Fluke 6105A - Non-Sinusoidal Voltage Example; Apparent Power (S) Accuracy Calculations

Introduction
Electrical Specifications 1
1-23
∑
=
=
N
i
iiRMSc
VucVu
1
)()(
where
RMS
i
i
V
V
c =
and is known as the sensitivity coefficient.
1-57. Non-sinusoidal Voltage Example
The waveform is a 60 Hz, 110 V rms waveform, from the 168 V range, comprising 10 % 95
th
harmonic, 30 % 3
rd
harmonic with the remainder contributed by the fundamental frequency. Using the 6100B voltage uncertainty values
in “Voltage and Sine Amplitude Specifications” and “Voltage DC and Harmonic Specifications”, determine the 1-year
accuracy.
3
rd
Harmonic rms voltage = 0.3 x 110 = 33 V
95
th
Harmonic rms voltage = 0.1 x 110 = 11 V
Fundamental rms voltage = √(110
2
- 33
2
- 11
2
) = 104.3552 V
Accuracy contribution from the fundamental:
112 ppm of output +4.4 mV = (104.3552 x 0.000112) + 0.0044 = 0.011688 + 0.0044 = 0.016088 V
Modified by the sensitivity coefficient = 0.016088 x 104.3552 ÷ 110 = 0.015262 V
Accuracy contribution from the 3
rd
Harmonic (180 Hz):
122 ppm of 3
rd
harmonic value +4.4 mV = (0.000122 x 33) + 0.0044 = 0.008426 V
Modified by the sensitivity coefficient = 0.008426 x 33 ÷ 110 = 0.002528 V
Accuracy contribution from the 95
th
Harmonic (5700 Hz):
512 ppm of 95
th
harmonic value + 4.4 mV = (0.000512 x 11) + 0.0044 = 0.010032 V
Modified by the sensitivity coefficient = 0.010032 x 11 ÷ 110 = 0. 001003 V
Combining the uncertainties:
Total amplitude uncertainty = 0.015262 + 0.002528 + 0.010032 = 0.018793 V
Voltage Accuracy = 110 ±0.018793 V
1-58. Apparent Power (S) Accuracy Calculations
For the purpose of calculation of apparent power (S) for non-sinusoidal outputs the following equations are used:
∑∑
=
nn
nn
IVS
22
VA
To calculate the accuracy of apparent power (S), the amplitude accuracy specifications of voltage harmonic
components must be combined as described in “Determining Non-Sinusoidal Waveform Amplitude Specifications”
above. Current components are combined using the same method. As apparent power is the product of two different
quantities, uncertainties are conveniently combined using relative values. Note that 6100B voltage and current
components are generated independently and are therefore largely uncorrelated.
As
222
.
RMSRMS
IVS =
;
22
2
2
]
)(
[]
)(
[
)(
RMS
RMS
RMS
RMSc
I
Iu
V
Vu
S
Su
+=
where
)(Su
c
is the combined uncertainty of the apparent Power,
)(
RMS
Vu
is the uncertainty of the rms voltage and
)(
RMS
Iu
is the uncertainty of the rms current.