Power Quality Analyzer Model 3945-B
95
Calculation of Harmonic Bins
Harmonic bins are calculated by FFT with 16 bit resolution (1024 samples on
4 cycles) without windowing (IEC 1000-4-7). From real and imaginary compo
-
nents, each bin ratio is calculated on each phase Vharm[3][51], Uharm[3][51]
and Aharm[3][51] in proportion to the fundamental value and the phase angles
Vph[3][51], Uph[3][51] and Aph[3][51] between each bin and the fundamental.
This calculation is accomplished using the following principle:
cos
sin
=
+
×
=
+
×
=
+
=
+
=
∑
∑
∑
=
=
=
1024
0
0
1024
0
1024
0
2
2
1024
1
512
512
1
512
512
1
s
s
s
k
s
k
s
k
s
k
k
k
k
k
k
F
c
s
k
F
a
s
k
F
b
b
a
ja
b
c
ϕ
π
ϕ
π
100
mod
1
×
=
c
c
k
k
=
k
k
k
b
a
arctan
ϕ
module in %:
with
angle in degree:
ck: amplitude of the component with a frequency of
1
4
f
k
f
k
=
Fs: sampled signal
co: DC component
k: ordinal number (spectral bin)
Multiplying the voltage harmonic factor with the current harmonics factor gives the
power harmonic factor. Differentiating voltage harmonic phase angle with current
harmonic phase angle gives power harmonic phase angle.
VAharm[3][51] , VAph[3][51]
Distortion Factor Calculation (DF)
Two global values giving the relative quantity of harmonics are computed: the THD
in proportion to the fundamental and the DF in proportion to the RMS value.
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[]
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[]
[]
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[]
i
Arms
n
i
Aharm
i
Urms
n
i
Uharm
i
Vrms
n
i
Vharm
n
n
n
∑
∑
∑
=
=
=
=
=
=
50
2
2
50
2
2
50
2
2
2
1
i
Adf
,
2
1
i
Udf
,
2
1
i
Vdf