Finding PHASE between two sinusoids with FFT/DFT (ArduinoFFT w/ C)

Supplement on the nature of your source data

While testing my pll software simulator, I ran it on the voltage/current datasets of your github reference and noticed an unusual behavior of the phase detector output (phase error). Intrigued, I've computed fft of your dataset voltages/currents.

The voltage's FFT is quite smooth, phase noise at the end of the range is due to quantization noise:

But the current's FFT shows a nonlinearity of voltage-to-current conversion (if the dataset's current is generated from the dataset's voltage by some electronic circuit). Notice third and fifth harmonics in an ABS(FFT) graph and nearly full circle phase noise in ARG(FFT):

Nonlinearity in current can be attributed to a phase modulation sort of $$ cos(2pi{omega}t + (alpha + beta cos^2(2pi{omega}t))gamma cos^2(2pi{omega}t)*normalDistRandomFunc(mu,sigma)) $$ which generates FFT like in the below picture It would be interesting to know the origin of those github datasets and how they are related with phase noise/phase distortion.

This strong phase noise is hardly noticed when inspecting dataset current waveforms. Yet, when present, it aggravates processing of affected signals.

A couple of things I’ve noticed, the combination of which likely is at the root of the issue. First, when you apply a window, you are applying a linear phase shift to the frequency transform. You could subtract it out, and it would probably fix the issue. This wouldn’t necessarily be a problem except...

Second, your code calculates the max values for the magnitudes independently for the current and voltage. This means that you are comparing the phase for different bins. Again, this would not be an issue (mostly) if not for the phase shift resulting from the windowing.

You could either remove the phase shift from the windowing, be sure to use the same bin for voltage and current phase, or do both. Mr Dawg is right that there are other/better ways to do this, but I wanted to help out considering this technique should work.

Edit: Also, I don’t know how that library works, but you may want to restrict your search for peaks to the first half of the Transform output. Phases in the second half will be negative.

You can't do better than this for accuracy in my experience.

• A Two Bin Solution

Select a frame size of 1 1/2 cycles or 2 1/2 cycles.

You only need to calculate two bins, either 1 and 2, or 2 and 3. No need for a full DFT. So it is very efficient as well. By placing the frequency squarely near the center of the two bins you minimize noise effects and avoid needing to deal with near bin frequencies which call for a different set of equations for the fitting vector.

The alternative form is for when the frequency is really close to a bin.

• DFT Bin Value Formulas for Pure Real Tones
• An Alternative Form of the Pure Real Tone DFT Bin Value Formula

There are other tricks to do it point by point. I'll let others provide those.