User's Manual

Fluke 434-II/435-II/437-II
Users Manual
A-4
W - Active Power (P)
The active power (all frequency components) is directly calculated from the samples
measured on the voltage and current inputs:
Active phase power:
() ()
∑
+
=
⋅=
NK
Kn
XXX
ninu
N
1
P
Active system power Υ: P
Y
= P
A
+ P
B
+ P
C
System power is the sum of the phase powers!
Active system power Δ:
() () () ()
∑
+
=
Δ
⋅−⋅=
NK
Kn
CBCAAB
ninuninu
N
1
P
W fund - Fundamental Active Power(P1)
The fundamental powers (50/60 Hz component only) are calculated using he FFT results
which are calculated according to IEC 61000-4-7 grouping into the first harmonic
subgroup. These rms values are here called U
1X
for voltage and I
1X
for current. The phase-
angle between voltage and current is ϕu
1x
- ϕi
1x
.
Fundamental active phase power:
(
)
X1X1X1X1X1
iucosIUP
ϕ
−
ϕ
⋅
⋅
=
Fundamental active system powerΥ:
(
)
+++++
ϕ−ϕ⋅⋅=
11111
iucosIU3P
In this case the system power is NOT the sum of the phase powers! The system power is
calculated from the positive sequence components of voltage and current, eliminating all
unbalance components. This component is also called Effective power as it is the most
effective way to transfer power (electrical into mechanical) if it would only consist of the
positive sequence power component.
Fundamental active system powerΔ:
(
)
()
C1BC1C1BC1
A1AB1A1AB11
iucosIU
iucosIUP
ϕ−ϕ⋅⋅−
ϕ
−
ϕ
⋅
⋅
=
Δ
VA – Apparent Power (S)
The apparent power (all frequency components) is calculated from the rms values of
voltage U
X
and current I
X
.
Apparent phase power:
XXX
IUS
⋅
=
Apparent system power Υ:
(
)
(
)
2
C
2
B
2
A
2
C
2
B
2
AY
IIIUUUS ++⋅++=
Apparent system power is NOT the sum of the phase powers!
Apparent system power Δ:
(
)
(
)
3/IIIUUUS
2
C
2
B
2
A
2
CA
2
BC
2
AB
++⋅++=
Δ