Relationship between power angle and real and apparent in ECO dataset
Hi, my question is mostly about the mathematical relation between
  power angle, apparent power and real power, I believe the kind of
  device is irrelevant


Real devices and loads can take highly non-sinusoidal currents and hence phase angle measurements are irrelevant. The power triangle of apparent, real and reactive powers as shown below is irrelevant when the load is non-linear.

 

The power triangle above assumes that loads are linear. A typical appliance current might look like this: -



How would you measure or determine a meaningful phase angle from the current waveform above?