There are many studies/papers in the field. A common definition for active power (in non-sinusoidal regime) is (acc. Budeanu) P= U0I0 +Sum(UkIkcos(phi)k and for reactive power  Q= Sum(UkIkcos(phi)k (k - harmonic rank). You can also consult the IEEE Std 1459 – 2000 for these definitions.

Try to create a block in Simulink (using maybe Powergui FFT Analysis).

Dear Mustafa

It doesn't matter whatever the wave shape is.The phase shift between voltage and current decides the active and reactive power. The components used decides the power factor like resultant inductance and capacitance of the circuit.Any vector can be resolved in to its Horizontal and Vertical components likewise the power supplied to the circuit is the vector  sum of its horizontal & vertical components of the load.

                          ps=VICOSθ+JVISINθ

Dear Mustafa,

there is a golden rule:

Only the fundamental frequency contributes to power generation.

Once you add an FFT and get the fundamental frequency's amplitude for both, current and voltage as well as the phase shift, a simple block that calculates Usin*Isin*cos(phi) will do the trick.

Cheers - Martin

There are many studies/papers in the field. A common definition for active power (in non-sinusoidal regime) is (acc. Budeanu) P= U0I0 +Sum(UkIkcos(phi)k and for reactive power  Q= Sum(UkIkcos(phi)k (k - harmonic rank). You can also consult the IEEE Std 1459 – 2000 for these definitions.

Try to create a block in Simulink (using maybe Powergui FFT Analysis).

Hi Mustafa,

• Split the voltage and current waveforms - each into harmonic series by Fourier Analysis. Make sure the base frequency is the same for both (preferably the fundamental frequency of the periodic waveforms).
• The golden rule is: Only voltage and current component-pairs of identical frequency contribute to the overall active and reactive power. 
• These work out to the expressions suggested by Marian in his reply. Please note that the U0I0 mentioned by him is nothing but the active power contribution by DC (that is, zero frequency components).

-Sanjay

Hi Mustafa,

you can multiply each voltage and current sample value to a power instantaneous sample value. Then sum each power instantaneous sample values over the cycle duration of the fundamental (or integer multiple of the fundamental cycle duration) and divide by the number of the samples -- this is the active power.

Mario

The active power in a system is the average power in a period of time. So, you can find the average value of the multiplication of the instantaneous voltage and current in a period. When you find the average power naturaly you will consider only the power generated by harmonics of the same frequency, like wrote Mr. Roy, due to the ortogonality of functions. You can find a good definition of power in a system with harmonics in: R. W. Erickson; D. Maksimovic. Fundamentals of Power Electronics. Page 589, Chapter 16. Springer, 2001. DOI: 10.1007/b100747.

dearest abdel

hopefully the pictures could help

Dear and halim

Your pic's speaks appropriately than many words.

dear mus and vasantha

i am soorry because of not to make a words

i also have an experience with children from their

birht until universy grading laveling

here may help

Thanks  All Colleagues for the encouraging suggestions.

Based on the answers, specially from Adriano and Mario,  I have the attached Figure of the Instantaneous Power (Multiplicastion of Voltage and Current) from SIMULINK simulation.

The average is show as 12.6 W.  can this average Simply be considered as the Active POWER?

Thanks 

Yes it is. But your Signal seems to be very complicated! Take care, very small time shift between voltage and current signal will distort your active power completely. Also calculation errors caused by resolution or rounding error can lead to false results.

regards Mario

More questions like an answer:

1) Does somebody try FFT in REAL power measurements to measure and calculate active power?

2) how many FFT bins (and bin frequency width) and what about FFT "windows"? Witch one from about 15? We look on non-sinusoidal and sometimes poorly periodical process.

3) what about 3rd, 5th.etc harmonics in power calculation?

4) what a difference between Σ(Asin(ωt[k])*Bsin(ωt[k])) and Σ((Ireal[k]*Ureal[k]) + (Iimg[k]*Uimg[k])) for k-harmonics?

4) I'm pretty sure (after many real life experiments and calculations) - Budeanu theory is just a theory without any value or meaning for practical results in non-sinusoidal power value calculation. From practical point - forget it. Simulink is great, Simulink can prove not so great theory...:)

Many points, many practical results, many suggestions etc. - will be shown on my near future publications.

Please see the attached file !