ELENG0901—Procedure for uncertainty determination for calibration consoles
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Category: Electricity
Procedure: ELENG0901
Document(s) : SE01, SE02, SS02, Bulletin E29
Distribution date: 20111205
Effective date: 20111205
Table of contents
 1.0 Scope
 2.0 References
 3.0 General guidelines
 4.0 Basic reduction equation for calibration console uncertainties
 4.1 Determination of burden uncertainty
 4.2 Determination of uncertainty due to number of meters under test
 4.3 Determination of uncertainty due to position to position errors
 4.4 Uncertainty due to current switching effects
 4.5 Uncertainty due to regulation
 4.6 Reference standard uncertainty
 4.7 Uncertainty due to interchangeable console reference meters
 5.0 Uncertainty determination using commercially available software
 6.0 Examples
 6.1 Example 1
 6.2 Example 2
 6.2.1 Uncertainty due to burden effects
 6.2.2 Uncertainty due to number of meters under test
 6.2.3 Uncertainty due to position to position errors
 6.2.4 Uncertainty due to current switching effects
 6.2.5 Uncertainty due to regulation
 6.2.6 Uncertainty due to the reference standard used for console calibration
 6.2.7 Calculations
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
 SE01 — Specifications for the calibration, certification and use of electricity calibration consoles
 SE02 — Specifications for the verification and reverification of electricity meters
 SS02 — 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 SE01, 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 (SE01 clause 7.1.5a)
 Burden Effect (SE01 clause 7.2)
 Number of Meters Under Test (SE01 clause 7.3)
 Variation from Position to Position (SE01 clause 7.4)
 Current Switching Effects (SE01 clause 7.7)
 Regulation (SE01 clause 7.6)
 Calibration reference standard
The uncertainty is established by reviewing the data gathered in respect of the requirements of the SE01 clauses above. This data can be extracted from the worksheets which are completed during the certification process of an electricity calibration console under SE01.
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 E29 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 SE01. This data can be resolved by the following equation to provide an uncertainty for the calibration console.
Description of Equation 1
The combined standard uncertainty of the console u_{c(con)} is equal to the square root of the sum of the squares of the following uncertainties:
 u_{be }/3 = Uncertainty due to burden divided by 3
 u_{nm} /3 = Uncertainty due to # of meters divided by 3
 u_{ptp} /3 = Uncertainty due to position to position errors divided by 3
 u_{cse} /3 = Uncertainty due to current switching effects divided by 3
 u_{cre} /3 = Uncertainty due to load regulation (1hour test)^{1} divided by 3
 u_{crm} /3 = Uncertainty due to load regulation (1minute test)^{1} divided by 3
 u_{rs} /2 = Uncertainty due to reference standard used to calibrate console divided by 2
 u_{rm} /2 = Uncertainty due to interchangeable console reference meter divided by 2 ^{Footnote A}
Footnotes
 Footnote A

this value is included for the case of Section 7.9 certification
where:
 u_{c(con)} = Combined Standard Uncertainty of console
 u_{be} = Uncertainty due to burden
 u_{nm} = Uncertainty due to # of meters
 u_{ptp} = Uncertainty due to position to position errors
 u_{cse} = Uncertainty due to current switching effects
 u_{cre} = Uncertainty due to load regulation (1hour test)^{Footnote 1}
 u_{crm} = Uncertainty due to load regulation (1minute test)^{Footnote 1}
 u_{rs} = Uncertainty due to reference standard used to calibrate console
 u_{rm} = Uncertainty due to interchangeable console reference meter^{Footnote 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. SE01 requires assessment of burden effects under several criteria. The criteria are identified in section 7.1.5.1 of SE01. Additional criteria for burden are also identified in Measurement Canada bulletin E29: Electricity Meter Calibration Console Burden Effects. A simplified breakdown of this criteria results in burdens for selfcontained singlephase meters, burdens for transformer type meters, and burdens for singlephase 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 SE01 or Bulletin E29 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 SE01 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 multiposition consoles. Section 7.3 of SE01 provides the information needed to establish this contribution. The difference in console error with only the reference standard in the meterundertest 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 SE01 establishes position to position errors for multiposition 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 SE01, 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 SE01, current switching effects applies only to automatic and semiautomatic 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 SE01, 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 SE01 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 7.27.7 of SE01 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 addin 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
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 multiposition board used to verify many different types of meters, including singlephase and polyphase meters. As a result, there is calibration data for singlephase 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
Figure 2
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 SE01 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 E29 will have the uncertainty determined on the basis of the spread of errors which includes the capacitive and inductive burdens.
Figure 3
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
Figure 4
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
Figure 5
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
Figure 6
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.
Description of Equation 2
The combined standard uncertainty of the console u_{c(con)} equals the square root of the sum of the squares of the following quantities:
 u_{be} /3 which is the uncertainty due to burden and is equal to 0.01% divided by 3
 u_{nm} /3 which is the uncertainty due to # of meters and is equal to 0.00% divided by 3
 u_{ptp} /3 which is the uncertainty due to position to position errors and is equal to 0.01% divided by 3
 u_{cse} /3 which is the uncertainty due to current switching effects and is equal to 0.03% divided by 3
 u_{rs} /2 which is the uncertainty due to reference standard used to certify the console and is equal to 0.005% divided by 2
where:
 u_{c(con)} = Combined Standard Uncertainty of console
 u_{be} = 0.01% Uncertainty due to burden
 u_{nm} = 0.00% Uncertainty due to # of meters
 u_{ptp} = 0.01% Uncertainty due to position to position errors
 u_{cse} = 0.03% Uncertainty due to current switching effects
 u_{rs} = 0.005% Uncertainty due to reference standard used to certify the console
Description of Equation 3
The combined standard uncertainty of the console u_{c(con)} equals the square root of the sum of the squares of the following quantities:
 u_{be} /3 which is the uncertainty due to burden and is equal to 0.01% divided by 3
 u_{nm} /3 which is the uncertainty due to # of meters and is equal to 0.00% divided by 3
 u_{ptp} /3 which is the uncertainty due to position to position errors and is equal to 0.01% divided by 3
 u_{cse} /3 which is the uncertainty due to current switching effects and is equal to 0.03% divided by 3
 u_{rs} /2 which is the uncertainty due to reference standard used to certify the console and is equal to 0.005% divided by 2
 = ±.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:
Description of Equation 4
The combined standard uncertainty of the console u_{c(con)} equals the square root of the sum of the squares of the following quantities:
 u_{be} /3 which is the uncertainty due to burden and is equal to 0.02% divided by 3
 u_{nm} /3 which is the uncertainty due to # of meters and is N/A because each position is being calibrated
 u_{ptp} /3 which is the uncertainty due to position to position errors and is N/A because each position is being calibrated
 u_{cse} /3 which is the uncertainty due to current switching effects and is equal to 0.03% divided by 3
 u_{rs} /2 which is the uncertainty due to reference standard used to certify the console and is equal to 0.005% divided by 2
where:
 u_{c(con)} = Combined Standard Uncertainty of console
 u_{be} = 0.02% Uncertainty due to burden
 u_{nm} = N/A Uncertainty due to # of meters (because each position is being calibrated)
 u_{ptp} = N/A Uncertainty due to position to position errors (because each position is being calibrated)
 u_{cse} = 0.03% Uncertainty due to current switching effects
 u_{rs} = 0.005% Uncertainty due to reference standard used to certify the console
Description of Equation 5
The combined standard uncertainty of the console u_{c(con)} equals the square root of the sum of the squares of the following quantities:
 u_{be} /3 which is the uncertainty due to burden and is equal to 0.02% divided by 3
 u_{nm} /3 which is the uncertainty due to # of meters and is N/A because each position is being calibrated
 u_{ptp} /3 which is the uncertainty due to position to position errors and is N/A because each position is being calibrated
 u_{cse} /3 which is the uncertainty due to current switching effects and is equal to 0.03% divided by 3
 u_{rs} /2 which is the uncertainty due to reference standard used to certify the console and is equal to 0.005% divided by 2
 = ±.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
Figure 7
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 2element burden results in an error difference of 0.03% . Since the 2element 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
Figure 8
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
Figure 9
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
Figure 10
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.
Figure 11
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.
Description of Equation 6
The combined standard uncertainty of the console u_{c(con)} equals the square root of the sum of the squares of the following quantities:
 u_{be} /3 which is the uncertainty due to burden and is equal to 0.03% divided by 3
 u_{nm} /3 which is the uncertainty due to # of meters and is equal to 0.04% divided by 3
 u_{ptp} /3 which is the uncertainty due to position to position errors and is equal to 0.03% divided by 3
 u_{cse} /3 which is the uncertainty due to current switching effects and is equal to 0.02% divided by 3
 u_{cre} /3 which is the uncertainty due to load regulation (1hour test) and is equal to 0.0025% divided by 3
 u_{crm} /3 which is the uncertainty due to load regulation (1minute test) and is equal to 0.15% divided by 3
 u_{rs} /2 which is the uncertainty due to reference standard used to certify the console and is equal to 0.005% divided by 2
where:
 u_{c(con)}= Combined Standard Uncertainty of console
 u_{be} = 0.03% Uncertainty due to burden
 u_{nm} = 0.04% Uncertainty due to # of meters
 u_{ptp} = 0.03% Uncertainty due to position to position errors
 u_{cse} = 0.02% Uncertainty due to current switching effects
 u_{cre} = 0.0025% Uncertainty due to load regulation (1hour test)
 u_{crm} = 0.15% Uncertainty due to load regulation (1minute test)
 u_{rs} = 0.005% Uncertainty due to reference standard used to calibrate console
Description of Equation 7
The combined standard uncertainty of the console u_{c(con)} equals the square root of the sum of the squares of the following quantities:
 u_{be} /3 which is the uncertainty due to burden and is equal to 0.03% divided by 3
 u_{nm} /3 which is the uncertainty due to # of meters and is equal to 0.04% divided by 3
 u_{ptp} /3 which is the uncertainty due to position to position errors and is equal to 0.03% divided by 3
 u_{cse} /3 which is the uncertainty due to current switching effects and is equal to 0.02% divided by 3
 u_{cre} /3 which is the uncertainty due to load regulation (1hour test) and is equal to 0.0025% divided by 3
 u_{crm} /3 which is the uncertainty due to load regulation (1minute test) and is equal to 0.15% divided by 3
 u_{rs} /2 which is the uncertainty due to reference standard used to certify the console and is equal to 0.005% divided by 2
 = ±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
 Footnote 2

this value is included for the case of Section 7.9 certification
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