What I want to do, is calculate the active power (P) and the reactive power (Q) or something proportional to those. This is to be done with a DSP mcu, btw.
I have been running figures in Excel, and I am getting confused.
Only the product of the terms having the same frequency have an average non-zero value. The active power is then:
P = 1/sqrt(2) * A/sqrt(2) *cos(-φa)
Only the first harmonic (the fundamental) transpoorts the active power.
Then, you have the reactive power which is similar:
Q=A/2 * sin(- φa);
The rest of the harmonics would only be of interest if you need the Total Harmonic Distortion (THD) Ratio . That one I don't always remenber well so I refer you to this: https://en.wikipedia.org/wiki/Total_harmonic_distortion