How to measure the average
power of distorted waveforms
precisely
Michael Rietvelt
Technical Engineer T&M
Power and Energy Specialist
Yokogawa Europe
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Precision Making
Making
Precision
Definition of Measurement
Any measurement of an object can be judged by the
following meta-measurement criteria values:
 level of measurement (which includes magnitude)
 dimensions [units]
 uncertainty
Source: Wikipedia
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23/06/2015
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Examples Measurement Uncertainty
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Three Gorges Dam, China  22.5 [GW] maximum power
• Is this a value, a measurement, an
indication or a calculated guess?
• It is certainly not a measurement,
because:
• 22.5 [GW] ± ?? [MW]
• It would read for a measurement for
instance:
• 22.5 [GW] ± 19.5 [MW]
• Can we ignore 19.5 [MW]
uncertainty?
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Uncertainty in efficiency measurement
99,5% or 102,2% efficiency?
Combustion Engine
Converter
Battery
DC
AC
eMotor
Generator
Source: PPA55xx series START UP GUIDE
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<Document Number>
Copyright © Yokogawa Electric Corporation
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Uncertainty calculation of
average power for
pure sine waveforms
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Pure sine wave voltage across- and current through the load
i
u
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Specifications
This table is the starting point for uncertainty calculations.
Additional uncertainties might follow..
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Source: Yokogawa WT3000
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The average electrical power for pure sine waveforms:e
average electric power for sinusoidal waveforms is:
Pavg = Urms . Irms . cos [W]
Every multiplication factor contributes in its own way to the total uncertainty:
Pavg = (Urms ± unc) . (Irms ± unc) . (cos ± unc)
2
2
Pavg,unc   Uunc  Iunc  cos()unc
2
[W]
[%]
When measuring power, additional uncertainties might appear……..
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Factors that influence the total error for power are:










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Current shunt drift by continuous high currents
Amplitude
Frequency of the fundamental of the input signal
Crest Factor of the input signal (BW)
Crest Factor setting of the Power Meter
Power Factor
Temperature
Use of filters
Use of protection diodes
Stability of Period Time detection
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Pavg = (Urms ± unc) . (Irms ± unc) . (cos ± unc) [W]
Focus on internal phase shift uncertainty
(cos ± unc)
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Internal phase shift uncertainty of ANY two channel instrument
δ
u(t)
Attenuator
A/D
DSP
i(t)
i(t) u(t)
SHUNT
Main part of the phase delay is
caused by this shunt due to its,
although very small, inductance.
Amplifier
A/D
The VOLTAGE input often needs a big attenuation
(e.g. 600V to 3V).
The small voltage drop across the CURRENTshunt on the other hand needs a very high gain
(e.g. μV to 3V).
OPAMPs show different amplitude gain
characteristics.
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23/06/2015
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Consequently there
will be an additional
internal
phase shift between the voltage and current input.
Effect of internal phase shift uncertainty
p(t) = u(t) x i(t)
Real DUT values!
p’(t) = u(t) x i(t)
Measured Values!
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4
3
2
Pavg
P’avg1
u(t)
0
i(t)
p(t)
-1
i'(t)
p'(t)
-2
-3
cosφ
-4
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ƍ
-5
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Uncertainty calculation
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This uncertainty calculation is only valid
for one frequency of pure sine waves
What if the waveforms of voltage across
- and current through the load are
distorted?
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Switching-mode Power Supply
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Distorted waveform
Distorted wave
resolve
fundamental wave
3rd harmonic wave
5th harmonic wave
7th harmonic wave
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A measurement challenge
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Power Measurement of DISTORTED WAVEFORMS
Instantaneous Power transmission = Inst. Voltage x Inst. Current [VA]
values, including a mix of all higher harmonics !
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DEFINITION of Pavg :
1 T
1 T
Paverage  T 0 p(t )  dt  T 0 u(t )  i(t )  dt
The most difficult task for the power meter is to find the period time
T correctly!
Especially with distorted signals this can be very difficult.
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The Measurement Challenge
Zero Crossing?
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How to measure distorted waveforms
Superposition principle
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Superposition Principle
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A Complex Task
?
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Superposition Principle Part 1
Input is organised (decomposed);
-
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for instance sorted on the same size of apple
or sorted on the same frequency (HRM analysis)
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Superposition Principle Part 2
Input is one by one fed through the “Black Box”;
-
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for instance size by size
or frequency by frequency
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Superposition Principle Part 3
[W]
All the individual outputs are
summed.
+
The superposition principle
states that this result (Pavg)
is the same when all apples
(frequencies) are processed
in the black box (power
meter) at the same time.
[W]
+
+
[W]
+
.
.
frequency
frequency
frequency
=
=
[W]
frequency
4+2+1 = 7[W]
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Measurement uncertainty of distorted waveforms
• One has to measure the power of each frequency
component related to the total distorted signal.
• A High Precision Harmonic measurement is
required to know the harmonic uncertainty.
• For each frequency component we have to apply
the former explained uncertainty calculation formula
for sine waves.
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How many harmonics need to be
included?
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Voltage, Current & Power Harmonics Spectrum of DISTORTED WAVEFORMS
Switching-mode Power Supply
Voltage across the load
Current trough the load
Instantaneous Power consumed by the load
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Voltage, Current & Power Harmonics Spectrum of DISTORTED WAVEFORMS
Pulse-Width-Modulated Electric Motor
Voltage across the load
Current trough the load
Power consumed by the load
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Advice to minimize the uncertainty:
Before you calculate, calibrate!
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Accuracy of Electrical Power Measurement WT3000
Guaranteed Catalogue Specifications for Electrical Power based on
Production Line Standards in Japan;
0.02% of reading + 0.04% of range @ 45Hz – 66Hz
0.05% of reading + 0.05% of range @ 66Hz – 1kHz
0.15% of reading + 0.1 % of range @ 1kHz – 10kHz
0.014 x f % of reading + 0.2% of range @ 100kHz
= 0.06% @ 50Hz
= 0.1 % @ 1kHz
= 0.25% @ 10kHz
= 1.6% @ 100kHz
Typical Accredited Calibration Value (NMi-VSL), 100V, 1A, PF=1.000;
0.004% @ 50Hz
0.003% @ 1kHz
0.023% @ 10kHz
0.15% @ 100kHz
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Three Gorges Dam, China  22.5 [GW] maximum power
• Uncertainty based on Production
Line Standards specificaitions
• Uncertainty based on Accredited
Calibration.
• 22.5 [GW] ± 19.5 [MW]
• 22.5 [GW] ± 0.9 [MW]
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Thank you for
your attention
Questions?
Michael.Rietvelt@nl.yokogawa.com
tmi.yokogawa.com
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