CLC/TR 50462:2008

Rules for the determination of uncertainties in the measurement of the losses on power transformers and reactors

This Technical Report illustrates the procedures and criteria to 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, the document can be also used for the measurements of reactor losses, when applicable.

Regeln zur Bestimmung der Messunsicherheiten von Verlusten in Leistungstransformatoren und Drosselspulen

Pravila za ugotavljanje negotovosti pri meritvah izgub na močnostnih transformatorjih in dušilkah

General Information

• Status: Published
• Publication Date: 03-Jul-2008
• ICS: 29.180 - Transformers. Reactors
• Technical Committee: CLC/TC 14 - Power transformers
• Drafting Committee: IEC/TC 14 - IEC_TC_14
• Parallel Committee: IEC/TC 14 - IEC_TC_14
• Current Stage: 6060 - Document made available - Publishing
• Start Date: 04-Jul-2008
• Completion Date: 04-Jul-2008
• Ref Project: SIST-TP CLC/TR 50462:2008 - Rules for the determination of uncertainties in the measurement of the losses on power transformers and reactors

Standards Content (Sample)

SLOVENSKI STANDARD
01-november-2008
3UDYLOD]DXJRWDYOMDQMHQHJRWRYRVWLSULPHULWYDKL]JXEQDPRþQRVWQLK
WUDQVIRUPDWRUMLKLQGXãLONDK
Rules for the determination of uncertainties in the measurement of the losses on power
transformers and reactors
Regeln zur Bestimmung der Messunsicherheiten von Verlusten in
Leistungstransformatoren und Drosselspulen
Ta slovenski standard je istoveten z: CLC/TR 50462:2008
ICS:
29.180 Transformatorji. Dušilke Transformers. Reactors
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

TECHNICAL REPORT
CLC/TR 50462
RAPPORT TECHNIQUE
July 2008
TECHNISCHER BERICHT
ICS 29.180
English version
Rules for the determination of uncertainties in the measurement
of the losses on power transformers and reactors

This Technical Report was approved by CENELEC on 2008-03-07.

CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Cyprus, the
Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.

CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung

Central Secretariat: rue de Stassart 35, B - 1050 Brussels

© 2008 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. CLC/TR 50462:2008 E
Foreword
This Technical Report was prepared by the Technical Committee CENELEC TC 14, Power
transformers.
The text of the draft was submitted to vote in accordance with the Internal Regulations, Part 2,
Subclause 11.4.3.3 (simple majority) and was approved by CENELEC as CLC/TR 50462 on
2008-03-07.
__________
– 3 – CLC/TR 50462:2008
Contents
Introduction. 5
1 Sc op e . . 6
2 Normative references . 6
3 Definitions . 6
4 Symbols . 6
4.1 General symbols . 6
4.2 Symbols for uncertainty . 7
5 Power measurement, systematic deviation and uncertainty . 8
6 Procedures for no-load loss . 8
6.1 General . 8
6.2 Model function for no-load losses at reference conditions . 9
6.3 Uncertainty budget . 10
7 Procedures for load loss . 11
7.1 General . 11
7.2 Model function for load loss at reference conditions . 11
7.3 Uncertainty budget for measured power P referred to rated current . 12
7.4 Uncertainty budget for reported load loss . 14
8 Three-phase calculations . 14
8.1 Power . 14
8.2 Reference voltage (current) . 15
9 Reporting . 15
9.1 Unc e r t a i nt y . 15
9.2 Traceability . 15
10 Estimation of corrections and uncertainty contributions . 15
10.1 Ratio error of instrument transformers . 15
10.2 Phase displacement of instrument transformers . 17
10.3 Power meter . 21
10.4 Voltage measurement in no-load loss . 22
10.5 Ampere meter in load loss measurement . 22
10.6 Correction to sinusoidal waveform . 23
10.7 Winding temperature θ at load loss test . 23
10.8 Winding resistance . 24
Annex A (informative) Example of load loss uncertainty evaluation for a large power
transformer . 26
A.1 Introduction . 26
A.2 Transformer rating . 26
A.3 Measuring method and instrumentation used . 26
A.4 Model of the measurand (see 7.2) . 27
A.5 Results of the measurements . 27
A.6 Uncertainty of load loss . 28
A.7 Estimates of the single contributions to the uncertainty . 30
Annex B (informative) Example of load loss uncertainty evaluation for a distribution
transformer . 34
B.1 Introduction . 34
B.2 Transformer rating . 34
B.3 Measuring instrumentation . 34

B.4 Model of the measurand (see 7.2) . 34
B.5 Results of the measurements . 35
B.6 Uncertainty of load loss . 36
B.7 Estimate of the single contributions to the uncertainty formation . 37
Annex C (informative) General rules for the uncertainty estimate . 40
C.1 The basic concepts . 40
C.2 Measurements, estimates and uncertainties . 40
C.3 Evaluation of the input quantity uncertainties. 41
C.4 Evaluation and expression of the expanded uncertainty . 44
Annex D (informative) Sensitivity coefficients for uncertainty contributions due to phase
displacement correction of measurements at low power factor . 45
D.1 Introduction . 45
D.2 Sensitivity factors . 46
Annex E (informative) Model function for load loss temperature correction . 51
E.1 General . 51
E.2 Model function . 51
E.3 Sensitivity coefficients . 52
E.4 Estimation of temperature during load loss test . 53
E.5 Simplified analysis. 53
Annex F (informative) Measurement of winding resistance . 55
F.1 Description of the measurement . 55
F.2 Inductive voltage drop . 56
Bibliography . 58
Figures
Figure D.1 – Sensitivity coefficient for uncertainty in power, current and voltage . 48
Figure F.1 – Equivalent circuit . 55
Tables
Table 1 – No-load loss uncertainty, general case . 10
Table 2 – No-load loss uncertainty without correction for phase displacement . 11
Table 3 – Uncertainty in the general case . 13
Table 4 – Uncertainty without correction for phase displacement . 13
Table 5 – Standard and expanded uncertainty for load loss . 14
Table 6 – Procedures for uncertainty analysis . 18
Table A.1 – Uncertainty contribution . 29
Table A.2 – Calibration of voltage and current transformers ratio error. 30
Table A.3 . 31
Table A.4 – Calibration of voltage and current transformer phase displacement . 32
Table B.1 . 35
Table B.2 – Uncertainty contribution . 36
Table B.3 . 38
Table B.4 . 38
Table C.1 – Combined uncertainties for uncorrelated quantities . 43
Table E.1 . 53

– 5 – CLC/TR 50462:2008
Introduction
Although the efficiency of a power transformer is very high, the losses (no load and load losses) are
object of guaranty and penalty in the majority of the contracts. As a matter of fact, considering the long
power transformer life (20 years and more) the cost of the losses play an important role in the
evaluation of the total (service) costs and therefore in the investments involved.
A further reason that justifies the attention paid to the losses is that from the generation to the final
user, the energy is passing through a number of transformers: step up transformers of generation
power stations, interconnecting units for transmission systems, distribution transformers for primary
systems (from 100 kV to 400 kV), medium voltage to low voltage transformers in small distribution
substations (from 10 kV to 20 kV feeders).
The sum of the losses accrued in the transformer chains may be significant and therefore of
importance in nationwide efforts to save energy. A large number of European Countries have
instituted measures to conserve energy where losses in electric transmission are an important part.
In power transformers the direct measurement of the efficiency is not recommended because of the
uncertainty of this method.
The indirect method based on the measurement of the losses is largely preferred even if the
conditions in which such losses are measured differ a little from those that occur in operation.
EN ISO/IEC 17025 requires that the result of any measurement shall be qualified with the evaluation
of its uncertainty. A further requirement is that known corrections shall have been applied before
evaluation of uncertainty.
This document 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 estimate itself.
It is well known that when a test result is expressed as numerical quantity it is not an exact number but
suffers from uncertainty.
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 test objects.
The submitted test results is to be considered the most correct estimate and therefore this value has to be
accepted as it stands.
The uncertainty shall not be involved in the judgment of compliance for guarantees, tolerances and penalties
thresholds.
Guaranty and penalty calculations should refer to the estimated values without consideration of the
measurement uncertainties.
1 Scope
This Technical Report illustrates the procedures and criteria to 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, the document can be also used for the
measurements of reactor losses, when applicable.
2 Normative references
The following referenced documents are indispensable for the application 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.
EN 60076 series, Power transformers (IEC 60076 series)
EN 60076-1:1996, Power transformers – Part 1: General (IEC 60076-1:1993, mod.)
3 Definitions
For the purposes of this document, the terms and definitions given in EN 60076 apply.
4 Symbols
4.1 General symbols
c sensitivity factor for contribution to uncertainty, see C.3.4;
F parameter related to correction of power for effect of phase displacement in measuring
D
circuit;
I current measured by the ammeter (normally corresponding to rated current);
M
I reference current (normally rated current);
N
k rated transformation ratio of the current transformer;
CN
k rated transformation ratio of the voltage transformer;
VN
P power;
P power measured at load loss test, but referred to the reference current I ;
2 N
P load loss at reference conditions and corrected for known systematic deviations in the
LL
measurement;
P no-load loss at reference conditions and corrected for known errors in the measurement;
NLL
P power measured by the power meter;
W
R winding resistance measured at cold winding resistance test according to EN 60076-1,
10.1;
R winding resistance estimated for the load loss test;
R winding resistance at reference temperature according to EN 60076-1, 10.1;
r
t parameter related to the thermal coefficient of winding resistance;

– 7 – CLC/TR 50462:2008
U voltage measured with an instrument having average rectified mean response;
avg
U voltage measured;
M
U rated voltage;
N
U voltage measured using an instrument with true r.m.s. response;
rms
θ temperature;
temperature of transformer winding at cold winding resistance test according to
θ
EN 60076-1, 10.2;
temperature of transformer winding during load loss test;
θ
reference temperature for transformer winding according to EN 60076-1, 10.1;
θ
r
ε actual phase displacement of the current transformer (rad);
C
ε actual phase displacement of the power meter (rad);
P
actual phase displacement of the voltage transformer (rad);
ε
V
accuracy of the phase displacement declared in the calibration certificate for the voltage
α
εV
transformer;
accuracy of the phase displacement declared in the calibration certificate for the current
α
εC
transformer;
actual current error of the current transformer (%);
η
C
η actual voltage error of the voltage transformer (%);
V
actual phase angle between voltage and current;
ϕ
phase angle between voltage and current measured with power meter.
ϕ
M
4.2 Symbols for uncertainty
u, U uncertainty – lower case denotes standard uncertainty and upper case denotes
expanded uncertainty, the tilde ~ is used to denote absolute uncertainty;
u uncertainty of current transformer ratio;
C
u uncertainty of calibration;
cal
u uncertainty defined by instrument transformer class limit for ratio error or phase
class
displacement;
u uncertainty contribution to u related to uncertainty in current measurement;
F(IM) pd
u uncertainty contribution to u related to uncertainty in power measurement;
F(PW) pd
u uncertainty contribution to u related to uncertainty in voltage measurement;
F(UM) pd
uncertainty contribution to u related to uncertainty in phase displacement of instrument
u
pd
F(ε)
transformers;
u uncertainty of current measurement;
IM
u uncertainty of an interpolation procedure;
interpol
u uncertainty of the load loss power;
LL
u uncertainty of the no-load loss power;
NLL
u uncertainty of P ;
P2 2
u uncertainty of term F ;
pd D
u uncertainty of P ;
PW W
u uncertainty of resistance R ;
R1 1
u uncertainty of thermal sensors;
th
u uncertainty of setting of rated voltage at no-load loss test;
U
u uncertainty of voltage measurement;
UM
u uncertainty of voltage transformer ratio;
V
u uncertainty of correction to sinusoidal waveform for no-load-loss;
wf
u uncertainty of phase displacement for complete measuring system;
ε
uncertainty of current transformer phase displacement;
u
εC
uncertainty of voltage transformer phase displacement.
u
εV
5 Power measurement, systematic deviation and uncertainty
In the following, it is assumed that the transformer losses be measured in the conditions prescribed by
EN 60076-1 and further that only digital instruments are connected in the measuring circuit.
For three-phase transformers, losses are intended to be measured using three independent
single-phase measuring systems.
In general losses are measured using current transformers and voltage transformers in conjunction
with a power meter (power analyser). Each is associated with a small systematic deviation and a
corresponding uncertainty that has to be evaluated. Systems using electronically aided or electronic
based current and voltage transducers can in this analysis be treated the same way as systems with
conventional instrument transformers.
The measuring system usually has a known systematic deviation (error). This systematic deviation
could be corrected for, or not, and the two cases ask for different approach in the uncertainty analysis.
The measuring system used has an unknown difference between the true value of the input quantity
and the value shown on the instrument. This is the uncertainty of the measurement.
6 Procedures for no-load loss
6.1 General
The result of the no-load loss measurement shall be valid at rated voltage. The uncertainty of the loss
with respect to the possible difference between measuring voltage and rated voltage is required.
Systematic deviations related to measuring equipment can be characterised by calibration. The
current drawn by the test object is distorted, 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
EN 60076-1, as well as a limit for the permissible distortion.

– 9 – CLC/TR 50462:2008
6.2 Model function for no-load losses at reference conditions
The no-load loss will exhibit a non-linear relation to applied voltage. The non-linear relation can be
established for each object by measurements repeated at different voltages, but usually a power law
approximation is sufficient. The model function used for no-load loss uncertainty estimation is given by
the following approximation:
n
 
 
U U
1 1 P U
  avg rms
W N
P k k 1 
−
NLL CN VN
η η 1  
1 ε ε tan  U
= ⋅ ⋅ ⋅ ⋅ + Eq. 1
C V
1 1 k U
V C avg
 
−()− ⋅ ϕ 
VN M
η
100 100  
+ + ⋅ ⋅
V
 
+
 
 
where
– k ⋅
CN
η
is a parameter related to the ratio error of the current transformer;
C
1 +
– k ⋅
VN
η is a parameter related to the ratio error of the voltage transformer;
V
1 +
–
is a parameter related to the correction for phase displacement;
1 −()ε −ε ⋅tanϕ
V C
n
 
 
 
U
is a parameter related to the actual measuring voltage where the
 N 
–
  exponent is related to the non-linear behaviour of no-load loss;
k ⋅ ⋅U
 
VN M
η
V
 
1 +
 
 100 
is defined in EN 60076-1 and is used to compensate for the influence of
 U −U 
avg rms
the distortion on the voltage waveform on the no load loss. Here U is
avg
 
– 1 +
 
the indication of a mean value responding instrument and U the
U
rms
avg
 
indication of an r.m.s. responding instrument.
Eq. 1 can also be expressed as:
n
n−1
 
  U −U
1 η 1 U
  avg rms
V N
 
P = k ⋅ ⋅k ⋅1 +  ⋅P ⋅ ⋅ ⋅ 1 +
NLL CN VN W  
Eq. 2
 
η
100 1 −()ε −ε ⋅tanϕ k ⋅U U
C
 
V C  VN M avg
1 +  
The known systematic deviations of the power meter have been assumed to be negligible. The phase
angle ϕ of the loss power is obtained from
 
P
W
 
ϕ = ϕ −ε +ε = arccos −ε +ε
Eq. 3
M V C V C
 
I ⋅U
 M M
It has been assumed that the power meter establishes the power factor from measurement of power
and apparent power at the fundamental frequency of the test voltage.

When the power factor at no-load loss is larger than 0,3, the term relating to phase displacement can
be neglected and we have
n
n−1
 
  U −U
1 η U
 
avg rms
V N
 
P = k ⋅ ⋅k ⋅1 +  ⋅P ⋅ ⋅ 1 +
NLL CN VN W  
Eq. 4
 
η
100 k ⋅U U
C  
 VN M avg
1 +  
NOTE 1 The formula uses 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. This factor is often approximated by n = 2.
NOTE 2 In the written formula, some secondary influencing quantities have been disregarded such as frequency, wave
shapes, effect of the voltage transformer leads, etc.
NOTE 3 IEEE C57.123-2002 identifies a small temperature effect on no-load losses and gives - 1 % per 15 °C. This effect is
not well known and is not identified within IEC. The effect has been disregarded.
6.3 Uncertainty budget
6.3.1 General
An uncertainty budget should list all possible contributions to uncertainty, and an estimate of their
magnitudes should be made.
The sensitivity to different uncertainty contributions can in general be deduced form the model
function. Contributions to uncertainty in loss measurements from statistical random processes are in
general small compared to other contributions and are not further treated here.
Rated values, such as U are considered constants and are not included in uncertainty evaluations.
N
6.3.2 Standard and expanded uncertainty for no load loss
Table 1 – No-load loss uncertainty, general case
See
Standard Sensitivity Uncertainty
Quantity Estimate Variance sub-
uncertainty coefficient contribution
clause
CT ratio error
10.1.2
η u 1 u u
C C C C
2 2
VT ratio error
u n-1 10.1.2
η (n-1) ⋅ u (n-1) ⋅ u
V V V V
Power meter 10.3
P u 1 u u
W PW PW PW
Phase 10.2.3
displacement u = 0 1 0 0 or
pd
1 −()ε −ε ⋅tanϕ
V C
10.2.4
2 2
Voltage
10.4
U u n N ⋅ u n ⋅ u
N U U U
U U
avg rms
Correction to
1 −
U
sinusoidal + 10.6
u 1 u u
wf wf wf
avg
waveform
Standard uncertainty u =√(right) =sum(above)
NLL
Expanded uncertainty U =2 ⋅ above

NLL
– 11 – CLC/TR 50462:2008
Table 2 – No-load loss uncertainty without correction for phase displacement
See
Standard Sensitivity Uncertainty
Quantity Estimate Variance sub-
uncertainty coefficient contribution
clause
CT ratio error
10.1.2
η u 1 u u
C C C
C
2 2
VT ratio error
u n-1 (n-1) u (n-1) u 10.1.2
η * *
V V V V
Power meter 10.3
P u 1 u u
W PW PW PW
Phase 2
1 u 1 u u 10.2.2
pd pd pd
displacement
2 2
Voltmeter
U u n n u 10.4
n ⋅ u *
N U U U
Correction to
U −U
avg rms
1 +
sinusoidal
u 1 u u 10.6
wf wf wf
U
waveform avg
=√(right) =sum(above)
Standard uncertainty u
NLL
Expanded uncertainty U =2 ⋅ above
NLL
Where the standard uncertainty in both cases is calculated as
2 2 2 2 2 2 2 2
Eq. 5
u = u +()n −1 ⋅u + u + u + n ⋅u + u
NLL C V PW pd u wf
and the expanded relative uncertainty is U = 2*u , which corresponds to a coverage probability of
NLL NLL
approximately 95 %.
7 Procedures for load loss
7.1 General
In load loss measurements the reported loss shall be valid at the rated current and at the reference
temperature. In general the measurement is not performed at the precise current and temperature
level intended and the value valid at reference conditions must be deduced.
7.2 Model function for load loss at reference conditions
EN 60076-1 requires that the measured value of load loss be corrected with the square of the ratio of
rated current to test current. The power thus obtained is then recalculated from actual to reference
temperature.
The model function for the measured power P referred to the rated current I
2 N
 
 
 
1 1 1 I
N
Eq. 6
 
P = k ⋅ ⋅k ⋅ ⋅P ⋅ ⋅
2 CN VN W
η η 1
1 −()ε −ε ⋅tanϕ  
C V
V C
1 + 1 + k ⋅ ⋅I
CN M
 
η
100 100
C
1 +
 
 100 
which is rearranged to
 
η 1 1 I
 
C N
P = k ⋅1 +  ⋅k ⋅ ⋅P ⋅ ⋅
Eq. 7
2 CN VN W  
η
100 1 −()ε −ε ⋅tanϕ k ⋅I
  V
V C  CN M
+
where
 I 
N
– is a parameter related to the actual current measured during the test related to the
 
k ⋅I
 CN M
reference current for which the transformer shall be tested;
– other terms are as defined in 6.2.
The known systematic deviations of the power meter have been assumed to be negligible. The phase
angle ϕ of the loss power is obtained from
 P 
W
 
ϕ = ϕ −ε +ε = arccos −ε +ε
Eq. 8
M V C V C
 
I ⋅U
 M M
It has been assumed that the power meter establishes the power factor from measurement of power
and apparent power at the fundamental frequency of the test voltage.
And finally, as given in Annex E, the load loss power P referred to rated current I and to reference
LL N
temperature θ
r
 
t +θ t +θ t +θ t +θ
2 2 r 2 2
 
P = P ⋅ + I ⋅R ⋅ − ⋅
Eq. 9
LL 2 N 1
 
t +θ t +θ t +θ t +θ
r  1 1 r
Here t is a constant set to 235 for copper and to 225 for aluminium windings. The winding resistance
R has been determined at “cold winding resistance” at a temperature θ . The temperature of the
1 1
winding θ at the time of the load loss test will in general be determined at the time of test and can be
different from θ . In the event that the load loss test is made in immediate conjunction with the winding
resistance measurement, θ =θ can be assumed.
2 1
Eq. 9 is identical to the procedure given in EN 60076-1, Annex E for temperature corrections.
In most cases it is however possible to assume that the relative uncertainty of ohmic loss is
representative of the uncertainty of the temperature correction. This is given in the uncertainty budget
below.
NOTE In the written formula, some secondary influencing quantities have been disregarded, such as frequency, wave shapes,
effect of the voltage transformer leads, etc.
7.3 Uncertainty budget for measured power P referred to rated current
7.3.1 General
An uncertainty budget should list all possible contributions to uncertainty, and an estimate of their
magnitudes should be made.
The sensitivity to different uncertainty contributions can in general be deduced form the model
function. Contributions to uncertainty in loss measurements from statistical random processes are in
general small compared to other contributions and are not further treated here.
Rated values, such as I and θ are considered constants and are not included in uncertainty
N r
evaluations.
– 13 – CLC/TR 50462:2008
7.3.2 Standard and expanded uncertainty for measurement of measured load loss power P
at ambient temperature
Table 3 – Uncertainty in the general case
See
Standard Sensitivity Uncertainty
Quantity Estimate Variance sub-
uncertainty coefficient contribution
clause
CT ratio error
1 10.1.2
η u u u
C C C
C
VT ratio error
u 1 u u 10.1.2
η
V V V V
Power meter 1 10.3
P u u u
W PW PW PW
Phase 10.2.4
1 ε ε tan
displacement 1 or
u u u
pd pd pd
V C
−()− ⋅ ϕ
10.2.3
Ampere meter
2 10.5
I u 2 ⋅ u 4 ⋅ u
M IM
IM IM
Winding
~ ~ ~
2 2
u c = c ⋅u c ⋅u 10.7
temperature θ 3
3 θ
θ 3 θ
t +θ
Standard uncertainty u =√(right) =sum(above)
P2
Expanded uncertainty U =2 ⋅ above

P2
Table 4 – Uncertainty without correction for phase displacement
See
Standard Sensitivity Uncertainty
Quantity Estimate Variance sub-
uncertainty coefficient contribution
clause
CT ratio error
η u 1 u u 10.1.2
C C C C
VT ratio error
10.1.2
η u 1 u u
V V V
V
Power meter
P u 1 u u 10.3
W PW PW PW
Phase 10.2.2
displacement 1 u 1 u u or
pd pd pd
10.2.3
Ampere meter
I u 2 2 ⋅ u 4 ⋅ u 10.5
M IM IM IM
Winding
~ 2 2
~ ~
c = 10.7
θ u c ⋅u c ⋅u
temperature 3
3 θ
θ 3 θ
t +θ
=√(right) =sum(above)
Standard uncertainty u
P2
Expanded uncertainty U =2 ⋅ above
P2
NOTE 1 The parameter t relates to thermal coefficient of winding resistance, and is taken as 235 for copper and as 225 for
aluminium.
NOTE 2 In the case that temperature change during load loss test is significant, e.g. in tests on large transformers with
measurements on several tap changer positions, more appropriate procedures are given in E.3.

The standard uncertainty is in both cases calculated as
~
2 2 2 2 2 2 2
u = u + ⋅u + u + u + 4 ⋅u + c ⋅u Eq. 10
P2 C V PW pd IM 3 θ
and the expanded uncertainty is U = 2 ⋅ u , which corresponds to a coverage probability of
P2 P2
approximately 95 %.
7.4 Uncertainty budget for reported load loss
The results of the load loss test are to be recalculated to the reference temperature. The uncertainty of
this process is given by the table below where the sensitivity coefficients are discussed in E.5.
Table 5 – Standard and expanded uncertainty for load loss
See
Standard Sensitivity Uncertainty
Quantity Estimate Variance sub-
uncertainty coefficient contribution
clause
Loss power
2 2
7.3
P u c = 1 c ⋅ u c ⋅ u
2 P2 1 1 P2 1 P2
measurement
Winding
R u c = 1 u u 10.8
1 R1 2 R1 R1
resistance
Standard uncertainty u =√(right) =sum(above)
LL
Expanded uncertainty U =2 ⋅ above =2 ⋅ above
LL
The standard uncertainty of the load loss is calculated as
2 2
Eq. 11
u = u + u
LL P2 R1
and the expanded relative uncertainty is U = 2 ⋅ u , which corresponds to a coverage probability of
LL LL
approximately 95 %.
8 Three-phase calculations
8.1 Power
Power measurement is usually performed using three independent single-phase measuring systems,
adding the three terms. This measuring method is recommended.
In this case the criteria for calculating 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
T
the total power is obtained by the formula:
~ ~ 2 ~ 2 ~ 2
Eq. 12
u = u +u + u
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 W.

– 15 – CLC/TR 50462:2008
The relative uncertainty is:
~
u
T
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. Such circuits are not recommended.
8.2 Reference voltage (current)
The reference voltage (or current) is measured during no-load loss (load loss) tests. If the three-phase
system can be considered practically symmetrical (or equilibrated), it is acceptable to use the mean
value of the three indications of the reference voltage (current). The quantities are considered not
correlated and any scattering of values are due to the system.
9 Reporting
9.1 Uncertainty
The total uncertainty of the measurement of losses shall be estimated in accordance with this
Technical Report and the reported expanded uncertainty of measurement shall be stated as the
standard uncertainty of measurement multiplied 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 shall be based on traceable calibrations. The chain of
traceability should be indicated in the report.
10 Estimation of corrections and uncertainty contributions
10.1 Ratio error of instrument transformers
10.1.1 General
An instrument transformer is in general characterised by a calibration performed at different currents
(voltages) and at two different burdens. Depending on the needs of the measurement situation there
are several options for estimation of errors and uncertainty.
The method using class index will usually be sufficient for analysis of both no-load loss and load loss.
In some cases, when the estimated uncertainty of the loss is too large, use of the reference procedure
may be indicated.
In measuring systems conventional instrument transformers consisting of a simple magnetic circuit is
often used. There are however today advanced devices employing technologies that enhance
accuracy and stability. These types are treated separately due to the difference in characteristics.
Examples of advanced devices are for current scaling:
– zero flux current transformers;
– two-stage current transformers;
– amplifier-aided current transformers.

These transformers operate on the principle of reducing flux in the active core of the current
transformer to near zero, thereby reducing both ratio errors and phase displacement to very small
values.
Advanced voltage transducers utilise standard compressed gas capacitors in conjunction with various
active feedback circuits to minimise ratio errors and phase displacement. The compressed gas
capacitor is sufficiently stable and has a relatively low loss, however the electronics associated with
the divider generally drift over time and hence should be calibrated periodically.
10.1.2 Using class index procedure for ratio error
10.1.2.1 Ratio error of conventional instrument transformers
The analysis is based on estimating the uncertainty as u = class index of the instrument
class
transformer. In this case the ratio error is estimated to η = 0. A necessary prerequisite for this
C
method is that the transformer is used within the burden range and current (voltage) range for which it
has been qualified.
u
class
Eq. 13
u =
C
10.1.2.2 Ratio error of advanced instrument transformers
The analysis is based on estimating the uncertainty as u = class index of the instrument
class
transformer. In this case the ratio error is estimated to η = 0. A necessary prerequisite for this
C
method is that the transformer is used within the burden range and current (voltage) range for which it
has been qualified.
u
class
Eq. 14
u =
C
10.1.3 Reference procedure for ratio error
10.1.3.1 Ratio error of conventional instrument transformers
Highest accuracy is obtained if the error η is interpolated from the available data in the calibration
C
certificate. Interpolation must be performed to obtain the value valid at the current (voltage) measured,
and at the total burden connected to the terminals of the instrument transformer. Best results will be
obtained if the calibration has been performed at the actual burden.
The uncertainty of η is composed of the calibration uncertainty and the uncertainty in the
C
interpolation. Possible long-term drift of the instrument transformer is disregarded.
2 2
Eq. 15
u = u + u
C cal interpol
where
– u is the standard uncertainty obtained as the expanded uncertainty given in a calibration
cal
certificate, divided by the coverage factor. In cases where the coverage factor is not given
explicitly, it is common procedure to assume a rectangular distribution and to divide by √3;
– u is the standard uncertainty obtained as part of the interpolation procedure.
interpol
– 17 – CLC/TR 50462:2008
10.1.3.2 Ratio error of advanced instrument transformers
Highest accuracy is obtained if the error η is interpolated from the available data in the calibration
C
certificate. Interpolation must then be performed to be valid at the current (voltage) measured, and at
the total burden connected to the terminals of the instrument transformer. The uncertainty of η will
C
then be composed of the calibration uncertainty and the uncertainty in the interpolation. Possible drift
of the instrument transformer since the last calibration is disregarded.
2 2
Eq. 16
u = u + u
V cal interpol
where
– u is the standard uncertainty obtained as the expanded uncertainty given in a calibration
cal
certificate, divided by the coverage factor. In cases where the coverage factor is not given
explicitly, it is common procedure to assume a rectangular distribution and to divide by √3;
– u is the standard uncertainty obtained as part of the interpolation procedure.
interpol
10.2 Phase displacement of instrument transformers
10.2.1 General
The combined phase displacement of current and voltage transformers has an effect on the
measurement of power at low power factor. See Annex D. Evaluation of effect of phase displacement
must therefore be made for the system rather than for each component.
A current (voltage) transformer is in general characterised by a calibration performed at different
currents (voltages) and at two different burdens. Depending on the needs of the measurement
situation there are several options for estimation of phase displacement and uncertainty.
Highest accuracy is obtained if the phase displacement ε is interpolated from the available data in the
C
calibration certificate. Interpolation must then be performed to be valid at the current measured, and at
the total burden connected to the terminals of the current transformer. Best results will be obtained if
the calibration has been performed at the actual burden.
Depending on the power factor and on the magnitude of the combined phase displacement, it may be
possible to make simplified analysis. In practice, the simplified analysis is satisfactory if the estimated
uncertainty of the loss measurement is low enough. If not, the more elaborate method should be used.
Three procedures for uncertainty analysis are identified, Reference procedure, Simplified procedure
and Using class index. Exact applicability will be determined by the required uncertainty of the
measurement and on the combination of power factor and known phase displacement in the
measuring chain. As a first guide Table 6 can be used.

Table 6 – Procedures for uncertainty analysis
Procedure Description Salient features
Using class inde Requires the least work and could give The term F is estimated as F = 1.
D D
acceptable results if the power factor
x The uncertainty is obtained from the
is > 0,3
maximum phase displacement defined
10.2.2
for the accuracy class and the
corresponding maximum value of F
D
for the range of power factors
considered.
Simplified Could give acceptable results if power The term F is calculated in Eq. 2 and
D
procedure factor is > 0,05 and if the combined Eq. 7 respectively, using average
phase displacement is < 2 min estimates for the known phase
10.2.3
displacements.
The uncertainty is estimated from
spread in known phase displacement.
Reference Is most correct and will usually be The term F is calculated in Eq. 2 and
D
procedure needed when the power factor is Eq. 7 respectively, using the best
< 0,05 and/or if the combined phase estimates for the known phase
10.2.4
displacement is > 2 min displacements.
The uncertainty is estimated from the
uncertainty of the known phase
displacements
10.2.2 Using class index procedure for phase displacement
No correction for the effect of phase displacement is effectuated and in Eq. 2 and Eq. 7
F = ≈1 , is used.
D
1 −()ε −ε ⋅tanϕ
V C
The uncertainty is calculated from the maximum value the term F could assume for the range of
D
values of tan ϕ expected to occur.
1 1 1
u = 1 − max(F ) = max1 −
Eq. 17
pd D
1 −()ε −ε ⋅tanϕ
3 3
V C
where
– ε = negative class limit (expressed in rad) for the current transformer phase displacement;
C
– ε = positive class limit (expressed in rad) for the voltage transformer phase displacement.
V
10.2.3 Simplified procedure for phase displacement
10.2.3.1 Formulas
...