Fluke 6105A - Apparent Power Example

6100B/6105A
Users Manual
1-24
1-59. Apparent Power Example
Voltage channel fundamental frequency output is 109 V on the 1 V range at 60 Hz. A 15 V 3
rd
harmonic has been
added. The current channel output is 7 A at 60 Hz on the 10 A range with 3
rd
and 5
th
harmonics at 0.7 A and 0.3 A
respectively. Phase angles are not relevant to the calculation of apparent power. Voltage uncertainty values are
given in “Voltage and Sine Amplitude Specifications” and “Voltage DC and Harmonic Specifications”, current
uncertainty values are given in “Current Sine Amplitude Specifications” and “Current DC and Harmonic Amplitude
Specifications”. The accuracy used is that of the 6100B.
The voltage rms value is
V02727.11015109
22
=+
Accuracy contribution from the voltage fundamental:
112 ppm of 109 V + 4.4 mV = (109x0.000112) + 0.0044 = 0.012208 + 0.0044 = 0.016608 V
Modified by the sensitivity coefficient = 0.016608 x 109 ÷ 110.02727 = 0.016453 V
Accuracy contribution from the voltage 3
rd
harmonic:
122 ppm of 15 V + 4.4 mV = (15x0.000112) + 0.0044 = 0.01830 + 0.0044 = 0.006230 V
Modified by the sensitivity coefficient = 0.006230 x 15 ÷ 110.02727 = 0.000849 V
Combined voltage uncertainty:
000157.0
02727.110
000849.0016453.0
)(
=
+
=
RMS
RMS
V
Vu
(or 157 ppm).
The current rms value is
041307.73.07.07
222
=++
Accuracy contribution from the current fundamental:
164ppm of 7 A + 240 μA = (7x0.000164) + 0.000240 = 0.001148 + 0.000240 = 0.001388
Modified by the sensitivity coefficient = 0.001388 x 7 ÷ 7.041307 = 0.001380 A
Accuracy contribution from the current 3
rd
harmonic:
191 ppm of 0.7 A + 240 μA = (0.7x0.000191) + 0. 000240 = 0.000134 + 0.000240 = 0.000374
Modified by the sensitivity coefficient = 0. 000374 x 0.7 ÷ 7.041307 = 0.000037 A
Accuracy contribution from the current 5
th
harmonic:
191 ppm of 0.3 A + 240 μA = (0.3x0.000191) + 0. 000240 = 0.000058 + 0.000240 = 0.000297
Modified by the sensitivity coefficient = 0.000297 x 0.3 ÷ 7.041307 = 0.000013 A
Combined current uncertainty:
000204.0
041307.7
000013.0000037.0001388.0
)(
=
++
=
RMS
RMS
I
Iu
(or 204 ppm).
Now,
VAIVS
RMSRMS
7358.774041307.702727.110.
222
=×==
Apparent Power uncertainty:
0002574.0000204.0000157.0]
)(
[]
)(
[
)(
2222
=+=+=
RMS
RMS
RMS
RMS
I
Iu
V
Vu
S
Su
giving:
VASu
c
1994.0735748.7740002574.0)( =×=
Apparent Power Accuracy = 774.7358± 0.1994 VA