Arbiter Systems Portable Power Sentinel 933A, Руководство по эксплуатации

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absolute phase. This is because the subtraction is actually one of time;
the purpose being to ’realign’ the reference point to correspond to zero
degrees on the fundamental. The phase angle corresponding to this time
shift is proportional to the frequency.
9.14 Harmonics
Harmonics are measured using overlapping Hanning window FFT’s of 1024
samples and 100 ms window length. Based on the instantaneous frequency,
the location of the bins containing significant energy for each harmonic are
determined. This is a total of three bins, one approximately centered on
the harmonic and those two adjacent to it. Then, the energy in those three
bins is totaled, resulting in the energy for that harmonic. This can then
easily be expressed as a percentage of the rms signal level, or in whatever
form is required. While there is a closed-form correction, which can be
employed to find the harmonic magnitude in the presence of frequency
errors, this approximation was chosen because it is much faster and gives
adequate performance.
There is an error in this approximation, due to the fact that there will
be a small amount of energy leakage into nearby bins, which will not be
included in the three measured bins. This is generally of little consequence
when the frequency is close to being accurate (which is most of the time),
since the amount of energy outside of the three bins summed is so low.
Finally, with the Hanning window, there is no signal at all outside of
these three bins if the frequency is exact. In the real world, however, the
frequency will be off somewhat, and it is reasonable to ask how large the
error can be. For small frequency errors, say 0.01 Hz, the 50th harmonic
will be 0.5 Hz from the center of the nominal bin. This results in an
error of about 0.005%, which is insignificant. The worst-case error will
occur when a harmonic is very nearly centered between two bins. In this
case, the algorithm described above will ’miss’ a bin containing a signal
with amplitude of about 17% of the actual harmonic amplitude.
The
energy contained in this bin is then (0.17)
2
or about 2.9% of the total
energy, resulting in a measured energy 0.971x what it should be. The
measured harmonic amplitude will then be (0.971)0.5 or about -1.5% in
error.
This is well within the specification limits (5%) of IEC 61000-
4-7. This worst-case error would occur for the 50th harmonic with a
fundamental frequency error of 0.1 Hz. At lower harmonics, the frequency
error must be progressively greater; for example, to result in a -1.5% error
in measuring the 9th harmonic would require a fundamental frequency
offset of 0.556 Hz. The phase angle of the harmonics is determined by
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