Siemens SICAM P 7KG7750 - Formulas and Calculation of Derived Quantities

3
3.2 Formulas and Calculation of Derived Quantities
44 Power Meter SICAM P 7KG7750/55, Manual
E50417-B1076-C340-A6, Edition 09.2013
3.2 Formulas and Calculation of Derived Quantities
3.2.1 Calculation of Derived Quantities
Line Derived Quantity Formula Note
1 RMS value voltage,
distorted waveform included
∑
=
=
64
1
2
64
1
ν
ν
uV
2 RMS value voltage,
fundamental component U
1
only
2
22
1
ba
V
+
=
From the Fourier coefficients a
and b of the fundamental
component
3 RMS value current,
distorted waveform included
∑
=
=
64
1
2
64
1
ν
ν
iI
4 RMS value voltage,
fundamental component I
1
only
2
22
1
ba
I
+
=
From the Fourier coefficients a
and b of the fundamental
component
5 Active power P
Std
∑
=
=
64
1
64
1
ν
νν
ivP
From sample values
6 Active power P
Four
1111
IbVbIaVaP +=
From the Fourier coefficients
of the fundamental component
7 Active power P
DIN
)(
21
1
nn
n
nn
IbVbIaVaP +=
∑
=
From the Fourier coefficients
of the fundamental component
and from the harmonics.
8 Reactive power Q
Std
∑
=
−
⋅=
64
1
2
1
64
1
ν
π
νν
j
eivQ
Standard up to now, additional
fault for distortions
1
9 Reactive power Q
Four
1111
IaVbIbVaQ +=
10 Reactive power Q
DIN
)(
21
1
nn
n
nntot
IaVbIbVaQ +=
∑
=
From the Fourier coefficients
of the fundamental component
11 Apparent power S
Std
332211
IVIVIVS
NNN
⋅+⋅+⋅=
From the RMS values
according to line 1 and 3
12 Apparent power S
Four
2
3
2
2
2
1
2
3
2
2
2
1
IIIVVVS
NNN
++⋅++=
From the RMS values
according to line 1 and 3
13 Apparent power S
DIN
2
3
2
2
2
1
2
3
2
2
2
1
IIIVVVS
NNN
++⋅++=
From the RMS values
according to line 2 and 4
14 Power factor
S
P
=
ϕ cos
or
DIN
S
P
1
No sign!
15 Power factor DIN
DIN
S
P
=
ϕ cos
No sign!
16
Power factor cos ϕ
1
1
cos
S
P
= ϕ
Four quadrants according to
note 4
17 Phase Angle
1
1
arctan
P
Q
= ϕ
From the fundamental
component only!
1
According to classic measuring devices (electrodynamic power meter)