HT instruments VEGA78 User Manual
Page 120
VEGA78
EN - 118
10.4. POWER AND POWER FACTOR: DEFINITIONS
In a standard electrical installation powered by three sine voltages the following are to be
defined:
Phase Active Power:
(n=1,2,3)
)
cos(
n
n
nN
actn
I
V
P
Phase Apparent Power:
(n=1,2,3)
n
nN
appn
I
V
P
Phase Reactive Power:
(n=1,2,3)
2
2
actn
appn
reactn
P
P
P
Phase Power Factor:
(n=1,2,3)
appn
actn
n
F
P
P
P
Total Active Power:
3
2
1
act
act
act
act
P
P
P
P
Total Reactive Power:
3
2
1
react
react
react
react
P
P
P
P
Total Apparent Power:
2
2
react
act
app
P
P
P
Total Power Factor:
app
act
F
P
P
P
where:
V
nN
=
RMS value of voltage between phase n and Neutral.
I
n
=
RMS value of n phase current.
f
n
=
Phase angle between voltage and current of n phase.
In the 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
actn
cos
0
Phase Apparent Power:
(n=1,2,3)
n
nN
appn
I
V
P
Phase Reactive Power:
(n=1,2,3)
2
2
actn
appn
reactn
P
P
P
Phase Power Factor:
(n=1,2,3)
appn
actn
n
F
P
P
P
Distorted Power Factor
(n=1,2,3)
dPF
n
=cos
f
1n
=
phase displacement between the
fundamentals of voltage and
current of n phase
Total Active Power:
3
2
1
act
act
act
act
P
P
P
P
Total Reactive Power:
3
2
1
react
react
react
react
P
P
P
P
Total Apparent Power:
2
2
react
act
app
P
P
P
Total Power Factor:
app
act
F
P
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.