A Parametrization Scheme for High
Performance Thermal Models of Electric
Machines using Modelica
Anton Haumer ∗ Christian Kral ∗∗ Vladimir Vukovic ∗∗
Alexander David ∗∗∗ Christian Hetteisch ∗∗∗
Attila Huzsvar ∗∗∗
Austrian Institute of Technology, Gienggasse 2, A-1210 Vienna,
Austria (e-mail: Anton.Haumer@ait.ac.at).
∗∗
Austrian Institute of Technology, Gienggasse 2, A-1210 Vienna,
Austria
∗∗∗
University of Applied Sciences Technikum Vienna, Höchstädtplatz
5, A-1200 Vienna, Austria
∗
Abstract:
Thermal models oer great advantages for enhancement of design, protection and control of
electric machines. Detailed thermal models take a great number of time constants into account
and provide accurate prediction of the temperatures. However, to parameterize such models
detailed geometric data are needed. Whenever such detailed information is not available, or the
performance of the detailed models is not satisfying, simplied thermal models as described in
this paper are advantageous.
The calculation of parameters is described in detail, in order to achieve best accordance with
temperatures obtained from measurements or from simulations with detailed thermal models.
Thermal resistances are calculated from end temperatures of a test run with constant load (and
known losses). Thermal capacitances are obtained using optimization to minimize deviation
of simulated and measured temperatures during the whole test run. The thermal model of an
asynchronous induction machine with squirrel cage is coupled with an electrical model of the
drive.
For validation, simulation results of an optimally parameterized simplied model are compared
with temperatures obtained by simulation of a detailed thermal model, which in turn has been
validated against measurement results, both for continuous duty S1 and intermittent duty S6
(6 minutes no-load followed by 4 minutes of 140% nominal load). The deviations are not more
than 4 K which is quite satisfying.
Keywords: Electric machines, Induction machines, Thermal models, Model reduction,
Parameter identication, Parameter optimization.
1. INTRODUCTION
For many applications of electric drives it is desired to
have a thermal model of the electric machine. Being
able to simulate the relevant temperatures allows to take
advantage of the thermal inertia during non-steady duty
cycles, cooling down the machine during a period of low
load condition after overload operation. The possibility
to enhance the machine's design in an early stage of the
engineering process has been shown in Haumer et al.
(2010). However, such detailed thermal models also
described in Kral et al. (2005) require detailed geometric
data of the machine to calculate the parameters of the
thermal model. In many cases, such a detailed thermal
machine model is not performant enough, or detailed
geometric data is not available from the manufacturer. In
both cases a simplied thermal model is desired.
An application of a simplied thermal model is checking
whether a chosen machine is sucient for a given duty
cycle with varying speed and load during an early design
stage of the drive. Another application is the thermal protection of the machine during such load cycles, without using too many thermal sensors. A third case is represented
by high precision inverter control of an asynchronous induction machine with squirrel cage rotor: Measurement of
the rotor temperature is nearly impossible for practical
applications, but knowing the rotor temperature allows to
adjust the controller parameters.
The thermal model suggested in Section 2 covers three
relevant temperatures of an asynchronous induction machine with squirrel cage rotor even during non-steady
operation: temperatures of the stator winding, the rotor
cage and the stator core. Parametrization can be done from
measurement results, as described in Section 3. For this
work, simulation results obtained with a detailed thermal
model which has been validated in Haumer et al. (2010)
instead of measurement results have been used.
• friction losses
• stray load losses
However, rotor core losses are nearly zero during normal
operation with small slip of an asynchronous induction
machine. A big part of the friction losses are used to
transport the medium. For simplicity reasons, these two
losses as well as the stray load losses are dissipated
to thermal sinks with constant temperatures, whereas
the other three losses are fed to the simplied thermal
equivalence circuit.
The DAE system can be obtained from gure 1 as equations:
dTsw
= Psw − Rsw sc (Tsw − Tsc )
dt
dTrc
Crc
= Prc − Rrc sc (Trc − Tsc )
dt
dTsc
Csc
= Psc + Rsw sc (Tsw − Tsc )
dt
+Rrc sc (Trc − Tsc )
Csw
Figure 1. Simplied thermal model
For both the thermal model and the drive model as
described in Section 4, the modeling language Modelica
is used. Modelica is a non-proprietary, object-oriented,
equation based language to conveniently model complex
physical systems containing, e.g., mechanical, electrical,
electronic, hydraulic, thermal, control, electric power or
process-oriented subcomponents.
®
®
Section 5 compares simulation results achieved with the
suggested simplied thermal model with the results obtained with a detailed thermal model.
2. THERMAL MODEL
A simplied thermal model is only capable of describing a
limited number of relevant temperatures. In this case, it is
suggested to model the following ones as shown in gure
1:
• sw: temperature of the stator winding, averaged over
slot and end winding region
• sc : temperature of the stator core, averaged over the
whole cross-section of the stator core
• rc : temperature of the rotor cage, averaged over slot
and end ring region
The three regions are represented by thermal capacitors,
they are connected with thermal resistors respectively
conductors. Additionally, the coolant ow is modeled by
means of a sub-library of the Modelica Standard Library
the FluidHeatFlow library as described in Kral et al.
(2005). A varying coolant inlet temperature is enabled by
the signal input inletTemperature. The parameter record
in the upper left summarizes the losses and the end
temperatures of the machine, as used in Section 3 for
calculation of the thermal resistances. The thermal port
as described in Haumer et al. (2009); Kral and Haumer
(2011) contains a thermal connector for each loss source:
•
•
•
•
ohmic losses of the three stator phases
stator core losses
ohmic losses of the rotor cage
rotor core losses
−Rsc c (Tsc − Tc )
cp ṁ (TcOut − TcIn ) = Rsc c (Tsc − Tc )
(1)
(2)
(3)
(4)
Tc = TcIn + tapT (TcOut − TcIn ) (5)
The coolant temperature (index c) that is relevant for the
heatow from the stator core to the coolant is interpolated
by parameter tapT between inlet and outlet temperature
of the coolant.
3. PARAMETRIZATION
Knowing the losses and the temperatures at the end of a
test run (or a simulation with a detailed thermal model),
from equations 1 - 5 the thermal resistances as well as the
coolant's mass ow rate can be obtained since in steady
state the derivatives of temperatures with respect to time
are zero, i.e. all losses have to be dissipated to the coolant.
Psw = Rsw sc (Tsw − Tsc )
(6)
Prc = Rrc sc (Trc − Tsc )
(7)
Psc + Prc + Psw = Rsc c (Tsc − Tc )
(8)
cp ṁ (TcOut − TcIn ) = Psc + Prc + Psw
(9)
After determination of the thermal resistances which are
summarized in table 1, the thermal capacitances have to
be calculated. Having temperature characteristics versus
time during the above mentioned test run, it is possible
to vary the thermal capacitances and compare simulated
with measured temperatures (or results obtained with
a detailed thermal model). During motor type test for
obtaining rotor temperature measurements, either a device
as described in Ganchev et al. (2010) or an infrared optical
sensor has to be used.
Using an aggregating criterion, e.g. integrating the absolutes of the deviations with respect to time and summing up the integrals, it is possible to utilize optimization
methods to determine best-t thermal capacitances. For
optimization, the freely available Java-based application
GenOpt http://gundog.lbl.gov/GO/ has been used.
Psw [W ]
Prc [W ]
Psc [W ]
779.2
483.4
409.7
Tsw [°C]
Trc [°C]
Tsc [°C]
TcIn [°C]
TcOut [°C]
96.0
132.9
78.1
20.0
29.6
Table 1. Losses and temperatures
Csw [J/K]
Crc [J/K]
Csc [J/K]
5150
13672
40469
Table 2. Thermal capacitances
GenOpt writes the tuning parameters in this case the
three thermal capacitances to an input text le, starts
the simulation model which reads the parameter le and
writes the criterion to a result le. GenOpt reads the result
and varies the tuning parameters to minimize the criterion
which is dened as the integral of the absolutes of the
deviations between reference and simulated temperatures
with respect to time.
Estimating start values for the thermal capacitances from
masses, the optimization with algorithm GPSCoordinateSearch unveils the optimal thermal capacitances summarized in table 2.
4. DRIVE MODEL
The model of the asynchronous induction machine with
squirrel cage see gure 2 is explained in detail in
Kral and Haumer (2005); Haumer et al. (2009); Kral
and Haumer (2011) and models the transient electromagnetic behavior as well as the generation of losses. The
ohmic resistances depend on the simulated temperatures
as shown in the thermal port.
Figure 2. Model of the asynchronous induction machine
with squirrel cage
The complete model coupling the electro-mechanical
model with the simplied thermal model is shown in
gure 3. The characteristic of the load torque can easily be
changed from a continuous load S1 to an intermittent load
S6: 6 minutes no-load followed by 4 minutes 140% nominal
load. The block combiTimeTable reads the temperatures
obtained by measurement or simulation of a detailed model
from a text le; the coolant inlet temperature is fed to the
thermal model.
5. VALIDATION
To ease the handling of reference results, instead of measurements a detailed thermal model as shown in gure
4 has been used. This model has been validated using
measurements in Haumer et al. (2010).
The temperatures for comparison are dened as:
• stator winding: averaged over slot and end windings
• stator core: averaged over the whole cross-section
• rotor cage: averaged over slots and end rings
Temperature sensors require very careful mounting to ensure optimal contact for measurements. Additonally, a sufcient number of temperature sensors has to be distributed
over the cross section of interest to enable averaging which is quite challenging without destroying the iron core.
For obtaining rotor temperature measurements, a device
as described in Ganchev et al. (2010) or special brushes
Figure 3. Model of the complete drive
and sliprings have to be used to transfer measurements
from the rotating part. A feasible solution was to validate
local temperatures of the detailed model compared with
measuements, and using these simualtion results for averaging reference temperatures.
Figures 5, 6 and 7 compare reference temperatures with
simulation results of stator core, stator winding and rotor
cage for continuous duty S1. The maximum deviations are
for stator core 3.4 K, for stator winding 0.6 K and for rotor
cage 1.8 K. These deviations are satisfactory low and can
be explained by the fact that compared with a detailed
temperature [degC]
140
Figure 4. Detailed thermal model
120
100
80
60
rotorCage reference
rotorCage simulated
40
20
0
0
0.5
1
1.5
time [s]
Figure 7. Comparison of reference and simulated rotor cage
temperatures for continuous duty S1
120
100
140
80
60
statorCore reference
statorCore simulated
40
20
0
0
0.5
1
1.5
time [s]
2
4
x 10
Figure 5. Comparison of reference and simulated stator
core temperatures for continuous duty S1
temperature [degC]
temperature [degC]
140
120
100
80
60
120
statorCore reference
statorCore simulated
40
20
0
0
140
5000
10000
time [s]
15000
Figure 8. Comparison of reference and simulated stator
core temperatures for intermittent duty S6
100
80
140
60
statorWinding reference
statorWinding simulated
40
20
0
0
0.5
1
1.5
time [s]
2
4
x 10
Figure 6. Comparison of reference and simulated stator
winding temperatures for continuous duty S1
thermal model time constants are omitted that inuence
the temperature versus time characteristic.
Figures 8, 9 and 10 compare reference temperatures with
simulation results of stator core, stator winding and rotor
cage for intermittent duty S6 (6 minutes no-load followed
by 4 minutes 140% nominal load). The maximum devia-
temperature [degC]
temperature [degC]
2
4
x 10
120
100
80
60
40
20
0
0
statorWinding reference
statorWinding simulated
5000
10000
time [s]
15000
Figure 9. Comparison of reference and simulated stator
winding temperatures for intermittent duty S6
models for electric machines. Proceedings of the 7th
Modelica Conference, 847854.
Kral, C. and Haumer, A. (2005). Modelica libraries for DC
machines, three phase and polyphase machines. International Modelica Conference, 4th, Hamburg, Germany,
549558.
Kral, C., Haumer, A., and Plainer, M. (2005). Simulation
of a thermal model of a surface cooled squirrel cage
induction machine by means of the SimpleFlow-library.
temperature [degC]
140
120
100
80
60
rotorCage reference
rotorCage simulated
40
20
0
0
5000
10000
time [s]
15000
Figure 10. Comparison of reference and simulated rotor
cage temperatures for intermittent duty S6
tions are for stator core 3.8 K, for stator winding 2.1 K and
for rotor cage 2.8 K. Although these deviations are a little
bit higher than those for continuous duty S1, the results
are suitable for the applications mentioned in Section 1.
6. CONCLUSION
A simplied thermal model comprising three relevant
temperatures has been suggested. The parameters of this
model have been determined using reference data either
from measurements or simulations with a detailed thermal
model:
• Thermal conductances have been calculated from
losses and temperatures in a thermal equilibrium.
• Thermal capacitances have been derived from minimizing deviations of simulated and reference temperatures versus time.
The detailed thermal model used to obtain reference temperatures for validation takes into account approximately
50 time constants (with an axial discretization of 5 regions). Reducing the order of the model to 3 time constants
increases performace substantially, although the loss in
precision a deviation of not more than 4 K is satisfactorily low.
It is planned to adapt and validate the model as well
as the parameterization algorithm for permanent magnet
synchronous machines, which are of interest for applications in electric vehicles.
Furthermore, investigations shall me made to nd a mathematical method for model reduction.
REFERENCES
Ganchev, M., Kubicek, B., and Kapeller, H. (2010). Rotor
temperature monitoring system. Proceeding of the XIX
International Conference on Electrical Machines.
Haumer, A., Bäuml, T., and Kral, C. (2010). Multiphysical
simulation improves engineering of electric drives. 7th
EUROSIM Congress on Modelling and Simulation.
Haumer, A., Kral, C., Kapeller, H., Bäuml, T., and Gragger, J.V. (2009). The AdvancedMachines library: Loss
International Modelica Conference, 4th, Hamburg, Germany, 213218.
Kral, C. and Haumer, A. (2011). Object Oriented Modeling
of Rotating Electrical Machines. INTECH.