Amprobe DM-111S Current-Data-Logger User Manual
Page 57
DMIIIS
EN - 55
16.3. POWER AND POWER FACTOR: DEFINITIONS
In a standard electric installation powered by three sine voltages the following is defined:
Phase Active Power:
(n=1,2,3)
)
cos(
n
n
n
n
I
V
P
Phase Apparent Power:
(n=1,2,3)
n
n
n
I
V
S
Phase Reactive Power:
(n=1,2,3)
2
2
n
n
n
P
S
Q
Phase Power Factor:
(n=1,2,3)
n
n
n
F
S
P
P
Total Active Power:
3
2
1
P
P
P
P
TOT
Total Reactive Power:
3
2
1
Q
Q
Q
Q
TOT
Total Apparent Power:
2
2
TOT
TOT
TOT
Q
P
S
Total Power Factor:
TOT
TOT
TOT
F
S
P
P
where:
V
n
=
RMS value of voltage between phase n and Neutral.
I
n
=
RMS value of n phase current.
f
n
=
Phase displacement angle between voltage and current of n phase.
In presence of distorted voltages and currents the previous relations vary as follows:
Phase Active Power:
(n=1,2,3)
)
(
I
V
P
n
k
n
k
n
k
k
n
cos
0
Phase Apparent Power:
(n=1,2,3)
n
nN
n
I
V
S
Phase Reactive Power:
(n=1,2,3)
2
2
n
n
n
P
S
Q
Phase Power Factor:
(n=1,2,3)
n
n
n
F
S
P
P
Distorted Power Factor:
(n=1,2,3)
dPF
n
=cosf
1n
=
phase displacement
between the
fundamentals of
voltage and current of n
phase
Total Active Power:
3
2
1
P
P
P
P
TOT
Total Reactive Power:
3
2
1
Q
Q
Q
Q
TOT
Total Apparent Power:
2
2
TOT
TOT
TOT
Q
P
S
Total Power Factor:
TOT
TOT
TOT
F
S
P
P
where:
V
kn
=
RMS value of kth voltage harmonic between n phase and Neutral.
I
kn
=
RMS value of kth current harmonic of n phase.
f
kn
=
Phase displacement angle between kth voltage harmonic and kth current harmonic
of n phase.