non-integer harmonics included in the THD computation

[Jones]

I have voltage and current data recorded from a cyclo-convertor, which produces harmonic energy at integer and non-integer multiple of the fudamental 60Hz frequency. Does LabVIEW have a vi or function that includes non-integer as well as integer frequencies of the fundamental frequency in computing the THD?

[LocalDSP]

A harmonic is by definition an integer multiple of the fundamental frequency and a THD measurement will not (and is not supposed to) include "non-integer multiple" tones in the calculation.

There is one exception to this rule though, and it is if the tones are actually true harmonics that appear in your spectrum as aliased signals. For example if you are sampling your signal at 500 Hz, then the 10th harmonic of 60 Hz, that is 600 Hz, will appear as a 600-500 = 100 Hz signal. The high-level Harmonic Distortion Analyzer.vi gives you an option to either include these aliased signals or not in your THD calculation.

So try to use this VI (in the Analyze>>Waveform Measurements palette) to see if your "non-integer harmonics" are caused by aliasing.

If they are no
t, then most likely the tones you see are spurious tones that are not related to the 60 Hz signal or intermodulation with another signal (your main signal?). In this case, try to use the SINAD Analyzer.vi and see if it gives you are more useful result.

[Jones]

I appreciate your response, but I am afraid that I have run into a non-integer producing animal (i.e. a cycloconverter). Please go to the following site for a better explanation of the cycloconverter.
http://grouper.ieee.org/groups/harmonic/iharm/docs/ih519.pdf. Also from what I have heard, arc furnaces are producers of non-integer harmonics. Somehow these non-integer harmonics need to be included in the THD formula for my application. I know the FFT bandwidth can be adjusted by changing the sampling frequency and number of samples, but can I modifiy the THD formula in lab view?

[LesHammer]

The reason that the Fast Fourier Transform (FFT) is fast is because it makes some basic assumptions - the prime assumption being that the harmonics are integer multiples of the base frequency. It's been many years, but I seem to recall that a true Fourier Transform doesn't make these assumptions. You may need to go back to that. (Where did I put that old text book? 🙂

Or, if you can find the magnitude and phase of the fundamental frequency, subtract that from your signal. What you have left is your distortion. You should be able to get an RMS reading on it and compare it to the fundamental magnitude. I had an HP meter many years ago that did that automatically. It sat right next to the spectrum analyzer - which scanned all the frequenc
ies too. You could use the spectrum analyzer to get all the information you need.

Or you could limit your array to a size that has a base frequency that makes that distortion an integer harmonic. Be careful of aliasing though.

A lot depends upon what those non-integer harmonics look like (are they constant frequency, related to the fundamental, or what? how big are they?), and how much you can spend on test equipment. But a simple FFT is probably not the answer.

Les.Hammer@CompleteTest.com

[LocalDSP]

I am sure your signal is full of inter-harmonics, but again the THD VI will not find these automatically. I see 3 options you could try, (the first one being a little "dirty").

1 - If your inter-harmonics are multiple of a common frequency (like n* 10 Hz), you may be able to use the THD VI with some modifications. Make your fundamental search around 10 Hz, (assuming there is a tone there, even though it may be small). Then the THD VI will return a THD value that is useless (since it considers your 60 Hz tone as a harmonic), but the VI also returns an array of RMS values (DC, 10 Hz, 20 Hz ...). You can then extract the components you are interested in (like everything but DC and 60 Hz) and compute your measurement value. This is, as mentioned, a
dirty trick but it might work for you (no guarranties though!)

2 - You can save the THD VI in another name and location and edit the diagram to your specifications. You can see on the diagram, that the FFT is only computed once, and that the spectrum is passed to a sub-vi called "Extract single tone Information from Hann Spectrum.vi". The VI is used to compute the fundamental and then in the For loop to compute the different harmonics. You can modify the harmonic list to fit your requirements.

3 - last but not least, the SINAD VI could be worth trying. This VI will return the ratio between the signal minus fundamental and the signal. The measurement will therefore include all your inter-harmonics, but also all noise. So depending on your uncorrelated noise level, the result may or may not accurate enough for your application.