Amprobe DM-4 Power-Quality-Recorder - Manual (Page 53)

In presence of distorted voltages and currents the previous relations vary as follows:
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 wave-
forms, 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 together contribute 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 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 dis-
crepancy between the values 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.
52
DM-4 Power Quality Recorder
Phase Active Power:
(n=1,2,3)
P
n
= V
kn
I
kn
cos(Θ
Θ
kn
)
Phase Apparent Power:
(n=1,2,3)
S
n
= V
nN
• I
n
Phase Reactive Power:
(n=1,2,3)
Q
n
= S
n
- P
n
Phase Power Factor:
(n=1,2,3)
P
F n
=
Distorted Power Factor:
(n=1,2,3)
dPF
n
=cosf
1n
=
phase
displacement between the
fundamentals of voltage and current
Total Active Power:
P
TOT
= P
1
+ P
2
+ P
3
Total Reactive Power:
Q
TOT
= Q
1
+ Q
2
+ Q
3
Total Apparent Power:
S
TOT
= P
TOT
2 + Q
TOT
2
Total Power Factor:
P
F TOT
=
∞
k=1
∑
√
2 2
P
n
S
n
√
P
TOT
S
TOT