Hameg HM8115-2 Manual page 34

O p e r a t i n g c o n t r o l s a n d d i s p l a y s
Power factor (PF)
In this mode the power factor will be measured, the LED will
light up, the display
by apparent power. The HM8115-2 allows the measurement
of the average of the instantaneous power irrespective of the
waveform as long as the specifications for crest factor and
frequency are observed.
Please note that a power factor can only be shown
u
for AC or AC + DC signals of sufficient minimum
i
amplitu-des. If the signal amplitude of either
voltage or current or both is insufficient horizontal
û
î
bars will be displayed, this will also be the case if
DC is being measured.
ig
t-
cos ϕ is only defined for truly sinusoidal signals. As
ϕ
en
soon as at least one of the signals is distorted a cos ϕ
h-
derived from the phase shift between voltage and
V
current will not be identical to the true power factor.
ergibt sich für die Wirkleistung
Connectors
P = U · I
eff eff
MONITOR (BNC)
5
Der Ausdruck cosϕ wird als Leistungsfaktor bezeichnet.
This is an analog output representing
11
the instantaneous active power e.g.
for display on a scope.
Die Momentanleistung ist die Leistung zum Zeit-
punkt (t) und errechnet sich aus dem Produkt des
Stromes und der Spannung zum Zeitpunkt (t).
The instantaneous power
TiPP
is the product of voltage
11
p = i · u
and current at time (t)
(t) (t)
bei Sinus gilt: p(t) = i(t) · u(t)
p = û sin (ωt + ϕ) · î sin ωt
(t)
in case of sine wave:
57
p = û sin (ωt + ϕ) · î sin ωt
Die effektive Leistung, die sogenannte Wirkleistung, ist der
(t)
zeitliche arithmetische Mittelwert der Momentanleistung. Wird
The active power is the average of the instantaneous power
über eine Periodendauer integriert und durch die Periodendau-
integrated over the interval T = period divided by the period T:
er dividiert ergibt sich die Formel für die Wirkleistung.
15
1
∫
P =
—
T
0
î · û · cosϕ
= ———————
= U · I
eff
g)
The monitor output will always deliver the instantaneous power
Das Maximum des Leistungsfaktors cos
no matter which function was selected. For positive instanta-
sich bei einer Phasenverschiebung von
neous power the output will be positive, for negative instanta-
wird nur in einem Wechselstromkreis ohne Blindwi-
nd
neous power it will be negative. If DC is being measured the
derstand erreicht.
k-
monitor output will hence deliver a DC signal.
m,
ie In einem Wechselstromkreis mit einem idealen
The BNC terminal outer conductor is connected to the instrument
ch Blindwiderstand beträgt die Phasenverschiebung
housing, however, the signal is isolated by a transformer.
= 90°. Der Leistungsfaktor cos
ϕ
strom bewirkt dann keine Wirkleistung.
TiPP
The temperature dependent drift is automatically corrected
n-
for by disconnecting the input/output terminals, during this
n.
interval (100 ms) there will thus be no monitor signal. After
Blindleistung (Einheit var, Kurzzeichen Q)
or
instrument turn-on the autozero will be activated every 3 se-
en Die Blindleistung errechnet sich aus der effektiven Spannung
conds for the first minute, after warm-up the breaks will occur
und dem Blindstrom. Im Zeigerdiagramm ist der Blindstrom
every 2 minutes.
die Stromkomponente senkrecht zur Spannung. (var = Volt
Ampere réactif)
The average of the monitor output voltage will be 1
n-
V if the input signals are such that the WATT display
ch
shows full scale. There is no indication of the po-
ft Wenn: Q = Blindleistung
wer range, the range has to be calculated and is the
n- U = Spannung Effektivwert
eff
product of the VOLT and AMPERE ranges.
en
I = Strom Effektivwert
eff
er = Phasenverschiebung
ϕ
ie zwischen U und I
34
Subject to change without notice
ergibt sich für die Blindleistung
will show the power factor = active/
4
ω
ϕ
ωt
· cosϕ
(t)
1
T
î sin ωt û sin ( ωt + ϕ) dt
·
2
· cos ϕ
eff
= 0. Der Wechsel-
ϕ
Examples:
50 V x 0,16 A
150 V x 16,0 A
500 V x 1,6 A
If both voltage and current are equal to their full
scale values in the ranges selected and if both are
sinusoidal the monitor output signal will be 2 V
the power is purely active the signal will oscillate
between 0 and 2 V
U
For DC full scale values the monitor output will be
1 V
Icos ϕ
I
Example 1:
A wirewound resistor of 1.47 kΩ is connected to 70 V
picture shows the voltage across the resistor and the monitor
output. The ranges selected are 150 V and 0.16 A which yields
a 24 W full scale 1 V average signal at this output. There is no
phase shift.
R : 1,47 k
Ω
L
5
The scope shows an undistorted instantaneous power signal.
The negative peak is equal to 0 V, the positive peak equals 0.27
V, thus the average equals 0.135 V.
This average value multiplied by the full scale value 24 W equals
= 1 ergibt
ϕ
3.24 W which is the average power.
= 0°. Die
ϕ
The HM8115-2 displays the following results:
V
I
P
Example 2:
A wirewound resistor of 311 ohms is connected to 50 Vrms/50
Hz. The picture shows the voltage across the resistor and the
monitor output.
The ranges are 50 V and 0.16 A, the full scale power is hence 8
W corresponding to 1 V average at the monitor output.
There is no phase shift with this purely resistive load. The scope
shows an undistorted signal. The negative peak equals 0 V, the
positive peak 2 V, the average is thus 1 V.
= 2408 W
➔
= 2400 W
➔
= 800 W
➔
, the average of this is 1 V.
p
.
DC
= 70 V
rms
= 0,048 A
rms
= 3,34 W
1 V (average)
1 V (average)
1 V (average)
. If
pp
. The
rms
Voltage
at R
L
100 V
50 V
GND
Monitor
Signal
100 Vm
GND
Q = 0,2 var
S = 3,32 VA
PF = 1,00