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7FINDING REFERENCE VALUES TO CALIBRATE TWO ALTERNATING CURRENTS COMPARATOR
Isaiev V.
Ukraine, Kyiv, State Enterprise "Ukrmetrteststandart", senior researcher
Abstract. The urgency of this work is conditioned by the need for the measure of two AC currents difference, that is some device with well-defined metrological characteristics. Such a need arose in Ukraine after 2016 due to changes in the features of metrological support. Metrological traceability should guarantee the correlation of the calibration results with the international system of SI units, and the values of the measurement uncertainty should be small enough for modern means of comparing. The reference values for calibration service of comparators in the working range of 5 amps are obtained according to the results. Associated measurement uncertainties was also evaluated.
Keywords: alternating current, comparator, ratio error, phase displacement, current transformer, measurement uncertainty
Introduction. A measuring device for verifying instrument transformers K507, manufactered by plant "Tochelectroprylad" in Kiev, was widely used in the departments for metrological support of current transformers in the 70s of the last century. It was replaced by the calibration unit K535 developed by the specialists of the same company in the 80s years. Over and above the company "OLTEST" produced an analogous device comparator CA507 on a modern element base in the 2000s. The comparators like AITTS-98 and others are also used in Ukraine in addition to the listed measuring instruments. The new law on metrology entered into force in 2016 as well as such a metrological service as a calibration expanded earlier. Two reasons mentioned above raise the issue of problem of the measurement uncertainty determining during calibration of the indicated measuring instruments.
Overview and Purpose. The typical accuracy of the AC comparators is about 1 or 2 percent of the difference between two currents according to manufacturers' specifications. But such values of permissible errors occur only for the alternating current differences equal 0.1 or more percent and the alternating current values of more than 1 amp [1]. This metrological characteristic can reach 20 percent for alternating current difference of about 0.005 %. The method of determining the measurement uncertainty for the amplitude component of alternating current difference is given in [2] as well as the calculation for the angular component in [3]. Both methods are based on analytical expressions.
However, there is a path for an empirical determination of some reference values which should be compared with reading of the investigated comparator. The development of this idea should be to create a measure of the alternating current difference.
The purpose of the work is to establish the reference values of the metrological characteristics of alternating current comparators at the points of working range. It is also necessary to estimate measurement uncertainty of these reference values.
Research Method. A comparation method with help of a comparator is implemented in practice in calibrating laboratories to determinate corrections for the ratio error and phase displacement of scale converters of alternating current (current transformers). The RMS value of investigated current transformer output signal and the RMS value of reference current transformer output signal with known corrections are compared by means of this method.
The ratio error of the current transformer is determined through relative difference between the secondary current value multiplied by the transformation coefficient and the primary current. The phase displacement of the current transformer is determined through the angle between the vector of the primary current and the vector of secondary current displaced of 180 degrees [4].
The comparator compares two input signals, each of one has unique values of metrological characteristics, during calibration of current transformers according to equations
5comp 5 S >
comp
(1)
where sx is ratio error of investigated current transformer; sS is ratio error of reference current transformer.
^comp =A9x -A9S ,
(2)
where is phase displacement of investigated current transformer;
A^S is phase displacement of reference current transformer.
It is necessary to create the reference amplitude difference of two alternating currents and the reference phase difference of two alternating currents. The last statement follows from Equations (1) and (2) in order to check the correctness of the comparator reading.
This condition can be met by using two current transformers. Two precise current transformers were selected to find the reference value: H515, accuracy class 0.2 and H512, accuracy class 0.05. The combination of two precise scale transducers with highly stable metrological characteristics on a permanent basis allows them to be used as a measure of the alternating current difference.
The research and the search for the reference value for comparison with comparator reading when determining their metrological characteristics were made using the scheme [5] shown in Fig. 1.
Fig. 1. Scheme for finding reference values to calibrate AC comparators
The one and the same current flows through the primary windings of the reference and investigated transformers from the source of an alternating current. The currents have amplitude difference and phase shift when flowing out from the secondary windings of transformers. The comparator measures the difference between secondary currents of the investigated and reference scale transducers [1].
15 comparators of the mentioned above types were investigated by the methods [2] and [3] during the search for reference values. The observations of these measuring instruments were made at points of 1, 5, 20, 100 and 120 percents of 5 amps during one year. In this case, the averaged values of ratio errors and phase displacements (between precise current transformers type H515, accuracy class 0.2, and H512, accuracy class 0.05) readings were fixed.
Research Results and Measurement Uncertainty. The obtained results for the ratio errors, phase displacements and their mean arithmetic values are given in Table 1.
It is important to evaluate the associated uncertainty of measurement for the use of arithmetic mean as reference value. Since the reference values were determined as arithmetic average of 15 comparators readings, the functional relationship for ratio error in accordance with [6] is the following
s t =
ref
4 sK535 ^ 5 sK507 ^ 5 sCA507 ^ sAITTS
15
(3)
where sK535 is averaged value of calibration units K535 readings of ratio error;
sK507 is averaged value of devices for verifying instrument transformers K507 readings of ratio error;
sCA507 is averaged value of calibrators CA507 readings of ratio error;
Saitts is averaged value of calibrator AITTS-98 reading of ratio error.
Table 1. Measurement results of metrological characteristics of comparators
Number The value of the ratio error depending on the observation point, % The value of the phase displacement depending on the observation point, min.
1 5 20 100 120 1 5 20 100 120
1 -0.3220 -0.0610 0.0528 0.0698 0.0702 -4.60 -2.60 -0.77 0.42 0.40
2 -0.2190 -0.0516 0.0499 0.0658 0.0662 -3.84 -4.22 -0.76 0.47 0.48
3 -0.2110 -0.0505 0.0505 0.0668 0.0672 -3.99 -4.29 -0.82 0.44 0.46
4 -0.2640 -0.0610 0.0474 0.0659 0.0665 -1.32 -3.91 -0.84 0.30 0.31
5 -0.2190 -0.0510 0.0529 0.0682 0.0687 -3.15 -4.20 -0.88 0.48 0.49
6 -0.2020 -0.0490 0.0488 0.0640 0.0641 -5.40 -4.20 -0.62 0.54 0.55
7 -0.2180 -0.0532 0.0491 0.0654 0.0659 -3.73 -4.06 -0.62 0.59 0.66
8 -0.1810 -0.0440 0.0545 0.0710 0.0715 -4.78 -4.65 -1.00 0.42 0.40
9 -0.2090 -0.0475 0.0405 0.0665 0.0675 -2.25 -4.20 0.10 0.15 0.25
10 -0.2090 -0.0483 0.0529 0.0697 0.0703 -4.12 -4.41 -0.93 0.40 0.41
11 -0.2160 -0.0460 0.0520 0.0700 0.0710 -3.15 -4.45 -0.40 0.25 0.25
12 -0.2430 -0.0550 0.0480 0.0660 0.0670 -3.20 -4.20 -0.30 0.50 0.50
13 -0.2470 -0.0520 0.0460 0.0660 0.0670 -3.40 -4.30 -0.50 0.40 0.40
14 -0.1820 -0.0460 0.0540 0.0701 0.0708 -5.01 -4.72 -1.01 0.37 0.39
15 -0.2000 -0.0490 0.0527 0.0698 0.0703 -4.11 -4.42 -0.94 0.37 0.39
Mean -0.2228 -0.0510 0.0501 0.0677 0.0683 -3.74 -4.19 -0.69 0.41 0.42
The functional relationship for phase displacement in accordance with [6] is the following
A = 4 • 535 + 5 • 507 + 5 • A9ca507 + A9AITTS (4)
ref 15
where A^^j is averaged value of calibration units K535 readings of phase displacement; a9Kjo7 is averaged value of devices for verifying instrument transformers K507 readings of phase displacement;
AqCA507 is averaged value of calibrators CA507 readings of phase displacement; A^aitts is averaged value of calibrator AITTS-98 reading of phase displacement. The uncertainty of measurement for ratio error for each investigated point was calculated according to Expression (3) by the formula
116 • 535) + 25 ' (u(sk507) + U(sca507) ) + U(2
JJ _ 2 I (sK535) 1 ^ V"(sk507) "(sca507)/ (¡AITTS) ...x
s - 'A/ 225 '
where u(ek535) is standard uncertainty of calibration units K535 readings for ratio error; U(ekso7) is standard uncertainty of devices for verifying instrument transformers K507 readings for ratio error;
U(zca507) is standard uncertainty of comparators CA507 readings for ratio error; U(zaitts) is standard uncertainty of comparators AITTS-98 readings for ratio error. The uncertainty of measurement for phase displacement for each investigated point was calculated according to Expression (4) by the formula
j j I16 ' U(A*K535) + 25 ' (u(a<pk507) + u(a*ca507)) + u(a*aitts) ¡¿s
Ua* - 2 'V 225 ' (6)
Where U(A(fK535) is standard uncertainty of calibration units K535 readings for phase displacement;
U(AqtK5o7) is standard uncertainty of devices for verifying instrument transformers K507 readings for phase displacement;
U(Aq,cA507) is standard uncertainty of comparators CA507 readings for phase displacement; U{A<fAiTTS) is standard uncertainty of comparators AITTS-98 readings for phase displacement.
The budget of measurement uncertainty (see Table 2) was compiled for each investigated point in the general form according to Expressions (5) and (6).
Table 2. Budget of measurement uncertainty
Estimate of input quantity Estimate of standard uncertainty Sensitivity coefficient Contribution to combined uncertainty Output quantity Expanded uncertainty
sK535 u(sK535) 0.267 0.267- u(sK535) sref according to formula (3) Us according to formula (5)
SK507 u(sK507) 0.333 0.333- u(sK507)
SCA507 u(sCA507) 0.333 °.333- u(CA507)
SAITTS u(sAITTS) 0.067 0.067- u(sAITTS)
A^K535 u(AwK535) 0.267 0.267- u(A(K535) Atyref according to formula (4) UA9 according to formula (6)
AtyK507 u(A<oK507) 0.333 °.333- u(AtsK507)
AtyCA507 u(AwCA507) 0.333 °.333^ u(AwCA507)
AtyAITTS u(AisAITTS) 0.067 0.067- u(A<aitts)
The dispersal of the measurement results depending on the meter type was also taken into account for each input quantity in accordance with the formulas
F — F
e _ max mm
dif " 2-V3 '
where smax, smin is the maximum and minimum values of reading of the same type comparators for ratio error;
A<p _ A9max — A9 mm
Udf ~ 2>-V3 '
where A^max, A^min is the maximum and minimum values of reading of the same type comparators for phase displacement.
The reference values and the corresponding measurement uncertainties for each investigated point are summarized in the Table 3.
Table 3. Results of defining of reference values and measurement uncertainties
Alternating current percentage Reference value for Measurement uncertainty of reference value for Coverage factor Confidence level
ratio error, % phase displacement, min. ratio error, % phase displacement, min.
1 -0.2228 -3.74 0.0339 0.99 2 0.95
5 -0.0510 -4.19 0.0090 0.57
20 0.0501 -0.69 0.0061 0.44
100 0.0677 0.41 0.0050 0.31
120 0.0683 0.42 0.0050 0.31
Estimated values of measurement uncertainty are somewhat higher than those normally attributed to modern comparators, which is explained by their resolution in particular. By contrast, analogous characteristics have improved for older devices.
Conclusions. According to the results of the research work, the reference values of ratio error and phase displacement found to determine the metrological characteristics of the alternating current comparators for investigated points of 1, 5, 20, 100, 120 percent of 5 amps.
The values of the associated measurement uncertainty of the obtained reference values were calculated as well.
The use of reference values for comparison with reading of comparator under metrological investigation significantly simplifies and accelerates the calibration process.
REFERENCES
1. AMAK.411439.001 РЭ. Comparator CA507. Manual. Part 1, Kiev, "Oltest" LLC, 86 p.
2. V. Isaiev, "The problem of defining comparation accuracy of AC current amplitude values", Science and Education a New Dimension. Natural and Thechnical Sciences, V(13), Issue: 121, 2017, P. 57-60.
3. V. Isaiev, "The method of measuring the phase shift angle between two voltages using a precision voltmeter", Ukrainian Metrological Journal, Vol. 2, 2017, P. 3-7.
4. IEC 61869-1, International standard. Instrument transformers - Part 1: General requirements, Geneva: International Electrotechnical Commission, 2007, 134 p.
5. flCTY 6097, Metrology. Current transformers. Method of verification, Kyiv: SE "UkrSRTC", 2009, 18 p.
6. JCGM 100:2008 (GUM 1995), Evaluation of measurement data - Guide to the expression of uncertainty in measurement, Joint Committee for Guides in Metrology, 2008, 134 p.
