Capacitive Switching

Switching of Harmonic Filter Banks

Why switching a harmonic filter bank is not the same as switching a capacitor bank — the large series tuning reactor makes energising milder (lower inrush, frequency and overvoltage) but de-energising more onerous, with a trapped voltage above 1 pu, a recovery voltage reaching 3–3.5 pu, and inductive-type chopping and restrike overvoltages. Covers single-tuned and de-tuned banks, energising, back-to-back, recovery voltage, restrike and outrush. Follows CIGRE TB 817 and IEC 61642, with APS engineering interpretation.

Reading time ≈ 14 min

Section 1

Filter Banks Are Not Just Capacitor Banks

A harmonic filter bank is not just a capacitor bank. It provides a low-impedance path at a chosen frequency to divert a harmonic current away from the network, and electrically it is a series R-L-C branch designed to be low-impedance at that harmonic. Its large series tuning reactor — far larger than the small current-limiting reactor of a plain capacitor bank — changes the switching behaviour markedly: a plain bank is mainly capacitive, whereas a filter is resonant, so the reactor and capacitor exchange energy and the switching waveform can carry both capacitive and inductive features. That reactor reduces the energising inrush, but it also changes the trapped voltage, recovery voltage and restrike behaviour on de-energising.

This page develops the filter-bank duty introduced in the general application overview, focusing on why harmonic filters are usually milder to energise than plain capacitor banks but can be more onerous to de-energise because of the series tuning reactor and the trapped capacitor voltage. It follows CIGRE TB 817 and IEC 61642 and treats the two most common passive filters in utility practice: single-tuned and de-tuned banks. For the capacitor-bank energising duty see the APS note on energising capacitor banks.

Table 1 — Passive filter types.

Type	Construction	Use
Single-tuned	Series R-L-C tuned to one harmonic (R is the reactor’s intrinsic resistance); usually a group, each tuned to a different order.	The most common industrial filter; bypasses a specific harmonic.
De-tuned	Same components as single-tuned but tuned below the lowest harmonic, typically between 4.0 and 4.4.	Power-factor correction that also mitigates harmonics while avoiding resonance.
Damped (C-type / MSCDN)	A broad band-pass filter with a resistor in parallel with the inductor, damping frequencies above the tuning point.	Attenuates more than one harmonic; the most widespread damped type (out of scope in detail here).

A single-tuned filter is deliberately tuned close to one harmonic order, so that harmonic current flows into the filter instead of into the network. A de-tuned filter is tuned away from the dominant harmonic frequencies, providing reactive-power support while avoiding a harmful resonance with the system.

The decisive difference is the size of the series inductance. A capacitor bank uses a small current-limiting reactor — typically a few hundred microhenries — whereas a filter’s tuning reactor is set by the system voltage, power frequency, reactive power and harmonic order, and is normally in the millihenry range, largest for the lowest-order filters. That larger inductance in the switching path normally lowers both the peak and the frequency of the energising inrush, but on de-energising the same reactor can produce a more severe recovery-voltage waveform — the trade-off this page turns on.

Table 2 — Typical parameters of four single-tuned filters on a 35 kV, 50 Hz bus.

Filter Order	Size (Mvar)	Tuned Order	Inductance (mH)	Capacitance (µF)
2nd	26.6	1.90	56.2	50.0
3rd	30.7	2.86	17.6	70.0
4th	16.5	3.86	17.0	40.0
5th	20.2	4.59	9.6	50.0

Section 2

Energising a Single Filter Bank

When a filter bank is energised, the series tuning reactor limits how fast the current can rise, so the energising inrush is normally lower in magnitude and frequency than that of a plain shunt capacitor bank of similar rating. A single filter energised from the bus is a series R-L-C loop of the source impedance (\(R_{S},L_{S}\)) and the filter (\(L_{1},C_{1}\)). Its under-damped natural response — the inrush — and the peak and frequency are:

\[ i(t) = V_{m}\sqrt{\dfrac{C_{1}}{L_{eq}}}\,\sin\!\left(\dfrac{t}{\sqrt{L_{eq}C_{1}}}\right), \qquad \hat{\imath}_{\text{peak}} = V_{m}\sqrt{\dfrac{C_{1}}{L_{eq}}}, \qquad f_{\text{inrush}} = \dfrac{1}{2\pi\sqrt{L_{eq}C_{1}}} \]

\(V_{m}\): crest of the driving voltage
\(L_{eq}\): loop inductance, \(L_{S}+L_{1}\) (source plus tuning reactor)
\(C_{1}\): filter capacitance

Key idea — energising is milder than a capacitor bank

The equations are identical in form to a single capacitor bank, but \(L_{eq}\) is dominated by the large tuning reactor rather than a small current-limiting one. Both the inrush magnitude and its frequency are therefore much lower than for a plain capacitor bank, and because the inrush is smaller the energising transient overvoltage is smaller too. Setting aside pre-strikes, a filter bank stresses the switchgear less on closing than a comparable capacitor bank — the opposite of what people often expect. Even so, lower inrush does not mean the duty can be ignored: the breaker, the reactor, the capacitor units and the protection circuits should still be checked for the calculated peak current, frequency and pre-strike behaviour.

Section 3

Energising Back-to-Back Filter Banks

Filters are usually installed as a group, each tuned to a different order, so energising one onto a bus that already carries others is the back-to-back case. As with capacitor banks the already-energised branch can contribute to the transient, but a filter’s large tuning reactor normally limits the current far more strongly than the small connection inductance of a plain capacitor-bank back-to-back case. The switching sequence matters: energise from the lowest harmonic order upward and de-energise from the highest order downward. The order matters because each branch changes the network’s harmonic impedance, so switching in the wrong order can momentarily create or excite a parallel resonance.

Which inrush dominates depends on how the source inductance compares with the tuning reactors:

\[ \begin{aligned} L_{S}\gg L_{1},L_{2}:\ \ &\hat{\imath}_{\text{peak}} = V_{m}\sqrt{\dfrac{C_{eq}}{L_{eq}}},\quad f_{\text{inrush}} = \dfrac{1}{2\pi\sqrt{L_{eq}C_{eq}}},\quad C_{eq}=\dfrac{C_{1}C_{2}}{C_{1}+C_{2}},\ L_{eq}=L_{1}+L_{2} \\[14pt] L_{S}\ll L_{1},L_{2}:\ \ &\hat{\imath}_{\text{peak}} = V_{m}\sqrt{\dfrac{C_{2}}{L_{S}+L_{2}}},\quad f_{\text{inrush}} = \dfrac{1}{2\pi\sqrt{C_{2}(L_{S}+L_{2})}} \end{aligned} \]

\(C_{eq},L_{eq}\): series-combination capacitance and loop inductance of the two banks
\(L_{S}\gg L\): resonant-between-banks case (as for capacitor banks): the resonant current flows between the two banks
\(L_{S}\ll L\): large-tuning-reactor case: the inrush is set by the source and the switched filter, exactly like a single-bank energisation

Because a filter’s tuning reactor is large, the second condition normally holds and back-to-back energising behaves like single-bank energising. The general case — needed for higher-order filters or higher voltages, where the reactors are smaller — requires the full fourth-order solution. Either way the conclusion is the same: back-to-back filter energising produces markedly lower inrush magnitude, frequency and overvoltage than back-to-back capacitor-bank switching. Case studies and site measurements on multi-branch arc-furnace filter banks confirm this, and match EMTP® simulation closely.

Section 4

Pre-strike on Making

Pre-strikes — breakdown of the closing gap before galvanic contact — occur on every capacitive making operation; how many depends on the device type (breaker or contactor) and medium (vacuum or SF₆). On a capacitor bank a pre-strike merely starts the inrush early, and the high \(du/dt\) stresses the capacitors rather than the switchgear. On a filter bank there is an extra hazard: the pre-strike transient can impose an unbalanced voltage distribution across the reactor windings and damage the inductor, so the reactor winding insulation must be rated for it. More generally, fast pre-strike, reignition or restrike transients need not distribute uniformly along the reactor winding, so its first turns can see a higher insulation stress than the power-frequency voltage alone would suggest.

Section 5

Recovery Voltage on De-energising — the Hard Part

For filter banks the more severe duty is often de-energising, not energising: where they are easier to close, they are harder to open. After the current is interrupted the filter capacitor keeps a trapped voltage, the source side goes on following the power-frequency voltage, and the reactor and connected capacitances add an oscillation — so the breaker sees more than a smooth capacitive recovery voltage. The current is chopped just before its natural zero, the source voltage is near its crest, and a 1 − cosine recovery voltage builds across the contacts. Two things make it worse than a plain capacitor bank.

The trapped capacitor voltage exceeds 1 pu

On a capacitor bank the trapped voltage equals the source crest. On a filter the reactor and capacitor divide the fundamental-frequency voltage, and because the branch is capacitive below its tuning order the trapped capacitor voltage rises above the source — the more so for low-order filters, where the reactor most strongly alters the relationship between the bus voltage and the capacitor voltage. The rise is by exactly the factor already familiar from a series reactor:

\[ V_{C} = \dfrac{n^{2}}{n^{2}-1}\ \text{pu}, \qquad n = \dfrac{f_{\text{tune}}}{f} \]

\(V_{C}\): trapped capacitor voltage, in per unit of the source crest
\(n\): tuning ratio (tuned harmonic order)

Table 3 — Trapped capacitor voltage and first-pole recovery voltage by filter order (parameters of Table 2).

Filter Order	Trapped Voltage \(V_{C}\) (pu)	Ungrounded First-Pole RV (pu)
2nd	1.38	3.08
3rd	1.14	2.71
4th	1.07	2.61
5th	1.05	2.58
Plain capacitor bank (\(V_{C}\approx V_{S}\))	1.00	2.50

Low-order filters — a second- or third-harmonic filter — are therefore the more severe on de-energising, because their capacitor voltage sits well above the bus voltage and that raises the recovery voltage the breaker sees after the first pole opens. The peak power-frequency recovery voltage on the first pole to clear follows from the trapped voltage and the neutral shift. For an ungrounded bank, interrupting phase A unbalances the system and lifts the neutral by half the trapped voltage:

\[ \text{ungrounded:}\quad V_{AA'} = V_{S} + 1.5\,V_{C} \qquad\qquad \text{grounded:}\quad V_{AA'} = V_{S} + V_{C} \]

\(V_{AA'}\): peak power-frequency recovery voltage across the first pole to clear
\(V_{S}\): source crest voltage (1 pu)

With \(V_{C}\approx V_{S}\) an ungrounded capacitor bank reaches the familiar 2.5 pu; a 2nd-harmonic filter, with \(V_{C}=1.38\), reaches about 3.08 pu. Earthing the star point (with the reactor on the neutral side, an HV practice) removes the neutral shift and lowers the recovery voltage; ungrounded connection is common at medium voltage to block third-harmonic flow.

A superimposed high-frequency transient

The slow 1 − cosine is only half the story. The filter inductance \(L_{f}\) resonates with the small load-side cable capacitance \(C_{eq}\), superimposing a fast transient reminiscent of inductive switching (motors, reactors). Its frequency changes when the second and third poles clear:

\[ f_{1} = \dfrac{1}{2\pi\sqrt{1.5\,L_{f}C_{eq}}}\quad\text{(A cleared, B and C still in)} \qquad f_{2} = \dfrac{1}{2\pi\sqrt{L_{f}C_{eq}}}\quad\text{(B and C cleared)} \]

This resonant transient pushes the ~3 pu power-frequency peak up towards 3.5 pu. Current chopping is really an inductive-switching effect, and it is the tuning reactor that brings that inductive behaviour, so de-energising a filter involves both a capacitive recovery voltage and an inductive chopping overvoltage: the classic inductive hazards apply — a chopping overvoltage and multiple reignitions at short contact gaps. The chopping overvoltage scales with the surge impedance of the resonant load loop:

\[ U_{\max} = \sqrt{\dfrac{L_{f}}{C_{eq}}}\;I_{\text{chop}} \]

\(U_{\max}\): superimposed transient overvoltage from current chopping
\(I_{\text{chop}}\): chopping current of the circuit breaker
\(L_{f},C_{eq}\): filter reactor inductance and load-side cable capacitance

Design consequence

The values around 3 to 3.5 pu quoted here indicate the severity of the relevant low-order filter cases; they are not universal and should be re-checked against the actual filter order, earthing, network capacitance and breaker arrangement. Because even the “normal” recovery voltage already reaches ~3 pu, surge arresters alone are often not sufficient: an arrester limits the voltage at its own location, but it cannot fully control the breaker recovery voltage, the reactor winding stress or the energy of repeated restrikes. It may be necessary to apply a breaker of higher voltage rating, or two interrupters in series, to withstand the TRV. The capacitive-plus-filter current also carries harmonic content, which can create extra current zeros and premature interruption — worth a separate grid study, though rarely a problem for modern breakers. Because the duty depends on the filter tuning, nearby capacitance, breaker pole timing, trapped charge, surge-arrester operation and the surrounding network impedance — interactions that simple steady-state calculations do not capture — an EMT simulation is the reliable way to confirm a severe or unusual case.

Section 6

Restrike Overvoltage

It is worth separating the two failure modes. A reignition occurs shortly after current interruption, before the recovery voltage has built up significantly; a restrike occurs later, after that voltage has grown across the open contacts. In a filter bank either event can excite the reactor–capacitor circuit and raise the component stress. If the gap fails to hold off the recovery voltage, a restrike reconnects the charged bank to the source. For a plain capacitor bank with the trapped voltage equal to the source crest, the capacitor voltage after a restrike at the source peak is

\[ \begin{aligned} \text{capacitor bank:}\quad &V_{C} = -V_{m} + 2V_{m}\left(1-\cos\omega_{0}t\right) \\[14pt] \text{filter bank:}\quad &V_{C} = V_{C0} + \left(V_{m}-V_{C0}\right)\left(1-\cos\omega_{0}t\right) \end{aligned} \]

\(V_{C0}\): voltage trapped on the filter capacitor before the restrike
\(\omega_{0}\): natural angular frequency of the restrike loop

The capacitor-bank voltage peaks at 3 pu, and a second restrike a half-cycle later drives it to 5 pu. For a filter the higher trapped voltage makes it worse still: with the 2nd-harmonic filter’s \(V_{C0}=-1.38\) pu the first restrike can reach about 3.38 pu, and a second may swing from +3.38 to about −5.38 pu. Either way, each successive half-cycle restrike escalates the voltage by roughly 2 pu — the well-known runaway of a restriking capacitive interruption. In short, each restrike transfers more charge and energy into the filter branch, and because the filter starts from a higher trapped capacitor voltage than a plain bank, the resulting overvoltage can escalate more severely.

Section 7

Outrush Into a Nearby Fault

Outrush is the discharge current that flows from an already-charged filter bank into a nearby fault or other low-impedance path. When a short circuit occurs close to the bank, the charged filter discharges through the low-impedance fault path, and the outrush is of the same order as a back-to-back inrush:

\[ \hat{\imath}_{\text{peak}} = V_{m}\sqrt{\dfrac{C_{1}}{L_{eq}}}, \qquad f = \dfrac{1}{2\pi\sqrt{L_{eq}C_{1}}}, \qquad L_{eq} = L_{1} + L_{\text{line}} \]

\(L_{1}\): filter tuning reactor
\(L_{\text{line}}\): inductance between the bank and the fault

As on energising, the large tuning reactor works in the engineer’s favour here: a filter bank produces an outrush of much lower magnitude and frequency than a plain capacitor bank of the same rating. Even so, the outrush duty should still be checked for the breaker, the reactor and the protection equipment.

Section 8

Common Mistakes

The recurring errors come from switching a filter bank as if it were a plain capacitor bank — checking the mild energising inrush but overlooking the more onerous de-energising recovery voltage, the raised trapped capacitor voltage of low-order filters, and the inductive behaviour the tuning reactor brings.

Common mistakes to avoid

Assuming a filter bank switches like a capacitor bank — it is milder on energising but more onerous on de-energising.
Sizing the breaker on the making duty and overlooking the recovery voltage, which for a low-order filter can reach ~3–3.5 pu (well above the 2.5 pu of an ungrounded capacitor bank).
Treating de-energising as a purely capacitive duty and missing the inductive-switching behaviour — chopping overvoltage \(U_{\max}=\sqrt{L_{f}/C_{eq}}\,I_{\text{chop}}\) and reignitions.
Relying on surge arresters alone when even the restrike-free TRV is ~3 pu; a higher-rated breaker or two series interrupters may be needed.
Energising or de-energising a multi-branch group in the wrong order — energise lowest-order first, de-energise highest-order first — and exciting a parallel resonance.
Ignoring the reactor winding insulation, which pre-strike transients can stress unevenly.

Section 9

Key Points

Filter-bank switching checklist

A filter bank is a series R-L-C branch, not a plain capacitor bank: its large tuning reactor (millihenries, not the hundreds of microhenries of a capacitor bank’s current-limiting reactor) usually makes energising milder but can make de-energising more severe.
On energising the large reactor cuts the inrush magnitude, frequency and overvoltage — a filter is milder to close than a capacitor bank, single or back-to-back.
Energise a multi-branch group from the lowest harmonic order up and de-energise from the highest down, to avoid parallel resonance.
On de-energising, low-order filters give the highest duty: the trapped capacitor voltage rises to \(n^{2}/(n^{2}-1)\) pu (1.38 pu for a 2nd-harmonic filter), so the ungrounded first-pole recovery voltage \(V_{S}+1.5V_{C}\) reaches ~3 pu — around 3–3.5 pu once the reactor–capacitor oscillation is added — against 2.5 pu for a plain capacitor bank.
A resonance between the reactor and load-side cable capacitance superimposes a fast inductive-type transient (up to ~3.5 pu), with chopping overvoltage \(\sqrt{L_{f}/C_{eq}}\,I_{\text{chop}}\) and possible reignitions.
Restrikes escalate as for any capacitive interruption — ~3 pu then 5 pu for a capacitor bank, and higher (3.38 pu, −5.38 pu) for a filter because of its larger trapped voltage.
Surge arresters alone may not suffice: consider a higher-rated breaker or two series interrupters, and confirm severe or unusual duties by EMT simulation — especially with low-order filters, long cables, multi-branch switching or nearby capacitor banks.

Section 10

References and Further Reading

The standards and technical brochures behind this guide.

CIGRE, Shunt Capacitor Switching in Distribution and Transmission Systems, Technical Brochure 817. Paris, France: CIGRE, 2020.
IEC 61642:1997, Industrial a.c. Networks Affected by Harmonics – Application of Filters and Shunt Capacitors. Geneva, Switzerland: International Electrotechnical Commission, 1997.
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 18-2012, IEEE Standard for Shunt Power Capacitors. New York, NY, USA: IEEE, 2012.
IEEE Std 1036-2010, IEEE Guide for the Application of Shunt Power Capacitors. New York, NY, USA: IEEE, 2011.
J. C. Das, Transients in Electrical Systems: Analysis, Recognition, and Mitigation. New York, NY, USA: McGraw-Hill, 2010.

Part 7 Reading now

Switching of Harmonic Filter Banks

Why the large tuning reactor makes filter banks milder to energise but more onerous to de-energise, with the inrush, recovery-voltage, chopping and restrike equations.

Series progress 7 of 8

Part 8

Devices for Limiting Capacitor-Switching Transients

Controlled switching, pre-insertion resistors, current-limiting reactors, solid-state and hybrid diode switches — how each limits the transient, and what it costs.