IEC 60076-19-1:2023

IEC 60076-19-1 ®
Edition 1.0 2023-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Power transformers –
Part 19-1: Rules for the determination of uncertainties in the measurement of the
losses of power transformers
Transformateurs de puissance –
Partie 19-1: Règles pour la détermination des incertitudes de mesure des pertes
des transformateurs de puissance
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IEC 60076-19-1 ®
Edition 1.0 2023-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Power transformers –
Part 19-1: Rules for the determination of uncertainties in the measurement of the

losses of power transformers
Transformateurs de puissance –

Partie 19-1: Règles pour la détermination des incertitudes de mesure des pertes

des transformateurs de puissance

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 29.180  ISBN 978-2-8322-7024-0

– 2 – IEC 60076-19-1:2023 © IEC 2023
CONTENTS
FOREWORD . 5
INTRODUCTION . 7
1 Scope . 9
2 Normative references . 9
3 Terms and definitions . 9
4 Symbols . 11
4.1 General symbols . 11
4.2 Symbols for uncertainty . 12
4.2.1 General designations . 12
4.2.2 Specific designations . 12
5 Power measurement, systematic deviation and uncertainty . 12
5.1 General . 12
5.2 Traceability . 13
5.3 Model function . 13
5.4 Measuring systems . 13
6 Procedures for no-load loss measurement . 13
6.1 General . 13
6.2 Model function for no-load losses at reference conditions . 14
6.3 Uncertainty budget for no-load loss . 15
7 Procedures for load loss measurement . 16
7.1 General . 16
7.2 Model function for load loss measurement at rated current . 16
7.3 Model function for load loss at rated current and reference temperature . 17
7.4 Uncertainty budget for the measured power P recalculated to rated current . 18
7.4.1 General . 18
7.4.2 Uncertainties of measured load loss power P at ambient temperature θ . 18
2 2
7.5 Uncertainty budget for reported load loss at reference temperature . 18
8 Three-phase power calculations . 19
9 Reporting. 20
10 Estimate of corrections and uncertainty contributions . 20
10.1 Instrument transformers . 20
10.1.1 General . 20
10.1.2 Ratio error of instrument transformers . 21
10.1.3 Phase displacement of instrument transformers . 22
10.2 Voltage and current measurements . 24
10.3 Power meter . 25
10.4 Advanced system with specified system uncertainty . 25
10.5 Correction to sinusoidal waveform . 26
10.6 Winding resistance measurement . 26
10.7 Winding temperature at load loss measurement . 27
10.7.1 General . 27
10.7.2 R and θ determined from temperature measurement . 27
2 2
10.7.3 R and θ determined by resistance measurement . 28
2 2
Annex A (informative) Example of no-load loss uncertainty evaluation – Advanced
measuring system . 30

A.1 General (intent of example) . 30
A.2 Transformer specification . 30
A.3 Measuring system . 30
A.4 Measurements . 31
A.5 Correction of measured values. 31
A.6 Calculation of uncertainty . 31
A.7 Reported loss and uncertainty estimate . 32
Annex B (informative) Example of no-load loss uncertainty evaluation – Calibration
based procedure . 33
B.1 General . 33
B.2 Transformer specification . 33
B.3 Measuring system . 33
B.4 Measurements . 34
B.5 Correction of measured values. 35
B.6 Uncertainty calculation . 35
B.7 Reported loss and uncertainty estimate . 36
Annex C (informative) Example of load loss uncertainty evaluation class index
procedure . 37
C.1 General . 37
C.2 Transformer specification . 37
C.3 Measuring system . 37
C.4 Measurements . 38
C.5 Calculation in accordance with IEC 60076-1 . 39
C.6 Uncertainty calculation . 39
C.7 Reported loss and uncertainty estimate . 41
Annex D (informative) Determination of exponent n in expression for no-load loss . 42
Annex E (informative) Measurement uncertainty and test results . 44
E.1 General . 44
E.2 Test results, guarantees, tolerances, uncertainty limits . 44
E.3 Traceability as tool for quality assurance . 44
E.4 Means and methods to prove uncertainty claims and traceability . 45
E.4.1 Calibration . 45
E.4.2 Calibration certificate . 46
E.4.3 Guidance on scope of a calibration . 47
Annex F (normative) Calculation of uncertainty of losses with different reference
temperatures and/or winding material . 48
Bibliography . 49

Figure D.1 – Evaluation of exponent n from data in Table D.1 . 43

Table 1 – Measured no-load loss uncertainties . 16
Table 2 – Measured load loss uncertainties at ambient temperature . 18
Table 3 – Absolute uncertainty of load losses P reported at reference temperature θ . 19
LL r
Table 4 – Measured no-load loss uncertainties, advanced system . 25
Table 5 – Measured load loss uncertainties at ambient temperature, advanced system . 26
Table A.1 – Three-phase transformer oil immersed transformer . 30
Table A.2 – Uncertainty specification of the power measuring system . 30

– 4 – IEC 60076-19-1:2023 © IEC 2023
Table A.3 – Measured data . 31
Table A.4 – Corrected values . 31
Table A.5 – Uncertainty of no-load loss (according to Table 1) . 32
Table B.1 – Three-phase transformer oil immersed transformer . 33
Table B.2 – Uncertainties of measuring system current and voltage transducers. 34
Table B.3 – Uncertainties of power meter . 34
Table B.4 – Measured data . 34
Table B.5 – Corrected values . 35
Table B.6 – Uncertainty of no-load loss (according to Table 1) . 35
Table C.1 – Three-phase transformer dry type transformer . 37
Table C.2 – Uncertainties of measuring system current and voltage transducers . 38
Table C.3 – Measured data . 38
Table C.4 – Results based on measured data . 39
Table C.5 – Derivation of standard uncertainty contributions . 39
Table C.6 – Uncertainty budget for measured load loss at ambient temperature
(Table 2) . 40
Table C.7 – Uncertainty budget for absolute uncertainty of load loss reported at

reference temperature (Table 3) . 40
Table D.1 – Example of measured no-load loss versus applied voltage . 42

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
POWER TRANSFORMERS –
Part 19-1: Rules for the determination of uncertainties in
the measurement of the losses of power transformers

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international
co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent
rights. IEC shall not be held responsible for identifying any or all such patent rights.
IEC 60076-19-1 has been prepared by IEC technical committee 14: Power transformers. It is
an International Standard.
The text of this International Standard is based on the following documents:
Draft Report on voting
14/1105/FDIS 14/1107/RVD
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.

– 6 – IEC 60076-19-1:2023 © IEC 2023
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/standardsdev/publications.
A list of all parts in the IEC 60076 series, published under the general title Power transformers,
can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The "colour inside" logo on the cover page of this document indicates that it
contains colours which are considered to be useful for the correct understanding of its
contents. Users should therefore print this document using a colour printer.

INTRODUCTION
The losses of power transformers (no-load and load losses) are the object of guarantee and
penalty in many contracts and play an important role in the evaluation of the total (service)
costs and therefore in the investments involved. Furthermore, regional regulations, such as the
Ecodesign Directive of the European Union (Directive 2009/125/EC), can also pose
requirements on the establishment of reliable values for losses.
According to ISO/IEC 17025 and ISO/IEC Guide 98-3, the result of any measurement should
be qualified with the evaluation of its uncertainty. A further requirement of those documents is
that known corrections shall have been applied before evaluation of uncertainty. These
provisions have been applied in this document.
Corrections and uncertainties are also considered in IEC 60076-8 where some general
indications are given for their determination.
This document deals with the measurement of the losses, which from a measuring point of view
consist of the estimate of a measurand and the evaluation of the uncertainty that affects the
measurand itself. The procedures can also be applied to loss measurements of power
transformers:
• as evaluation of the achievable performance of a test facility in the course of prequalification
processes,
• as estimations of achievable uncertainty in the enquiry stage of an order or prior to beginning
final testing at the manufacturer's premises; and for
• evaluations of market surveillance measurements.
Evaluation of uncertainty in testing is often characterized as "top-down" or "bottom-up", where
the first one relies on inter-laboratory comparisons on a circulated test object to estimate the
dispersion and hence the uncertainty. The latter method instead relies on the formulation of a
model function, where the test result y is expressed as a function of input quantities. This
function is often the formula used for the calculation of the result. The "bottom-up" method is
applied in this document.
The uncertainty range depends on the quality of the test installation and measuring system, on
the skill of the staff and on the intrinsic measurement difficulties presented by the tested objects.
The procedures developed in this document for evaluation of measurement uncertainty are
provided as a tool to assess the soundness of results of loss measurements. Uncertainty is
understood as a "parameter, associated with the result of a measurement, that characterizes
the dispersion of the values that could reasonably be attributed to the measurand" [SOURCE:
IEV 311-01-02].
In cases where the losses are required to conform to stated tolerance limits, it is recommended
that measurement systems are of such quality that their estimated uncertainty is less than the
tolerance limit. (As an example, a measurement with a 5 % uncertainty on a test where the
tolerance limit is 5 % is acceptable if the measured value lies within the tolerance limit.) This
situation can occur for example in market surveillance activities. It can be noted that an
uncertainty 3 % is regarded as state-of-the-art for uncertainty of loss.
Treatment of measurement results is defined as follows in IEC 60076-8:1997, 10.1: "The
submitted test result shall contain the most correct estimate that is possible, based on the
measurements that have been carried out. This value shall be accepted as it stands. The
uncertainty margin shall not be involved in the judgement of compliance for guarantees with no
positive tolerance or tolerance ranges for performance data of the test object."

– 8 – IEC 60076-19-1:2023 © IEC 2023
In Annex A to Annex C of this document, examples of uncertainty calculations are reported for
no-load and load loss measurements on large power and distribution transformers. Annex D
provides information on determination of the exponent for applied voltage in no-load loss
measurement. Annex E provides information on uncertainty in measurement. Annex F provides
information on calculation of uncertainty of losses with different reference temperatures and/or
winding material.
International Standards, Technical Reports and Guides which are mentioned in the text of this
document, but which are not indispensable to its application, are listed in the Bibliography at
the end of this document.
Loss of reactors is not within the scope of this document. A separate part of IEC IEC60076-19
to handle loss of reactors is under consideration.
A problem with symbols has been rectified, where the symbol for voltage has been changed
from U to V to avoid confusion with expanded uncertainty. The new symbol is accepted in
IEC 60050-121:2002, 121-11-27 for the case when the corresponding electric field is
irrotational.
POWER TRANSFORMERS –
Part 19-1: Rules for the determination of uncertainties in
the measurement of the losses of power transformers

1 Scope
This part of IEC 60076 defines the procedures that are applied to evaluate the uncertainty
affecting the measurements of no-load and load losses during the routine tests on power
transformers.
This document centres on measuring systems utilizing digital instruments, although the
procedures can be adapted to evaluation of systems with analogue instruments where further
uncertainty sources have to be taken into account.
This document specifies how to determine measurement uncertainty and how to apply
corrections for known errors in the measurement chain. Information vis-à-vis judgement and
traceability are given in IEC 60076-8:1997, 10.1 and 10.2.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60076-1, Power transformers – Part 1: General
IEC 60076-2, Power transformers – Part 2: Temperature rise for liquid-immersed transformers
IEC 60076-11:2018, Power transformers – Part 11: Dry-type transformers
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60076-1,
IEC 60076-2, and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at https://www.electropedia.org/
• ISO Online browsing platform: available at https://www.iso.org/obp
3.1
uncertainty
parameter, associated with the result of a measurement, that characterizes
the dispersion of the values that could reasonably be attributed to the measurand
[SOURCE: ISO/IEC Guide 98-3:2008, 2.2.3, modified – Notes to entry omitted.]

– 10 – IEC 60076-19-1:2023 © IEC 2023
3.2
standard uncertainty
uncertainty of the result of a measurement expressed as a standard deviation
[SOURCE: ISO/IEC Guide 98-3:2008, 2.3.1]
3.3
combined standard uncertainty
standard uncertainty of the result of measurement when that result is obtained from the values
of a number of other quantities, equal to the positive square root of a sum of terms, the terms
being the variances or covariances of these other quantities weighted according to how the
measurement result varies with changes in these quantities
[SOURCE: ISO/IEC Guide 98-3:2008, 2.3.4]
3.4
expanded uncertainty
quantity defining an interval about the result of a measurement that may be expected to
encompass a large fraction of the distribution of values that could reasonably be attributed to
the measurand
[SOURCE: ISO/IEC Guide 98-3:2008, 2.3.5, modified – Notes to entry omitted.]
3.5
coverage factor
numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an
expanded uncertainty
[SOURCE: ISO/IEC Guide 98-3:2008, 2.3.6, modified – Note to entry omitted.]
3.6
traceability
property of a measurement result whereby the result can be related to a reference through a
documented unbroken chain of calibrations, each contributing to the measurement uncertainty
[SOURCE: ISO/IEC Guide 99:2007, 2.41, modified – "metrological" omitted from the term and
notes to entry omitted.]
3.7
accuracy class
class of measuring instruments or measuring systems that meet stated metrological
requirements that are intended to keep measurement errors or instrumental uncertainties within
specified limits under specified operating conditions
[SOURCE: ISO/IEC Guide 99:2007, 4.25, modified – Notes to entry omitted.]

4 Symbols
4.1 General symbols
F
Parameter related to correction of power for phase displacement in measuring circuit
D
I
Current measured by the ammeter
RMS
I
Current measured by an advanced measuring system
S
I
Reference current (normally corresponding to rated current)
N
k
Rated transformation ratio of the current transformer
CN
k
Rated transformation ratio of the voltage transformer
VN
P Power
Power measured at the load loss measurement corrected for known systematic deviations and referred
P
to the reference current I
N
P
Load loss at reference conditions and corrected for known errors in the measurement
LL
P
No-load loss at reference conditions and corrected for known errors in the measurement
NLL
P
Power measured by the power meter
W
P
Power measured by an advanced measuring system
S
P
Additional loss at reference temperature
ar
P Additional loss at temperature θ
a2 2
R Resistance of the windings at temperature θ
1 1
R Resistance of the windings at temperature θ
2 2
R
Resistance of the windings at reference temperature
r
t Parameter related to the thermal coefficient of winding resistance
V
Voltage measured with an instrument having rectified mean response
avg
V
Rated voltage
N
V
Voltage measured using an instrument with true RMS response
RMS
θ Temperature (°C)
θ
Temperature of transformer winding at cold winding resistance test according to IEC 60076-1 (°C)
θ
Temperature of transformer windings during load loss test (°C)
Θ
Reference temperature for transformer windings according to IEC 60076-1 (°C)
r
Δ
Actual phase displacement of the current transformer (rad)
φC
Δ
Actual phase displacement of the voltage transformer (rad)
φV
ε
Actual ratio error of the current transformer (% of nominal ratio)
CT
ε
Actual ratio error of the voltage transformer (% of nominal ratio)
VT
φ Actual phase angle between voltage and current (rad)
φ
Phase angle between voltage and current measured with power meter (rad)
M
– 12 – IEC 60076-19-1:2023 © IEC 2023
4.2 Symbols for uncertainty
4.2.1 General designations
u Relative standard uncertainty

u Absolute standard uncertainty
U Relative expanded uncertainty

Absolute expanded uncertainty
U
4.2.2 Specific designations
u
Uncertainty of current transformer ratio (expressed in percent of the ratio)
CT
u
Uncertainty of current measurement
IRMS
u
Uncertainty of current measured by an advanced measuring system
IS
u
Uncertainty of the load loss
LL
u
Uncertainty of the no-load loss
NLL
u
Uncertainty of P
P2 2
u Uncertainty of term F
FD D
u
Uncertainty of the power indicated by the power meter
PW
u
Uncertainty of the power indicated by an advanced measuring system
PS
u
Uncertainty of the resistance R
R1
u Uncertainty of the resistance R
R2 2
u
Uncertainty of resistance of current shunt
SH
u
Uncertainty of rectified mean voltage measurement
Vavg
u
Uncertainty of RMS voltage measurement
VRMS
u
Uncertainty of voltage transformer ratio
VT
u
Uncertainty of correction to sinusoidal waveform for no-load-loss
WF
u
Uncertainty of phase displacement for complete measuring system
Δφ
u
Uncertainty of current transformer phase displacement
ΔφC
u
Uncertainty of voltage transformer phase displacement
ΔφV
NOTE Specific designations can be identified as relative or absolute as defined in the list of general designations.
5 Power measurement, systematic deviation and uncertainty
5.1 General
In this document, it is assumed that the transformer losses are measured in the conditions
prescribed by IEC 60076-1 by means of digital instruments.
For three-phase transformers, losses are measured using three independent (uncorrelated)
single-phase measuring systems. These systems may comprise separate instruments or be
combined in a three-phase instrument.

In general, losses are measured using current and voltage transformers in conjunction with a
power meter. Voltage and current values can be measured with separate instruments or using
built-in functions of the power meter. Currents are assumed to be measured as line currents
and voltages as line-to-earth voltages.
Any measurement system can be characterised with a systematic deviation (error) and an
uncertainty. When known, the systematic deviation should be corrected. If it cannot be
corrected, it should be considered as an added uncertainty.
Inductive instrument transformers and resistive shunts used to measure current are considered
to have negligible drift and therefore the evaluation of their performance can be appreciably
enhanced by using calibration results to correct for known errors and as the basis for estimation
of uncertainty.
All other measurement devices should be evaluated from their technical specifications (or
accuracy class). Corrections are not applied and uncertainty estimates are based on the
specifications. The residual deviations should be considered in the uncertainty estimations. For
these cases calibration primarily verifies the specification.
Certain advanced measuring systems employ measuring principles that lead to negligible
systematic deviations – but not negligible uncertainties. This should however always be
carefully evaluated.
5.2 Traceability
Measurement devices used to establish losses shall have traceable calibrations.
5.3 Model function
The uncertainty estimation includes uncertainties in the measuring system as well as in the
tested object (transformer).
The model functions presented in 6.2, 7.2 and 7.3 include both the measuring system and the
test object in one equation.
5.4 Measuring systems
Measuring systems can be characterized either by a stated overall uncertainty verified by
system-wide calibration, or by specifications of their components verified by component
calibrations.
This document focuses mainly on uncertainty analysis based on component calibrations.
For systems characterized by an overall uncertainty, simplifications in the uncertainty analysis
are possible, see 10.4.
6 Procedures for no-load loss measurement
6.1 General
The test procedure is given in IEC 60076-1.
The no-load loss measurement shall be performed at rated voltage and frequency and no
corrections are to be applied for deviations from rated voltage in the test as there is no formula
defined by IEC for such correction. A further consequence is that the uncertainty estimated in
this document does not include contributions due to the non-linear behaviour of no-load loss as
a function of test voltage.
– 14 – IEC 60076-19-1:2023 © IEC 2023
The current drawn by the test object is non-sinusoidal, and this may cause a distortion in the
voltage that leads to erroneous values for the losses. A correction for the transformer losses is
prescribed in IEC 60076-1, as well as a limit for the permissible distortion.
6.2 Model function for no-load losses at reference conditions
The single-phase model function used to calculate no-load loss (and to use as the basis for
uncertainty estimation) is given in Formula (1):
n
 
 
 
VV−
cosφ
( ) V
11 avg RMS
N
 
(1)
Pk ⋅ k ⋅ P ⋅ 1+
NLL CN VN W

εε  1 
V
CT VT cosφ + (Δ − Δ)
avg
( )
φφVC 
1+ 1+ kV⋅
VN avg
 
ε
100 100
VT
 1+ 
 100 
where
is the term combining the nominal ratio k of the current transformer
CN
k
CN
ε (CT) and the correction for the known ratio error ε ;
CT CT
1+
is the term combining the nominal ratio k of the voltage transformer
VN
k
VN
ε (VT) and the correction for the known ratio error ε ;
VT VT
1+
is the term related to the correction for phase displacement (F ) of the
cosφ
( ) D
current and voltage transformers;
cosφ + (Δ − Δ)
( )
φφVC
P is the reading of the wattmeter, and the wattmeter is considered to
W
have no known errors, thus no correction term;
n
 
is the parameter related to the actual voltage where the exponent n
 
(taken as 2 in the absence of other information) is related to the
 
V non-linear behaviour of no-load loss, and since IEC 60076-1 requires
N
 
that the applied voltage be as close as possible to the nominal voltage,
 
kV
VN avg
  no corrections are to be applied although uncertainty has to be
ε
VT
 1+ 
considered;
 
is used to compensate for the influence of the distortion on the voltage
VV−
avg RMS
waveform on the no-load loss. V is the indication of a rectified mean
1+
avg

V
avg

value responding instrument and V is the indication of an RMS
RMS
responding instrument (see IEC 60076-1).

NOTE 1 The actual exponent n can be estimated by analysis of measurement of no-load loss at slightly different
voltages, see Annex D.
=
Formula (1) can for the purpose of uncertainty analysis be rearranged as:
n
  VV− 
V
1 1 cosφ avg RMS
N
Pk ⋅ ⋅ P ⋅  ⋅ 1+
NLL CN W
n−1
ε 
VV
CT cosφ + (Δ −Δ )
( )  avg  avg

φφVC   
1+
(2)

k

VN
ε
VT

1+

100
The true phase angle φ between voltage and current under sinusoidal conditions is obtained by
correcting for the known phase displacement difference between CT and VT (Δ − Δ) :
φφVC
P
W
φφ=−−(Δ Δ )=arccos −−(Δ Δ )
(3)

M φφVC φφVC
I ⋅V
RMS RMS
which is not strictly applicable in many cases for no-load loss where distortion is present, but
still suitable for the purpose of this document.
P
W
The term in Formula (3) is the power factor as measured by the power meter.
I ⋅V
RMS RMS
NOTE 2 It is observed that the formula of the loss determination is expressed only through the product of a number
of factors to facilitate the estimation of the total relative uncertainty of the measurement.
NOTE 3 In Formula (1), some secondary influencing quantities have been disregarded, such as frequency, under
the assumption that the test frequency is close to the rated frequency.
NOTE 4 IEEE C57.123:2019 identifies a small temperature effect on no-load losses and gives −1 % per 15 K
temperature rise. This effect, not well known and not identified within IEC, has been disregarded.
6.3 Uncertainty budget for no-load loss
The uncertainty estimate of no-load loss power is obtained as given in Table 1, having taken
into consideration all possible contributions to uncertainty. Propagation of uncertainties is
estimated from partial derivatives of the model function as defined in ISO Guide 98 3, which
also gives the background for Table 1.
The uncertainty related to the phase displacement can be disregarded when the power factor
is greater than 0,2, which is the normal case for no-load loss.
=
– 16 – IEC 60076-19-1:2023 © IEC 2023
Table 1 – Measured no-load loss uncertainties
Quantity Component Standard Sensitivity Contribution See
uncertainty coefficient to standard subclause
uncertainty
ε u u
CT ratio error 1 10.1.2
CT CT CT
ε u (n – 1)u
VT ratio error (n – 1) 10.1.2
VT VT VT
P u u
Measured power 1 10.3
W PW PW
cos(φ)
≈ 0
u
Phase displacement 1 ≈ 0 10.1.3
Δφ
cos φ +−(Δ Δ)
( )
φφVC
V u n ∙ u
Voltage n 10.2
N Vavg Vavg
V - V
avg RMS
Correction to
1 + u u
1 10.5
WF WF
sinusoidal waveform
V
avg
2 2 2 2 22 2
Combined standard relative uncertainty calculated as: u u+ n− 1⋅ u+ u+ nu⋅ + u
( )
NLL CT VT PW Vavg WF
The expanded relative uncertainty is Uu= 2 , which corresponds to a coverage probability of
NLL NLL
approximately 95 %.
7 Pr
...