Definition of Reactive Power 2

[SSLA]

The IEEE Standard 1459-2000, section 3.1.1.3 defines reactive power as the contour integral of v*di divided by 2*PI. Does anyone know the origins of this definition?

 

[cuky2000]

...Does anyone know the origins of this definition?

Reactive power (Q) is usually calculated using RMS value from the conventional power triangle relationship.

Q=SQRT(S²-P²) or Q= S.Sin[cos^-1(PF)]

This relation may contain significant error in unbalance or waveforms other than perfect sinusoidal conditions.

The formula proposed in the IEEE Std 1459 is intended for not only perfect sinusoidal waves, but also to distorted sinusoidal and non-sinusoidal waves in balance or unbalance conditions.

This definition provide a challenger benchmark for manufacturers of new digital revenue meters and monitoring devices to measuring reactive power (Q) and total power (S) with better accuracy than conventional methods.

 

[electricpete]

The countour integral applies to a complex function. If we are considering non-sinusoidal waveforms, we cannot consider v a vector. So I don't understand mathematically what that expression represents.

One sanity check though. Using the chain rule:
integral v di /(2Pi) = integral v(t) * (di/dt) dt / (2Pi)

If we looked at the pure sinusoidal case, di/dt will be 90 degrees ahead of i(t). If v(t) and i(t) were in phase, then v(t) and di/dt will be 90 degrees out of phase and integral over one cycle will be zero as expected.

If v(t) led i(t) by 90 degrees such as inductive power, then then v(t) and di/dt will be in-phase and the integral over one cycle would be positive.

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[stevenal]

Note that this standard is a "trial use" standard and does not have ANSI approval. The approved ANSI standard for revenue meters is C12.1 from NEMA. This standard uses a sum the harmonics approach. Even with a wider definition, the tests described in the standard are all at or very near the fundamental with no harmonics.

There is a bibliography in 1459. Sorry I cannot narrow it down.