where:
k
................... index of the order of each harmonic
N
.................. highest harmonic (63)
U
1
,k
,
I
1
,k
....... k-th harmonic of voltage and current (1
st
phase)
∆
ϕ
1
,k
............ angle between
U
1
,k
,
I
1
,k
(1
st
phase)
Apparent and Distortion power (per phase, three phase):
S
1
=
U
1
×
I
1
,
3
S
=
S
1
+
S
2
+
S
3
D
1
=
q
S
2
1
−
P
2
1
−
Q
2
1
,
3
D
=
p
3
S
2
−
3
P
2
−
3
Q
2
Power factor (per phase, three phase):
P F
1
=
|
P
1
|
S
1
,
3
P F
=
|
3
P
|
3
S
3.3
Harmonic distortion of voltages and currents
is continuously evaluated by FFT up to 63rd harmonic. The calculation is performed by using a rectangular
window of each measurement cycle. Following parameters are evaluated from the harmonic analysis:
Fundamental (1
st
) harmonic of voltage and current:
U f h
1
, If h
1
The absolute angle of the fundamental harmonic voltage and current phasors:
ϕU
1
, ϕI
1
The angle between the corresponding phasors of the fundamental harmonic components of voltage and
current:
4
ϕ
1
The angle between a voltage and the corresponding current phasors of the i-th order:
4
ϕ
i
Total harmonic distortion of voltage and current (as defined in 61000-4-30):
T HDU
=
q
P
40
i
=2
U h
2
i
U h
1
×
100
, T HD R
U
=
pP
max
i
=2
U h
2
i
U
×
100 [%]
T HDI
=
q
P
40
i
=2
Ih
2
i
Ih
1
×
100
, T HD R
I
=
pP
max
i
=2
Ih
2
i
I
×
100 [%]
28