# Power Factor Correction – Harmonic Resonance Calculation in Power-Factor Correction

harmonicspower-factor-correction

Eaton's Power factor correction:
a guide for the plant engineer
states,

Capacitors and transformers can create dangerous resonance
conditions when capacitor banks are installed at the service
entrance. Under these conditions, harmonics produced by
nonlinear devices can be amplified manyfold.
Problematic amplification of harmonics becomes more likely as
more kVAR is added to a system that contains a significant amount
You can estimate the resonant harmonic by using this formula:

$$\ h = \sqrt {\frac {kVA_{sys}}{kVAR}} \$$

kVAsys = short-circuit capacity of the system
kVAR = amount of capacitor kVAR on the line
h = the harmonic number referred to a 60 Hz base

If h is near the values of the major harmonics generated by a
nonlinear device—for example, 3, 5, 7, 11—then the resonance
circuit will greatly increase harmonic distortion.

Two questions:

1. Why would resonance depend on the short-circuit capacity of the system? (Can you explain the formula?)

2. I can't find a similar equation for 50 Hz. Any suggestions?

For reference, this is for a 1 MVA transformer (short-circuit capacity not known at this time) and 350 kVAr PF bank).

$$\f_0 = \frac{1}{2 \pi\sqrt{LC}}\$$