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
Technical Committee
Drafting Committee
Parallel Committee
Current Stage
6060 - Document made available
Due Date
04-Jul-2008
Completion Date
04-Jul-2008

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SLOVENSKI STANDARD
SIST-TP CLC/TR 50462:2008
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
SIST-TP CLC/TR 50462:2008 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TP CLC/TR 50462:2008
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SIST-TP CLC/TR 50462:2008
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
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SIST-TP CLC/TR 50462:2008
CLC/TR 50462:2008 – 2 –
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.
__________
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SIST-TP CLC/TR 50462:2008
– 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

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SIST-TP CLC/TR 50462:2008
CLC/TR 50462:2008 – 4 –

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

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SIST-TP CLC/TR 50462:2008
– 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.
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SIST-TP CLC/TR 50462:2008
CLC/TR 50462:2008 – 6 –
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

circuit;
I current measured by the ammeter (normally corresponding to rated current);
I reference current (normally rated current);
k rated transformation ratio of the current transformer;
k rated transformation ratio of the voltage transformer;
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

measurement;

P no-load loss at reference conditions and corrected for known errors in the measurement;

NLL
P power measured by the power meter;

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;
t parameter related to the thermal coefficient of winding resistance;
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SIST-TP CLC/TR 50462:2008
– 7 – CLC/TR 50462:2008
U voltage measured with an instrument having average rectified mean response;
avg
U voltage measured;
U rated voltage;
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
EN 60076-1, 10.2;
temperature of transformer winding during load loss test;
reference temperature for transformer winding according to EN 60076-1, 10.1;
ε actual phase displacement of the current transformer (rad);
ε actual phase displacement of the power meter (rad);
actual phase displacement of the voltage transformer (rad);

accuracy of the phase displacement declared in the calibration certificate for the voltage

transformer;

accuracy of the phase displacement declared in the calibration certificate for the current

transformer;
actual current error of the current transformer (%);
η actual voltage error of the voltage transformer (%);
actual phase angle between voltage and current;
phase angle between voltage and current measured with power meter.
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;
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

F(ε)
transformers;
u uncertainty of current measurement;
u uncertainty of an interpolation procedure;
interpol
u uncertainty of the load loss power;
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SIST-TP CLC/TR 50462:2008
CLC/TR 50462:2008 – 8 –
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;
u uncertainty of setting of rated voltage at no-load loss test;
u uncertainty of voltage measurement;
u uncertainty of voltage transformer ratio;
u uncertainty of correction to sinusoidal waveform for no-load-loss;
u uncertainty of phase displacement for complete measuring system;
uncertainty of current transformer phase displacement;
uncertainty of voltage transformer phase displacement.
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.
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SIST-TP CLC/TR 50462:2008
– 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:
 
 
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
100 100  
+ + ⋅ ⋅
 
100
 
 
where
– k ⋅
is a parameter related to the ratio error of the current transformer;
1 +
100
– k ⋅
η is a parameter related to the ratio error of the voltage transformer;
1 +
100
is a parameter related to the correction for phase displacement;
1 −()ε −ε ⋅tanϕ
V C
 
 
 
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
 
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
rms
avg
 
indication of an r.m.s. responding instrument.
Eq. 1 can also be expressed as:
n−1
 
  U −U
1 η 1 U
  avg rms
V N
 
P = k ⋅ ⋅k ⋅1 +  ⋅P ⋅ ⋅ ⋅ 1 +
NLL CN VN W  
Eq. 2
 
100 1 −()ε −ε ⋅tanϕ k ⋅U U
 
V C  VN M avg
1 +  
100

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
 
 
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.
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SIST-TP CLC/TR 50462:2008
CLC/TR 50462:2008 – 10 –

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−1
 
  U −U
1 η U
 
avg rms
V N
 
P = k ⋅ ⋅k ⋅1 +  ⋅P ⋅ ⋅ 1 +
NLL CN VN W  
Eq. 4
 
100 k ⋅U U
C  
 VN M avg
1 +  
100

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.

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
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 −
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
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SIST-TP CLC/TR 50462:2008
– 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
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
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
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
 
100 100
1 +
 
 100 
which is rearranged to
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SIST-TP CLC/TR 50462:2008
CLC/TR 50462:2008 – 12 –
 
η 1 1 I
 
C N
P = k ⋅1 +  ⋅k ⋅ ⋅P ⋅ ⋅
Eq. 7
2 CN VN W  
100 1 −()ε −ε ⋅tanϕ k ⋅I
  V
V C  CN M
100
where
 I 

– 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 
 
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
 
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 ti
...

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