Uncertainty Determination of Electricity Meter Types

Uncertainty Determination of Electricity Meter Types (PDF, 59 KB, 8 pages)

Category: Electricity
Procedure: EL-ENG-09-02
Document(s) : S-E-01, S-E-02, S-S-02, Bulletin E-29
Distribution Date:
Effective Date:
Supersedes :

Record of Changes
Revision Date Description
Rev. 0 Initial Release

Table of Contents

1.0 Scope

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

2.0 References

  • GUM — Guide to the Expression of Uncertainties
  • S-E-01 — Specifications for the Calibration, Certification and Use of Electricity Calibration Consoles
  • S-E-02 — Specifications for the Verification and Reverification of Electricity Meters
  • S-S-02 — Measurement Uncertainty and Meter Conformity Evaluation Specifications

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 by International Standards Organization (ISO) document: Guide to the Expression of Uncertainties (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 numbers of element. Where an uncertainty is required under specified meter tests of S-E-02, the uncertainty of the respective test point may be applied or optionally the largest value of the uncertainties described above may be applied.

Each uncertainty determination for a given meter Type is applicable only for the organization which established the uncertainty and is applicable 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 Sources of uncertainty

The uncertainty of an energy meter shall be established at all applicable verification test points for one energy (typically watt hour) function. Verification tests are normally conducted with meter elements connected in series/parallel configuration or connected as individual elements. The three series points are traditionally referred to as light load (LL), high load unity power factor (HL, unity power factor) and high load power factor (HL power factor). These relate to load currents of 2.5%Imax (LL), 25% Imax (HL, unity power factor) and 25% Imax 0.5pF (HL power factor). The voltage shall be the rated voltage of the meter. For multi-rated meters the lowest standard approved voltage shall be used. For 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 individual uncertainty determined in respect of 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 ony to the electronic demand meter type. The uncertainty for demand meters shall 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
  • X̄ = sample mean
  • n = number of runs

For the purpose of 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 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

A single-phase 1.5 element, 3-wire meter is tested at three test points with 10 repeated runs. The table below provides the results.

Example 1: Singlephase, 1.5 element, 3-wire meter

  2.5%Imax 1.0pF 25%Imax 1.0pF 25%Imax 0.5pF Series
Xi (X−X̄) (X−X̄)2 Xi (X−X̄) (X−X̄)2 Xi (X-X̄) (X-X̄)2
X̄ 0.012   0.138   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 0.018738 0.092592 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 0.005925476 0.029280161 0.008666538
Run #1 0.03 0.018 0.000324 0.14 0.002 0.000004 0.08 −0.012 0.000144
Run #2 0.01 −0.002 4.00E-06 0.15 0.012 0.000144 0.06 −0.032 0.001024
Run #3 0.01 −0.002 4.00E-06 0.2 0.062 0.003844 0.09 −0.002 0.000004
Run #4 −0.01 −0.022 0.000484 −0.1 −0.238 0.056644 0.09 −0.002 0.000004
Run #5 0.02 0.008 0.000064 0.16 0.022 0.000484 0.04 −0.052 0.002704
Run #6 0.01 −0.002 4.00E-06 0.09 −0.048 0.002304 0.11 0.018 0.000324
Run #7 0.04 0.028 0.000784 0.13 −0.008 0.000064 0.09 −0.002 0.000004
Run #8 −0.02 −0.032 0.001024 0.21 0.072 0.005184 0.12 0.028 0.000784
Run #9 0 −0.012 0.000144 0.22 0.082 0.006724 0.11 0.018 0.000324
Run #10 0.03 0.018 0.000324 0.18 0.042 0.001764 0.13 0.038 0.001444

In this example the meter repeatability uncertainties expressed as standard uncertainties are:

  • 2,5 %Imax 1,0pF : us=±0,0059 % ou ±0,01 % (2 significant digits)
  • 25 %Imax 1,0pF : us=±0,0293 % ou ±0,03 % (2 significant digits)
  • 25 %Imax 0,5pF : us=±0,0087 % ou ±0,01 % (2 significant digits)

The standard uncertainties established above can be stated to 2 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.

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. The table below provides the results.

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

  2.5%Imax 1.0pF 25%Imax 1.0pF 25%Imax 0.5pF Series 25%Imax 0.5pF (Left) 25%Imax 0.5pF (Right)
Xi (X−X̄) (X−X̄)2 Xi (X−X̄) (X−X̄)2 Xi (X-X̄) (X-X̄)2 Xi (X−X̄) (X−X̄)2 Xi (X-X̄) (X-X̄)2
X̄ 0.012   0.138   0.092   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 0.018738 0.092592 0.027406 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 0.005925476 0.029280161 0.008666538 0.017448336 0.011035297
Run #1 0.03 0.018 0.000324 0.14 0.002 0.000004 0.08 −0.012 0.000144 0.04 −0.02 0.0004 0.11 0.022 0.000484
Run #2 0.01 −0.002 4.00E-06 0.15 0.012 0.000144 0.06 −0.032 0.001024 −0.01 −0.07 0.0049 0.1 0.012 0.000144
Run #3 0.01 −0.002 4.00E-06 0.2 0.062 0.003844 0.09 −0.002 0.000004 −0.02 −0.08 0.0064 0.09 0.002 4E-06
Run #4 −0.01 −0.022 0.000484 −0.1 −0.238 0.056644 0.09 −0.002 0.000004 0.03 −0.03 0.0009 0.06 −0.028 0.000784
Run #5 0.02 0.008 0.000064 0.16 0.022 0.000484 0.04 −0.052 0.002704 0.04 −0.02 0.0004 0.01 −0.078 0.006084
Run #6 0.01 −0.002 4.00E-06 0.09 −0.048 0.002304 0.11 0.018 0.000324 0.13 0.07 0.0049 0.08 −0.008 6.4E-05
Run #7 0.04 0.028 0.000784 0.13 −0.008 0.000064 0.09 −0.002 0.000004 0.05 −0.01 1E-04 0.11 0.022 0.000484
Run #8 −0.02 −0.032 0.001024 0.21 0.072 0.005184 0.12 0.028 0.000784 0.09 0.03 0.0009 0.14 0.052 0.002704
Run #9 0 −0.012 0.000144 0.22 0.082 0.006724 0.11 0.018 0.000324 0.12 0.06 0.0036 0.08 −0.008 6.4E-05
Run #10 0.03 0.018 0.000324 0.18 0.042 0.001764 0.13 0.038 0.001444 0.13 0.07 0.0049 0.1 0.012 0.000144

In this example the meter repeatability uncertainties expressed as standard uncertainties are:

  • 2.5%Imax 1.0pF: us=±0.0059% or ±0.01% (2 significant digits)
  • 25%Imax 1.0pF: us=±0.0293% or ±0.03% (2 significant digits)
  • 25%Imax 0.5pF: us=±0.0087% or ±0.01% (2 significant digits)
  • 25%Imax 0.5pF (Left element) : us=±0.0174% or ±0.02% (2 significant digits)
  • 25%Imax 0.5pF (Right element): us=±0.011% or ±0.01% (2 significant digits)

The standard uncertainties established above can be stated to 2 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.

A polyphase 3 element, 4-wire demand meter is tested at one series test points with 10 repeated runs. The tests were conducted for the VA demand function. The table below provides the results.

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

  25%Imax 0.5pF
Xi (X−X̄) (X−X̄)2
X̄ 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
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

In this example the meter repeatability uncertainty for the demand function is expressed as a standard uncertainty is:

  • 25%Imax 0.5pF: us=±0.0109% or ±0.01% (2 significant digits)

The standard uncertainties established above can be stated to 2 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.