Capacitor Banks and VFDs: How Resonance Actually Happens

Article

October 26, 2026

A capacitor bank is the cheapest way to correct a power factor, and on the wrong network it is also the fastest way to destroy itself. The mechanism is parallel resonance between the bank's capacitance and the inductance of the supply — the transformer and the cabling — excited by the harmonic currents that variable-speed drives inject. Nothing about it is exotic; it is predictable from three numbers on a nameplate and one measurement.

This article sets out the formula, works an example, describes what failure actually looks like on site, and states plainly what a detuned reactor protects against and what it does not.

A Capacitor Bank Does Not Create Harmonics — It Amplifies Them

The distinction matters, because it decides who is responsible for the problem and what the remedy is.

The bank is not a harmonic source. It draws no harmonic current of its own. What it changes is the impedance of the network as seen by the harmonic currents already flowing. Every harmonic current produced by the drives has to flow somewhere, and it divides between the supply and the capacitor according to their impedances at that frequency. Near the resonant frequency, the impedance of the supply-plus-capacitor combination rises sharply, so a modest harmonic current produces a large harmonic voltage — and that voltage drives a much larger current around the loop formed by the transformer and the capacitor.

The practical consequence: a site can have perfectly acceptable distortion before the bank is installed, install a correctly sized bank, and see distortion and capacitor current both climb. The bank did not add harmonics. It moved the network's impedance into a range where the harmonics already present became destructive.

The Formula You Can Actually Use

For a bank connected at a busbar fed by a transformer, the parallel resonant order is:

h = √(S_sc / Q_c)

where S_sc is the short-circuit capacity at that busbar, in kVA, and Q_c is the connected capacitor rating, in kvar. For a transformer, S_sc ≈ transformer kVA ÷ per-unit impedance. The resonant frequency is h × the fundamental frequency.

Two things follow immediately, and both surprise people. First, the resonant order falls as the bank gets larger — so a bigger bank is not automatically safer, it simply moves the resonance somewhere else. Second, the resonance is determined by the network, not by the drives: change the transformer or add a second bank and the resonant point moves, even though the drives are untouched.

Worked Example: A 1,250 kVA Transformer and Three Bank Sizes

Take a 1,250 kVA transformer with 6% impedance feeding a 400 V busbar. The short-circuit capacity is 1,250 ÷ 0.06 ≈ 20,800 kVA. Now size a bank three different ways on a 50 Hz system:

• 200 kvar: h = √(20,800 ÷ 200) = √104 ≈ 10.2, so about 510 Hz — close to the 11th harmonic at 550 Hz;
• 400 kvar: h = √52 ≈ 7.2, so about 360 Hz — sitting almost exactly on the 7th harmonic at 350 Hz;
• 600 kvar: h = √34.7 ≈ 5.9, so about 295 Hz — between the 5th at 250 Hz and the 7th at 350 Hz.

The third case is the worst, and it is the one that gets installed most often, because 600 kvar is a round number and the calculation is rarely done. A resonance between two dominant orders amplifies both, and there is no clean way to detune around it without changing the bank size.

The useful question is therefore not "how big should the bank be" but "where does the resonance land relative to the orders my drives actually produce". Those two questions have different answers, and only the second one protects the equipment.

Why the Fifth and Seventh Dominate

A six-pulse rectifier — the front end of almost every standard variable-speed drive — draws current in pulses, and the resulting spectrum contains the characteristic orders 5, 7, 11, 13, 17, 19 and so on, with amplitudes falling roughly as 1/5, 1/7, 1/11. The fifth and seventh therefore carry most of the harmonic energy in a typical drive-fed network, which is why a resonance that lands on them is the expensive one.

Single-phase loads — office equipment, LED drivers, small chargers, the switch-mode supplies in an internet café — add third harmonic and the other triplen orders. In a three-phase four-wire system these do not cancel in the neutral, so they accumulate there. They sit well below any realistic resonant point, so they are not a resonance problem, but they are a conductor-loading and transformer-heating problem, and they are the reason a site can have a poor power factor and hot cables without any large motor in sight.

What Failure Looks Like in the Field

Resonance is rarely diagnosed from a calculation after the fact; it is usually diagnosed from a pattern of failures that keep recurring after each replacement. The signs, roughly in order of how often they appear:

• capacitor cans bulging, leaking or with the internal over-pressure device operated, often within months of installation;
• fuses or the bank's breaker tripping with no identifiable overload and no fault on the load side;
• contactors with pitted, blackened or welded contacts, and step switching that becomes erratic;
• an audible buzz from the reactor or the capacitor enclosure at a distinct, steady pitch that changes when steps are switched;
• capacitor case temperature more than 15 K above ambient, and a bank room that is noticeably hotter than the rest of the switchroom;
• the transformer running hotter than its load justifies, with no change in load since the bank was installed.

One test settles it, and it costs nothing: measure voltage total harmonic distortion with the bank switched off, then with it switched in, at the same load. If distortion rises when the bank is connected and falls when it is disconnected, the bank is participating in a resonance. That single comparison is worth more than any catalogue claim.

Measure current in the capacitor branch at the same time. A capacitor current well above its rated 1.3 times, with a distorted waveform, confirms the diagnosis.

What a Detuned Reactor Buys You — and What It Does Not

The standard remedy is a reactor in series with each capacitor step. Its reactance is quoted as a percentage p of the capacitor's reactance at fundamental frequency, and it moves the series resonance of the branch to:

h_r = √(1 / p)

At p = 7%, h_r = √(1 ÷ 0.07) = 3.78, which is 189 Hz on a 50 Hz system. Below that frequency the branch is capacitive; above it the branch is inductive. Since the fifth harmonic at 250 Hz and everything above it now sits in the inductive region, the branch no longer forms a parallel resonance with the supply at those orders, and the fifth and seventh are absorbed rather than amplified. The reactor also limits the inrush current at switching and shields the capacitor from the higher-frequency components that shorten its life.

What it does not do. It is not a filter. A detuned bank absorbs a proportion of the fifth and seventh but does not remove them; residual distortion remains, and if the site needs a specific distortion limit the answer is a tuned filter or an active filter, not a detuned bank. It does not address the third harmonic, which lies below 189 Hz; sites dominated by single-phase load may need a different topology. It does not help if the resonance was between the bank and a separate filter, or between two banks on the same busbar.

And it imposes a design constraint that is routinely missed: the reactor raises the voltage across the capacitor. U_C = U ÷ (1 − p), so at 400 V with p = 7% the capacitor sees 430 V. Capacitors rated 400 V will not survive that; 440 V types are required. A quotation that pairs 400 V capacitors with a 7% reactor has a design error built into it, and it will fail inside the warranty period.

The Measurements to Take Before Anyone Sizes a Bank

A bank sized from a nameplate and a rule of thumb is a guess. Six measurements make it an engineering decision:

1. Power factor over a full operating day, with minimum, maximum and mean, not a single spot reading taken at a convenient moment.
2. Current and voltage THD at the point of common coupling, plus individual harmonic orders up to at least the 25th, so the dominant orders are known rather than assumed.
3. Transformer kVA and impedance, from the nameplate or the test certificate — this is the S_sc in the formula and it is not optional.
4. The non-linear load inventory: how many drives, of what rating, with which rectifier type — six-pulse, twelve-pulse or active front end — and their total kW.
5. Whether significant single-phase load returns through the neutral, which determines whether triplen harmonics are part of the problem.
6. The history of any existing compensation: what was installed, when, what failed, and what was replaced with what.

A quotation issued without the first three is not a quotation, it is a price for a box.

If You Already Have a Bank That Keeps Failing

The diagnostic sequence is short and mostly consists of comparing two states. Measure with the bank off and with the bank on, at the same load, recording THD, individual orders and capacitor branch current. Then check four things against the design: the capacitor voltage rating against the reactor percentage; whether the calculated resonant order falls within about ten percent of a dominant harmonic order; whether the step sequence leaves a small step connected at light load, where over-compensation and the sharpest resonance usually occur; and whether a second bank or a filter shares the same busbar.

If the answer is a resonance inside the fifth-to-thirteenth band, the remedy is a detuned or filtered bank — not a larger one, and not a straight replacement of the failed capacitors with the same specification. Replacing like with like reproduces the failure on the same schedule.

Where Our Standard Cabinet Fits — and Where It Does Not

Our power loss regulating equipment is a parallel, continuously adjusting compensation unit rated 15–100 kW at 380–415 V, 50/60 Hz, with harmonic control stated as keeping total harmonic distortion below 8%. It is a compensation product. It is not a harmonic filter, and it does not ship with a detuned reactor as standard.

That distinction matters on this page more than on any other, so it is worth being explicit. If the site is a workshop or a restaurant with a handful of small drives and a power factor around 0.75, the unit's continuous adjustment and its 8% THD target are a reasonable fit. If the site runs a dozen six-pulse drives at high load and the measured current THD is 25% or more, a standard capacitor-based cabinet is the wrong product and we will say so before quoting: that site needs a measured harmonic study and probably a detuned or active solution, not a compensation cabinet with a harmonic claim attached to it.

The correct sequence is measure, then size, then choose the topology. Choosing the topology first and measuring afterwards is how banks end up failing in their first year.

What to Send Us

For a site with drives, five items are enough to give a defensible answer rather than a price:

• transformer kVA and impedance percentage;
• a 24-hour power factor log, or the utility's metering data;
• a harmonic measurement, even a one-day portable analyser log;
• the number and rating of drives, and the rectifier type if it is known;
• whether the tariff charges kVA demand or reactive energy.

With those we will tell you whether a compensation cabinet is appropriate at all, what rating it should be, and whether a detuned variant is required. If the honest answer is that compensation is not the right first step, that is what the reply will say.

The specification and selection route for the unit are on the power loss regulating equipment page. If the question behind the question is whether compensation can reduce the bill at all, the companion article on what actually moves an industrial power bill starts one step earlier.