HT instruments SIRIUS89N - Manual (Page 126)

SIRIUS89N
EN - 124
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
the increasing of power losses due to harmonics is added to that introduced by the
presence of reactive power. In effect, even if the two phenomena contribute together to the
increase of power losses in line, it is not true in general that these causes of the power
losses are in phase between each other and therefore that can be added one to the other
mathematically.
The above given relation is justified by the relative simplicity of calculation of the same and
by the relative discrepancy between the value obtained using this relation and the true
value.
It is to be noted moreover, how in case of an electric installation with harmonics, another
parameter called distorted Power Factor (dPF) is defined. In practice, this parameter
represents the theoretical limit value that can be reached for Power Factor if all the
harmonics could be eliminated from the electric installation.