How calculate three phase kilowatt hour from time sampled data [closed]

Question

My problem is I want to calculate three phase power from time sampled data of current and voltages.

My questions:

1. How can I calculate the energy (unit kilowatt hour) from time sampled data? Are any equations available?

2. Is it needed to take the phase shift in account? (How can I calculate the phase shift? How do I link this to calculating the three phase power?)

3. Is some better platform is available for solving my question?

I get the instantaneous sample value (not continuous). (I have some sensors that gives the current and voltage - I convert this to digital for processing). Around 50 samples are got per second. (Is it to be zero when we some up all the power of three phase - due to phase shift of 120?) How can I calculate total three phase energy from these sampled values? I am processing my data in Arduino.

(I don't know this is the place to ask my question (if I can get a better help from some where else please suggest me).)

Answer 1

Numerical calculus to the rescue.

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If you have several samples of voltage and current, then you also have that many samples of momentary power: P(t) = U(t) * I(t).

Now you have power and you have time, you can integrate the power with respect to time. A simple numeric approach is the trapezoidal rule. This question is tagged "Arduino" and I know C reasonably well so here's some pseudo-C that illustrates the technique:

int n_samples = 1000; // or however many samples you have
double integral = 0.0;
for (int i = 0; i < n_samples - 1; i++) {
    integral += (samples[i] + samples[i + 1]) / 2;
}

integral *= (t_max - t_min) / n;

Where t_min and t_max are the beginning and ending time of the sampling, respectively, n_samples is the number of samples you got, samples is an array (presumably of double or so) that contains the calculated momentary power values. integral will hold the result.