Calculating active and reactive component of power signal

[iggyboy]

We start with a sinwave for voltage:

U(t)=sin(ωt).

Then we have current flowing, which looks like:

I(t)= A*sin(ωt-φa) + B*sin(3ωt-φb) + C*sin(5ωt-φc) + D*sin(7ωt-φd) + ...

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.

Regards,

iggyboy

 

[tzushky]

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


cos(-φa) is the power factor.

Hope it helps
Bye