush current is always less than the available short-circuit current at the bank terminals. Because a breaker must in any case meet the system making-current requirement, the inrush current is not a limiting factor for single-bank applications, and mitigation is generally not required.

When a bank is energised against one or more banks already on the bus, the charging current of the incoming bank is supplied largely by the energised bank(s) through the small inter-bank inductance. The source contribution is at a much lower frequency and is usually negligible. The peak and frequency are governed by the equivalent capacitance and the equivalent inductance between the banks.

Typical back-to-back inrush amplitudes are several tens of kiloamperes, with frequencies ranging from around 2 kHz for distribution banks to about 15 kHz for EHV transmission banks; compact designs can give higher frequencies. A restrike on opening can produce currents up to about twice the maximum closing inrush, at the same frequency.

The practical equations (using bank currents and the equivalent inductance per phase) are summarised in Section 7. The inter-bank inductance is composed of the bus inductance between switching devices, the inductance between each device and its bank, and the inductance of the banks themselves. As a guide, capacitor-bank internal inductance is of the order of 10 µH for banks above 52 kV and 5 µH below 52 kV, with a single capacitor unit typically 0.7 to 1.2 µH.

Capacitor units have their own inrush/outrush withstand. Without internal fuses, typical single-unit capabilities are 10 kA (units 300 kvar and smaller), 15 kA (301 to 599 kvar) and 20 kA (600 kvar and larger); internally fused units can withstand up to about 100 times continuous current. The bank capability is obtained by multiplying the per-unit capability by the number of parallel units or strings per phase (see IEEE Std 1036 for guidance).

For modern SF₆ and vacuum interrupters, the natural frequency of the inrush is a lesser concern than was historically assumed. If the inrush magnitude is within the tested value, the frequency may exceed the tested frequency provided the product \(i \times f\) stays below four times the tested \(i \times f\). If the inrush magnitude is below 10% of the tested back-to-back value, no upper limit on frequency need be applied. The quantity that actually needs to be limited is the inrush-current integral (ICI) rather than the peak current or the frequency; lower frequencies can in fact be more onerous for contact erosion.

The breaker is selected for the capacitive current it must interrupt, including the effects of operating voltage, capacitance tolerance, and harmonics.

In the absence of specific data, a total multiplier of about 1.25 on nominal current is conservative for ungrounded-neutral operation, and about 1.35 for effectively grounded operation. For the inrush calculation itself, the harmonic multiplier is omitted (inrush depends on inductive reactance, so higher-frequency harmonics are not relevant); a combined voltage-and-tolerance multiplier of about 1.15 is used.

The grounding of both the system neutral and the bank neutral largely determines the recovery voltage the breaker must withstand, and hence the single-phase test voltage factor \((k_{c})\).

Voltage factors for single-phase tests range from 1.0 for effectively grounded systems to 1.7 for ungrounded systems in the presence of single- or two-phase-to-ground faults. The maximum recovery voltage listed for switching an unfaulted shunt bank is 2.8 pu, which corresponds to an ungrounded bank where the second and third poles clear 90° after the first (true for modern breakers). For certain older devices where the later poles do not clear 90° after the first, this factor rises to 4.1.

Most class C₁ and C₂ breakers have a low restrike probability, so the majority of switching transients in service arise from energisation rather than de-energisation. The effects appear both locally and at remote points on the network.

High inrush currents during back-to-back switching can also induce voltages in control cables by capacitive and electromagnetic coupling, and can stress wound-type current transformers through high \(di/dt\). These effects can be reduced by cable shielding, radial cable routing to avoid inductive loops, and metal-oxide varistors on control circuits.

The relationships below summarise IEEE Std C37.012-2022 for estimating inrush-current peak and frequency. The bank being switched is assumed uncharged and closed at a voltage crest. Currents should include the voltage and capacitance-tolerance effects (a combined multiplier of about 1.15 in the absence of specific data); the harmonic multiplier is not included. The calculated peak is without damping — in practice the first peak is about 90% of this value.

Frequencies in the back-to-back expressions are in kHz. With an ungrounded neutral, the current in the first two phases to close is about 87% of the calculated value, while the last phase reaches the full calculated value; inherent circuit resistance then reduces these further. These results apply to both grounded and ungrounded banks and to wye and delta connections.

The standard works through a 138 kV (145 kV rated) example with three 32.4 Mvar banks (nominal 136 A each, source short-circuit current 18 kA). The breakers are rated 145 kV, 1600 A continuous, 40 kA short-circuit, and 400 A single and back-to-back capacitive switching, with a preferred back-to-back inrush peak rating of 16 kA. Applying the combined voltage-and-tolerance multiplier of 1.155 gives a per-bank inrush current of about 157 A.

A detailed electromagnetic-transient simulation of the same arrangement gave a back-to-back inrush of about 26.5 kA at 15.6 kHz, confirming the need for mitigation. The simplified equations are intended for a first estimate; detailed simulation is appropriate where the result is close to a rating limit or where mitigation effectiveness must be quantified.

Several techniques limit the transients associated with capacitor-bank switching. Each addresses a different combination of inrush current and overvoltage, and each has practical costs.

For the 138 kV back-to-back case above, the standard quantifies the mitigation options by simulation (tested \(i \times f\) taken as the reference).

Reclosing can produce up to twice the normal inrush current, because the bank may still hold a near-peak trapped voltage when the breaker recloses against it. High inrush on reclose can be avoided by isolating the bank from other loads after tripping and before reclosing (using the regular capacitor switching device), or by increasing the reclose time delay so that the discharge resistors reduce the residual voltage. Discharge curves should be obtained from the capacitor supplier; a typical discharge time constant is 40 s.

Outrush is the transient discharge of a charged bank into an external short circuit — most often a breaker closing into a nearby fault, for example on a reclose or when safety grounds have been left on by mistake. The breaker involved may be a general-purpose station breaker not intended for capacitive making, such as an older oil circuit breaker, which is sensitive to both the peak current and its \(di/dt\).

Significant damaging outrush events are rare and, to be serious, generally require the fault to be close to the station; the higher the system voltage, the further out a fault can be and still matter. A risk analysis is the appropriate way to weigh the low probability of a damaging outrush against the cost of mitigation, and any regulator requirements should also be considered.

Where parallel banks share a busbar, a breaker connected to that bus can be exposed during a fault to the total discharge of all banks behind it. The worst case is a bolted three-phase fault with ungrounded banks, or a three-phase-to-ground / line-to-ground fault with effectively grounded banks. For class C₁ and C₂ breakers, such a discharge is permissible up to about twice in the breaker’s life without additional maintenance, provided the peak does not exceed the close-and-latch rating. Class C₀ breakers (and oil breakers generally) may also require a \(di/dt\) check with the manufacturer.

Transient inrush and outrush currents can also flash over the secondaries of linear couplers or bushing current transformers and their wiring. Appropriately sized metal-oxide varistors can clamp these secondary overvoltages. A bus-section (tie) breaker with banks on both sides deserves particular attention: in a fault-clearing sequence it can be left to switch the parallel banks remaining on a section and must be rated and equipped for that duty, or the clearing sequence arranged so the tie breaker clears first.

Capacitive switching stresses interrupter technologies differently. The following is general guidance based on laboratory and field experience.

The presence of a fault can increase both the capacitive current and the recovery voltage. For capacitor banks, the standard does not make these specific cases mandatory tests, for several reasons: the probability of a fault coinciding with minimum operating conditions is very small; the faulted phase is likely to discharge before contact separation; the single-phase test voltage factor already exceeds the service condition; laboratory tests use a minimal voltage step (short arcing times, a more severe condition than service); and with an ungrounded neutral the two healthy poles end up in series, so each sees less than rated voltage.

Indicative results from the standard for a faulted bank: with a fault to neutral in one phase, the highest recovery voltage (about 3.46 pu) occurs when a healthy phase is the first pole to clear, and the highest current (about three times the reference) when the faulted phase clears first. With a fault to ground in one phase, the most severe case is an ungrounded source with an effectively grounded bank neutral. The maximum recovery voltage listed for an unfaulted bank is 2.8 pu, and these faulted values may exceed it.

• Use a higher-rated breaker where ground faults on ungrounded systems push recovery voltage and/or current beyond the standard requirements.
• Reduce the bank size so the faulted-condition current stays within the rated capacitive switching current.
• Use a high-speed switch to ground the source or bank neutral before switching under faulted conditions.
• Use a delta configuration for the bank instead of an ungrounded wye.

Controlled (point-on-wave) switching times the breaker operation relative to the voltage or current waveform to minimise transients. For capacitive loads, closing is timed so that the voltage across the contacts is near zero (i.e. closing near the appropriate point on the wave so the applied step is minimised), and opening is timed to current zero. Effective implementation depends on accurate, repeatable breaker operating time, real-time waveform information, and a control algorithm that adjusts the firing instant to compensate for changing conditions.

Among the available techniques, controlled switching offers a strong combination of precision, repeatability and adaptability, and can be made robust to temperature-induced timing drift, auxiliary-supply variation, and mechanical scatter. The controller does, however, add complexity and can influence breaker availability.

For a solidly grounded bank neutral, the three phases are electrically independent for closing purposes, so each pole can be closed at its own optimum instant on its phase reference. The result is uniform phase charging, minimal transient energy and overvoltage, and a cleaner waveform with reduced electromagnetic interference. The requirements are high-resolution per-phase voltage tracking and low-scatter, well-synchronised pole closure.

For an ungrounded or delta-connected bank the phases are coupled, so a staggered closing strategy is needed: the first pole closes at the optimum instant on its phase reference, and the remaining poles close at instants determined by the interphase voltages (or a calculated optimum). Each pole’s timing is computed independently. This balances the transient energy across phases and suppresses interphase surges, which suits harmonic-rich environments, but it demands precise low-scatter breakers, more complex control logic, high-speed computation, and reliable sensors.

The following consolidates the key decisions when applying a circuit breaker to shunt capacitor-bank switching.