EL-ENG-09-01 — Procedure for Uncertainty Determination for Calibration Consoles

Category: Electricity
Procedure: EL-ENG-09-01
Document(s) : S-E-01, S-E-02, S-S-02, Bulletin E-29
Distribution Date: 2011-12-05
Effective Date: 2011-12-05
Supersedes :


Table of Contents


1.0 Scope

This document establishes a procedure for determining measurement uncertainty for calibration console certification.

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 Guidelines

Typically the certified errors of a console will be provided with uncertainty figures determined by analysing the process(es) provided in this document. The uncertainty will be established using guidelines and recommendations found in the International Standards Organization (ISO) document, Guide to the Expression of Uncertainties (GUM). The uncertainty contributors are determined by assessments made under section 7 of S-E-01, Specifications for the Calibration, Certification and Use of Electricity Calibration Consoles. The procedure provided in this document applies specifically to certification errors used in verifying single phase, network, and polyphase electronic energy and demand meters as well as electromechanical energy meters.

Uncertainty in console calibration is influenced by the following contributors:

  • Test Burden (S-E-01 clause 7.1.5a)
  • Burden Effect (S-E-01 clause 7.2)
  • Number of Meters Under Test (S-E-01 clause 7.3)
  • Variation from Position to Position (S-E-01 clause 7.4)
  • Current Switching Effects (S-E-01 clause 7.7)
  • Regulation (S-E-01 clause 7.6)
  • Calibration reference standard

The uncertainty is established by reviewing the data gathered in respect of the requirements of the S-E-01 clauses above. This data can be extracted from the worksheets which are completed during the certification process of an electricity calibration console under S-E-01.

The test burden data is used to identify the burden effects data which in turn is used in uncertainty determination. Calibration consoles are certified to assess many types of meters. The data gathered when certifying consoles needs to be reviewed for the intended application. In this respect Bulletin E-29 also applies for determining applicable burdens and the resulting uncertainty.

For the case of consoles which are equipped with interchangeable standards, an additional source of uncertainty is also applicable. This is the uncertainty of the reference meter which is being exchanged.

4.0 Basic Reduction Equation for Calibration Console Uncertainties

As mentioned above the console uncertainties are established on the basis of data gathered through the assessment of requirements of the relevant sections of S-E-01. This data can be resolved by the following equation to provide an uncertainty for the calibration console.

where:

  • uc(con) = Combined Standard Uncertainty of console
  • ube = Uncertainty due to burden
  • unm = Uncertainty due to # of meters
  • uptp = Uncertainty due to position to position errors
  • ucse = Uncertainty due to current switching effects
  • ucre = Uncertainty due to load regulation (1-hour test)Footnote 1
  • ucrm = Uncertainty due to load regulation (1-minute test)Footnote 1
  • urs = Uncertainty due to reference standard used to calibrate console
  • urm = Uncertainty due to interchangeable console reference meterFootnote 2

The value determined by the equation above is the standard uncertainty. A coverage factor of 2 is applied to provide an expanded uncertainty value.

4.1 Determination of Burden Uncertainty

The burden effects uncertainty is a Type B uncertainty contributor. S-E-01 requires assessment of burden effects under several criteria. The criteria are identified in section 7.1.5.1 of S-E-01. Additional criteria for burden are also identified in Measurement Canada bulletin E-29: Electricity Meter Calibration Console Burden Effects. A simplified breakdown of this criteria results in burdens for self-contained single-phase meters, burdens for transformer type meters, and burdens for single-phase and/or polyphase self contained meters. The relevant uncertainty contributor is determined on the basis of the errors which are being established for a console. This will be the error of the burden which is used when calibrating the console for the given test points.

If a console is calibrated with only one set of errors then the test burden which has been identified under 7.1.5.1 of S-E-01 or Bulletin E-29 is used to establish the uncertainty contribution due to burden effects. In this case the results of the spread of errors between high burden and low burden will be used for the uncertainty figure.

If a console has an error for each position, as in the case of testing with 1:1 transformers, then the burden error established under 7.2.2.3 of S-E-01 shall be used for the uncertainty errors with 1:1 transformers.

4.2 Determination of Uncertainty due to Number of Meters Under Test

This uncertainty contributor is a type B source. It is only applicable for multi-position consoles. Section 7.3 of S-E-01 provides the information needed to establish this contribution. The difference in console error with only the reference standard in the meter-under-test position versus the error with the reference meter and meters in all other test positions establishes the uncertainty.

4.3 Determination of Uncertainty due to Position to Position Errors

Section 7.4 of S-E-01 establishes position to position errors for multi-position consoles. A single position console will not have any uncertainty contribution due to position to position errors. This uncertainty is a Type B value. The value of the maximum spread between the errors established under this assessment of section 7.4 establishes the uncertainty resulting from position to position errors.

Where a console has position to position errors between 0.1% and 0.2% as defined by the criteria of section 7.8.2.5 of S-E-01, the uncertainty due to position to position errors does not apply. In this situation each position is required to be calibrated. When each position is calibrated then an associated uncertainy applies to each position.

4.4 Uncertainty Due to Current Switching Effects

Current switching effects provides a Type B uncertainty contribution to overall console uncertainty. As identified in S-E-01, current switching effects applies only to automatic and semi-automatic consoles. The maximum spread between the errors observed during the assessment of current switching errors in section 7.7 provides the value of uncertainty.

4.5 Uncertainty Due to Regulation

Consoles which are used to verify demand meters will have an uncertainty in the certified demand errors due to the console regulation. Console regulation is assessed using three criteria. First the test load is assessed in terms of its stability over a one hour period. Second the test load is assessed for its stability at one minute intervals. Finally the test load is assessed for its variations between one minute intervals. There are two contributors to uncertainty from these assessments. The first is the one hour load stability. The uncertainty due to the load variation is determined by using the variation figure established under the test of section 7.6.1.1 of S-E-01, and dividing it by four. This applies for block interval demand meters having a fifteen minute demand. The second uncertainty contributor relates to the variation between one minute energy readings. The maximum variation from the expected energy as established under section 7.6.1.2 of S-E-01 provides the value of the uncertainty.

The regulation assessment is performed at two loads. This can provide two uncertainty values which can be applied for test loads which are representative of the assessment loads. A second option which is acceptable is to use the higher uncertainty value for all demand meter calibrations.

4.6 Reference Standard Uncertainty

The reference standard which is used to calibrate the console and to establish the influence errors of sections 7.2-7.7 of S-E-01 is a source for uncertainty in console calibration. The uncertainty of the reference standard can be found on the calibration certificate for the standard.

Note: Measurement Canada Laboratories are in the process of updating certificates of calibration for reference meters which will include uncertainty figures. In the interim a default uncertainty figure of 0.005% may be used for all reference meters provided by Radian Research. Uncertainties for other reference meter types will need to be established prior to their use in console calibration.

4.7 Uncertainty Due to Interchangeable Console Reference Meters

Consoles which are being certified with errors for interchangeable reference meters will have an additional uncertainty associated with the reference meter which would be interchanged. The uncertainty of this reference meter will be found on the certificate of errors for the reference meter.

5.0 Uncertainty Determination Using Commercially Available Software

The electricity industry has standardized on a software package from Quametec which is Uncertainty Toolbox. This procedure is not intended to be a guide to using the program specifically. It is intended to provide guidance in identifying appropriate parameters to allow the software to calculate an uncertainty value for console certification. For the purposes of this program a base template is being provided. This procedure will identify the parameters which can be updated to enable the program to calculate the uncertainty value. A basic template is provided which can be executed on any excel program which has been updated with the Quametec Uncertainty Toolbox add-in program.

The basic template is an Excel file with filename: "Console Calibration Template.xls". The tab labelled "Budget" provides the tools to determine console uncertainties on the basis of the console calibration data described above. In order to determine the uncertainty value for a given console simply update column "E" (Parameter Uncertainty Limits) with the appropriate values obtained from the console worksheets.

Figure 1
An Example of the "Console Calibration template.xls" built from the Quametec Uncertainty Toolbox (the long description is located below the image)

An Example of the "Console Calibration template.xls" built from the Quametec Uncertainty Toolbox. The sheet represents the Uncertainty Budget Tab which can be used to determine the uncertainty value for a given console by updating it with the appropriate values obtained from the console worksheets.

6.0 Examples

6.1 Example 1

Extracts from a worksheets representing data from a console calibration exercise will be used to establish an uncertainty for the console calibration. In this example, the console is a multi-position board used to verify many different types of meters, including single-phase and polyphase meters. As a result, there is calibration data for single-phase meters (1:1 transformers are in circuit) as well as data for all other meter types. In this particular example the 1:1 transformers are used for energy meter testing only. There may be situations where the demand meter testing may also require the use of 1:1 transformers. In this case the uncertainty due to regulation will need to be included as well.

There are two sets of calibration errors established for this console. The uncertainty contributors are identified first.

6.1.1 Uncertainty due to burden effects

In this example the test burden is established for the two conditions of use. One is the test burden with the 1:1 transformers in circuit and the other is the test burden for all other applications. Data is established for each 1:1 transformer position under S-E-01 section 7.8, console calibration. This means that there will be an uncertainty figure associated with each of the 1:1 positions. The data from section 7.2.5.2 is used for the uncertainty figures for each position. As an example for the case of position 3, the spread of errors between high burden and low burden is 0.02%. This represent the uncertainty figure which will be used in the uncertainty budget. It should be noted here that a console for which burden errors are also established as determined by the requirements of bulletin E-29 will have the uncertainty determined on the basis of the spread of errors which includes the capacitive and inductive burdens.

For the case of calibration when 1:1 transformers are not in circuit the uncertainty is determined using the data for both single phase and polyphase meters. From the worksheets, the uncertainty is the error spread identified in entry "C" of the table in Section 7.1.4. This spread is 0.01%.

6.1.2 Uncertainty due to number of meters under test

The uncertainty due to number of meters under test is determined by looking at the difference in the error with the reference meter only in circuit and the error with burdens in all meter under test positions. In the case of the example, from section 7.3 of the worksheets, the difference is 0.0%

This uncertainty contributor only applies to the uncertainty determination for the case when one 1:1 transformers are not in circuit.

6.1.3 Uncertainty due to position to position errors

The uncertainty contribution from position to position errors only applies to the case when 1:1 transformers are not in circuit. In this case the difference between the greatest and smallest errors represents the uncertainty due to position to position errors. For this example, from section 7.4 of the worksheets, the maximum spread is 0.01%.

6.1.4 Uncertainty due to current switching effects

The uncertainty contribution due to current switching effects is established from the spread of errors observed over five runs. In this case table 7.7 indicates a spread of 0.03%.

6.1.5 Uncertainty due to the reference standard used for console calibration

The reference standard which is used to certify the console will have an uncertainty found on the certificate of calibration for the standard. For this example a value of 0.005%.

6.1.6 Calculations

Use the formula below with the applicable contributors.

For the case when 1:1 transformers are not in circuit.

where:

  • uc(con) = Combined Standard Uncertainty of console
  • ube = 0.01% Uncertainty due to burden
  • unm = 0.00% Uncertainty due to # of meters
  • uptp = 0.01% Uncertainty due to position to position errors
  • ucse = 0.03% Uncertainty due to current switching effects
  • urs = 0.005% Uncertainty due to reference standard used to certify the console
  • = ±.01% (rounded to 2 decimal places)

This uncertainty represents the combined standard console uncertainty for the errors established for the case of no intervening transformers (1:1)

A coverage factor of k=2 provides an expanded uncertainty value of ±0.02%

This value should be stated on the certificate of errors.

For the case when 1:1 transformers are in circuit an uncertainty figure will be established for each position of the console. For each case the uncertainty will be stated with the respective console position errors established under section 7.8.

As an example for position # 3 in the data sheets the relevant contributors are:

where:

  • uc(con) = Combined Standard Uncertainty of console
  • ube = 0.02% Uncertainty due to burden
  • unm = N/A Uncertainty due to # of meters (because each position is being calibrated)
  • uptp = N/A Uncertainty due to position to position errors (because each position is being calibrated)
  • ucse = 0.03% Uncertainty due to current switching effects
  • urs = 0.005% Uncertainty due to reference standard used to certify the console
  • = ±.01% (rounded to 2 decimal places)

With similar entries in the Quamatec software a standard uncertainty of ±0.01% is also established.

The expanded uncertainty of ±0.02% with k=2 can be stated on the certificate of errors for position #3 with 1:1 transformers in circuit.

6.2 Example 2

This example relates to a console used to assess an electronic polyphase transformer type demand meter. The extracts from worksheets relevant to uncertainty determination are provided. This is a multi position console used for testing both single phase and polyphase meters.

6.2.1 Uncertainty due to burden effects

The worksheets provide burden data for three scenarios. Under section 7.1.4 of the worksheets, the section "B" results provide data for the case of testing polyphase transformer type meters. In this case the 2-element burden results in an error difference of 0.03% . Since the 2-element meter will be used as the burden for console calibration, an uncertainty of 0.03% is used as the value in establishing the combined uncertainty for the console calibration.

6.2.2 Uncertainty due to number of meters under test

The uncertainty due to number of meters under test is determined by looking at the difference in the error with the reference meter only in circuit and the error with burdens in all meter under test positions. In the case of the example, from section 7.3 of the worksheets, the difference is 0.04%

6.2.3 Uncertainty due to position to position errors

The uncertainty contribution from position to position errors only applies to the case when 1:1 transformers are not in circuit. In this case the difference between the greatest and smallest errors represents the uncertainty due to position to position errors. For this example, from section 7.4 of the worksheets, the maximum spread is 0.03%.

6.2.4 Uncertainty due to current switching effects

The uncertainty contribution due to current switching effects is established from the spread of errors observed over five runs. In this case table 7.7 indicates a spread of 0.02%.

6.2.5 Uncertainty due to regulation

The uncertainty due to console regulation has two components. The first is the contribution due to the load holding capability of the console. This is determined from the one hour load monitoring test result. The data for this console shows that the load was held to within 0.01%. over one hour. The uncertainty contribution over a fifteen minute period is them determined to be 0.0025% (= 0.01/4).

The second component to uncertainty due to regulation relates to the consoles ability to provide steady loads over one minute intervals. For this contribution the maximum departure from the expected energy for one minute establishes the uncertainty.

For the case of this example, from section 7.6 of the worksheets, the variation is 0.15% to −0.11%. 0.15% is the maximum excursion and therefore is the value used to establish an uncertainty contribution of 0.15% due to one minute load regulation test.

6.2.6 Uncertainty due to the reference standard used for console calibration

The reference standard which is used to certify the console will have an uncertainty found on the certificate of calibration for the standard. For this example a value of 0.005%

6.2.7 Calculations

Use the formula below with the applicable contributors.

where:

  • uc(con)= Combined Standard Uncertainty of console
  • ube = 0.03% Uncertainty due to burden
  • unm = 0.04% Uncertainty due to # of meters
  • uptp = 0.03% Uncertainty due to position to position errors
  • ucse = 0.02% Uncertainty due to current switching effects
  • ucre = 0.0025% Uncertainty due to load regulation (1-hour test)
  • ucrm = 0.15% Uncertainty due to load regulation (1-minute test)
  • urs = 0.005% Uncertainty due to reference standard used to calibrate console
  • = ±0.0547%
  • = ±0.05% (rounded to two decimal places)

This uncertainty represents the standard console uncertainty for the errors established for the case of a console used for assessing transformer type polyphase demand meters. This example provides the standard uncertainty at the low load test point as provided under the regulation assessments. This uncertainty can be applied for all transformer type meters. Another assessment can be performed for the high load regulation assessment and this would be applied for self contained meters.

The uncertainty for polyphase energy meters would be the same as above except the uncertainties for regulation would be removed from the formula.

The expanded uncertainty with a k=2 factor for the example above is ±0.10%

Footnotes

Footnote 1

Applicable to demand calibration test points

Return to footnote 1 referrer

Footnote 2

this value is included for the case of Section 7.9 certification

Return to footnote 2 referrer