resonance - Cut Off Frequency in three phase LC filter

Good afternoon all

My question is what will be the formula to calculate cut off frequency of attached LC filter.

Its a three phase LC filter.

\$(L1=L2=L3= 6.1 \mathrm{mH}) \;\mathrm{and} \;(C1=C2=C3=29\mathrm{uF}). \$

I know formula for single phase LC filter is \$\dfrac{1}{2 \pi \sqrt{LC}}\$.

What wondering same will apply to three phase system or its different. Please Help. Also what is doffrence between cut off frequency and resonance frequency.

Answer

If I were you I'd simulate this circuit in LTSpice to see the exact relationship between filtering frequency and inductors and capacitors in this low pass filter.

See this graph for cut-off frequency and resonant frequency.

The blue curve is for a Q of 0.7071 and at the normalized frequency, the response is 3dB down compared to the value at much lower frequencies. As Q increases to 1 a small resonant peak develops at about 0.8 x normalized frequency. As Q rises higher there becomes a peak at the normalized frequency and the cut-off frequency - now the 3dB response has shifted to a slightly higher frequency.

This response is typical of an LC low pass filter and controlling what could be a massive peak is very important in 3 phase inverters. You need to ensure that the normal running frequency produced (50Hz or 60Hz) does not correspond with any peaks as shown above or the thing will rapidly get very warm and blow fuses or catch fire.