Detuning Reactor Formulas: Capacitor Banks

Detuned capacitor bank formulas: reactor reactance from the percentage, resonance frequency and harmonic order, capacitor voltage rise and net kVAR.

The formulas

V is the line voltage, Qc the capacitor rating in VAR at that voltage and p the reactor as a fraction of the capacitor reactance. The reactor is chosen so that the series resonance is below the lowest harmonic of the network, which stops the bank and the supply resonating with the harmonics. The common values are 5.67% (210 Hz at 50 Hz), 7% (189 Hz) and 14% (134 Hz). The capacitors must be rated for the higher voltage across them, and the reactor for the harmonic currents. Take the final design from the maker and a harmonic study.

Worked example: 50 kVAR bank at 400 V, 7% reactor

1. Xc = 400² / 50,000 = 3.2 Ω, so XL = 0.07 × 3.2 = 0.224 Ω
2. L = 0.224 / (2π × 50) = 0.713 mH
3. fr = 50 / √0.07 = 189 Hz, which is harmonic order 3.78
4. The capacitor voltage is 400 / (1 − 0.07) = 430.1 V
5. The net reactive power is 400² / (3.2 − 0.224) = 53.76 kVAR

Resonance by reactor percentage (50 Hz)

Frequently asked questions

Why add a reactor in series with a capacitor bank?

The capacitor and the supply inductance can resonate at a harmonic frequency and amplify it. A reactor moves the resonance of the bank below the lowest harmonic, so it cannot be excited.

Which percentage should I use?

Use 7% if the 5th harmonic is the lowest large one, and 14% if the 3rd is also present. Use 5.67% where the maker or the utility advises it, for example to keep clear of a ripple-control signal frequency. Check with a measurement.

Why is the capacitor voltage higher?

The reactor and the capacitor are in series and the voltage across the capacitor is the supply voltage divided by (1 − p) at the fundamental frequency.

Does the reactor change the reactive power?

Yes. The net reactive power at the fundamental is a little higher than the capacitor rating at the line voltage, as in the example, so the bank has to be rated for the result.

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