IEC 60034-28:2012

IEC 60034-28 ®
Edition 2.0 2012-12
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Rotating electrical machines –
Part 28: Test methods for determining quantities of equivalent circuit diagrams
for three-phase low-voltage cage induction motors

Machines électriques tournantes –
Partie 28: Méthodes d’essai pour la détermination des grandeurs des schémas
d’équivalence des circuits pour moteurs à induction à cage basse tension
triphasés
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IEC 60034-28 ®
Edition 2.0 2012-12
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Rotating electrical machines –

Part 28: Test methods for determining quantities of equivalent circuit diagrams

for three-phase low-voltage cage induction motors

Machines électriques tournantes –

Partie 28: Méthodes d’essai pour la détermination des grandeurs des schémas

d’équivalence des circuits pour moteurs à induction à cage basse tension

triphasés
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
CODE PRIX U
ICS 29.160 ISBN 978-2-83220-553-2

– 2 – 60034-28 © IEC:2012
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms, definitions, symbols and conventions . 7
3.1 Terms and definitions . 7
3.2 Symbols . 8
3.3 Subscripts . 9
3.4 Winding connection . 9
4 Test requirements . 10
4.1 General . 10
4.2 Frequency and voltage . 10
4.3 Instrumentation . 10
4.3.1 Measuring instruments for electrical quantities, speed and frequency . 10
4.3.2 Instrument transformers . 10
4.3.3 Temperature measurement . 10
5 Approximations and uncertainties . 10
6 Test procedures . 11
6.1 General . 11
6.2 Stator d.c. line-to-line resistance measurement . 11
6.3 Load-test at rated load . 11
6.4 Load curve test. 12
6.5 No-load test . 12
6.6 Reverse rotation and locked rotor tests . 13
6.6.1 General . 13
6.6.2 Reverse rotation test . 13
6.6.3 Locked rotor test. 13
7 Determination of motor quantities . 13
7.1 General . 13
7.2 Resistance of stator winding R . 15
s
7.3 Total stator inductance L = L + L . 15
ts m σs
7.3.1 General . 15
7.3.2 Determination procedure . 15
7.4 Equivalent resistance of iron losses R . 16
feΓ
7.4.1 Constant losses . 16
7.4.2 Friction and windage losses. 17
7.4.3 Iron losses . 17
7.5 Total leakage inductance L . 18
tσ
7.5.1 General . 18
7.5.2 Distribution of leakage inductances between stator and rotor. 18
7.5.3 Determination of total leakage inductance from a reverse rotation or
locked rotor test (6.6) . 18
7.5.4 Determination of total leakage inductance from a load curve test (6.4) . 20
7.6 Magnetizing inductance L and voltage U . 21
m m
7.6.1 From a reverse rotation or locked rotor test (6.6) . 21
7.6.2 From a load curve test (6.4) . 21

60034-28 © IEC:2012 – 3 –
7.7 Stator and rotor leakage inductances L and L ’ . 22
σs σr
7.7.1 From a reverse rotation or locked rotor test (6.6) . 22
7.7.2 From a load curve test (6.4) . 22
7.8 Inductances for calculations at constant flux (rated load) . 22
7.9 Resistance of rotor cage R ’ referred to the stator winding and frequency . 23
r
7.10 Equivalent resistance of iron losses R . 25
fe
Annex A (informative) Sample calculation . 26

Figure 1 – Type-T equivalent circuit diagram . 14
Figure 2 – Type-T equivalent circuit diagram (iron losses disregarded) . 14
Figure 3 – Type-L equivalent circuit diagram (iron losses disregarded) . 14
Figure 4 – Type-Γ equivalent circuit diagram. 15
Figure 5 – Typical characteristics of inductance L over current I . 16

– 4 – 60034-28 © IEC:2012
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ROTATING ELECTRICAL MACHINES –

Part 28: Test methods for determining quantities of equivalent circuit
diagrams for three-phase low-voltage cage induction motors

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-
governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely
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
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
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4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence
between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in
the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
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.
International Standard IEC 60034-28 has been prepared by IEC technical committee 2:
Rotating machinery.
This second edition cancels and replaces the first edition published in 2007. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition.
a) The formulae are now all given for equivalent star-connection equivalent circuit diagrams.
They are applied even in the case of delta connected windings. All formulae for delta-
connected equivalent circuit diagrams have been moved to notes.
b) Procedures for the determination of equivalent circuit parameters from a load curve test as
an alternative to the reverse rotation and locked rotor tests have been added.

60034-28 © IEC:2012 – 5 –
The text of this standard is based on the following documents:
FDIS Report on voting
2/1685/FDIS 2/1688/RVD
Full information on the voting for the approval of this standard 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.
NOTE A table of cross-references of all IEC TC 2 publications can be found in the IEC TC 2 dashboard 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
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
– 6 – 60034-28 © IEC:2012
INTRODUCTION
Equivalent circuits are widely used in the control of adjustable speed drives with induction
motors supplied by frequency inverters. The motor parameters are required for the realisation
of flux oriented control or other model-based control algorithms. Their knowledge is required
by suppliers and system engineers, especially when motors and frequency inverters from
different suppliers are combined.
This standard provides a standardized test procedure to determine the electric motor
parameters. At the same time the draft offers an improved understanding of the equivalent
circuit method. The procedures can be carried out in laboratories equipped for standard
electric machinery tests.
NOTE This standard’s main purpose is for assistance in modelling frequency controlled motors. Due to the
simplifications the results cannot be used to determine motor performance or efficiency accurately.
A related technical specification is IEC/TS 60034-25 where required motor parameters are
listed, but their definition and methods of determination are not included.

60034-28 © IEC:2012 – 7 –
ROTATING ELECTRICAL MACHINES –

Part 28: Test methods for determining quantities of equivalent circuit
diagrams for three-phase low-voltage cage induction motors

1 Scope
This part of the IEC 60034 series applies to three-phase low-voltage cage induction motors of
frame numbers 56 to 400 as specified in IEC 60072-1.
This standard establishes procedures to obtain values for elements of single phase equivalent
circuit diagrams from tests and defines standard elements of these diagrams.
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 60034-1:2010, Rotating electrical machines – Part 1: Rating and performance
IEC 60034-2-1, Rotating electrical machines – Part 2-1: Standard methods for determining
losses and efficiency from tests (excluding machines for traction vehicles)
IEC 60034-2-2, Rotating electrical machines – Part 2-2: Specific methods for determining
separate losses of large machines from tests – Supplement to IEC 60034-2-1
IEC 60034-2-3 , Rotating electrical machines – Part 2-3: Specific test methods for
determining losses and efficiency of converter-fed AC motors
IEC/TS 60034-25 , Rotating electrical machines – Part 25: A.C. Motors when used in power
drive systems - Application guide
IEC 60044 (all parts), Instrument transformers
IEC 60051-1, Direct acting indicating analogue electrical measuring instruments and their
accessories – Part 1: Definitions and general requirements common to all parts
IEC 60072-1, Dimensions and output series for rotating electrical machines – Part 1: Frame
numbers 56 to 400 and flange numbers 55 to 1080
3 Terms, definitions, symbols and conventions
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60034-1:2010
apply.
———————
To be published.
A revision of this publication is currently under preparation.

– 8 – 60034-28 © IEC:2012
3.2 Symbols
The following symbols apply:
cos ϕ is the power factor
cos ϕ is the rated power factor
N
f is the stator supply frequency, Hz
f is the frequency of the rotor current (slip frequency), Hz
r
f is the rated frequency, Hz
N
h is the height of the rotor-conductor bar, m
H is the motor frame size according to IEC 60072-1 (distance from the centre-line of
the shaft to the bottom of the feet (basic dimension)), mm
I is the stator line current, A
I is the stator phase current, A
s
I ’ is the rotor phase current, A
r
I is the magnetizing current, A
m
is the rated stator current, A
I
N
k is the skin effect factor for inductances
i
k is the reciprocal of the temperature coefficient of resistance at 0 °C of the rotor
r
conductor material, see Note 1
k is the reciprocal of the temperature coefficient of resistance at 0 °C of the stator
s
conductor material, see Note 1
k is the ratio of the stator to the rotor leakage inductances
σ
L is the magnetizing inductance, H
m
L is the stator leakage inductance, H
σs
L ’ is the rotor leakage inductance, H
σr
L is the total leakage inductance (= L + L ’), H
tσ σs σr
L is the total leakage inductance disregarding the skin effect, H
σa
L is the total stator inductance (= L + L ), H
ts m σs
L ’ is the total rotor inductance (= L + L ’), H
tr m σr
–1
n is the operating speed, min
–1
n is the rated speed, min
N
–1
n is the rated synchronous speed, min
syn
p is the number of pole pairs
P is the electrical input power, W
S
P is the mechanical output power, W
2N
P is the constant losses, W
k
P is the friction and windage losses, W
fw
P is the iron losses, W
fe
R is the line-to-line resistance, Ω
R is the equivalent circuit resistance of iron losses, Ω
fe
R , is the stator line-to-line resistance at initial winding temperature, Ω
ll m
R is the stator phase-resistance corrected to a temperature of 25 °C, Ω
s,25°
R ’ is the rotor cage resistance, Ω
r
R ’ is the rotor resistance corrected to an ambient temperature of 25 °C, Ω
r,25°
60034-28 © IEC:2012 – 9 –
R , ’ is the rotor resistance at initial winding temperature, Ω
r m
s is the slip, in per unit value of synchronous speed
s is the rated slip
N
U is the stator terminal voltage, V
is the stator phase voltage, V
U
s
U is the voltage drop over the magnetizing inductance, V
m
U is the rated terminal voltage, V
N
X is the magnetizing reactance (= 2πf ⋅L ), Ω
m N m
X is the stator leakage reactance (= 2πf ⋅L ), Ω
σs N σs
X ’ is the rotor leakage reactance (= 2πf ⋅L ’), Ω
σr N σr
X is the total leakage reactance (= 2πf ⋅L ), Ω
tσ N tσ
X is the total leakage reactance disregarding the skin effect (= 2πf ⋅L ), Ω
σa N σa
X is the total stator reactance (= 2πf ⋅L ), Ω
ts N ts
X ’ is the total rotor reactance (= 2πf ⋅L ’), Ω
tr N tr
Z is the line impedance, Ω
γ is the conductivity of rotor conductor, S/m, see Note 2
r
θ is the temperature of the cold winding at initial resistance measurement, °C
θ is the temperature of the winding at the end of the thermal load test, °C
L
θ is the temperature of the winding at the end of the thermal no-load test, °C
NL
NOTE 1 For copper, use k = 235, for aluminium, use k = 225, unless otherwise specified.
6 6
NOTE 2 For copper rotor-bars, use γ = 56 × 10 S/m, for aluminium rotor-bars, use γ = 33 × 10 S/m unless
r r
otherwise specified.
NOTE 3 For calculations in this standard, voltages and currents are r.m.s. magnitude values (different from
vectors in complex calculations).
NOTE 4 All rotor values are referred to the stator winding and frequency.
3.3 Subscripts
L, NL, 0 test conditions
m, ma, mb magnetizing quantities
N rated value
r, tr rotor quantities
s, ts stator quantities
σ, tσ leakage quantities
3.4 Winding connection
The mathematical model of the machine shall be regarded as Y-connected, regardless of the
actual connection of the motor (delta or star). The quantities in the equivalent circuit diagram
shall be presented as per phase values in equivalent Y-connection.
NOTE For reference purposes the formulae required to calculate a delta-connected equivalent circuit diagram are
also given as notes. In case of delta connected motors these formulae can be used to create an equivalent circuit
diagram which represents the internal winding currents better than a circuit diagram in equivalent Y-connection.

– 10 – 60034-28 © IEC:2012
4 Test requirements
4.1 General
The tests shall be carried out with regard to the requirements for the tests given in
IEC 60034-2-1, IEC 60034-2-2, IEC 60034-2-3 and IEC/TS 60034-25, as applicable.
4.2 Frequency and voltage
The frequency shall be within ± 0,3 % of specified test frequency during measurements. The
form and symmetry of the supply voltage shall conform to the requirements of 8.3.1 of
IEC 60034-1:2010.
4.3 Instrumentation
4.3.1 Measuring instruments for electrical quantities, speed and frequency
The measuring instruments shall have an accuracy class of 0,5 or better in accordance with
IEC 60051-1. However, accuracy class for the measurement of resistance shall be 0,1.
Since instrument accuracy is generally expressed as a percentage of full scale, the range of
the instrument chosen shall be as low as practical.
4.3.2 Instrument transformers
Instrument transformers shall have an accuracy class of 0,2 according to IEC 60044.
4.3.3 Temperature measurement
The instrumentation used to measure temperatures shall have an accuracy of ± 1 °C.
5 Approximations and uncertainties
The procedures described to obtain the values of the equivalent circuit diagram include
approximations. Furthermore, the equivalent circuit diagram is an approximation in itself.
The inductances are determined depending on current in order to take saturation effects of
the iron core into account. However, iron losses are disregarded in the determination formulae
of all inductances.
Eddy current effects on inductances and resistances are disregarded because the application
of the obtained equivalent circuit parameters is not intended to the start-up process of the
motor (i.e. application to slips between 0 to ± 0,3).
The assumption of short-circuited rotor resistance during the determination of the total
leakage inductance L (7.4) will typically result in an error less than 5 % on the obtained
tσ
value. The effect on the magnetizing inductance L (7.6) is negligible.
m
NOTE For very small motors (rated power less than 1 kW) the error can increase due to the relatively large values
of rotor resistance.
Furthermore the relatively large rotor frequencies (at s = 2 or s = 1) during the tests for total
leakage inductance require skin effect compensation. Unless rotor design data are available,
the calculation must be based on an estimated rotor conductor-bar height (see 7.5.3.3). But
rotor design data is preferable. This standard introduces an alternative procedure (7.5.4) for
the determination of leakage inductances from a load curve test that avoids these difficulties.

60034-28 © IEC:2012 – 11 –
The distribution of the total leakage inductance L into stator and rotor leakage inductances
tσ
(L and L ’, see 7.7) is based on rough assumptions and cannot be performed accurately by
σs σr
the methods described in this standard.
The difference between the rotor and winding temperature is neglected during the
determination of rotor resistance R ’ (7.9).
r
While iron losses in the stator are included, those in the rotor are disregarded. This is a valid
assumption for slips between 0 and breakdown slip. Therefore, the start-up situation cannot
be represented correctly.
Furthermore this simplification gives rise to errors in the determination of leakage inductances
from the reverse rotation test (see 6.6.2) since the rotor frequency becomes twice the rated
frequency in this case.
To adjust the equivalent iron loss resistance to frequencies other than rated frequencies the
distribution of hysteresis losses versus eddy current losses needs to be known. This standard
presents a suitable approximation (see 7.4.3).
6 Test procedures
6.1 General
The subtests that make up this test procedure shall be performed in the sequence listed. It is
not essential that the tests are carried out immediately one after another. However, if the
subtests are performed individually, then the specified thermal conditions shall be re-
established prior to obtaining the test data.
The arithmetic average of the three line currents and voltages shall be used. The stator line-
to-line resistance is the value across any two terminals for which a reference value has been
measured at known temperature.
It is recommended that whenever measurements of voltage, current, speed or power for a
certain load point are required the actual test data is an average value of several samples
taken in short time intervals to compensate for load fluctuations.
6.2 Stator d.c. line-to-line resistance measurement
The temperature of the winding when the resistance is measured shall not differ from the
coolant by more than 2 K.
Measure and record R , . The resistance shall be taken as the average value from
ll m
measurements of all three phases. Measure and record the winding temperature θ according
to 8.6.2 of IEC 60034-1:2010.
6.3 Load-test at rated load
Before starting to record data for this test, the temperature of the stator winding shall be
within 2 K of the temperature obtained from a rated load thermal test (see IEC 60034-1).
Apply rated voltage of rated frequency to the terminals. Increase the load until the line current
I equals rated current I .
N
Measure and record U, I, P and n. Measure and record the winding temperature θ according
S L
to 8.6.2 of IEC 60034-1:2010. The first reading of resistance shall be taken within the time
specified in Table 5 of IEC 60034-1:2010.

– 12 – 60034-28 © IEC:2012
6.4 Load curve test
This test is only required for the determination procedure according to 7.5.4 and is an
alternative to the reverse rotation and locked rotor tests (6.6).
Before starting to record data for this test, the temperature of the stator winding shall be
within 5 K of the temperature obtained from a rated load thermal test (see IEC 60034-1).
Apply the load to the machine for at least 10 points. The load points should be chosen to be
approximately equally spaced between not less than 25 % and up to and including 125 %
load. When loading the machine, start at the highest load value and proceed in descending
order to the lowest. The tests shall be performed as quickly as possible to minimize
temperature changes in the machine during testing.
Measure the line-to-line resistance R before the highest and after the lowest reading. The
resistance for 100 % load and higher loads shall be the value determined before the highest
load reading. The resistance used for loads less than 100 % shall then be determined as
linear with load, using the reading before the test for the highest load and after the lowest
reading for the lowest load.
Preferably, resistances may also be determined by measuring the stator winding temperatures
using a temperature-sensing device installed on the winding. Resistances for each load point
may then be determined from the temperature of the winding at that point in relation to the
resistance and temperature measured before the start of the test.
Measure and record for each load point U, I, P and n.
S
Determine R for each load point.
6.5 No-load test
The no-load test shall be started after the load test. Decouple the motor from any load or
other machine. Run the motor without load until the no-load losses have stabilized.
This test should be done with a slip as close to zero as possible. Therefore, seals or other
devices causing additional friction should be removed if suitable.
By adjusting the supply voltage at rated frequency, measure and record U, I and P for at
S
least 10 values of voltage.
The highest voltage shall be selected according to the capabilities of the laboratory. However,
it shall be not less than 110 % of the rated voltage of the motor and not exceed the value that
will result in a no-load current greater than 150 % of rated current.
The lowest voltage shall be approximately 20 % of rated voltage. However, it shall not fall
below the value where further reduction increases the current.
One of the test voltages shall be the rated voltage of the machine.
The test shall be carried out as quickly as possible with the readings taken in descending
order of voltage.
After the test, measure and record the winding temperature θ according to 8.6.2 of
NL
IEC 60034-1:2010. The first reading of resistance shall be taken within the time specified in
Table 5 of IEC 60034-1:2010.
60034-28 © IEC:2012 – 13 –
6.6 Reverse rotation and locked rotor tests
6.6.1 General
Reverse rotation and locked rotor tests are only required for the determination procedure
according to 7.5.3 and are an alternative to the load curve test (6.4).
For motors which do not use double-cage or deep bar rotor designs (i.e. small current
displacement) the reverse rotation test (6.6.2) is recommended to improve accuracy. This is
usually the case for motors up to frame size 132. For larger motors, the locked rotor test
(6.6.3) may give better results. This test is not recommended for motors less than 1 kW rated
output power (due to the inaccuracies resulting from the large rotor resistance of these
machines).
6.6.2 Reverse rotation test
Couple the tested motor to an external machine. Drive the tested motor at synchronous speed
n by the external machine. Apply a low voltage of opposite phase sequence to the
syn
terminals of the machine (f = –f ). The slip will become 2,0. Increase the voltage until the line
N
current I equals 1,5 times rated current I
N.
The rate of temperature rise in rotor bars of 2-pole machines can be very large. In these
cases, in order to avoid the rotor from being destroyed, a maximum current of 1,25 times
rated current is recommended.
Measure and record U, I and P for at least 10 values of current approximately equally
S
spaced between 150 % and 10 % of rated current I including one reading at rated current.
N
It is recommended that the current values used for this test match the values used in (6.5) at
the best. The test shall be carried out as quickly as possible with the readings taken in
descending order of voltage and current.
6.6.3 Locked rotor test
Lock the rotor and apply low voltage of rated frequency f = f to the terminals. The slip is then
N
1,0. Increase the voltage until the line current I reaches up to 1,5 times rated current I
N
maximum.
The rate of temperature rise in rotor bars of 2-pole machines can be very large. In these
cases, in order to avoid the rotor from being destroyed, a maximum current of 1,25 times
rated current is recommended.
Measure and record U, I and P for at least 10 values of current approximately equally
S
spaced between maximum 150 % and 10 % of rated current I including one reading at rated
N
current.
It is recommended that the current values used for this test match the values used in (6.5) at
the best. The test shall be carried out as quickly as possible with the readings taken in
descending order of voltage and current.
7 Determination of motor quantities
7.1 General
The type-T equivalent circuit diagram (Figure 1) is normative for the motors addressed in this
standard. A simplified variant without the equivalent resistance of iron losses is given in
Figure 2.
– 14 – 60034-28 © IEC:2012
R jX
jX′
s σs σr
I
I′
s
r
I I
m fe
R′ /S
r
jX R
U U
s m m fe
IEC  2349/12
Figure 1 – Type-T equivalent circuit diagram

R jX jX′
σs
s σr
I
I′
s r
I
m
R′ /S
r
jX
U U m
s m
IEC  2350/12
Figure 2 – Type-T equivalent circuit diagram (iron losses disregarded)
Resistances are corrected to an ambient temperature of 25 °C. They shall be converted to the
actual motor temperature by the user before application of the values (for example by the
frequency inverter depending on readings of a temperature sensing device).
The equivalent resistance of iron losses R however shall not be temperature but frequency
fe
corrected when applying a frequency other than rated frequency.
The type-L (Figure 3) diagram is provided for illustrative purposes. Both type-L and type-Γ
(Figure 4) diagrams are mathematically identical to the type-T diagram.

X
m
X –
jX = j
ts
tσ
R
X′
s
tr
I
s
2 2
X X R′
m m r
U j ×
s
X′ S
tr X′
tr
IEC  2351/12
Figure 3 – Type-L equivalent circuit diagram (iron losses disregarded)

60034-28 © IEC:2012 – 15 –
R jX′
s tσ
I
s
R′ /S
rΓ
jX
U U R
s i ts feΓ
IEC  2352/12
Figure 4 – Type-Γ equivalent circuit diagram
7.2 Resistance of stator winding R
s
The stator winding resistance R is determined from the measured line-to-line resistance R ,
s ll m
(see 6.2) corrected to a reference winding temperature of 25 °C
1 k + 25
s
R = ⋅ R ⋅
s,25 ll,m
2 k +θ
s 0
3 k + 25
s
NOTE For the calculation of an equivalent circuit diagram for delta-connection:
R = ⋅ R ⋅
s,25 ll,m
2 k +θ
s 0
7.3 Total stator inductance L = L + L
ts m σs
7.3.1 General
At s = 0, the equivalent rotor resistance R ’ / s becomes infinite and therefore the reactive part
r
of the measured impedance results only from the serial connection of the two inductances.
2 22
L LL
m mm
LL+= − +=L
NOTE See Figure 3:
tσ ts ts
L LL
tr tr tr
In this case, the line-current I is equal to the magnetizing current I .
m
7.3.2 Determination procedure
For each of the measured no-load points (6.5):
U
Determine the line impedance Z =
s=0
I ⋅ 3
U ⋅ 3
NOTE 1 For the calculation of an equivalent circuit diagram for delta-connection: Z =
s=0
I
P
Determine the power factor: cosϕ =
U ⋅ I ⋅ 3
Determine the resistance:
RZ ⋅ cosϕ
s 0 s 0
Determine the magnetizing-current: I = I
m
==
=
– 16 – 60034-28 © IEC:2012
I
NOTE 2 For the calculation of an equivalent circuit diagram for delta-connection: I =
m
Determine the total stator reactance: XZ − R
ts s 0 s 0
X
ts
Determine the total stator inductance:  L =
ts
2π ⋅ f
N
Plot the values of L against the values of I (see Figure 5 for a typical characteristic of
ts m
inductance L against current I).

L
ts
L
L
m
For s = 0
0 A
5,00 A/Div. 50,0 A
I
IEC  2353/12
Figure 5 – Typical characteristics of inductance L over current I
Determine the inner machine voltage:
 
U
 2 
 
U = − R ⋅ I ⋅cosϕ + 1− (cosϕ) ⋅ R ⋅ I
 
i,s =0 s =0 m s =0 m
 
3  
 
NOTE 3 For the calculation of an equivalent circuit diagram for delta-connection:
2  2 
U = (U − R ⋅ I ⋅cosϕ) + 1− (cosϕ) ⋅ R ⋅ I
 
i,s =0 s =0 m s =0 m
 
Plot the values of L against the values of U .
ts i,s=0
7.4 Equivalent resistance of iron losses R
feΓ
7.4.1 Constant losses
Subtracting the no-load stator winding losses from the no-load power input gives the constant
losses P which are the sum of the friction, windage and core losses.
k
==
=
60034-28 © IEC:2012 – 17 –
For each value of voltage recorded in 6.5, subtract the no-load stator winding losses from the
input power to obtain the constant losses:
k + θ
s NL
PP−⋅3 I ⋅ R ⋅
k s s s,25°
k + 25
s
where I = I .
s
NOTE For the calculation of an equivalent circuit diagram for delta-connection: I = I / 3 .
s
7.4.2 Friction and windage losses
From the no-load loss values (6.5) use all those that show no significant saturation effect and
develop a curve of constant losses (P ), as determined in 7.4.1, against the voltage squared
k
(U ). Extrapolate a straight line to zero voltage. The intercept with the zero voltage axis is the
friction and windage losses P .
fw
Friction and windage losses are considered to be independent of load. They are not included
in the equivalent circuit diagram but can be taken into account by reduction of the calculated
mechanical output power.
Friction losses are linearly dependent on motor speed n. Windage losses depend on the third
power of the speed n .
7.4.3 Iron losses
Determine the iron losses from P = P – P .
fe k fw
Determine the equivalent resistance of iron losses for the type-Γ equivalent circuit diagram
(Figure 4) for rated voltage U and frequency f :
N N
3⋅U
i,s=0
R =
feΓ
P
fe
with U being the inner voltage as determined in 7.3 at the test-point at rated voltage.
i,s=0
The resistance R must not be temperature corrected when applying the equivalent circuit
feΓ
diagram.
However, the resistance R shall be corrected to R ’ when calculating the equivalent circuit
feΓ feΓ
for a frequency f other than rated frequency f by the following formula:
N
 
U
15,
f ⋅
05,
 
 f
f P ' U ² R
 
fe feΓ
R ' R ⋅ since  ⋅ ~

feΓΓfe
f PR '
U
N fe feΓ
 U 
N
15,
N
f ⋅
 
N
f
N
 
The power value of 1,5 related to frequency variations is a compromise between the two parts
that make up the iron losses (hysteresis losses ~ f and eddy current losses ~ f ) and well-
suited for electro sheet with losses of about 6,5 to 8,0 W/kg at 50 Hz, 1,5 T. For motors with
electro sheet with losses of 4,0 W/kg or better, lower values may be more appropriate due to
reduced impact of eddy current losses.
= =
=
– 18 – 60034-28 © IEC:2012
NOTE The formula for R ’ applies to standard saturation of motors; it does not apply to oversaturated motors in
feΓ
which the R value decreases.
feΓ
7.5 Total leakage inductance L
tσ
7.5.1 General
The total leakage inductance can either be determined from a reverse rotation or locked rotor
tests (6.6) or alternatively from a load curve test (6.4). The latter procedure is more accurate
especially for motors with deep rotor bars since the rotor frequencies during the test are
closer to the frequency at rated speed. A current displacement correction is not required for
this procedure.
7.5.2 Distribution of leakage inductances between stator and rotor
The methods described in this standard permit only to determine the sum of the stator and
rotor leakage inductances.
If design details are available, use the calculated ratio k = L / L ’. Otherwise, for special
σ s r
design motors (such as double-cage or deep bar rotors) the ratio k = L / L ’ = 0,67 and for
σ σs σr
single cage motors the ratio k = L / L ’ = 1 shall be used by definition.
σ σs σr
7.5.3 Determination of total leakage inductance from a reverse rotation or locked
rotor test (6.6)
7.5.3.1 General
At large slip values
...