How to measure the average power of distorted waveforms precisely Michael Rietvelt Technical Engineer T&M Power and Energy Specialist Yokogawa Europe 1 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 2 23/06/2015 Precision Making Examples Measurement Uncertainty 3 Precision Making 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? 4 Precision Making Uncertainty in efficiency measurement 99,5% or 102,2% efficiency? Combustion Engine Converter Battery DC AC eMotor Generator Source: PPA55xx series START UP GUIDE 5 <Document Number> Copyright © Yokogawa Electric Corporation Precision Making Uncertainty calculation of average power for pure sine waveforms 6 Precision Making Pure sine wave voltage across- and current through the load i u 7 Precision Making Specifications This table is the starting point for uncertainty calculations. Additional uncertainties might follow.. 8 Source: Yokogawa WT3000 Precision Making 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…….. 9 Precision Making Factors that influence the total error for power are: 10 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 Precision Making Pavg = (Urms ± unc) . (Irms ± unc) . (cos ± unc) [W] Focus on internal phase shift uncertainty (cos ± unc) 11 Precision Making 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. 12 23/06/2015 Precision Making 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! 5 4 3 2 Pavg P’avg1 u(t) 0 i(t) p(t) -1 i'(t) p'(t) -2 -3 cosφ -4 13 ƍ -5 Precision Making Uncertainty calculation 14 Precision Making 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? 15 Precision Making Switching-mode Power Supply 16 Precision Making Distorted waveform Distorted wave resolve fundamental wave 3rd harmonic wave 5th harmonic wave 7th harmonic wave 17 Precision Making A measurement challenge 18 Precision Making Power Measurement of DISTORTED WAVEFORMS Instantaneous Power transmission = Inst. Voltage x Inst. Current [VA] values, including a mix of all higher harmonics ! 19 Precision Making 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. 20 Precision Making The Measurement Challenge Zero Crossing? 21 Precision Making How to measure distorted waveforms Superposition principle 22 Precision Making Superposition Principle 23 Precision Making A Complex Task ? 24 Precision Making Superposition Principle Part 1 Input is organised (decomposed); - 25 for instance sorted on the same size of apple or sorted on the same frequency (HRM analysis) Precision Making Superposition Principle Part 2 Input is one by one fed through the “Black Box”; - 26 for instance size by size or frequency by frequency Precision Making 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] 27 Precision Making 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. 28 Precision Making How many harmonics need to be included? 29 Precision Making 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 30 Precision Making 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 31 Precision Making Advice to minimize the uncertainty: Before you calculate, calibrate! 32 Precision Making 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 33 Precision Making 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] 34 Precision Making Thank you for your attention Questions? Michael.Rietvelt@nl.yokogawa.com tmi.yokogawa.com 35 Precision Making