User Manual
88
The angle with respect to the fundamental in degrees [°] ⇔
4
arctan
ϕϕ
−
=
k
k
k
b
a
with
=
+⋅=
+⋅=
+=+=
∑
∑
∑
=
=
=
1024
0
0
1024
0
1024
0
22
1024
1
512
cos
512
1
512
sin
512
1
s
s
s
ksk
s
ksk
kkkkk
Fc
s
k
Fa
s
k
Fb
bajabc
ϕ
π
ϕ
π
c
k
is the amplitude of the component of order
4
k
m =
with a frequency
4
4
f
k
f
k
=
.
F
s
is the sampled signal at the fundamental frequency
4
f
.
c
o
is the DC component.
k is the index of the spectral spike (the order of the harmonic component is
4
k
m = ).
Note: The power harmonic factors are calculated by multiplying the phase-to-neutral voltage harmonic factors by the current
harmonic factors. The power harmonic angles (VAharm[i][j] and VAph[i][j]) are calculated by differentiating the phase-to-
neutral voltage harmonic angles with the current harmonic angles. In the case of a 2-wire two-phase distribution source,
the phase-to-neutral voltage V1 is replaced by the phase-to-phase voltage U1 and one obtains the harmonic power levels
UAharm[0][j] and the harmonic power angles UAph[0][j].
16.1.3.2. Harmonic distortions
Two global values giving the relative quantity of the harmonic are calculated:
the THD as a proportion of the fundamental (also noted THD-F),
the THD as a proportion of the total RMS-AC value (also noted THD-R) (for the C.A 8333 only).
Total harmonic distortion of phase (i+1) with i ∈ [0; 2] (THD-F)
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1
iAthdf ,
1
i Uthdf,
1
iVthdf
50
2
2
50
2
2
50
2
2
iAharm
niAharm
iUharm
niUharm
iVharm
niVharm
nnn
∑∑∑
===
===
Total harmonic distortion of channel (i+1) with i ∈ [0; 2] (THD-R) (for the C.A 8333 only).
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∑
∑
∑
∑
∑
∑
=
=
=
=
=
=
===
50
1
2
50
2
2
50
1
2
50
2
2
50
1
2
50
2
2
iAthdr , i Uthdr, iVthdr
n
n
n
n
n
n
niAharm
niAharm
niUharm
niUharm
niVharm
niVharm
The THD as a proportion of the RMS-AC value (THD-R) is also called the distortion factor (DF).
50
50
50
50
50
50
50
50
50