Is it possible to analyze a transient using the FFT (which is the case with the inrush current when energizing a power transformer)? Or is this technique applicable only to waves with armonic distortion? in other words, we are assuming that the inrush current is a transient and does not generate armonic distortion. Please clarify.
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armonic vs trnasient analysis 1
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electricpete
Electrical
The time domain and frequency domain are two different ways of looking at the same thing. In theory there is a 1:1 correspondence between a spectrum (with phase) and a time waveform. If you have digital data of one you should be able to transform to the other. Sampling and windowing issues can cloud the transformation a little.
Some behavior will be better understood by using time waveform... some is better understood using the spectrum. If you want to examine how harmonic restraint would behave, then use FFT. If you want to see the peak value obtained by the current, use the time waveform. In vibration analysis it is very common to routinely review both types of measurements on the same equipment.
Some behavior will be better understood by using time waveform... some is better understood using the spectrum. If you want to examine how harmonic restraint would behave, then use FFT. If you want to see the peak value obtained by the current, use the time waveform. In vibration analysis it is very common to routinely review both types of measurements on the same equipment.
electricpete
Electrical
javierac - numerically we can perform an FFT on any waveform we choose, periodic or not. How we should interpret the result in case of nonperiodic signal is a question worth asking, as you point out.
One way to interpret a FFT=DFT is as the discrete fourier series representation of the waveform which is a "periodic extension" of the original waveform. So if we sample 100 points, then we assume we have 100 samples of a waveform which continues to repeat itself every 100 samples and determine the discrete fourier series of that periodically-extended waveform. That can introduce errors whether the original waveform was periodic or not... For example if we sample a periodic waveform V=cos(2pi*f*t) for an interval from 0 1.5/f (one and a half periods), and then recreate that periodically, we have a discontinuity jump in the waveform which creates high frequency content that was not present in the original waveform. Windowing techniques are designed to reduce this kind of error.
There is yet another way to interpret the FFT=DFT. A transient waveform will have a continuous fourier transform (what you would see if you input into perfect spectrum analyser). That reflects the fact that a transient nonperiodic waveform CAN be decomposed into an infinite number of sinusoids (not sinusoids at discrete frequencies). For example exp(-alpha*t)*u(t) transforms to 1/(alpha+jw) which does not represent a single frequency or several discrete frequencies, but a contribution from infinite number of sinusoids. FFT/DFT is NOT capable of representing this type of continuous infinite number of frequencies, since it represents discrete frequencies. But the FFT=DFT does represents frequency "samples" of the continuous fourier transform sampled at frequency intervals of somewhere around 1/(2NT) where N is number of samples and T is time duration of the waveform.
In the case of transformer inrush, as has been discussed, there is at least one very useful application, which is examining how harmonic restraint can be used to differentiate a fault from an inrush.
One way to interpret a FFT=DFT is as the discrete fourier series representation of the waveform which is a "periodic extension" of the original waveform. So if we sample 100 points, then we assume we have 100 samples of a waveform which continues to repeat itself every 100 samples and determine the discrete fourier series of that periodically-extended waveform. That can introduce errors whether the original waveform was periodic or not... For example if we sample a periodic waveform V=cos(2pi*f*t) for an interval from 0 1.5/f (one and a half periods), and then recreate that periodically, we have a discontinuity jump in the waveform which creates high frequency content that was not present in the original waveform. Windowing techniques are designed to reduce this kind of error.
There is yet another way to interpret the FFT=DFT. A transient waveform will have a continuous fourier transform (what you would see if you input into perfect spectrum analyser). That reflects the fact that a transient nonperiodic waveform CAN be decomposed into an infinite number of sinusoids (not sinusoids at discrete frequencies). For example exp(-alpha*t)*u(t) transforms to 1/(alpha+jw) which does not represent a single frequency or several discrete frequencies, but a contribution from infinite number of sinusoids. FFT/DFT is NOT capable of representing this type of continuous infinite number of frequencies, since it represents discrete frequencies. But the FFT=DFT does represents frequency "samples" of the continuous fourier transform sampled at frequency intervals of somewhere around 1/(2NT) where N is number of samples and T is time duration of the waveform.
In the case of transformer inrush, as has been discussed, there is at least one very useful application, which is examining how harmonic restraint can be used to differentiate a fault from an inrush.
The inrush current when energising a transformer has a large 2nd harmonic component, which is transient. i.e. if trying to analyse with a FFT the period in which oscillations occur needs to be sampled at a frequency of at least twice the highest required harmonic. The FFT on this data would reveal the harmonic content. The inrush can be thought of as a 2nd harmonic superimposed on a transient decaying signal. Protection relays use this to ensure that they do not trip when inrush occurs.
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