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