http://ieeexplore.ieee.org/document/772312/
The question is related to the above paper. The authors after proposing the technique mention that the frequency can be calculated by taking the inverse sin of the imaginary part of the vector x_1. Since, sine inverse is only valid from -1 to 1, how will I be able to get the frequency for values other than the range.
http://ieeexplore.ieee.org/document/772312/
Hi Arif,
in equation (15) they said that
f=sin^-1{Im(x1)}/(2piDeltaT)
on the other hand, equation (6) says
x1=cos(kwDeltaT)+jsin(kwDeltaT), so Im(x1) is just sin(kwDeltaT)
Since it is a digital system, the Nyquist frequency is 1/(DeltaT*2). Therefore, it makes sense to consider that what is inside the sin is lower than pi. (worst case).
Of course, the range of frequencies you can consider is limited: from dc to the Nyquist frequency.
Anyway, I think that nowadays, the most reasonable way to do phase-angle/frequency estimation by digital implementations is by means of phase locked loop techniques.
Thank you Francisco. I have implemented it in Matlab and the Kalman Filter works fine in estimation. However, the value to frequency I calculate is always wrong. I am sure this has to do with the fact that as the value of "k" changes from 1:200 (let's assume I run it for 200 instances), the value of "2*pi*f*k*DeltaT" which is inside the sine keeps increasing and goes beyond pi. And as such I can never get back the original frequency. Could you let me know what would be a proper way of simulating the actual voltage signals in Matlab.
Hi Arif,
I think that what you identify as k has a different meaning. kw is the frequency to calculate, not k is each instance.
Anyway, have a look on the paper below. Section II.A shows a crystal clear simple method to get the frequency estimation with two/three samples. In that development, k indeed refers to sample number and w to frequency.
Cheers
Article Robust Frequency-Estimation Method for Distorted and Imbalan...
For computation, you can convert the value in 1 to -1 range by dividing the maximum value and then can take the inverse transformation for frequency calculation.
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