EL-ENG-09-02—Uncertainty determination of electricity meter types

Category: Electricity
Issue date:
Effective date:
Revision number: Rev. 1
Supersedes: N/A


Table of contents


1.0 Scope

This document establishes a procedure for determining the uncertainty of electricity meter types.

2.0 References

Guide to the Expression of Uncertainty in Measurement (GUM):1993 (corrected and reprinted 1995), BIPM/IEC/IFCC/ISO/IUPAC/IUPAP/OIML

3.0 General

An electricity meter is a measuring device, and as such, any measurement result provided by the meter has an uncertainty associated with it. This document provides a procedure for establishing the basic measurement uncertainty associated with an electricity meter. The measurement uncertainty is determined in accordance with recommendations and principles provided in the Guide to the Expression of Uncertainty in Measurement (GUM).

The uncertainty established by this procedure may be applied to all meters which are covered under the same Notice of Approval and have the same ratings and number of elements. Where an uncertainty is required under specified meter tests of S-E-02, the uncertainty of the respective test point may be applied or the largest value of the uncertainties described above may be applied.

Each uncertainty determined for a given meter type is applicable only for the organization which established the uncertainty and only when the same verification procedure which was used to establish the uncertainty is also used for the S-E-02 verification tests.

4.0 Test points for establishing uncertainty

4.1 Energy meters

The uncertainty of an energy meter must be established at all applicable verification test points for one energy (typically watt hour) function. Verification tests are normally conducted in series configuration as well as individual elements. The three series points are traditionally referred to as light load (LL), high load (HL) unity power factor and HL power factor. These relate to load currents of 2.5% Imax (LL), 25% Imax (HL unity power factor) and 25% Imax 0.5 pF (HL power factor). The voltage must be the rated voltage of the meter. For multi-rated meters, the lowest standard approved voltage must be used. In the case of polyphase meters, there can be two additional test points associated with the individual element assessments. For the purposes of establishing the meter uncertainty, each uncertainty determined for the test points identified above may be used with the respective meter test points. Alternatively, the highest uncertainty determined from the assessments described above can be applied for all test points.

4.2 Demand meters

Uncertainty determination for demand meters is currently applicable only to the electronic demand meter type. The uncertainty for demand meters must be determined at the demand meter test point applicable for each demand type (block or exponential) for which the meter is approved. The uncertainty determined for one demand function (watt, va or var) may be used for each demand function.

5.0 Uncertainty determination

The uncertainty of a meter due to repeatability is a Type A uncertainty. The standard uncertainty is established by determining the standard deviation of a sample of repeated runs using the formula below.

The sample standard deviation is equal to the square root of one divided by the number of runs times minus one and multiplied by the sum of the squares of each measured value minus the sample mean

Where:

s
= sample standard deviation
xi
= measured value
= sample mean
n
= number of runs

For the purpose of determining meter repeatability uncertainty, it is recommended that at least 10 repeated runs be conducted at each of the test points identified above. For meters which have large uncertainties due to repeatability, the number of runs can be increased to 30.

The uncertainty due to meter under test (MUT) repeatability can then be determined as follows.

The standard uncertainty due to the meter repeatability is equal to the sample standard deviation divided by the square root of the number of run times

Example 1: Single-phase 1.5-element 3-wire meter

A single-phase 1.5-element 3-wire meter is tested at three test points with 10 repeated runs. Tables 1 to 6 provide meter test results and uncertainty calculations.

Table 1: Test results at 2.5% Imax 1.0 pF
Test run 2.5% Imax 1.0 pF
xi (x−x̄) (x−)2
Run 1 0.03 0.018 0.000324
Run 2 0.01 −0.002 0.000004
Run 3 0.01 −0.002 0.000004
Run 4 −0.01 −0.022 0.000484
Run 5 0.02 0.008 0.000064
Run 6 0.01 −0.002 0.000004
Run 7 0.04 0.028 0.000784
Run 8 −0.02 −0.032 0.001024
Run 9 0 −0.012 0.000144
Run 10 0.03 0.018 0.000324
Table 2: Calculated values for tests at 2.5% Imax 1.0 pF
Uncertainty parameter Calculated value
0.012
The sample standard deviation is equal to the square root of one divided by the number of runs times minus one and multiplied by the sum of the squares of each measured value minus the sample mean 0.018738
The standard uncertainty due to the meter repeatability is equal to the sample standard deviation divided by the square root of the number of run times 0.005925476
Table 3: Test results at 25% Imax 1.0 pF
Test run 25% Imax 1.0 pF
xi (x− x̄) (x− x̄)2
Run 1 0.14 0.0020 0.000004
Run 2 0.15 0.0120 0.000144
Run 3 0.2 0.0620 0.003844
Run 4 −0.1 −0.2380 0.056644
Run 5 0.16 0.0220 0.000484
Run 6 0.09 −0.0480 0.002304
Run 7 0.13 −0.0080 0.000064
Run 8 0.21 0.0720 0.005184
Run 9 0.22 0.0820 0.006724
Run 10 0.18 0.0420 0.001764
Table 4: Calculated values for tests at 25% Imax 1.0 pF
Uncertainty parameter Calculated value
0.1380
The sample standard deviation is equal to the square root of one divided by the number of runs times minus one and multiplied by the sum of the squares of each measured value minus the sample mean 0.092592
The standard uncertainty due to the meter repeatability is equal to the sample standard deviation divided by the square root of the number of run times 0.029280161
Table 5: Test results at 25% Imax 0.5 pF
Test run 25% Imax 0.5 pF
xi (x− x̄) (x− x̄)2
Run 1 0.08 −0.0120 0.000144
Run 2 0.06 −0.0320 0.001024
Run 3 0.09 −0.0020 0.000004
Run 4 0.09 −0.0020 0.000004
Run 5 0.04 −0.0520 0.002704
Run 6 0.11 0.0180 0.000324
Run 7 0.09 −0.0020 0.000004
Run 8 0.12 0.0280 0.000784
Run 9 0.11 0.0180 0.000324
Run 10 0.13 0.0380 0.001444
Table 6: Calculated values for tests at 25% Imax 0.5 pF
Uncertainty parameter Calculated value
0.0920
The sample standard deviation is equal to the square root of one divided by the number of runs times minus one and multiplied by the sum of the squares of each measured value minus the sample mean 0.027406
The standard uncertainty due to the meter repeatability is equal to the sample standard deviation divided by the square root of the number of run times 0.008666538

In this example, the meter repeatability uncertainties are as follows.

The standard uncertainties established above can be stated to two significant digits after the decimal point.

For the purposes of uncertainty due to meter repeatability, the highest uncertainty determined above may be used for all meter tests or each individual uncertainty can be applied for the respective test point.

Example 2: Polyphase 3-element 4-wire energy meter

A polyphase 3-element 4-wire meter is tested at three series test points and two individual element test points, each with 10 repeated runs. The tests are conducted for the watthour function. Tables 7 to 14 provide meter test results and uncertainty calculations.

Table 7: Test results at 2.5% Imax 1.0 pF
Test run 2.5% Imax 1.0 pF
(xi− x̄) (xi− x̄)2
Run 1 0.03 0.018 0.000324
Run 2 0.01 −0.002 0.000004
Run 3 0.01 −0.002 0.000004
Run 4 −0.01 −0.022 0.000484
Run 5 0.02 0.008 0.000064
Run 6 0.01 −0.002 0.000004
Run 7 0.04 0.028 0.000784
Run 8 −0.02 −0.032 0.001024
Run 9 0 −0.012 0.000144
Run 10 0.03 0.018 0.000324
Table 8: Calculated values for tests at 2.5% Imax 1.0 pF
Uncertainty parameter Calculated value
0.012
The sample standard deviation is equal to the square root of one divided by the number of runs times minus one and multiplied by the sum of the squares of each measured value minus the sample mean 0.018738
The standard uncertainty due to the meter repeatability is equal to the sample standard deviation divided by the square root of the number of run times 0.005925476
Table 9: Test results at 25% Imax 1.0 pF
Test run 25% Imax 1.0 pF
xi− x̄) xi− x̄)2
Run 1 0.14 0.002 0.000004
Run 2 0.15 0.012 0.000144
Run 3 0.2 0.062 0.003844
Run 4 −0.1 −0.238 0.056644
Run 5 0.16 0.022 0.000484
Run 6 0.09 −0.048 0.002304
Run 7 0.13 −0.008 0.000064
Run 8 0.21 0.072 0.005184
Run 9 0.22 0.082 0.006724
Run 10 0.18 0.042 0.001764
Table 10: Calculated values for tests at 25% Imax 1.0 pF
Uncertainty parameter Calculated value
0.138
The sample standard deviation is equal to the square root of one divided by the number of runs times minus one and multiplied by the sum of the squares of each measured value minus the sample mean 0.092592
The standard uncertainty due to the meter repeatability is equal to the sample standard deviation divided by the square root of the number of run times 0.029280161
Table 11: Test results at 25% Imax 0.5 pF series
Test run 25% Imax 0.5 pF series
(xi) (xi)2
Run 1 0.08 −0.012 0.000144
Run 2 0.06 −0.032 0.001024
Run 3 0.09 −0.002 0.000004
Run 4 0.09 −0.002 0.000004
Run 5 0.04 −0.052 0.002704
Run 6 0.11 0.018 0.000324
Run 7 0.09 −0.002 0.000004
Run 8 0.12 0.028 0.000784
Run 9 0.11 0.018 0.000324
Run 10 0.13 0.038 0.001444
Table 12: Calculated values for tests at 25% Imax 0.5 pF series
Uncertainty parameter Calculated value
0.092
The sample standard deviation is equal to the square root of one divided by the number of runs times minus one and multiplied by the sum of the squares of each measured value minus the sample mean 0.027406
The standard uncertainty due to the meter repeatability is equal to the sample standard deviation divided by the square root of the number of run times 0.008666538
Table 13: Test results at 25% Imax 0.5 pF individual elements
Test Run 25% Imax 0.5 pF (left) 25% Imax 0.5 pF (right)
(xi−x̄) (xi−x̄)2 (xi−x̄) (xi−x̄)2
Run 1 0.04 −0.02 0.0004 0.11 0.022 0.000484
Run 2 −0.01 −0.07 0.0049 0.1 0.012 0.000144
Run 3 −0.02 −0.08 0.0064 0.09 0.002 0.000004
Run 4 0.03 −0.03 0.0009 0.06 −0.028 0.000784
Run 5 0.04 −0.02 0.0004 0.01 −0.078 0.006084
Run 6 0.13 0.07 0.0049 0.08 −0.008 0.000064
Run 7 0.05 −0.01 0.0001 0.11 0.022 0.000484
Run 8 0.09 0.03 0.0009 0.14 0.052 0.002704
Run 9 0.12 0.06 0.0036 0.08 −0.008 0.000064
Run 10 0.13 0.07 0.0049 0.1 0.012 0.000144
Table 14: Calculated values for tests at 25% Imax 0.5 pF individual elements
Uncertainty parameter Calculated value Calculated value
0.06 0.088
The sample standard deviation is equal to the square root of one divided by the number of runs times minus one and multiplied by the sum of the squares of each measured value minus the sample mean 0.055176485 0.034896673
The standard uncertainty due to the meter repeatability is equal to the sample standard deviation divided by the square root of the number of run times 0.017448336 0.011035297

In this example, the meter repeatability uncertainties expressed as standard uncertainties are as follows.

The standard uncertainties established above can be stated to two significant digits after the decimal point.

For the purposes of uncertainty due to meter repeatability, the highest uncertainty determined above may be used for all meter tests or each uncertainty can be applied for the respective test point.

Example 3: Polyphase 3-element 4-wire demand meter

A polyphase 3-element 4-wire demand meter is tested at one series test point with 10 repeated runs. The tests were conducted for the VA demand function. Tables 15 and 16 below provide the test results and uncertainty calculations.

Table 15: Demand meter test results
Test run 25% Imax 1.0 pF
(xi−x̄ (xi−x̄2
Run 1 0.08 0.062 0.003844
Run 2 −0.02 −0.038 0.001444
Run 3 −0.01 −0.028 0.000784
Run 4 −0.01 −0.028 0.000784
Run 5 0.04 0.022 0.000484
Run 6 0.03 0.012 0.000144
Run 7 0.05 0.032 0.001024
Run 8 −0.02 −0.038 0.001444
Run 9 0 −0.018 0.000324
Run 10 0.04 0.022 0.000484
Table 16: Calculated values for demand meter tests
Uncertainty parameter Calculated value
0.018
The sample standard deviation is equal to the square root of one divided by the number of runs times minus one and multiplied by the sum of the squares of each measured value minus the sample mean 0.034576807
The standard uncertainty due to the meter repeatability is equal to the sample standard deviation divided by the square root of the number of run times 0.010934146

In this example, the meter repeatability uncertainty for the demand function is expressed as a standard uncertainty is as follows.

The standard uncertainties established above can be stated to two significant digits after the decimal point.

For the purposes of uncertainty due to meter repeatability, this uncertainty can be applied to all meter demand functions.

Record of changes
Revision Date Description
Rev. 1
  • Updated the document format.
  • Removed references to S-E-01.
Date modified: