Virtual FFT Analyser for identification of harmonics and inter-harmonics metrological aspects

Transcription

1 NPL seminar 30 of November 005 Virtual FFT Analyser for identification of harmonics and inter-harmonics metrological aspects M. Jerzy Korczyński Institute of Theoretical Electrotechnics, Metrology and Material Science, Metrology Group, Technical University of Lodz, ul. B. Stefanowskiego 18/, Lodz, Poland,

2 British connection Joseph Mc Ghee & Ian Henderson

3 Activities of M&I research group 3 Research subjects: Some aspects of quality of electrical power: how to treat non-sinusoidal of current, voltage and as consequence - energy, which not only consists of active, reactive, apparent but one of the element is a deformation caused by harmonics. (DM FFT, JTFT, modelling of signals) Virtual Instrumentation development of new class of instruments Instrument calibration and traceability problems Software development supporting measurements Evaluation of uncertainties: Approximation methods Fast Fourier Transform based method Monte Carlo Method Teaching concern all subjects related to Measurement and Instrumentation

4 Overview: 4 INTRODUCTION Why are we interested in sinusoidal voltage and current of electrical power supply and what is disturbing electrical power supply? Sources of disturbances in electrical power net - loads? Impact of harmonics and interharmonics on electrical devices Do really harmonics and interharmonics exist? Parameters describing signal distortion Standards related to identification of harmonic contents Grouping of harmonics and interharmonics 00 ms window is a compromise - advantages and disadvantages of these 00ms window length transient states monitoring, sampling frequency requirements Uncertainties in grouping harmonics and interharmonic - how far can we be from the reality? Evaluation of uncertainties due to imperfection of probes, sensors, input transducers, analogue-to-digital converter How the uncertainty propagates through FFT procedure. Further work, foreseen development

5 INTRODUCTION: 5 The considerations cover the area of applications which concern electrical power net low and high voltage : current, voltage of 50 Hz ( 60 Hz) in consequence related power components and aggregated parameters, which characterise non-sinusoidal signals The metrological consequences of imperfections of virtual analyser will be presented for modelling the real world in calculation of: -Harmonic groups, interharmonic groups, harmonic subgroups and central interharmonic subgroups -Electrical power measurement How the compromised windowing of 00 effects measurement above parameters as it is a error due to applied methodology.

6 Why sinusoidal voltage and current? 6 - Ideal conditions for calculation of power consumption (Reactive, active and apparent power) Otherwise we are faced with deformation power, No payment so far for deformation in voltage, current - All electrical data of electrical equipment are presented for sinusoidal voltage power supply. - Some of instruments may fail if the voltage is to much distorted. What is causing distortion of current and voltage consequently?

7 Sources of harmonics and inter-harmonics 7 Power drives systems Cycloconverters Power frequency converters (inventers) Arc devices ferromagnetic devices (e.g. motors), fluorescent lamps, all office devices with rectifier at the input devices consuming power within a short period Typical scheme for frequency converter causing current distortion and how to identify these distortions

8 Source of distortions (transient states) 8 3 phase power supply Frequency converter LEM-based voltage and current sensors Data acquisition M N Gearbox stand N G 1 1 Energy flow

9 Virtual Instrument to calculate harmonics 9 A N A L Y S E D S I G N A L Input circuitry ADC- PCI CARD SENSORS & PROBES HARDWARE ANTy- ALIASING FILTERS WINDOWING Sampling frequency DATA HANDLING (DSP included)

10 Circuitry for steady or transient state analysis 10 M G voltage current LEM converter LEM converter Signal Conditioners electrical power net voltage current LEM converter LEM converter Samples at the same moment Controlling of frequency converters Human Machine Interface RS485 Computer PC PCI card 64 ports 1 bit A/C 1,5 MSamples\s

11 Taxonomy of applied to harmonics (50 Hz) 11 Higher harmonics whose frequencies are integer multiples of fundamental frequency Interharmonics harmonics whose frequencies are non-integer multiples of fundamental frequency and Sub-harmonics - harmonics non whose frequencies are below the fundamental frequency Steady state, quasi-stationary state and rapidly change states. f n = n* f 1

12 Harmonics and interharmonics in real world 1

13 Example of harmonic contents rms harmonicznych frequency converter off carrier frequency 7,5 khz carrier frequency 15 khz Rząd harmonicznych, prązki harmonicznych oddalone co 50 Hz

14 FIZYCZNY MODEL ODBIORNIKA NIELINIOWEGO 14 fundamental e 1 (t) R S1 X S1 R 0 e (t) R S L S (X S ) Non linear load N - load Equivalent circuitries higher harmonics R SK X SK X 0 i hhk R SN X SN Interharmonics i ihn

15 Measurement chain 15 Data acquisition: sampling frequency and windowing Fast Fourier Transform FFT Harmonic spectrum (harmonics and interharmonics) Grouping of harmonics and interharmonics Aggregated parameters Active electrical power

16 Permissible errors of instruments 16 Class Quantity Voltage Range U m 1% U n U m <1% U n Max permissible error ± 5%U m ± 0,05%U n I Current I m < 3% I n I 3% m I n ± 5%I m ± 0,15%I n Power P m 150W P m < 150W ±1,5W ±1%P n

17 Harmonic Group and interharmonic group 17 C r.m.s values of Harmonic Group and Interharmonic Group Harmonic group n+ Interharmonic group n+4 DFT output n Harmonic order n+1 n+ n+3 n+4 n+5 n+6 G g, n = C 4 k 5 + Ck+ i + i= 4 C k+ 5 9 G ig = C, n i= 1 k + i Harmonic Group Interharmonic Group

18 Grouping harmonics and interharmonics 18 C Harmonic subgroup n+ Interharmonic centred subgroup n+4 DFT output n Harmonic order n+1 n+ n+3 n+4 n+5 n+6 G sg, n = 1 i= 1 C k+ i Harmonic subgroup 8 G isg = C, n i= k+ i Interharmonic centered subgroup

19 19 According to IEC series - Measuring window - 00ms so 5 Hz resolution is assumed Aggregated parameters of non-sinusoidal signals = = H n n G G THD 1 = = H n g gn G G THDG 1 = = H n sg G G THDS 1 sgn Total Harmonic Distortion = = max min 1 H H n n G G n PWHD Group Total Harmonic Distortion Subgroup Total Harmonic Distortion Partial Weighted Harmonic Distortion

20 Calculation Example amplitudes time, s

21 Harmonic Content window of 1 s Fundamental Harmonic and Interharmonic of 1 Hz rms of fundamental and interharmonics realtive values Frequency, Hz

22 Harmonic Content window, 0. s rms of harmonics rms of amplitudain frequency, Hz

23 Real example 3 10 rms harmonicznych frequency converter off carrier frequency 7,5 khz carrier frequency 15 khz Rząd harmonicznych, prązki harmonicznych oddalone co 50 Hz

24 Example of calculating aggregated and their errors 4 True value True aggregated value Measured value using window 00 ms Aggregated measured value ERROR Fundamental harmonic % Harmonic group ,7 % Interharmonic group 1.1 brak ,15 % Harmonic subgroup brak brak % brak % Interharmonic cantered subgroup

25 Definition of Total Harmonic and Inter-harmonic Distortions and numerical example 5 TH & IHD = ( ) HG ( IHG) + IHG IHG HG HG DC TH & IHD ERROR _ rel = TH & IHD TH & IHD TH & IHD _ ref _ ref

26 Numerical example for arbitrary chosen signal 6 Fundamental frequency is 50 Hz, of amplitude of 5 units, and: 9 Hz of amplitude units, 167 Hz of amplitude units and frequencies: 67 Hz, 70 Hz, 73 Hz, 76 Hz, 79 Hz, 8 Hz, 85 Hz, 88 Hz, 91 Hz each of amplitude of 1

27 Ideal FFT of 1 Hz as needed and 5 Hz resolution 7 Harmonics and interharmonics of the arbitrarily chosen signal for f w =1Hz, f s =104 Hz, M=104 Spectrum of the signal analysed according to the IEC draft (f w =5 Hz, T w =00 ms, f s =510, M=104)

28 Inter and Harmonic Grouping IHG & HG 8 Interharmonic groups of the signal under consideration in logarithmic scale calculated according to the IEC Harmonic groups of the signal under consideration in logarithmic scale calculated according to the IEC

29 TH&IH ERROR_rel vs. variation of the fundamental 9 10 rectangular % error(thd&ihd) Blackman triangle Hamming Hanning % f1

30 TH&IH ERROR_rel vs. variation of a single interharmonic frequency Blackman triangle Hamming Hanning rectangular

31 TH&IH ERROR_rel vs. variation of percentage of missing samples rectangular Blackman triangle Hamming -40 Hanning

32 Conclusion from example 3 Defined TH&IHD parameter is a aggregated parameter which can be used for characterising of distortion in electrical power voltage and current, can be used to billing consumers for distortion of electrical power. The analysis of arbitrary chosen signals depicts that the rectangular window is most adequate but also most sensitive to variations of tested parameters. By applying the windows, the sensitivity is reduced significantly, but a displacement is observed. The displacement has a systematic character, hence it may be corrected.

33 Evaluation of uncertainties. 33

34 3*0,4 kv Evaluation of uncertainties - current in time domain A I B 34 I 1 I I 3 FC 1 FC 3*0,4 kv A M1 I M LinearB Load I 1 I I 3 FC 1 FC M1 M Linear Load amplitude 0 0,05 0,1 0,15 0, 30th of November 005, Teddington, time; UK s

35 Input samples, their imperfection 35 Input samples, their imperfection probability distribution functions of every input data 1. All sensors: current and voltage transformers. ADC converters (gain offset and quantisation) 3. and what left - FFT

36 Evaluation of uncertainties - current in time domain przed Serie

37 Evaluation of uncertainties - Harmonic content 37 Coverage interval Coverage probability A I 3*0,4 kv B I 1 I I 3 FC 1 FC M1 M Linear Load

38 Distribution of uncertainties through FFT procedure FFT algorithm - very well known, but the problem of calculation of uncertainties in harmonic contents is a problem What methods can be used? Calculation of standard uncertainty for type A and B? - discrete model is measurement equation - and k-factor? 1. Application of Law of Propagation of Uncertainty through measurement model to calculate uncertainties - Monte Carlo Method? 38 Disadvantages and advantages Two components were distinguished in input sampled data. The uniform distribution of errors and Normal and combing - Type A and type B - How it propagate through the digital calculation process.

39 What kind of signal was tested under MC method? 39 FFT parameters: Resampling / sampling 048 points, Window 00 ms 5 Hz resolution Uniform and Gaussian pdfs Input samples: 30 % of amplitude Uniform and Gaussian pdfs

40 Result of propagation of uncertainties through FFT procedure (uniform) 40 For 95 % of coverage probability the coverage interval for fundamental harmonic is <0,9993; 1,0007> (mean value equals to true value which is 1) and for THD rms coverage interval is <0,13 0,5> mean value 0,18%

41 Result of propagation of uncertainties through FFT procedure (Normal) 41 Normally distributed error over samples. For 95 % of coverage probability the coverage interval for fundamental harmonic is <0,9996-1,0004> (mean value equals to true value =1) and for THDrms coverage interval is 0,073-0,15 mean 0,10%

42 1 % of additive and % of multiplicative components of errors distributed over samples. 4 For 95 % of coverage probability the coverage interval for fundamental harmonic is <0,998-1,00> (mean value equals to true value which is 1) and for THDrms coverage interval is <0,1-0,45>, at mean 0,3 %.

43 Conclusion regarding evaluation of uncertainties 43 Evaluate how uncertainties propagate through model To find a simpler method than MCM (as MCM is time consuming) The harmonic contents should be presented with coverage interval at certain coverage probability

44 Conclusion 44 Grouping harmonics and interharmonics 00 ms window is a compromise, still 5 Hz bins are the assumed resolution This is an engineering approach resulting that sometimes we are far away from perfect modelling of a real world, have advantages of unification if widely applied. The transient stated in electrical power is still waiting for unification, but 00 ms window can be also used.

45 Further investigations 45 - Total Harmonic and Inter-harmonic Distortions may be present as relative coefficients (similar to THD) in relation to rms value or fundamental frequency. - TH&IHD for both steady states and transient states as a measure of non-linearity, induced be some devices in the net. - Investigation of signals, which can be used for testing instruments to validate build up procedures for analysing harmonics contents - Development of instruments, which can effectively measure distortion induced in the net by different devices - Estimation of uncertainties