Amprobe Multitest-2000 Continuity-Tester - Manual (Page 168)

AMPROBE
MULTITEST2000
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
ϕ
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
=cos f
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.
Note:
It is to be noted that the expression of the phase Reactive Power with non sine waveforms,
would be wrong. To understand this, it may be useful to consider that both the presence of
harmonics and the presence of reactive power produce, among other effects, an increase
of line power losses due to the increased current RMS value. With the above given relation