Capacitive Switching

Energising Capacitor Banks: Inrush and Back-to-Back Switching

Energising a shunt capacitor bank — the transient inrush current, why a single bank draws a modest source-limited inrush while back-to-back energising can reach tens of kiloamperes, the continuous-current rating, a full 138 kV worked example, capacitor-unit withstand and the mitigation options. Follows IEEE Std C37.012-2022, with APS engineering interpretation.

Reading time ≈ 18 min

Section 1

Overview: Two Energising Situations

Energising a shunt capacitor bank draws a transient inrush current as the capacitance charges. Its magnitude and frequency — and therefore the stress it places on the circuit breaker, the capacitor units and the network — depend almost entirely on what else is already energised on the same bus. IEEE Std C37.012-2022 distinguishes two situations:

Single (isolated) capacitor bank switching — the bank is energised from a bus on which no other capacitor banks, and no cables longer than 1000 m, are energised. The inrush is limited by the source inductance and the bank capacitance, and is comparatively modest.
Back-to-back capacitor bank switching — the bank is energised from a bus that already has other banks and/or long (> 1000 m) cables energised. The incoming bank is then charged mainly from the already-energised capacitance, and the limiting inductance is only the small connection inductance between the two banks — so the inrush can become much larger and much higher in frequency.

The distinction is electrical rather than purely geographical. A bank in a nearby substation (usually within about 10 km) can still contribute to back-to-back inrush if the electrical path between the banks is short and has low inductance. This page develops the capacitor-bank energisation duty introduced in the general application overview, with emphasis on the difference between single-bank and back-to-back inrush; it works through the inrush physics, the continuous-current rating, a full 138 kV worked example and the mitigation options. For the wider breaker duty during de-energisation see the APS note on switching of shunt capacitor banks.

Why shunt capacitor banks are installed

The switching duty exists because the banks earn their place in several ways. First, they provide reactive-power compensation: they supply VArs locally to inductive loads instead of drawing them from distant sources, which cuts the upstream reactive current and the voltage drop it causes. Second, they give voltage support by injecting reactive power at the point of connection, where line, cable and transformer impedance would otherwise pull the voltage down under load. Third, because network losses scale with the square of current, \(P_{\text{loss}} = I^{2}R\), removing that reactive current reduces losses.

This note concerns shunt banks, connected phase-to-earth or phase-to-phase. Series capacitors, installed in-line to cancel line reactance, are normally bypassed rather than energised, and are a different switching problem.

Assumption — the bank starts discharged

The inrush analysis assumes the bank is discharged before energisation. This is reasonable because capacitor units are fitted with discharge resistors; typical discharge times are of the order of 5 minutes (a time constant near 40 s). Any residual charge at closing, together with the point on the voltage wave at which the contacts touch, sets the actual peak in service.

What governs the inrush

The inrush current is controlled by the voltage at the instant of closing, the capacitance being connected, the inductance in the charging path, any residual charge, and the damping in the circuit.

Table 1 — Factors that set the magnitude and frequency of the inrush current.

Factor	Effect
Driving voltage at closing	The point on the voltage wave at which the contacts touch; the worst case is closing at a voltage peak.
Circuit capacitance	The bank being energised, and any parallel banks contributing charge.
Circuit inductance	Both amount and location — source inductance for a single bank, inter-bank inductance for back-to-back.
Residual charge	Any charge left on the bank at the instant of closing raises the peak.
Damping	Losses and any closing resistors reduce and shape the oscillation.

Section 2

Continuous-Current Rating

Before the inrush, the breaker must carry and interrupt the steady capacitive current, which is higher than the bank nameplate current. Three multipliers raise the nominal current to the value the breaker must be rated for.

Table 2 — Multipliers on nominal capacitor current for the continuous rating.

Factor	Multiplier	Reason
Voltage	up to 1.1	The kvar rating is scaled by (maximum service voltage / capacitor nameplate voltage); capacitors may run continuously up to 10% above rated voltage.
Capacitance tolerance	1.05 to 1.10	Manufacturing tolerance is −0 to +10% (more often −0 to +3%); the positive tolerance raises the current.
Harmonic component	1.1 earthed / 1.05 unearthed	A bank is a low-impedance path for harmonics; an unearthed neutral blocks zero-sequence (triplen) harmonics, so its multiplier is smaller.

Conservative default

Absent specific data, a total multiplier of 1.25 times the nominal current is usually conservative for an unearthed-neutral bank, and 1.35 for an effectively earthed-neutral bank. The continuous-current check is a steady-state thermal rating check, and it is separate from the transient inrush-current check: the harmonic multiplier used here belongs only in the continuous rating and is not carried into the inrush calculation.

Section 3

Single Capacitor Bank

For a genuinely single bank, the source is the only major source of charging current, so the source inductance limits the peak current and the duty is normally much less severe than back-to-back switching. With no other bank connected, the circuit reduces to the source inductance in series with the bank — a series RLC loop of \(L = L_{s}+L_{1}\), the loss resistance \(R\), and the bank capacitance \(C_{1}\). Applying a step voltage (closing at the peak) gives a second-order response whose form depends on the damping: it is under-damped in almost all practical cases, giving a decaying oscillation. Critical or over-damped responses arise only when closing resistors are added; the resistance that gives critical damping is \(R_{cd} = 2\sqrt{L/C_{1}}\). The peak and natural frequency then follow from the source short-circuit current and the bank current:

\[ \hat{\imath}_{\text{peak}} = \frac{\hat{u}}{Z} = \sqrt{2\,I_{sc}\,i_{1}} \qquad\qquad f_{i} = f_{s}\sqrt{\dfrac{I_{sc}}{i_{1}}} \qquad\qquad Z = \sqrt{\dfrac{L}{C_{1}}} \]

\(\hat{\imath}_{\text{peak}}\): peak inrush current
\(f_{i}\): inrush (natural) frequency
\(\hat{u}\): peak of the applied phase-to-earth voltage
\(Z\): surge impedance of the loop
\(I_{sc}\): source symmetrical short-circuit current (A rms)
\(i_{1}\): current of the bank being switched (A rms)
\(f_{s}\): power-system frequency (Hz)

Because the inrush is limited by the source, it is always less than the available short-circuit current at the bank terminals, and in practice rarely exceeds 20 times the bank rated current at a frequency approaching 1 kHz. Since a breaker must in any case meet the system making-current requirement, inrush is not a limiting factor for a genuinely single bank.

Key idea — the 20-times test

The 20-times value is a practical screening boundary. If the calculated peak inrush is below about twenty times the bank rated current, the duty can usually be treated as single-bank switching. If it is above that value — even where the layout appears to contain only one local bank — the duty must be treated as back-to-back, and the breaker selected on back-to-back (rather than isolated-bank) testing to class C₁ or C₂ as required.

The bus voltage transient and its propagation

The inrush current is only half the story: energising a bank also produces a voltage transient on the bus. Because the capacitor voltage cannot change instantaneously, the capacitor looks like a momentary short circuit at the instant of closing, so the bus voltage first dips — by an amount set by the source impedance behind the bus — and then recovers through a high-frequency oscillation. That recovery follows a 1 − cosine shape and, undamped, overshoots to about 2 per unit of the bus voltage:

\[ v_{c}(t) = V\left(1 - \cos\omega_{0}t\right), \qquad \hat{v}_{c} = 2V \ \text{at} \ \omega_{0}t = \pi, \qquad \omega_{0} = \frac{1}{\sqrt{L_{eq}C_{eq}}} \]

\(v_{c}(t)\): capacitor (and bus) voltage after closing
\(V\): driving (source) voltage crest
\(\omega_{0}\): natural angular frequency of the switching loop

The 2 pu figure is the ideal undamped value. In practice the actual overshoot is lower, because circuit damping and losses, the point on the wave at which the contacts close, and the network configuration all reduce it.

Worked illustration — a 6 Mvar bank at 13.8 kV

Switching a 6 Mvar bank onto a 13.8 kV distribution bus draws a peak inrush of about 4.6 kA at a natural frequency near 770 Hz, and swings the bus to roughly 22 kV crest — about 2 pu of the 13.8 kV rms rating — before the oscillation damps out over some six cycles. The damping comes only from the circuit resistance and losses, which at these distribution voltages is light.

What makes this voltage transient a system concern, rather than a purely local one, is that it is not always confined to the switched bus. The initial step and the oscillation propagate through the network much like a travelling wave: they reflect from impedance discontinuities and couple across transformer windings to other voltage levels, where they can be magnified.

If the transient’s dominant frequency is close to a transformer’s natural frequency, part-winding resonance can occur, and transformer failures from capacitor-switching transients have been documented. A related hazard is secondary resonance: when a large utility bank is switched while a smaller capacitor bank at a downstream low-voltage distribution system remains energised, the transient can be amplified at the downstream bank and trip the sensitive electronic and drive loads connected there. Surge arresters and surge capacitors limit these transferred overvoltages and also reduce their frequency.

Worked illustration — secondary resonance at 480 V

Switching the 6 Mvar, 13.8 kV bank while a 200 kvar bank on a downstream 2 MVA, 13.8/0.48 kV transformer stays energised drives the 480 V secondary to about 1220 V line-to-neutral crest — roughly 3.1 times the rated voltage — and pushes about 2200 A (≈ 6.5 times full-load current) through the 200 kvar bank. The amplification is worst when the secondary’s resonant frequency sits near the switched bank’s natural frequency and when damping is light, as it usually is in industrial distributions. The same mechanism can escalate the dc-link voltage of an adjustable-speed drive to about 2 pu and trip it. The practical rule is to apply capacitors at a single voltage level where possible; multi-level application needs a rigorous switching-transient study to locate and avoid the resonance points.

Section 4

Back-to-Back Energising

In back-to-back switching the already-energised bank behaves like a charged energy source: the incoming bank is charged mainly through the short connection path between the two banks, not through the full source impedance, which is why the peak current and frequency can be far higher than for a single bank. When a bank \(C_{1}\) is switched onto a bus that already carries an energised bank \(C_{2}\), the charge for \(C_{1}\) is supplied mostly by \(C_{2}\), not by the source. The oscillation is limited only by the two bank inductances and the series combination of the capacitances, so the peak and frequency follow the equivalent-circuit values:

\[ \hat{\imath}_{\text{peak}} = \hat{u}\,\sqrt{\dfrac{C_{eq}}{L_{eq}}} \qquad\qquad f_{i} = \dfrac{1}{2\pi\sqrt{L_{eq}\,C_{eq}}} \qquad\qquad C_{eq} = \dfrac{C_{1}\,C_{2}}{C_{1}+C_{2}},\; L_{eq} = L_{1}+L_{2} \]

\(C_{eq}\): series (equivalent) capacitance of the two banks
\(L_{eq}\): equivalent inductance between the banks
\(L_{1}, L_{2}\): inductance of the switched and the energised bank branches

The peak can reach extreme values, because \(L_{eq}\) — only the busbar and bank connections — can be arbitrarily small; the source contributes only a small, much lower-frequency component. When \(n\) equal banks are already energised and one more is switched in, the inrush peak approaches \(\hat{u}\,\tfrac{n}{n+1}\sqrt{C/L}\), tending to \(\hat{u}\sqrt{C/L}\) for large \(n\). For breaker application, the convenient current-based forms (with the units shown) are used:

\[ \hat{\imath}_{\text{peak}} = 13\,500\,\sqrt{\dfrac{U_{r}\,i_{1}\,i_{2}}{f_{s}\,L_{eq}\,(i_{1}+i_{2})}}\ \text{[A]} \qquad f_{i} = 9.5\,\sqrt{\dfrac{f_{s}\,U_{r}\,(i_{1}+i_{2})}{L_{eq}\,i_{1}\,i_{2}}}\ \text{[kHz]} \]

\(U_{r}\): rated voltage (kV rms)
\(i_{1}, i_{2}\): currents of the switched and the already-energised bank (A rms)
\(L_{eq}\): total equivalent inductance per phase between banks (µH)

Which current, and how big the real peak is

The currents \(i_{1}\) and \(i_{2}\) must include the voltage and capacitance-tolerance multipliers but not the harmonic multiplier — the inrush depends on inductive reactance, so higher-frequency harmonics are irrelevant to it. The equations give the undamped peak; circuit resistance reduces the measured first peak to about 90–98% of it. With an unearthed neutral, the first two phases to close carry roughly 87% of the calculated value, the last phase the full value. A restrike on opening can produce a discharge current up to twice the maximum closing inrush, at the same high frequency.

Section 5

The Inductance Between Banks

The smaller the inductance between the energised and switched banks, the higher the peak inrush current and the higher the natural frequency, so this inductance is the quantity the whole back-to-back calculation turns on. The limiting inductance \(L_{eq}\) is the sum along the loop between banks: the bus inductance between the switching devices \(L_{bus}\), the inductances between each device and its bank \(L_{1}\) and \(L_{2}\), the internal bank inductances \(L_{c1}\) and \(L_{c2}\), and any added reactor. The whole of this is usually less than 1% of the source inductance, which is why the source can be neglected. The bus inductance comes from conductor tables for the actual geometry; the internal bank inductance is of the order of 10 µH above 52 kV and 5 µH below, with a single unit contributing 0.7–1.2 µH.

Table 3 — Typical inductance between back-to-back banks (bank inductance excluded).

Rated Maximum Voltage (kV)	Busbar Inductance (µH/m)	Typical Inductance Between Banks (µH)
≤ 17.5	0.702	10 to 20
36	0.781	15 to 30
52	0.840	20 to 40
72.5	0.840	25 to 50
123	0.856	35 to 70
145	0.856	40 to 80
170	0.879	60 to 120
245	0.935	85 to 170

When switching against several banks at once the exact equivalent inductance is awkward: for a bank switched against three others, using \(L/3\) overestimates the current and \(3L\) underestimates it. A conservative estimate divides the inductance by the number of connected banks, accepting a result about 20–30% high.

Section 6

Worked Example — a 138 kV Bank

Consider a 138 kV system (rated \(U_{r}=145\) kV) with a source inductance of 11.75 mH (\(L_{s}=4.43\ \Omega\) at 60 Hz, giving \(I_{sc}\approx18\) kA) feeding a bus with three identical 32.4 Mvar banks, each of 136 A nominal current.

Continuous rating. The voltage ratio is 145/138 = 1.05; take +10% capacitance tolerance (1.1) and an earthed-neutral harmonic multiplier of 1.1. The total is 1.05 × 1.1 × 1.1 = 1.27, giving 1.27 × 136 = 173 A per bank; with two further banks energised, breaker CB2 carries 346 A. A breaker rated 145 kV, 1600 A continuous, 40 kA short-circuit, and 400 A single/back-to-back capacitive switching is selected.

Inrush currents. For the inrush the harmonic multiplier is dropped, so \(i_{1}=136\times(1.05\times1.1)=157\) A, and \(i_{2}=157\) A or 314 A. Using the busbar figure of 0.856 µH/m, each bank branch is \(L' = 6.10\text{ m}\times0.856 + 10 = 15.2\) µH and the inter-device bus is \(L_{bus}=(9.15+9.15)\times0.856 = 15.6\) µH. The three cases below all take bank 1 as the switched bank: Case I energises it alone, Case II against one already-energised bank, and Case III against two.

Table 4 — Inrush results for the three switching cases.

Case	L_eq (µH)	Peak Inrush	Frequency	Verdict
I — bank 1 alone (single)	—	2.38 kA	642 Hz	Below 20× the bank current; single duty, no mitigation needed.
II — bank 1 vs bank 2	46.0	27.4 kA	14.8 kHz	Exceeds the preferred back-to-back peak of 16 kA; mitigation required.
III — bank 1 vs banks 2 & 3	38.4	34.6 kA	14.0 kHz	Peak well above 16 kA; mitigation required.

Case I remains within the single-bank screening limit, while Cases II and III exceed the preferred back-to-back inrush rating, so mitigation is required before the arrangement can be accepted. In Case I, \(\hat{\imath}_{\text{peak}}=\sqrt{2\times18000\times157}=2377\) A and \(f_{i}=60\sqrt{18000/157}=642\) Hz, a rate of rise of about 9.6 A/µs; the 2.38 kA peak is below \(\sqrt{2}\times20\times157=4.4\) kA, confirming single-bank duty. In Case II, \(L_{eq}=L' + L_{bus} + L' = 46.0\) µH gives 27.4 kA at 14.8 kHz. In Case III, taking the two energised banks as an equivalent \(L'/2\), \(L_{eq}=7.6+15.6+15.2=38.4\) µH with \(i_{1}=157\) A and \(i_{2}=314\) A gives 34.6 kA at 14.0 kHz. Both exceed the preferred back-to-back rating, so the inrush must be limited. A detailed electromagnetic-transient (EMT) simulation of the same bus gives a comparable 26.5 kA peak and lets the mitigation options be compared quantitatively (Section 8).

Section 7

Typical Magnitudes and Unit Withstand

The breaker inrush rating is not the only limit: the capacitor units themselves must also withstand the transient current, and the permissible value depends on the unit construction and the number of parallel units or strings per phase. Back-to-back inrush currents are typically several tens of kiloamperes, at frequencies of about 2 kHz for distribution banks rising to 15 kHz for EHV transmission banks, and higher for compact designs. The stress is shared between the breaker and the capacitor units, so the units have their own withstand limits: internally fused units withstand up to about 100 times their continuous current, while non-fused units are limited by an absolute current that depends on their rating.

Table 5 — Inrush/outrush withstand of individual capacitor units.

Unit Type	Inrush Withstand
Internally fused	up to ~100 × continuous current
Non-fused, ≤ 300 kvar	10 kA
Non-fused, 301–599 kvar	15 kA
Non-fused, ≥ 600 kvar	20 kA

The withstand of the whole bank is the single-unit capability times the number of units or strings in parallel per phase; IEEE Std 1036 gives the detailed guidance.

Section 8

The i × f Limit and Mitigation

The breaker’s inrush capability was traditionally expressed as the product of peak current and natural frequency, \(i\times f\) (equivalently a \(di/dt\) limit). This limit was developed for shock-wave-limited devices such as oil breakers: during the pre-strike arc before galvanic contact, the rapidly rising current in an incompressible medium creates a shock wave that can damage nozzles and other internal parts. The class C₂ limit was historically about 100 kA × kHz.

Four decades of experience with SF₆ and vacuum interrupters have shown them far less shock-wave sensitive. Tests to 2500 kA × kHz on a 72.5 kV SF₆ breaker, and vacuum tests to 23.8 kHz, showed no shock-wave damage.

The quantity that actually needs limiting is the inrush current integral (ICI), not the peak and certainly not the frequency — a conclusion CIGRE WG A3.38 also reached. The ICI multiplied by the arc voltage is the pre-arc energy deposited on the closing contacts, and over a typical 1–3 ms pre-arc that energy can be comparable to a short-circuit making operation, so inrush erosion is not a lesser duty than fault making. Counter-intuitively, a lower frequency can be more damaging, because it lengthens the current pulse and increases contact erosion.

For a gas or vacuum breaker the practical limit is more often the control-system transients or the capacitors themselves than the interrupter. Two allowances follow: if the magnitude \(i\) is within the tested value \(i_{bb}\), the frequency may exceed \(f_{bb}\) provided \(i\times f < 4\,i_{bb}f_{bb}\); and if \(i < 0.1\,i_{bb}\) there is no upper limit on frequency. Where the nameplate or IEEE Std C37.04 peak is exceeded, the manufacturer should be consulted.

Three families of mitigation are available, and they work in different ways: they reduce the peak current, reduce the pre-arc energy, or control the closing instant so that the bank is energised at a less severe point on the voltage wave. For the 138 kV example the options compare as follows:

Table 6 — Inrush mitigation for the 138 kV example (from EMT simulation).

Mitigation	Peak (kA)	Frequency (kHz)	i × f (kA × kHz)	Multiple of Tested i × f
None	26.5	15.6	41.3	6.0
Fixed inductor (45 µH per bank)	15.6	9.1	14.2	2.1
Pre-insertion resistor (150 Ω, 6 ms)	6.4	15.6	10.0	1.5
Controlled closing (RDDS 90 kV/ms, ±0.5 ms)	6.0	15.6	9	1.4

Note — the fixed-inductor side effect

A fixed inductor cuts the peak effectively but roughly halves the frequency and — per IEEE Std C37.011 — can introduce a high-frequency transient recovery voltage that may exceed the standardised TRV envelope. Pre-insertion resistors and controlled closing achieve the deepest peak reduction (to ~6 kA here) without lowering the frequency. Whichever route is chosen, a detailed study is needed to confirm the mitigation is effective.

Note — two side effects of a series inrush reactor

A series inrush-limiting reactor is a passive, reliable option, but it changes the bank in two ways beyond limiting the inrush. First, it tunes the bank to a series-resonant frequency, so it must not be tuned close to a load-generated harmonic — otherwise the bank becomes an unintended single-tuned filter, offering a low-impedance path to that harmonic and overloading itself (unless it is deliberately designed as a filter). Second, it raises the net leading kvar rather than lowering it: the voltage drop across the reactor adds to the capacitor voltage, so the capacitor terminal voltage rises to \(V_{c} = \dfrac{n^{2}}{n^{2}-1}\,V\) (with \(n = f_{n}/f\) the tuning ratio), and because reactive output scales with the square of voltage the combination delivers more leading kvar — the capacitor rated voltage may therefore need to be increased. The reactor’s ohmic losses can also be significant and need a thermal check. See the APS note on devices for limiting capacitor-switching transients for how reactors, pre-insertion resistors and controlled switching compare.

Section 9

Bank Connections and Earthing

How the units are connected — and whether the bank neutral is earthed — shapes both the protection scheme and the switching duty. Six connections are in common use. Almost all substation banks are wye-connected; distribution banks may be wye or delta. The choice follows from the best use of the available unit voltage ratings, the fusing (externally fused, internally fused, fuseless or unfused) and the protective relaying.

Six common capacitor-bank connections drawn as three-phase schematics: (a) delta with three capacitors between phases; (b) grounded wye with the neutral earthed; (c) ungrounded wye with an isolated neutral; (d) ungrounded double wye, the two neutrals optionally tied; (e) grounded double wye with the common neutral earthed; (f) H configuration with the units bridged and a current transformer in each phase leg. — Figure 1 — Six common capacitor-bank connections. (a) delta; (b) grounded wye; (c) ungrounded wye; (d) ungrounded double wye (neutrals may or may not be tied); (e) grounded double wye; (f) H configuration — a current transformer in the bridge detects unbalance.

The delta connection is used only at distribution voltages, in small banks rated line-to-line with a single series group — common at 2400 V, where wye units are not readily available, and for the thyristor-switched capacitors of a static VAr compensator. Double-wye arrangements split a large bank into two sections to keep the parallel energy of a series group within the units’ or fuses’ limits, and they allow a simple, fast neutral-unbalance protection because any system zero-sequence unbalance affects both wyes equally. The H configuration bridges the units in each phase with a current transformer in the connecting branch; while every unit is healthy no current flows in it, and a failed unit is detected very sensitively — it suits large banks with many parallel units.

Table 7 — Grounded versus ungrounded wye banks.

Aspect	Grounded Wye	Ungrounded Wye
Surge / triplen-harmonic path	A low-impedance path to earth for lightning surge and triplen-harmonic currents — some surge protection, but possible communication interference and ground-relay operation on an open phase.	No path to earth for surge, zero-sequence or triplen-harmonic currents.
Neutral insulation	Neutral held at earth potential.	Neutral must be insulated for full line voltage — it reaches phase potential on switching or a unit failure.
Fault discharge current	Large discharge into a nearby earth fault.	Earth-fault discharge blocked; current through a faulted unit is limited to about 1.73× normal phase current, so current-limiting fuses are usually not needed.
First-pole recovery voltage on de-energising	Lower — about 2× the normal peak voltage.	Higher — up to about 3× the peak line-to-earth voltage.

Key idea — earth the neutral only on an effectively earthed system

Because the recovery voltage governs a breaker’s capacitive-switching capability, the lower recovery voltage of a grounded bank (~2 pu against ~3 pu ungrounded) makes it the easier switching duty, and IEEE Std C37.04 / ANSI C37.06 recommend earthing both the bank and the system at 121 kV and above.

But a grounded bank neutral on an otherwise ungrounded system can drive high transient overvoltages when an arcing earth fault restrikes, so the neutral should be earthed only where the system is effectively earthed — the delta tertiary of an auto-transformer, for instance, is an isolated network and grounding a bank there makes that side only capacitively earthed. Grounded-wye banks also inject high-frequency transient currents into the substation earth mat — worst on discharge into a nearby earth fault or on a restriking back-to-back operation — which must be managed with peninsula or single-point grounding (IEEE Std 1036) and with careful shielding of the relay circuits.

Section 10

Common Mistakes

Common mistakes to avoid

Classifying a bank as “single” from the physical layout instead of the calculated inrush — above ~20 times rated current it is a back-to-back duty.
Ignoring energised banks in nearby substations (within ~10 km), which can turn an apparently isolated bank into a back-to-back case.
Rating the breaker on the bank nameplate current, ignoring the voltage, tolerance and harmonic multipliers (about 1.25–1.35 in total).
Including the harmonic multiplier in the inrush current — it belongs only in the continuous rating.
Using \(L/3\) (too high) or \(3L\) (too low) for switching against three banks, instead of the conservative divide-by-number estimate.
Checking the breaker inrush rating but not the capacitor-unit withstand (100× for internally fused units; 10/15/20 kA for non-fused units).
Treating a high inrush frequency as the problem for SF₆/vacuum breakers, when the inrush current integral is the real concern — and a lower frequency can erode contacts more.
Adding a fixed inductor to cut the peak without checking the high-frequency TRV it can create (IEEE Std C37.011), or stopping at the hand calculation where the result is near a limit rather than confirming with an EMT simulation.

Section 11

Key Points

Inrush and rating checklist

Decide whether the duty is single-bank or back-to-back from the calculated inrush current, not the physical layout alone: below about 20× rated current is single-bank, above it is back-to-back. Count energised banks within about 10 km and cables longer than 1000 m if they are electrically connected.
Size the continuous current from the nominal bank current times the voltage, tolerance and harmonic multipliers (~1.25 unearthed to ~1.35 earthed).
Single bank: \(\hat{\imath}_{\text{peak}}=\sqrt{2\,I_{sc}\,i_{1}}\), \(f_{i}=f_{s}\sqrt{I_{sc}/i_{1}}\) — source-limited, rarely governs the breaker.
Back-to-back: \(\hat{\imath}_{\text{peak}}=\hat{u}\sqrt{C_{eq}/L_{eq}}\), or the current-based \(13\,500\) and \(9.5\) forms; use \(i_{1}, i_{2}\) with voltage and tolerance multipliers only (not harmonic).
Build \(L_{eq}\) from bus and bank inductances (~5 µH below, ~10 µH above 52 kV for the bank), dividing by the number of energised banks.
Compare the peak with the preferred \(i_{bb}\); in the worked example 27–35 kA exceeds the 16 kA rating, so mitigation is needed, and check the capacitor-unit withstand too.
For SF₆/vacuum breakers judge on the inrush current integral rather than frequency; choose mitigation by outcome (pre-insertion resistor or controlled closing for the deepest peak cut; a fixed inductor is simple but can raise the TRV) and confirm with an EMT simulation.

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 C37.04-2018, 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 C37.09-2018, 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 C37.06-2009, IEEE Standard for AC High-Voltage Circuit Breakers Rated on a Symmetrical Current Basis—Preferred Ratings and Related Required Capabilities for Voltages Above 1000 V. New York, NY, USA: IEEE, 2009.
IEEE Std C37.011-2019, IEEE Guide for the Application of Transient Recovery Voltage for AC High-Voltage Circuit Breakers with Rated Maximum Voltage Above 1000 V. New York, NY, USA: IEEE, 2019.
IEEE Std 1036-2010, IEEE Guide for the Application of Shunt Power Capacitors. New York, NY, USA: IEEE, 2011.
IEEE Std C37.99-2012, IEEE Guide for the Protection of Shunt Capacitor Banks. New York, NY, USA: IEEE, 2012.
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 2 Reading now

Energising Capacitor Banks: Inrush and Back-to-Back Switching

Single versus back-to-back inrush, the continuous-current rating, a full 138 kV worked example, capacitor-unit withstand and the mitigation options.

Series progress 2 of 8

Part 3

Unloaded Cable Switching

Cable charging current and capacitive reactance, screened versus belted recovery voltage, and single versus back-to-back cable inrush limited by the surge impedance.