U
SER MANUAL
–
ENERIUM
100/200/300
MS1-7352 ENERIUM100/200/300_ Ed04 User Manual
Page 77 / 86
22.9 Power factor
The monitors measure power factors (PF) "averaged over a second" on each of the three phases
PF
1
[1s], PF
2
[1s] and PF
3
[1s], as well as the three-phase power factor "averaged over a second" PF
[1s].
The measurements are derived from other measurements, according to the following formula:
•
]
1
[
]
1
[
]
1
[
s
S
s
P
s
PF
L
L
L
=
L = 1, 2, 3 or nothing for the three-phase quantity
Each of these quantities is associated with a quadrant. If P
x
[1s] and Q
x
[1s] (x = 1, 2, 3, or nothing for
the three-phase quantity) have the same sign, then the quadrant is inductive, otherwise it is capacitive.
22.10 Cos(
φ
)
The monitors measure cos(
ϕ
) "averaged over a second" on each phase cos(
ϕ
1
)[1s], cos(
ϕ
2
)[1s],
cos(
ϕ
3
)[1s], as well as the overall cos(
ϕ
) "averaged over a second", called cos(
ϕ
g
)[1s].
cos(
ϕ
) is calculated from the following formula:
•
∑
×
=
5
1
]
10
)[
cos(
5
1
]
1
)[
cos(
T
s
L
L
ϕ
ϕ
For F = 50Hz, L = 1, 2, 3
•
∑
×
=
5
1
]
12
)[
cos(
5
1
]
1
)[
cos(
T
s
L
L
ϕ
ϕ
For F = 60Hz, L = 1, 2, 3
And:
•
3
]
1
)[
cos(
]
1
)[
cos(
]
1
)[
cos(
]
1
)[
cos(
3
2
1
s
s
s
s
global
ϕ
ϕ
ϕ
ϕ
+
+
=
•
With:
])
10
[
_
_
]
10
[
_
_
cos(
]
10
)[
cos(
T
l
Fundamenta
I
Angle
T
l
Fundamenta
V
Angle
T
L
L
L
−
=
ϕ
•
And:
])
12
[
_
_
]
12
[
_
_
cos(
]
12
)[
cos(
T
l
Fundamenta
I
Angle
T
l
Fundamenta
V
Angle
T
L
L
L
−
=
ϕ
A quadrant is associated with each of these quantities.
•
If the angle is between 0° and 90° or between 180° and 270°, then the quadrant is inductive.
•
If the angle is between 90° and 180° or between 27 0° and 360°, then the quadrant is capacitive.
22.11 Peak factor
Measurements are derived from “10 averaged over period" real power measurements for a system set
at 50 Hz and "12 period" real power measurements for a system set at 60 Hz. The formulae are:
22.11.1 For voltages
∑
×
=
5
1
]
10
[
5
1
]
1
[
T
FC
s
FC
VL
VL
For F = 50Hz OR
∑
×
=
5
1
]
12
[
5
1
]
1
[
T
FC
s
FC
VL
VL
For F = 60Hz
With:
]
10
[
]
10
[
]
10
[
T
V
T
Vpeak
T
FC
VL
=
And:
]
12
[
]
12
[
]
12
[
T
V
T
Vpeak
T
FC
VL
=
With:
∑
×
=
1280
1
2
1280
1
]
10
[
L
v
T
V
And:
∑
×
=
1536
1
2
1536
1
]
12
[
L
v
T
V
•
With:
)]
(
max[
]
10
[
L
v
abs
T
Vpeak
=
•
And:
)]
(
max[
]
12
[
L
v
abs
T
Vpeak
=
•
L = 1, 2, 3
