Measuring AC parameters digitally - Basics 1

[atferrari]

AC voltage applied to a non linear load. Using a DSP processor, I digitize the resulting voltage and current along several periods (100 samples per period) and detect zero crossings, so I can calculate:

a) Vrms, by squaring each sample, summing all of them, taking its average and finally taking the square root of thatt average.

b) Irms, following same procedure as above.

c) Vrms times Irms = ???

d) Independent of the above, I multiply each sampled voltage - current pair. ( V*I) , add them succesively and find the average dividing by the number of pair of samples taken.

e) Measuring the time difference between both zero crossings I calculate how many electrical degrees the phase difference is. I asume> 1 full cycle = 360º.
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With the power diagram (or power triangle) in mind, composed by the three vectors: real power, apparent power and reactive power, my questions:

1 - The value obtained in c), is it real power or apparent power?

2 - The value obtained in d) is the average power which may be correlated to what vector in the triangle?

3 - What approach is better to get cos fi?: taking the cosine of the value obtained in e) or dividing somehow the values c) / d)?, or d) / c)?

As you can see I need help in basics of something that is far from my knowledge.

Please try to reply following the order of my questions. I will really appreciate that.

Please keep in mind we are talking non-linear voltages/currents.

I have been reading largely on this subject. The Google stage was exhausted already.

Sorry for the long posting. Gracias for any help.

Agustín Tomás

 

[electricpete]

Let's use single-phase for simplicity.

Is the voltage sinusoidal? If so there is a good simplification possible:

Vrms * Irms = Apparent Power
Apparent Power = Real Power * Displacement Power Factor * Distortion Power Factor

Distortion Power Factor = Ifundamental/Irms

Displacement power factor = cos(theta) where theta is angle between Ifundamental and V.

If voltage is sinusoidal than you need a more general approach. Average power is <p(t)>

"1 - The value obtained in c), is it real power or apparent power?" - Definitely not real. Possibly apparent.

"2 - The value obtained in d) is the average power which may be correlated to what vector in the triangle?" If we accept the assumption voltage is sinusoidal, then you have a triangle where the horizontal component is real power, the vertical component is imaginary power, and the hypoteneuse is real power / displacementPowerFactor which is not quite apparent power in this general case where harmonics are allowed.

"3 - What approach is better to get cos fi?:" I assume your fi (phi?) is the same as my theta. If you want to calculate it, then you need to take a fourier transform of your current to isolate the fundamental component.

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[electricpete]

Correction:
"If voltage is NOT sinusoidal than you need a more general approach. Average power is <p(t)>"

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[electricpete]

Also I should point out that Ifundamental is expressed on an rms basis as well. Irms refers to the total voltage waveform which also includes harmonics.

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[jghrist]

What do you mean by "non-linear voltages/currents"? Pure sinusoidal voltages and currents are non-linear. Do you mean non-linear loads with a sinusoidal source? The voltage measured may not be sinusoidal because it will be distorted by harmonic currents flowing through the source impedance. Your calculation of phase angle in (e) will not work with distorted currents; there may even be multiple zero crossings per cycle.

A better approach would be to use a discrete fast fourier transform to obtain the fundamental and harmonic components of the voltage and current. Then as ElectricPete pointed out, the displacement power factor can be determined by the fundamental components. The distortion power factor can then be determined by ElectricPete's relation between apparent power, real power, displacement power factor and distortion power factor.

c) Vrms times Irms = apparent power (VA)

 

[itsmoked]

Instantaneous voltage times the simultaneous instantaneous current is the real power.

Does your system take simultaneous readings?

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[ScottyUK]

If you take a look at section 7.5 of the Voltech PM6000 manual there is a good summary table of the mathematical equations used for the various calculations. It might help clear up some of the uncertainty.

100 samples per period (mains cycle?) instinctively feels too low a sampling rate to accurately digitise the higher harmonics. Can you speed it up if necessary?

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I don't suffer from insanity. I enjoy it...

 

[itsmoked]

Hi Scotty. The OP has never said what he's doing so low resolution may be fine...??

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[jghrist]

100 samples per mains cycle is sufficient to measure harmonics to the 50th order.

 

[ScottyUK]

At the theoretical Nyquist limit, yes that's true. To reconstruct the waveform with any degree of confidence, particularly on a heavily distorted wave, you don't want to be anywhere near the Nyquist limit. I would have major reservations about using data from an instrument operating at the absolute end of its tether. It's not a particularly challenging spec to sample at 1000 samples per cycle in these days of fast D/A's and DSPs with hundreds of time more horsepower than my first three computers combined. It would be entirely practical to build one using VXI-based parts from National Instruments, for example.

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I don't suffer from insanity. I enjoy it...

 

[atferrari]

Thanks to you all!!

Just to reply some of the questions:

a - Yes, I expect voltage essentially sinusoidal. Non-liner is the load. Sorry for the confusion.

b - Yes, I can increase a lot the number of samples/sec.

c - Readings are not simultaneous but consecutives and one of the parameters, V (or I for the case) would be the average of both (before/after). Have read that is a reasonable alternative.

After reading so many answers and the formulas used to calculate the parameters of interest (Voltech manual) I have now a much more clear idea about this. But, been honest I should devote more time and effort to understand all what's related with harmonics and its consequences.

I am happy of having asked in this forum. GRACIAS!

Agustín Tomás