IEC TS 60076-19:2013

IEC/TS 60076-19 ®
Edition 1.0 2013-03
TECHNICAL
SPECIFICATION
SPÉCIFICATION
TECHNIQUE
Power transformers –
Part 19: Rules for the determination of uncertainties in the measurement of the
losses on power transformers and reactors

Transformateurs de puissance –
Partie 19: Règles pour la détermination des incertitudes de mesure des pertes
des transformateurs de puissance et bobines d’inductance

IEC/TS 60076-19:2013
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IEC/TS 60076-19 ®
Edition 1.0 2013-03
TECHNICAL
SPECIFICATION
SPÉCIFICATION
TECHNIQUE
Power transformers –
Part 19: Rules for the determination of uncertainties in the measurement of the

losses on power transformers and reactors

Transformateurs de puissance –

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

des transformateurs de puissance et bobines d’inductance

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX W
ICS 29.180 ISBN 978-2-83220-693-5

– 2 – TS 60076-19 © IEC:2013
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Symbols . 8
4.1 General symbols . 8
4.2 Symbols for uncertainty . 9
5 Power measurement, systematic deviation and uncertainty . 10
5.1 General . 10
5.2 Model function . 10
5.3 Measuring systems . 10
6 Procedures for no-load loss measurement . 11
6.1 General . 11
6.2 Model function for no-load losses at reference conditions . 11
6.3 Uncertainty budget for no-load loss . 12
7 Procedures for load loss measurement . 13
7.1 General . 13
7.2 Model function for load loss measurement at rated current . 13
7.3 Reporting to rated current and reference temperature . 14
7.4 Uncertainty budget for the measured power P reported to rated current . 14
7.4.1 General . 14
7.4.2 Uncertainties of measured load loss power P at ambient temperature
θ . 14
7.5 Uncertainty budget for reported load loss at reference temperature . 15
8 Three-phase calculations . 16
8.1 Power measurement . 16
8.2 Reference voltage . 17
8.3 Reference current. 17
9 Reporting . 17
9.1 Uncertainty declaration . 17
9.2 Traceability . 17
10 Estimate of corrections and uncertainty contributions . 18
10.1 Instrument transformers . 18
10.2 Uncertainty contributions of ratio error of instrument transformers . 18
10.3 Uncertainty contribution of phase displacement of instrument transformers . 19
10.3.1 General . 19
10.3.2 Complete reference procedure . 19
10.3.3 Class index procedure . 20
10.4 Voltage and current measurements . 21
10.5 Power meter . 21
10.6 Correction to sinusoidal waveform . 22
10.7 Winding temperature at load loss measurement . 23
10.8 Winding resistance measurement . 23
Annex A (informative) Example of load loss uncertainty evaluation for a large power
transformer . 25

TS 60076-19 © IEC:2013 – 3 –
Annex B (Informative) Example of load loss uncertainty evaluation for a distribution
transformer . 33
Bibliography . 37

Table 1 – Measured no-load loss uncertainties . 12
Table 2 – Measured load loss uncertainties at ambient temperature . 15
Table 3 – Absolute uncertainty of the additional losses at temperature θ . 15
Table 4 – Absolute uncertainty of load losses P reported at reference temperature . 16
LL
Table 5 – Procedures for the determination of phase displacement uncertainties . 19
Table A.1 – Transformer ratings . 25
Table A.2 – Loss measurement results (one phase) . 27
Table A.3 – Calibration of voltage and current transformers . 27
Table A.4 – Uncertainty contributions. 29
Table B.1 – Transformer ratings . 33
Table B.2 – Measured quantities . 34
Table B.3 – Calibration of the current transformers . 35
Table B.4 – Uncertainty contribution . 36

– 4 – TS 60076-19 © IEC:2013
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
POWER TRANSFORMERS –
Part 19: Rules for the determination of uncertainties in the
measurement of the losses on power transformers and reactors

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 in addition to other activities, IEC publishes International Standards, Technical Specifications,
Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC
Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested
in the subject dealt with may participate in this preparatory work. International, governmental and non-
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with the International Organization for Standardization (ISO) in accordance with conditions determined by
agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
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between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
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5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
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6) All users should ensure that they have the latest edition of this publication.
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expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
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.
The main task of IEC technical committees is to prepare International Standards. In
exceptional circumstances, a technical committee may propose the publication of a technical
specification when
• the required support cannot be obtained for the publication of an International Standard,
despite repeated efforts, or
• the subject is still under technical development or where, for any other reason, there is the
future but no immediate possibility of an agreement on an International Standard.
Technical specifications are subject to review within three years of publication to decide
whether they can be transformed into International Standards.
IEC 60076-19, which is a technical specification, has been prepared by IEC technical
committee 14: Power transformers.
The text of this technical specification is based on the following documents:

TS 60076-19 © IEC:2013 – 5 –
Enquiry draft Report on voting
14/726/DTS 14/736A/RVC
Full information on the voting for the approval of this technical specification can be found in
the report on voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
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 publication will remain unchanged until
the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• transformed into an International Standard,
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
– 6 – TS 60076-19 © IEC:2013
INTRODUCTION
The losses of the transformers (no- load and load losses) are object of guaranty and penalty
in the majority of the contracts and play an important role in the evaluation of the total
(service) costs and therefore in the investments involved.
According to ISO/IEC 17025 the result of any measurement should be qualified with the
evaluation of its uncertainty. A further requirement is that known corrections shall have been
applied before evaluation of uncertainty.
Corrections and uncertainties are also considered in IEC 60076-8 were some general
indications are given for their determination.
This Technical Specification deals with the measurement of the losses that 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 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 submitted test results are to be considered the most correct estimate and therefore this
value has to be accepted as it stands.
In the annexes to this document, two examples of uncertainty calculations are reported for
load loss measurements on large power and distribution transformers.
Standards, technical reports and guides mentioned in the text are listed at the end of the
document.
It is stated that guaranty and penalty calculations should refer to the best estimated values of
the losses without considering the measurement uncertainties.

TS 60076-19 © IEC:2013 – 7 –
POWER TRANSFORMERS –
Part 19: Rules for the determination of uncertainties in the
measurement of the losses on power transformers and reactors

1 Scope
This part of IEC 60076, which is a Technical Specification, illustrates the procedures that
should be applied to evaluate the uncertainty affecting the measurements of no-load and load
losses during the routine tests on power transformers.
Even if the attention is especially paid to the transformers, when applicable the specification
can be also used for the measurements of reactor losses, except large reactors with very low
power factor.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60076-1:2011, Power transformers – Part 1: General
IEC 60076-2:2011, Power transformers – Part 2: Temperature rise for liquid-immersed
transformers
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60076-1 and
60076-2, as well as the following apply.
NOTE The following terms and definitions were taken from ISO/IEC Guide 98-3:2008.
3.1
uncertainty (of measurement)
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]
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
type A evaluation (of uncertainty)
method of evaluation of uncertainty by the statistical analysis of series of observations
[SOURCE: ISO/IEC Guide 98-3:2008, 2.3.2]

– 8 – TS 60076-19 © IEC:2013
3.4
type B evaluation (of uncertainty)
method of evaluation of uncertainty by means other than the statistical analysis of series of
observations
[SOURCE: ISO/IEC Guide 98-3:2008, 2.3.3]
3.5
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]
3.6
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]
3.7
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]
4 Symbols
4.1 General symbols
Parameter related to correction of power for phase displacement in measuring circuit

F
D
Current measured by the ammeter (preferably rated current)

I
M
Reference current (normally corresponding to rated current)

I
N
Rated transformation ratio of the current transformer

k
CN
Rated transformation ratio of the voltage transformer

k
VN
Power
P
Power measured at the load loss measurement corrected for known systematic deviations and referred

P
to the current I
N
Load loss at reference conditions

P
LL
No-load loss at reference conditions and corrected for known errors in the measurement
P
NLL
n Exponent related to the non-linear behaviour of no-load loss
Power measured by the power meter

P
W
Additional losses at reference temperature

P
ar
Additional losses at temperature
θ
P
a2
TS 60076-19 © IEC:2013 – 9 –
R
Equivalent resistance of the windings at temperature θ according to IEC 60076-1
Equivalent resistance of the windings at temperature
R θ
2 2
Equivalent resistance of the windings at reference temperature

R
r
t Parameter related to the thermal coefficient of winding resistance
Voltage measured with an instrument having average rectified mean response

U
avg
Voltage measured
U
M
Rated voltage
U
N
Voltage measured using an instrument with true r.m.s. response

U
rms
Temperature (expressed in degrees Celsius)
θ
Temperature of transformer winding at cold winding resistance test according to IEC 60076-1

θ
Temperature of transformer windings during load loss test (expressed in Celsius degrees)

θ
Reference temperature for transformer windings according to IEC 60076-1

θ
r
Actual phase displacement of the current transformer (rad)
Δ
ϕC
Actual phase displacement of the power meter (rad)

Δ
ϕP
Actual phase displacement of the voltage transformer (rad)
Δ
ϕV
Actual ratio error of the current transformer (%)

ε
C
Actual ratio error of the voltage transformer (%)

ε
V
ϕ
Actual phase angle between voltage and current (rad)
Phase angle between voltage and current measured with power meter (rad)

ϕ
M
4.2 Symbols for uncertainty
c Sensitivity factor for contribution to uncertainty
u
Standard uncertainty
 Absolute standard uncertainty
u
Expanded uncertainty
U

Absolute expanded uncertainty
U
Uncertainty of current transformer ratio (expressed in percent of the ratio)

u
C
Uncertainty of current measurement
u
IM
Uncertainty of the load loss at reference temperature

u
LL
Uncertainty of the no-load loss

u
NLL
Uncertainty of
u P
P2
Uncertainty of term
u F
FD
D
Uncertainty of the power indicated by the analyzer

u
PW
u Uncertainty of the equivalent resistance
R
R1
Uncertainty of the equivalent resistance
u R
R2
Uncertainty of voltage measurement

u
UM
– 10 – TS 60076-19 © IEC:2013
Uncertainty of voltage transformer ratio

u
V
Uncertainty of correction to sinusoidal waveform for no-load-loss

u
WF
Uncertainty of phase displacement for complete measuring system
u
Δϕ
Uncertainty of current transformer phase displacement
u
ΔϕC
Uncertainty of voltage transformer phase displacement
u
ΔϕV
5 Power measurement, systematic deviation and uncertainty
5.1 General
In the following, 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 intended to be measured using three independent
single-phase measuring systems. These systems may be made by separate instruments or a
combined in a three-phase instrument.
In general, losses are measured using current and voltage transformers in conjunction with a
power meter (power analyser).
The measuring system usually has a known systematic deviation (error) that can be corrected
for, or not, and the two cases ask for different approach in the uncertainty analysis.
Systematic deviations related to measuring equipment can be characterised by calibration.
If not negligible, systematic deviations introduced by the measuring system should be
corrected before the uncertainty estimate.
5.2 Model function
The uncertainty estimation includes uncertainties in the measuring system as well as in the
tested object (transformer or reactor).
Thus the model functions presented below includes both the measuring system and the test
object in one equation.
5.3 Measuring systems
Measuring systems can be characterized either by a stated overall uncertainty, or by
specifications of its components.
For systems characterized by an overall uncertainty, simplifications in the uncertainty analysis
are possible, but in this document this has not been utilized since calibration on the system
level are not generally available.
As a consequence, all type of measuring systems should be specified also on the component
level.
TS 60076-19 © IEC:2013 – 11 –
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 referred to rated voltage and frequency and to voltage
with sinusoidal wave shape.
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 no-load loss exhibits a non-linear relation to applied voltage that can be established by
measurements repeated at different voltages.
For the uncertainty determination at rated voltage, a power law approximation is sufficient.
The model function used for no-load loss uncertainty estimation is the following:
n
 
 
 
 
U − U
1 1 P U
avg rms
W N
   
P = k x k x x x 1 + (1)
NLL CN VN
 
ε ε 1
1 − (Δ − Δ )  
tanϕ U
C V
ϕV ϕC avg
 
1 + 1 + k U
VN M
 
ε
100 100
V
 1 + 
 100

where
1 is the parameter related to the ratio error of the current transformer

k
CN
ε (CT);
C
1+
1 is the parameter related to the ratio error of the voltage transformer

k
VN
ε (VT);
V
1 +
1 is the parameter related to the correction for phase displacement ( );
F
D
1 − (Δ − Δ )tanϕ
ϕV ϕC
n
is the parameter related to the actual measuring voltage where the
 
exponent is related to the non-linear behaviour of no-load loss;
 
 
U
N
 
 
k U
VN M
 
ε
V
 1+ 
 100 
is used to compensate for the influence of the distortion on the voltage
 U − U 
avg rms
 
1 +
waveform on the no load loss. is the indication of a mean value
U
 
avg
U
avg
 
responding instrument and the indication of an r.m.s. responding
U
rms
instrument (see IEC 60076-1).
Equation (1) can also be expressed as:

– 12 – TS 60076-19 © IEC:2013
n
n−1
 
  U −U
1 ε P U
  avg rms
V W N
 
P = k x k 1+  x x x 1+
NLL CN VN  
 
ε
100 1− (Δ − Δ )tanϕ k ×U U
(2)
C  
ϕV ϕC  VN M  avg
1+  
The known systematic deviations of the power meter may be assumed to be negligible.
The phase angle ϕ of the loss power is obtained from:
 P 
W
ϕ = ϕ − Δ + Δ = arccos  − Δ + Δ
M ϕV ϕC ϕV ϕC


(3)
I U
 M M 
NOTE 1 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 2 It has been assumed that the power meter establishes the power factor from measurement of active
power and apparent power at the fundamental frequency component of the test voltage.
NOTE 3 The Equations (1) and (2) use the simplified assumption that no-load loss is proportional to the voltage
raised to the power n, where n usually increases with the flux density. As this factor is often approximated by n = 2,
this exponent can be used for the uncertainty estimate.
NOTE 4 In the written formula, some secondary influencing quantities have been disregarded such as frequency.
NOTE 5 IEEE C57.123-2002 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 can be obtained as given in Table 1.
In the majority of the cases, the uncertainty estimate with the class index procedure described
in 10.3.3 is sufficiently accurate as in the determination of the standard uncertainty the
following contributions can be disregarded:
– the uncertainty related to the phase displacement when the power factor is greater than
0,2;
– the uncertainty on the correction to sinusoidal waveform when the indications of the
voltmeters responsive of the r.m.s. and mean voltages are equal within 3 %.
Table 1 – Measured no-load loss uncertainties
Quantity Component Standard Sensitivity Uncertainty See
uncertainty coefficient contribution subclause
ε u u
CT ratio error 1 10.2
C C C
VT ratio error ε u n-1 (n −1)u 10.2
V V V
Power meter P u 1 u 10.5
W PW PW
u ≈ 0
Phase displacement 1 ≈ 0 10.3
Δϕ
1 − (Δϕ − Δϕ )tanϕ
V C
U u n nu
Voltage 10.4
N UM UM
U - U
avg rms
Correction to
1 +
u 1 u 10.6
WF WF
sinusoidal waveform U
avg
2 2 2 2 2 2
Combined standard uncertainty calculated as:
u = u + (n −1) u + u + n u + u
NLL C V PW UM WF
The expanded relative uncertainty is , which corresponds to a level of confidence of
U = 2u
NLL NLL
approximately 95 %.
TS 60076-19 © IEC:2013 – 13 –
7 Procedures for load loss measurement
7.1 General
The test procedure is given in IEC 60076-1.
In load loss measurements the measured loss shall be referred to rated current or to be
reported at this current if performed at a reduced current. Moreover, the results of load loss
measurements shall be reported to the reference temperature.
7.2 Model function for load loss measurement at rated current
IEC 60076-1 requires that the measured value of load loss be corrected with the square of the
ratio of rated current to test current and the power obtained recalculated from actual to
reference temperature.
The model function for the measured power P referred to the rated current I is the
2 N
following:
 
 
 
1 1 P I
W N
 
P = k x k x x
2 CN VN
(4)
ε ε 1
( )  
1 − Δ − Δ tanϕ
C V
ϕV ϕC
k I
1 + 1 +
CN M
 
ε
100 100
C
 1 + 
 
which is rearranged to:
 
ε 1 P I
 
C W N
P = k 1 + x k x x
 
2 CN VN  
ε (5)
100 1 − (Δ − Δ )tanϕ k I
V
 
ϕV ϕC  CN M 
1 +
where
 I 
N
is the parameter related to the actual current measured during the test related to
 
k I
 CN M 
the reference current for which the transformer shall be tested;
other terms are as defined in 6.2.
NOTE 1 It is observed that also in this case 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 2 In the written formula, some secondary influencing quantities have been disregarded, such as frequency
and wave shapes.
The phase angle ϕ of the loss power is obtained from:
 P 
W
 
ϕ = ϕ − Δ + Δ = arccos − Δ + Δ (6)
M ϕV ϕC ϕV ϕC
 
I U
 M M 
– 14 – TS 60076-19 © IEC:2013
7.3 Reporting to rated current and reference temperature
The measured loss P is assumed to be composed of I R loss and additional loss P . The
2 a2
relation between these at the reference current I is:
N
P = I R + P
2 N 2 a2
The total load loss P at reference temperature as defined in IEC 60076-1:2011, Annex E is:
LL
t +θ t +θ
2 2 r 2
P = I × R + P = I R + P , (7)
LL N r ar N 2 a2
t +θ t +θ
2 r
where the equivalent resistance R of the windings during the load test performed at
temperature θ may be estimated from the equivalent resistance R obtained at temperature
2 1
θ by the relation:
t + θ
R = R
2 1
t + θ
where t is a parameter related to the thermal coefficient of winding resistance (235 for copper
and 225 for aluminium).
Likewise the resistance R at the reference temperature θ is given by:
r r
t + θ
r
R = R
r 2
t + θ
The additional loss at reference temperature is:
t + θ
P = P
ar a2
t + θ
r
7.4 Uncertainty budget for the measured power P reported to rated current
7.4.1 General
An uncertainty budget should list all possible contributions to uncertainty, and an estimate of
their magnitudes should be made.
Rated values, such as I and θ are considered constant and are not included in uncertainty
N r
evaluations.
7.4.2 Uncertainties of measured load loss power P at ambient temperature θ
2 2
The uncertainty estimate of load loss power should be obtained according to Table 2.
P
For large power transformers, the complete reference procedure described in 10.3.2 should
be applied.
TS 60076-19 © IEC:2013 – 15 –
For distribution transformer the class index procedure given in 10.3.3 may be sufficiently
accurate.
In many cases, when the power factor of the circuit is greater than 0,2, the contribution of the
phase displacement can be disregarded.
Table 2 – Measured load loss uncertainties at ambient temperature
Quantity Component Standard Sensitivity Uncertainty See
uncertainty coefficient contribution subclause
[%]
CT ratio error ε u 1 u 10.2
C C C
VT ratio error ε u 1 u 10.2
V V V
Power meter P u 1 u 10.5
W PW PW
Phase
u 1 u 10.3
FD FD
displacement 1 − (Δϕ − Δϕ )tanϕ
V C
Ampere meter I u 2 2u 10.4
IM IM IM
2 2 2 2 2
Combined standard uncertainty calculated as:
u = u + u + u + u + 4u
P2 C V PW FD IM
The expanded uncertainty is U = 2u which corresponds to a level of confidence of approximately 95 %.

P2 P2
7.5 Uncertainty budget for reported load loss at reference temperature
The results of the load loss test shall be reported to the reference temperature in accordance
with IEC 60076-1 (see 7.3).
The loss power and the associated uncertainty contributions are to be expressed in watt (i.e.
as absolute uncertainties) in order to obtain correct calculation of the total uncertainty at
reference temperature.
The estimate of the uncertainties affecting the I R and additional losses at temperature θ
N 2 2
are obtained as indicated in Table 3.
Table 3 – Absolute uncertainty of the additional losses at temperature θ
Quantity Component Absolute Sensitivity Contribution
measurement
 
Measured loss P u 1 u
2 P2 P2
2 2 2
 2
u
I R loss I R I R × u
I
R2 R2
N 2 N 2
2 2 2
 
The absolute uncertainty of the additional loss as: u = u + ( I R × u )
Pa2 P2 N 2 R2


The expanded absolute uncertainty is which corresponds to a coverage probability of
U = 2u
Pa2 Pa2
approximately 95 %.
The uncertainty of the total losses P reported at reference temperature can be determined
LL
starting from the model function given in 7.3:

– 16 – TS 60076-19 © IEC:2013
t +θ t +θ
2 2 r 2
P = I R + P = I R + P
LL N r ar N 2 a2
t +θ t +θ
2 r
In Table 4 the procedure is given for estimating the absolute uncertainty of the total losses
P reported at reference temperature.
LL
Table 4 – Absolute uncertainty of load losses P
LL
reported at reference temperature
Quantity Component Absolute Sensitivity Absolute
uncertainty uncertainty
contribution
t + θ t + θ
2 2
r r

I I R u
R u
I R loss
N N 2 R2
r R2
N r
t + θ t + θ
2 2
t + θ t + θ
2 2


u
Additional loss P u
Pa2
ar Pa2
t + θ t + θ
r r
t + θ t + θ
2 r r 2

≈ I R I R u
Mean winding
N r N r θ 2

u 2 2
θ
2 θ 2
temperature (t + θ ) (t + θ )
2 2
The total standard absolute uncertainty is calculated as:
t + θ t + θ t + θ
r 2 2 2 2 r 2 2
  
u = ( I R u ) + ( u ) + ( I R u )
LL N 2 R2 Pa2 N 2 θ 2
t + θ t + θ
(t + θ )
2 r


The expanded absolute uncertainty is which corresponds to a coverage probability of approximately
U = 2u
LL LL
95 %.

U
LL
The expanded relative uncertainty is obtained as:
U =
LL
P
LL

NOTE 1 In the table line one, the equality u = R u has been utilized.
R2 2 R2
NOTE 2 For typical liquid-immersed transformers and assuming t = 235, θ = 20 °C and θ = 75 °C, the
2 r
following sensitivities factors can be used:
t + θ 1 t + θ
t +θ
2 2
r 2 r
≅ 1,2 = I R ≅ 0,0048I R
N 2 N 2
t +θ t + θ
t + θ
r
2 (t + θ )
r
t + θ
For other temperature combinations (as for dry-type transformers) different sensitivity factors could be applied.
t +θ 1 t +θ
2 r 2 r
NOTE 3 In Table 4, the simplification − I R + P ≤ I R has been utilized.
N 2 a2 N 2
2 2
t +θ
(t +θ ) r (t +θ )
2 2
8 Three-phase calculations
8.1 Power measurement
For three-phase transformers, the power measurement should be performed using three
individual single-phase measuring systems, adding the three measurements.

TS 60076-19 © IEC:2013 – 17 –
In this case, the criteria for estimating the uncertainties for the power in each phase are the
same previously given for single-phase circuits.
Normally the three measurements of the power are not correlated, and the absolute

uncertainty u of the total power is obtained by the formula:
T
2 2 2
   
u = u + u + u (8)
T 1 2 3
where the symbols below the square root represent the absolute uncertainties of the power
measurements performed on the individual phases and expressed in watt.
The relative uncertainty is:

u
T
(9)
u =
T
P
W
where P is the sum of the power on all three phases.
W
All uncertainty contributions are assumed to be uncorrelated.
NOTE Three-phase power measuring circuits using reduced number of measuring elements are sometimes used.
It is however very difficult to make a valid uncertainty estimate for such circuits since sufficient knowledge of
influencing parameters are difficult to establish. Therefore such circuits are not recommended.
8.2 Reference voltage
The reference voltage is measured during no-load loss tests. If the three-phase system can
be considered practically symmetrical, it is acceptable to use the mean value of the three
indications of the reference voltage. The quantities can be considered not correlated.
8.3 Reference current
The reference current is measured during load loss tests. If the three-phase system can be
considered practically symmetrical, it is acceptable to use the mean value of the three
indications of the reference current. The quantities can be considered not correlated.
9 Reporting
9.1 Uncertainty declaration
In accordance with this Technical Specification, the total standard uncertainty of the loss
measurements and the expanded uncertainty should be declared.
The expanded uncertainties should be determined multiplying the standard uncertainty by the
coverage factor k = 2, which for a normal distribution corresponds to a coverage probability of
approximately 95 %.
9.2 Traceability
All measurements used to establish the losses should be based on traceable calibrations. The
chain of traceability should be indicated in the report.

– 18 – TS 60076-19 © IEC:2013
10 Estimate of corrections and uncertainty contributions
10.1 Instrument transformers
Instrument transformers are normally calibrated at different currents (voltages) and at least
two different burdens and the errors for the measuring conditions can be obtained by
interpolation from the available data given in the calibration certificate.
The calibration certificate should include the expanded uncertainty of the declared ratio errors
and phase displacements as well as the applied coverage factor.
In measuring systems conventional or advanced current transformers may be used:
– conventional transformers with simple magnetic circuit;
– zero flux current transformers;
– two-stage current transformers;
– amplifier-aided current transformers.
For conventional instrument transformers, higher accuracy can be obtained if the calibration is
performed at the actual burden during the loss measurement and this solution is
recommended for large power transformers.
The advanced devices that employ technologies that enhance accuracy and stability are
treated separately due to the difference in characteristics. They operate on the principle of
reducing flux in the active core to near zero, thereby reducing both ratio errors and phase
displacement to very small values.
In alternative to the conventional inductive voltage transformers, advanced voltage
transducers utilise standard compressed gas capacitors in conjunction with various active
feedback circuits that minimise ratio errors and phase displacement.
When the phase displacement uncertainty has to be evaluated also for the power meter the
2 2 2
u = u + u + u
u
Δϕ ΔϕV ΔϕC ΔϕP
ΔϕP
formula becomes the following where is the uncertainty
related to the phase displacement in the power meter.
10.2 Uncertainty contributions of ratio error of instrument transformers
This
...