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217

Dran-View 6 User Guide

19.1.9. Harmonic Watts

In a non-sinusoidal system it turns out that dissimilar voltage and current harmonics

do not interact to generate useable power. You can readily convince yourself of this

by graphically sketching the power curve resulting from a fundamental voltage

signal and a second harmonic of current. The power curve results from a point by

point multiplication of the two signals. The average power results from dividing the

area under the curve by the total time. You will be able to see that the average

power over one cycle of the fundamental and two cycles of the second harmonic

will average to zero (by symmetry you will see the positive lobes will cancel the

negative lobes). The result of this little mathematical bonus is that only harmonics

of the same order interact to generate power. This means that in the frequency

domain the average active power dissipation over one cycle of the fundamental in a

system rich in harmonics may be computed by summating the individual “harmonic

watts dissipations”.

Mathematically this is:

Average

= V

Where

RMS

Is rms voltage at the Jth harmonic

RMS

Is the rms current at the Jth harmonic

Is the difference between the phase angles Φ, of the voltage and current at the Jth

harmonic. (θ

= Φvoltage

- Φcurrent

). See previous discussion on how to compute

θ.

Is the power dissipation due to the dc components V

. It can usually be

ignored.

Caveats Harmonic watts may have dubious meaning if “Normalize to Own Fundamental” is

selected. Although Dran-View always gives the correct value, hand calculations

may be erroneous. Generally, the phase angles for the amperage harmonics are not

phase corrected for the lead/lag introduced by the probes. If this value proves to be

a significant proportion of the total phase difference between the volts and amps

signals then a significant error will be introduced. The phase accuracy decreases

significantly as a function of increasing harmonic frequency therefore the greater

the harmonic content the more error you are likely to see in the harmonic watts

calculations. It is possible for the phasors and the fundamental angles to disagree if

cosine expansion is chosen or if the phasors and DFT Chart and Text Label

normalization configuration disagree ("Always use Sine Expansion" is selected for

the Phasors).

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