I'd like to revisit this topic, last discussed over a year ago in this thread:

If you've got a relatively long integration period (say 10 seconds), and a really nasty looking current signal, should tan-1(reactive/real) always come out pretty close to real/(Vrms*Irms), or does reactive energy get "lost" as discussed in that previous thread?

When I've got a nice clean current signal (leading or lagging), the power triangle as described above works fine, but the minute I start feeding it a really nasty load (like pictured below), my reactive energy readings come out way smaller than expected. For the signal pictured for instance, my calibrated readings come out at:

Vrms = 254V

Irms = 1.029A

RealPower = 217W

ReactPower = -10.3VARS

so the power triangle is kinda' broken.

What is the algorithm used for calculating ReactEnergy? I thought the device simply delayed one signal by 90 degrees and re-calculated the sigma(V*I). And yet when I apply that algorithm in my spreadsheet, with the data in the picture, I get a ReactPower of about 39.4VARS which works out much closer to what the power triangle would suggest. So it seems the device has some other algorithm for calculating reactive energy.

Hi hmani,

Actually, my spreadsheet multiplied the 7 current harmonics by the fundamental voltage, which I agree is not what the IEEE definition of Reactive Power calls for. Your latest question prompted me to research and consult further, and I think I finally understand what's going on.

To recap my concern, PF as calculated correctly with RealPower, Vrms and Irms was much lower than PF calculated by completing the triangle with RealPower and ReactivePower. In other words, I was seeing a lot more current in the circuit than could be accounted for with RealPower and ReactivePower. Or mathematically:

RealPower / (Vrms * Irms) was coming out much much smaller than cos(tan-1(ReactPower/RealPower)).

If we go back to the IEEE definition of ReactivePower:

and then consider that in most environments (and certainly in my environment here where the above signal was captured) a very stiff voltage supply ensures that there are effectively no harmonics in V. In such an environment where V is a pure sine wave, all the terms in the above sum (except for the first) disappear because Vn is 0 when n > 1. In which case the formula degrades to just the fundamental case:

ReactPower = Vf * If * sin(phi)

I believe that is why ReactPower comes out lower than I originally expected. It's not that leading and lagging terms are cancelling each other out, but rather all the harmonic terms are dropped because there is no V at that frequency to keep them included in the calculation. They are effectively filtered out by the purity of the voltage signal. The "missing" current is all in the harmonics, and doesn't get included because there's no matching harmonic in V.