Detuned reactor — the p-factor as protection against resonance between a capacitor bank and network harmonics

The guide on power-factor correction covers why a capacitor bank is a standard solution against a low power factor (cosφ) with a lot of motor load. The [guide on harmonics & THD limits](/guides/nen-1010/harmonischen-thd) briefly mentions that a standard capacitor bank can worsen an existing THD problem through resonance. This article looks deeper at how that resonance arises and how a detuned reactor prevents it.

Why a capacitor bank can resonate with network harmonics

A capacitor bank forms an LC parallel circuit together with the network impedance (mainly the short-circuit impedance of the supplying transformer). Every LC combination has a resonant frequency at which the inductive and capacitive reactance cancel each other out. If that resonant frequency happens to lie close to a harmonic frequency already present in the network — typically originating from non-linear loads such as variable-frequency drives, LED drivers, or switch-mode power supplies (see the guide on measuring harmonics in practice) — the LC circuit amplifies that harmonic current instead of damping it. The result can be a substantially higher harmonic distortion than without the capacitor bank, with overload and accelerated ageing of the capacitors as a practical consequence.

The solution: a series reactor, tuned below the lowest relevant harmonic

By placing a reactor (coil) in series with the capacitor bank, the resonant frequency of the combination shifts to a lower value than that of the capacitor bank alone. If this reactor is chosen such that the resulting resonant frequency lies below the lowest harmonic order that is significant in the network, the combination behaves, for that harmonic and all higher harmonics, as an inductive impedance rather than a resonant or capacitive one — the bank then no longer amplifies the harmonic current, but instead offers it a certain resistance.

The p-factor and the corresponding tuning frequency

The degree of "detuning" is expressed as a percentage, the p-factor, defined as the ratio between the reactance of the reactor and that of the capacitor at the network frequency. The resulting tuning frequency follows from:

fr = f1 / √p (with p as a decimal fraction, for example 0.07 for 7%)

For a 50 Hz network this gives the following commonly used combinations:

p-factor	Tuning frequency	Tuning order	Typically applied when
5.67%	≈ 210 Hz	≈ 4.2nd	5th harmonic dominant, little 3rd-harmonic load
7%	≈ 189 Hz	≈ 3.8th	common standard choice with ample margin below the 5th harmonic
14%	≈ 134 Hz	≈ 2.7th	substantial share of single-phase, non-linear load (e.g. LED lighting) with elevated 3rd-harmonic content

Note: the exact choice of p-factor for a specific installation depends on the dominant harmonic order measured with a network analyser (see the guide on measuring harmonics) and on the manufacturer's system study/specification per IEC 61642; the values in the table are commonly used, rounded standard values, not an exhaustive list.

Why this is not the same as an active or tuned harmonic filter

A detuned reactor in series with a capacitor bank prevents resonance and provides a certain amount of damping of harmonic currents, but it is not the same as a dedicated tuned filter designed for one specific harmonic order to actively filter out that harmonic, nor the same as an active harmonic filter that actively compensates harmonic currents. An ordinary detuned-reactor bank remains, first and foremost, a reactive-power-compensation solution with resonance protection, not a dedicated harmonic filter.

Practical relevance

When specifying a capacitor bank for reactive-power compensation in an installation with a significant share of non-linear load (variable- frequency drives, LED lighting, UPS systems), it is worthwhile to measure the harmonic composition of the network beforehand and specify a capacitor bank with a suitably detuned reactor on that basis, rather than applying a standard, unfiltered capacitor bank that, with an unfortunate combination of network impedance and harmonic load, can actually lead to resonance and overload.

Common mistakes

Applying a standard, unfiltered capacitor bank in a network with a significant share of non-linear load, without checking whether resonance with a present harmonic is possible.
Choosing a p-factor without first measuring the dominant harmonic order in the network — a reactor that is not tuned to the harmonic composition actually present can itself lead to resonance problems or turn out needlessly heavy (and expensive).
Confusing a detuned reactor with a dedicated harmonic filter or an active filter — a detuned reactor prevents resonance and provides some damping, but is not a filter solution tuned to one specific harmonic.
Assuming a higher p-factor is always better — an unnecessarily high p-factor (for example 14% where 7% would suffice) increases the voltage drop across the reactor and hence the required overvoltage rating of the capacitors, without this being necessary for the actual harmonic composition.