Th4cl 5A METHOD, AND ITS INSTRUMENTATION, FOR MEASUREMENT OF SMALL DIFFERENCES OF

VECTORIAL VALUES

G.B. Gubler, E.Z. Shapiro*

St-Petersburg Technical University,Politechnicheskaya 21, St Petersburg, Russia

Abstract

The paper considers a measurement method thatdetermines small differences of vectorial values (lessthan 1% in magnitude and 0.02 rad in phase). Thesolution is based on the use of 2-channel digitalinstrument for non-coherent sampling of harmonicsignal instant values. Method description includesanalysis of methodic inaccuracies. The studydemonstrates that common off-the-shelf power analyzeris made applicable, due to the method proposed, toonsite calibration of instrument transformers ofcommercial frequency current or voltage.

Introduction

Vectorial values under review represent fundamentalharmonics of periodic signals. Small differences of suchvalues, typically within 1% in magnitude and 0.02 rad inangle, shall be measured each time we calibrate or checkfront-end converters ofAC voltage or amperage, such asinstrument transformers, current to voltage or voltage tocurrent converters, various voltage dividers or shunts.Measurement of the said differences is therefore aroutine task, and has a number of solutions. The mostaccurate and commonly used method represents signaldifference in analogue form, and then decomposes it intoin-phase and quadrature components [1]. This approachhas been further developed due to introduction ofprecision sampling instruments with error of full scaleless than 0.01%. As these instruments are typicallyprovided with features for harmonic analysis of signals,and mathematical processing of measured data, theymay constitute a base for new type of metrologyequipment [2] [3].

Basically two features are characteristic of themethod described below. First, differences acquired bysimultaneous samples of the two signals are processed inthe form of an array. Second, no coherent is requiredbetween frequencies of the signals and samplingfrequency. This mode of operation is used in mobile setcurrently designed to calibrate class 0.1-0.5 instrumenttransformers. With. such a set, calibration may beconducted under shop conditions, on an on-site basis.For power plants this means firstly, that samplingfrequency is never synchronized with Erequency of testsignal supplied from network. Secondly, the signal is ofpoor quality in tenns of its stability and distortion.

Ouantization effect, as detected in differentialmeasurement

* Mendeleyev Research Institute of Metrology(VNIIM) Moskovski Pr. 19, St Petersburg, Russia

As a general rule, subtraction of two time and leveldiscretized signals results in a differential signal withelevated quantization noise, provided that quantizationerrors of subtracted signals constitute two statisticallyindependent random values. If however, discretizedsignals of similar shape are subtracted, this is not alwaysthe case, for the following reason. Suppose, signaldifference and ADC increment are of the same range.Having said this, we cannot consider quantization noisesto be statistically independent. In fact, quantization noisedetected after subtraction of the said discretized valuesappears to be of the said intensity as that of an operandsignal.

Another finding is that the signal representingdifference shows no correlation with quantization noise(see Fig. 1). The effect described above makes itpossible to determine phase component. Moreover, itimproves resolution when magnitude of differentialsignal is determined. The effect takes oversampling asgeneral assumption, which is accompanied by noise-shaping under some circumstances. To illustrate the idealet us graphically demonstrate (Fig. 1) the difference oftwo sinusoidal signals discretized via 16-bit quantizer,magnitude difference being 0.01%, phase shift -0.00015rad (0.5 mi), and sampling rate of 12.8 kHz.

0.015

to 0.01CO

n 0.005

00

a- 005

0015

0 0.005 0.01 0.015 0.02bmes

0.025 0-03

Figure 1 Difference of two quantized signals

The reasoning behind the method proposed is onlywhen difference is found between signals of similarshape. The method is applicable to signals withadditional harmonics of higher order. The gainresolution tends to decrease in this case, but generalresults are still good. This is due to the fact that alladditional harmonics provide for the sort of dithering.They make it possible to find in frequency domain thesesensitive parameters of differential signal that belong tofundamental harmonics. As to precision of end results, itis never affected by the presence of higher hanmonics.

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Non-coherent samDling method, as avplied todetermination of differential sienal

Parameter finding procedure for a harnonic in frequencydomain follows the method of non-coherent samplingdescribed in [4]. Fig. 2 and 3 shows the results ofmodelling conducted to evaluate error in phase andmagnitude components. Measured signal constitutes thedifference of two harmonic signals. Modelling has beenmade under following conditions:Quantization mode: 15 bit + sign, sampling frequency12.8 kHzSampling interval 0.32 s (4096 points)Fundamental harmonic frequency 51.6 HzFundamental harmonic phases were randomDifference in magnitude varied within +0.25% to -0.25%; difference in phase varied within +20 min to -20minSignal under review contained 3-th and 20-th harmonics,their magnitudes being 0.1% and 0.7% of fundamentalharmonic, correspondingly.

El5

~0.0

000 02~~~~~~~10005 0-0.

phase rad 0.01 o04 magnitude %

Figure 2 Error in determination of magnitude component ofsignal difference

0.2

difference ±0.25%. Absolute error in phase would 0.1min (30. I0- rad) within the range of difference ±20 mi.As the curves show, absolute error decreases as signaldifference approaches zero. One of method advantagesis its capacity to precisely define parameter differencesbetween two channels of an instrment on specifiedfrequency. This is achieved by applying the same signalto both channel inputs. This way instrumental error ofdifferential measurement may be significantly reduced.

Conclusion

Commercially available power analyser "Energomonitor3.3" was used to implement the method in practice.Specially designed resistive-capacitive bridge has beenused to calibrate the instrument. The bridge made itpossible to set differences between two 1 V vectors so asto obtain magnitude difference within 0-2 % withabsolute uncertainty of 1-0- %, and phase differencewithin 0-30 min with uncertainty 0.2 min.

A series of measurements demonstrated that theinstrument's absolute uncertainty of results was 0.003 %and 0.2 min or less within the range of differences up to0.5 % in magnitude and 30 min in phase. The instrumentwas put in practical use for calibration of HVtransformers nominal voltage 10 kV, cl. 0.2.

References

[1] E. So "The application of the current-comparatortechnique in instrumentation and measurementequipment for the calibration of non- conventionalinstrument transformers with non-standard rated output"IEEE Trans. On Power Delivery, Vol.7, pp.46-52,January 1992

[2] R. Arseneau, P.S. Filipski, J.J. Zelle " An improvedthree phase digital recorder system for calibrating powerinstrumentations", IEEE Trans. On Instrumentation andMeasurement, Vol. 46, No. 2, pp.339 - 402, April 1997.

[3] B.C. Waltrip and T.L. Nelson, "A system to measurecurrent transformers performance", Conference DigestCPEM 2000, pp 272-273, June 2000.

[4] G.Gubler, V.Gutnikov, "DFT-based Method forAccurate Determination of Fundamental HarmonicParameters within Periodic Signal", Proceedings ofSENSOR 2003 Volume II pp. 419-423

0.005 04

0~~~~~~~~-0.005 -02phase -0.01 -04 magnitude %

Figure 3 Error in determination of phase component of signaldifference

Modelling results show the following. Absolute error inmagnitude appears to be 15 ppm witiin the range of

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