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windowing for range of frequencies

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gary36

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I have an input which has 50 Hz component and harmonics extending upto audio frequencies. The fundamental is likely to change from 48.5 to 52.5Hz . The goal is to extract the fundamental using FFT and compute the RMS. I am unclear how to select the window functions, adc sampling frequency and no of fft points to capture the range and compute rms accurately. RMS accuracy should be around +/-1%.
 

You can use e.g. the IEC 1000-3-2 measurement specification as a starting point.

- range up to 40th harmonic
- hanning window 4 to 30 fundamental periods. If rectangular window used, exact frequency synchronization required
- 50 dB attenuation for aliasing components.

In case of non constant harmonic magnitude, use 50 % overlapping hanning windows for averaging.

Sampling frequency according to Nyquist and aliasing specification
 

Hi,

If you want an FFT frequency resolution of 1% at 50Hz this means a delta frequency of 0.5Hz.
Thus you need a window size of 1/0.5Hz = 2 seconds.

For sure you may use a smaller window size ... but then you get larger frequency steps.
Then you may use interpolation to get better frequency resolution.

Klaus
 

I read the post so that the objective is accurate measurement of fundamental and harmonic magnitudes. Frequency precision usually isn't a problem for power quality measurement.
 

Hi FvM,
I need to accurately measure 50 Hz component that varies from 48.5 to 52.5Hz. I need to reject every other component outside this band. Should I really consider upto 40 harmonics?. I have to compute RMS within 200ms. To reduce computation time, I was considering 500 Hz ( 10 times fundamental) and using 64 point fft, which gives me 7.8 Hz resolution. I have to consider 6th and 7th bin for RMS computation. Can I use this line of approach?
 

40th harmonic is power quality measurement standard, e.g. referred in IEC 1000-3-2. But it may be unnecessary for your application. To measure 7th harmonic, you need at least 500 Hz sampling frequency (Nyquist rate), effectively more for input feasible filters.

I suggest that you estimate the error due to window length unequal to an integer multiply of fundamental period. If you feel it's too high, you may measure the fundamental frequency separately and adjust the window length. That's simple as long as the FFT length is larger or equal than the maximum window.
 

Hi,

. To measure 7th harmonic, you need at least 500 Hz sampling frequency (Nyquist rate), effectively more for input feasible filters.
Click to expand...
The 7th harmonic of a 50Hz fundamental is 350Hz. According nyquist you need a sampling frequency of more than 700Hz.
The closer you are at nyquist the larger the window you need for an FFT.

Thus - for calculating the RMS of the fundamental - I recommend to do a low pass filtering.
Try eliptic filter or Chebychev.

Klaus
 

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