LEM NORMA 5000 - Fundamental and Harmonics; Frequency Analysis; Uncertainty of Measurement

Formulas
66 Power Analyzer NORMA 4000, NORMA 5000
EO1111G REV G
∫
⋅= dtiuW )(
∫
−=
T
tytxrms
dtUU
T
U
0
)()(12
)²(
1
2
)
1107,1
(5,05,0
⋅
⋅+
=
rm
rms
cx
U
U
P
P
x = 1...6
10.3 Fundamental and harmonics
rms
Hrms
HnHH
HnHH
hc
U
UU
UUU
UUU
kU
²
²)....²²(
)²....²²(
01
2
21
32
−
=
+++
+++
==
01
2
01
2
01
32
)²....²²(
H
Hrms
H
HnHH
thd
U
UU
U
UUU
U
−
=
+++
=
rms
H
fc
I
I
I
01
=
1²²
=
+
⇒ fck
10.4 Frequency analysis
∫
∞
⋅+⋅=
0
)]sin()()cos()([)( ωωωωω dtStCtF
)(
ω
C Amplitude of cosine wave
)(
ω
S
Amplitude of sine wave
The coherence with f(p) results in:
[] )()()( ωωπ jSCpf −×=
amplitude spectrum:
)²)()²(()( ωωω SCF +=
phase angular:
)(
)(
)(tan
ω
ω
ωϕ
S
C
=
10.5 Uncertainty of measurement
2
22
3
2
WIUP
MMMM ++×=
M
U
Uncertainty of measurement - voltage
M
I
Uncertainty of measurement - current
M
W
Uncertainty of measurement - angle
Active energy:
Voltage phase to
phase:
Power corrected:
Harmonic content
(according to DIN):
Harmonic
distortion
(according to IEC):
Fundamental
content:
Fourier
transformation:
Uncertainty of
measurement -
power: