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Idiomas disponibles
Idiomas disponibles
B a s i c s o f P o w e r M e a s u r e m e n t
Please note that erroneous results will show if
the crest factor of a signal is higher than that of
the measuring instrument because it will be
overdriven.
STOP
Hence the accuracy of the rms value measurement will depend
on the crest factor of the signal, the higher the crest factor
the less the accuracy. Please note also that the crest factor
specification relates to the full scale value, if the signal is below
full scale its crest factor may be proportionally higher.
Form factors
Power
With DC power is simply derived by multiplying voltage and
current.
With AC the waveform and the phase angle resp. time
relationship between voltage and current have also to be taken
into account. For sine waves the calculation is fairly simple,
as the sine is the only waveform without harmonics. For all
other waveforms the calculation will be more complex.
As long as the instrument specifications for frequency and
crest factor are observed the power meter will accurately
measure the average of the instantaneous power.
Active, true Power (unit W, designation P)
As soon as either the source or the load or both contain
inductive or capacitive components there will be a phase ang-
le or time difference between voltage and current. The active
power is calculated from the rms voltage and the real
u
i
û
î
ϕ
30
Subject to change without notice
Crest- F o r m -
Crest-
Crest-
F o r m -
F o r m -
F o r m -
Crest-
Crest-
F o r m -
factor factor
factor
factor
factor
factor
factor
factor
factor
factor
C C C C C
F F F F F
π π π π π
2
= 1,11
2 2
π π π π π
2
= 1,11
2 2
π π π π π
2
= 1,57
2
3
= 1,15
2 2 2 2 2
3
ω
ϕ
Icos ϕ
ωt
I
component of the current as shown in the vector diagram
above.
Defining: P
= active power
V
= rms value of voltage
rms
I
= rms value of current
rms
ϕ
= phase angle
the active power is derived as follows:
P = V
· I
rms
cosϕ is the socalled power factor (valid for sine waves only).
The instantaneous power is the power at time t equal
to the product of voltage and current both at time t.
p
= i
· u
HINT
(t)
(t)
(t)
For sine waves the instantaneous power is given by:
= û sin (ωt + ϕ) · î sin ωt
p
(t)
The active power or true power is equal to the arithmetic mean
of the instantaneous power. The active power is derived by
integrating for a period T and dividing by the period T as
folllows:
T
∫
1
î sin ωt · û sin (ωt + ϕ) dt
P = ––
T
0
î · û · cos ϕ
P
= ––––––––––––––
2
P
= V
· I
rms
rms
The power factor will be maximum cos
phase shift. This is only the case with a purely
resistive circuit.
In an ac circuit which contains only reactances the
phase shift will be
ϕ
hence cos
HINT
Reactive Power (unit VAr, designation Q)
Reactive power equals rms voltage times reactive current.
With the designations:
Q
= reactive Power
V
= rms voltage
rms
I
= rms current
rms
ϕ
= phase angle between
voltage and current
a vector diagramm
can be drawn as follows:
The reactive power is derived by:
Q = V
· I
rms
rms
U
Reactive currents constitute a load on the public
mains. In order to reduce the reactive power the
phase angle ϕ must be made smaller. For most of
the reactive power transformers, motors etc. are
responsible, therefore capacitors in parallel to these
loads must be added to compensate for their
inductive currents.
HINT
· cosϕ
rms
· cos ϕ
ϕ
ϕ
= 90° and the power factor
= 0. The active power will be also zero.
· sinϕ
= 1 at zero
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