ELENG0902—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
 2.0 References
 3.0 General
 4.0 Test points for establishing uncertainty
 5.0 Uncertainty determination
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
 ELENG1201—Requirements for the Certification and Use of Measuring Apparatus — Electricity Meter Calibration Consoles
 SE02—Specifications for the Verification and the Reverification of Electricity Meters
 SS02—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 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 SE02, 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 SE02 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% I_{max} (LL), 25% I_{max} (HL unity power factor) and 25% I_{max} 0.5 pF (HL power factor). The voltage must be the rated voltage of the meter. For multirated 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.
Where:
 s
 = sample standard deviation
 x_{i}
 = measured value
 x̄
 = 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.
Example 1: Singlephase 1.5element 3wire meter
A singlephase 1.5element 3wire meter is tested at three test points with 10 repeated runs. Tables 1 to 6 provide meter test results and uncertainty calculations.
Test run  2.5% I_{max} 1.0 pF  

x_{i}  (x−x̄)  (x−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 
Uncertainty parameter  Calculated value 

x̄  0.012 
0.018738  
0.005925476 
Test run  25% I_{max} 1.0 pF  

x_{i}  (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 
Uncertainty parameter  Calculated value 

x̄  0.1380 
0.092592  
0.029280161 
Test run  25% I_{max} 0.5 pF  

x_{i}  (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 
Uncertainty parameter  Calculated value 

x̄  0.0920 
0.027406  
0.008666538 
In this example, the meter repeatability uncertainties are as follows.
 2.5% I_{max} 1.0 pF: U_{s}=0.0059 or 0.01 (two significant digits)
 25% I_{max} 1.0 pF: U_{s} =0.0293 or 0.03 (two significant digits)
 25% I_{max} 0.5 pF: U_{s} =0.0087 or 0.01 (two significant digits)
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 3element 4wire energy meter
A polyphase 3element 4wire 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.
Test run  2.5% I_{max} 1.0 pF  

x̄  (x_{i}− x̄)  (x_{i}− 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 
Uncertainty parameter  Calculated value 

x̄  0.012 
0.018738  
0.005925476 
Test run  25% I_{max} 1.0 pF  

x̄  x_{i}− x̄)  x_{i}− 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 
Uncertainty parameter  Calculated value 

x̄  0.138 
0.092592  
0.029280161 
Test run  25% I_{max} 0.5 pF series  

x̄  (x_{i} x̄)  (x_{i} x̄)^{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 
Uncertainty parameter  Calculated value 

x̄  0.092 
0.027406  
0.008666538 
Test Run  25% I_{max} 0.5 pF (left)  25% I_{max} 0.5 pF (right)  

x̄  (x_{i}−x̄)  (x_{i}−x̄)^{2}  x̄  (x_{i}−x̄)  (x_{i}−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 
Uncertainty parameter  Calculated value  Calculated value 

x̄  0.06  0.088 
0.055176485  0.034896673  
0.017448336  0.011035297 
In this example, the meter repeatability uncertainties expressed as standard uncertainties are as follows.
 2.5% I_{max} 1.0 pF: U_{s} =±0.0059% or ±0.01% (two significant digits)
 25% I_{max} 1.0 pF: U_{s} =±0.0293% or ±0.03% (two significant digits)
 25% I_{max} 0.5 pF: U_{s} =±0.0087% or ±0.01% (two significant digits)
 25% I_{max} 0.5 pF (left element): U_{s} =±0.0174% or ±0.02% (two significant digits)
 25% I_{max} 0.5 pF (right element): U_{s} =±0.011% or ±0.01% (two significant digits)
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 3element 4wire demand meter
A polyphase 3element 4wire 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.
Test run  25% I_{max} 1.0 pF  

x̄  (x_{i}−x̄  (x_{i}−x̄^{2}  
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 
Uncertainty parameter  Calculated value 

x̄  0.018 
0.034576807  
0.010934146 
In this example, the meter repeatability uncertainty for the demand function is expressed as a standard uncertainty is as follows.
 25% I_{max} 0.5 pF: U_{s} =±0.0109% or ±0.01% (two significant digits)
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.
Revision  Date  Description 

Rev. 1 

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