4.6.1 The approach in IEC 60060-2:2010
The uncertainty calculation has been significantly revised in the latest edition of IEC 60060-2:2010. The reasons for this major revision are mainly two fold.
First, the revision is to provide testing personnel a simple and practical method of estimating measurement uncertainties that is consistent with ISO 98-3, Guide on Uncertainty of Measurement (ISO GUM). The method is intended to cover most common cases of high-voltage testing.
Second, the approach described in the previous edition of IEC 60060-2 (Appendix H in IEC 60060-2:1994) is no longer considered consistent with the current edition of ISO Guide on Uncertainty of Measurement. That approach categorizes the uncertainty contributions as either “systematic” or “random”. Appendix H of IEC 60060-2:1994 also assumes that all systematic contributions can be covered by two types of distributions, the rectangular distribution and the Gaussian distribution. It also implies that systematic contributions can be considered to have infinite degrees of freedom. In fact, the use of “degrees of freedom”
is omitted in Appendix H. These assumptions and omissions are now considered not adequate for many practical applications. Appendix H also omitted the concept “sensitivity coefficient”, another important concept that is used in the current ISO GUM and that has now been adopted in IEC 60060-2:2010.
The major change advocated in the ISO GUM is to provide realistic estimates of measurement uncertainties, moving away from treating measurement uncertainty as a safe error limit, that is, treating measurement uncertainty as an estimate of maximum error that can possibly be expected for the measurement. By adopting the latest ISO GUM approach, it is possible to achieve measurement uncertainties that fit a specific testing purpose with less costly equipment and less time consuming procedures.
In the 1994 edition of 60060-2, specified fixed limits were given for individual uncertainty components, for example, a 1 % limit was specified for non-linearity of voltage measurement systems. Fixed numbers of repeated measurements were also specified. An example of this is that the number of repeated applied impulses during an impulse voltage calibration was specified to be at least 10. With the adoption of the ISO GUM approach in the 2010 edition, these limits are no longer specified as long as the total expanded uncertainty (expanded uncertainty is a defined term) is within the required limit. The removal of these limits becomes possible because of the adoption of the statistically more rigorous approach of the ISO GUM.
The 2010 edition of IEC 60060-2 also adopts an approach that is intended to provide practical help to users of the standard to better adapt to the new method of estimating measurement uncertainties.
The latest IEC 60060-2 lists typical sources of uncertainty contributions in measuring systems. It also added two completely new Annexes, Annex A and Annex B, dedicated to the topic of measurement uncertainty.
Annex A aims to provide an easy-to-understand explanation of the ISO GUM, assuming that a simplified procedure of the ISO GUM can be used for estimating measurement uncertainties for high-voltage tests in most cases. Annex B gives three examples of uncertainty calculation, all with the assumption the type B components often having high degrees of freedom. This practice is mainly for practical efficiency. It should be pointed out, type B components often do have low degrees of freedom and the “quality” of their estimates is often low. However, the degrees of freedom of individual components do not make a significant difference in the final calculated uncertainties. IEEE Std 4-2013 gives detailed explanation and examples how the degrees of freedom and sensitivity coefficients are determined and used.
4.6.2 Uncertainty Requirement Differences between IEC 60060-2:2010 and IEEE Std 4-2013 Table 7 below is a summary of the differences between the earlier editions and the latest editions of the standards in relation to estimation of measurement uncertainties. It should be emphasized that the differences in the two editions of IEC 60060-2 are significant, not only in details, but also in the general approach. The IEC 60060-2:2010 is very much harmonized with ISO Guide 98-3, while Annex H of IEC 60060-2:1994 was written before ISO Guide 98-3 was published and hence was not fully compatible with it. IEEE Std 4-2013 is also harmonized with ISO Guide 98-3. The main difference from IEC 60060-2: 2010 is that its uncertainty calculation examples contain more details.
Table 7: Uncertainty estimation in two editions of IEC60060-2 and IEEE Std 4-2013 IEC 60060-2:1994 IEC 60060-2:2010 IEEE Std 4-2013
Uncertainty definition
Clause H.2: pre-ISO/GUM of
“uncertainty” is used.
The general term “uncertainty” as defined in IEC 60050 is given in 3.6.
The general term “uncertainty” is not given. This makes no impact to the uncertainty calculation.
Type A uncertainty and Type B uncertainty, as defined in ISO GUM is given in D2.
Term for uncertainty result
H.3: Overall uncertainty 3.3.6 Expanded uncertainty (ISO
Guide 98-3) In D2, and interpreted definition of
“Expanded Uncertainty” as in “ISO Guide 98-3” is given.
Defined in 3.3.1 to 3.3.11, Including ISO/IEC definitions,
are described in Annex A and Annex B
Definitions and terms similar to those in IEC 60060-2:2010 are given in Annex D
Calculation
Detailed procedure described in D.2 to D.6 of Annex D (informative).
No procedure is given in the main text
Requirements also being specified.
No limits specified for individual components as long as the expanded uncertainty is within the specified value, e.g., 3% for test voltage and 10% for impulse time parameters. Also
calculation with one dominant component is acceptable.
No limits specified for components as long as the expanded uncertainty is within the specified value, e.g., 3% for test voltage and 10% for impulse time parameters. Also, there should be at least 3 dominant components of comparable magnitude for achieving reasonable effective degrees of freedom for the expanded uncertainty.
Number of
Not specified, as long as the expanded uncertainty is within the specified value, with the type A uncertainty achieved
Not specified, as long as the expanded uncertainty is within the specified value, with the type A uncertainty achieved
Principles Limited information Annex A: An informative annex explaining principles and concepts of ISO GUM
Terms are described Annex D
coverage factor
determination Assume to be 2 calculating coverage factor from effective degrees of freedom, assuming high degrees of freedom for individual type B components
Effective degrees of freedom for calculating coverage factor, estimating realistic degrees of freedom for individual type B components
Two very detailed examples in Annex D, demonstrating the uncertainty calculation steps and how intermediate values, such as standard uncertainty, degrees of freedom (type B component in particular), combined standard uncertainty, effective degrees of freedom and coverage factor, are determined.
4.6.3 Relationship between uncertainty and tolerance
Tolerance and uncertainty are different concepts that are specified in the standards for high-voltage and high-current testing.
Uncertainty is a statistical quantity used to estimate the accuracy of measurements. The uncertainty depends in the first instance on the metrological quality of the measuring system, and often a range of other factors that influence the measurement. According to IEC 60060-2:2010 the uncertainty of a high-voltage measurement shall be expressed as an expanded uncertainty with a coverage probability of approximately 95 %, corresponding to a coverage factor k=2 under the assumption of a normal distribution.
According to IEC 60060-1:2010, the tolerance constitutes the permitted difference between the measured value and the specified value.
According to IEC 60060-1:2010, the uncertainty interval and the tolerance interval are considered separately.
This is stated in terms 3.3.1 and 3.3.2 and associated notes. Typical tolerance is ±3 %, and the required expanded measurement uncertainty of test voltage for most high-voltage tests is 3 %. As long as both the tolerance and the uncertainty requirements are met, the test is considered valid. For example, an applied test voltage of 97.1 kV is considered just as valid as an applied voltage of 100.0 kV, for a test with a specified test voltage of 100 kV, as long as the expanded measurement uncertainty of the applied test voltage is within 3 % of the applied test voltage.
The tolerance of the test voltage is necessary because it is not possible to set the test voltage exactly at the specified value due to technical and operational limitations. For example, the peak impulse voltage at a given charging voltage may vary to some extend depending on the individual impulse generators. During a 60 second AC voltage withstand test, the output voltage may vary around the initially set voltage due to fluctuation of the input voltage to the high-voltage test transformer.
Every effort should be made to set the test voltage to the specified level as closely as possible. An operator should not purposely set the test voltage at the lower limit of the tolerance band.
In the case of the tolerance of impulse voltage time parameters, it is considered good practice to use time parameter values that provide efficient testing with available wave shaping components, as long as the time parameters are within the specified tolerance limits. For example, the tolerance limits for the lightning impulse front time are 0.84 µs to 1.56 µs. The true value of a time parameter may fall outside the tolerance limits, for example, the true front time value for a measured front time of 0.85 µs with an uncertainty of 5 % may be less than 0.84 µs, however, the front time of the applied impulse is still considered meeting the requirements of IEC 60060-1:2010 and IEC 60060-2:2010.