Explanation of phases of fridge cycle from power draw (power factor, reactive and active power)

It looks fairly straight-forward.

• We can see that there are three main modes in the chart: standby (low power), motor start and motor run.
• My guess is that in standby there is an air distribution fan running constantly, hence the standby power.
• The graph is showing a negative power consumption (yellow trace) in standby which, if true, means that it is generating power and feeding it back to the grid! This leads me to believe that there is a calibration or zero-offset error in your measurment setup. We would expect the fan power to be only a few watts however so the general position of the trace is correct.
• The reactive power is higher than the true power throughout the cycle so we can deduce that the fridge has a poor power-factor. This is confirmed by the power-factor trace. If we do a calculation for the running state we get 100 W + 133 VAr. Using the Omni Calculator we find that the calculated power factor is 0.601 which lines up nicely with the green trace on your chart. There isn't much point in trying to do a similar calculation for the standby condition as we suspect the readings have an offset.
• The motor start has an initial peak, a dip and then a rapid increase to the steady-state condition. The initial peak is just the motor start current which is always high due to the lack of back-EMF from the stationary / low speed motor. As it speeds up the current drawn decreases. It appears that the load switches after a minute and increases by a factor > 2. This suggests that the compressor is suddenly being loaded - either by a valve opening or something happening in the refrigerant to suddenly increase the back-pressure on the compressor, hence increasing its power demand.

The poor power-factor is tolerated by the power companies on domestic connections as it is typically only a small part of the overall load. In industrial connections it may cause problems for the utility company so they monitor reactive power and bill accordingly to incentivise power-factor correction at the user's premesis.

From the comments:

Why the power slightly goes down when the compressor is on? (I mean, look at the arc-shaped curve during the compressor cycle).

It must mean that it's getting easier to pump the fluid. That's a question for the mechanical guys, I suspect.

Why does the power factor spike to 1 exactly at the beginning?

It may represent that the motor is acting as a resistor at startup and it's inductance is playing a less significant role. It's a transient so it may not be all that accurate. I'd also check how much "headroom" the measurement system has: what is the peak current handling capability? how many samples per second can it handle?

The compr PF is only due to the charac of the compressor or there is more to it?

It will be determined by the characteristics of the motor. How do we know? Because the PF can be brought back to unity (1) by the addition of power-factor correction capacitors in parallel with the motor without affecting the operation of the motor itself (or its load).

Why during that compr phase the PF seems to be actively maintained to that value? Is it really like that?

It looks like the ratio of W:VAr is being maintained throughout the cycle. (Both curves have similar arcs). Therefore the PF is steady.

I've measured the idle power and it is 2W, 9VA, PF 0.180. Does it say something on the power supply? Why this low?

It doesn't say anything about the power supply - only the load. We can expect that the unloaded motor will run close to synchronous speed and back EMF will be at a maximum. Therefore the resistive losses will be low and the motor's inductance becomes more significant and the power-factor decreases as a result.