VEGA74
EN - 43
12.4. DEFINITIONS OF POWERS AND POWER FACTORS
In a standard electrical installation powered by three sine voltages the following are to be
defined:
Phase Active Power:
(n=1,2,3)
)
cos(
I
V
P
n
n
nN
n
=
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
=
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
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
