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Evolution and Modern Approaches for Thermal Analysis of Electrical Machines / Boglietti, Aldo; Cavagnino, Andrea; D.,
Staton; M., Shanel; M., Mueller; C., Mejuto. - In: IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS. - ISSN
0278-0046. - STAMPA. - 56:3(2009), pp. 871-882. [10.1109/TIE.2008.2011622]
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Evolution and Modern Approaches for Thermal Analysis of Electrical Machines
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 3, MARCH 2009 871
Evolution and Modern Approaches for Thermal
Analysis of Electrical Machines
Aldo Boglietti, Senior Member, IEEE, Andrea Cavagnino, Member, IEEE, David Staton,
Martin Shanel, Markus Mueller, and Carlos Mejuto
Abstract—In this paper, the authors present an extended sur-
vey on the evolution and the modern approaches in the thermal
analysis of electrical machines. The improvements and the new
techniques proposed in the last decade are analyzed in depth
and compared in order to highlight the qualities and defects of
each. In particular, thermal analysis based on lumped-parameter
thermal network, finite-element analysis, and computational fluid
dynamics are considered in this paper. In addition, an overview of
the problems linked to the thermal parameter determination and
computation is proposed and discussed. Taking into account the
aims of this paper, a detailed list of books and papers is reported
in the references to help researchers interested in these topics.
Index Terms—Computed fluid dynamic, electrical machines,
finite-element analysis (FEA), lumped-parameter thermal net-
work (LPTN), thermal model, thermal parameter identification.
I. INTRODUCTION
I
N THE PAST, the thermal analysis of electric machines has
received less attention than electromagnetic analysis. This is
clear from the number of technical papers published relating to
each of these particular subjects. This inequality is particularly
true for small- and medium-sized motors. Traditionally, for
such machines, motor designers have only superficially dealt
with the thermal design aspects, maybe by specifying a limiting
value of current density or some other rudimentary sizing
variable. The problem with such sizing methods is that they do
not give an indication of how the design may be improved to
reduce temperatures.
With the increasing requirements for miniaturization, energy
efficiency, and cost reduction, as well as the imperative to fully
exploit new topologies and materials, it is now necessary to
analyze the thermal circuit to the same extent as the electro-
magnetic design.
Manuscript received January 28, 2008; revised December 1, 2008. Current
version published February 27, 2009.
A. Boglietti and A. Cavagnino are with the Department of Electrical En-
gineering, Politecnico di Torino, 10129 Turin, Italy (e-mail: aldo.boglietti@
polito.it; andrea.cavagnino@polito.it).
D. Staton is with Motor Design Ltd., Ellesmere, SY12 OEG, U.K. (e-mail:
dave.staton@motor-design.com).
M. Shanel is with Cummins Generator Technologies, Stamford, PE9 2NB,
U.K. (e-mail: martin.shanel@cummins.com).
M. Mueller and C. Mejuto are with the Institute for Energy Systems,
University of Edinburgh, Edinburgh, EH9 3JL, U.K. (e-mail: markus.mueller@
ed.ac.uk; carlosmejuto@hotmail.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2008.2011622
In fact, there should be a strong interaction between the
electromagnetic and thermal designs as it is impossible to
accurately analyze one without the other, i.e., the losses are
critically dependent upon the temperature and vice versa.
Currently, the interest in thermal analysis involves not only
the electrical machine but also the drive and power converter
design [1], [2]. A possible reason why thermal analysis has
received less attention than electromagnetic analysis is that
electric-motor designers usually have an electrical engineering
background, while thermal analysis is a mechanical engineering
discipline.
Electric-motor thermal analysis can be divided into two basic
types: analytical lumped-circuit and numerical methods. The
analytical approach has the advantage of being very fast to
calculate; however, the developer of the network model must
invest effort in defining a circuit that accurately models the
main heat-transfer paths [3]–[6].
In its most basic form, the heat-transfer network is analo-
gous to an electrical network, and the analysis consists of the
calculation of conduction, convection, and radiation resistances
for different parts of the motor construction. The formulations
for such resistances are really quite simple. The conduction
resistance is equal to the path length divided by the product
of the path area and the materials’ thermal conductivity. The
convection and radiation resistances are equal to one divided by
the product of the surface area and the heat-transfer coefficient.
The radiation-heat-transfer coefficient is simply a function
of the surface properties, i.e., the emissivity and the view
factor. The emissivity is known for different types of surface,
and the view factor can be calculated based on the geometry.
The convection-heat-transfer coefficient is most often based on
empirical formulations based on convection correlations which
are readily available in the heat-transfer literature. Fortunately,
there is a wealth of convection correlations for most of the basic
geometric shapes used in electrical machines, both for natural
and forced convection cooling (i.e., cylindrical surfaces, flat
plates, open- and closed-fin channels, etc.). The most common
and useful convection correlations are even available in under-
graduate textbooks on heat transfer [7]–[12].
The main strength of numerical analysis is that any device
geometry can be modeled. However, it is very demanding in
terms of model setup and computational time. There are two
types of numerical analysis: finite-element analysis (FEA) and
computational fluid dynamics (CFD). CFD has the advantage
that it can be used to predict flow in complex regions, such as
around the motor end windings [13], [14]. FEA can only be
used to model conduction heat transfer in solid components.
0278-0046/$25.00 © 2009 IEEE
872 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 3, MARCH 2009
For convection boundaries, the same analytical/empirical algo-
rithms used in the lumped-circuit analysis must be adopted (i.e.,
convection correlations).
Taking into account the survey approach of this paper, a short
historical evolution on electrical-machine thermal analysis is
hereafter included.
Before the advent of computers, motor sizing was tradition-
ally made using the so-called D
2
L, D
3
L, and D
x
L sizing equa-
tions, where the designer provided limiting values of specific
magnetic and electric loadings and/or current density from past
experience [15]. This method of sizing does not involve thermal
analysis directly, the specific magnetic loading and current
density being limited to prevent overheating. At this time,
simple thermal-network analysis based on lumped parameters
were also used by some designers to perform rudimentary
thermal analysis; however, the thermal networks were kept as
simple as possible so they could be calculated by hand, e.g.,
maybe just one thermal resistances to calculate the steady-state
temperature rise of the winding. With the introduction of com-
puters to motor design, the complexity of the thermal networks
increased. A reference paper highlighting the introduction of
more complex thermal networks calculated using computers
was published in 1991 by Mellor et al. [3]. Thermal-network
analysis has become the main tool used by many researchers
involved in thermal analysis of electrical machines, both for
steady-state and transient analyses [16]. A further factor that
has led to increased interest in thermal-network analysis was
the introduction of induction motor inverter supplies. Several
authors have studied the effect of increased losses, resulting
from six-step and pulsewidth-modulation voltages, on motor
temperatures [17], [18].
Thermal analysis has always received less attention than
electromagnetic design. However, in the new century, the topic
had started to receive more importance due to market globaliza-
tion and the requirement for smaller, cheaper, and more efficient
electric motors. In many cases, the software used for the design
of electric machines has now adopted improved thermal model-
ing capabilities and features enabling better integration between
the electromagnetic and the t hermal designs [19], [20].
Several interesting papers have been published in recent
years on thermal analysis of electric machines. References [19]
and [20] deal with coupled electromagnetic and thermal analy-
sis with the thermal network solved using network analysis. In
[20], the losses are calculated using analytical methods [21],
while in [19], electromagnetic FEA is used. In [22], a thermal-
network method is proposed to account for combined air flow
and heat transfer, i.e., for forced air cooling in stator and rotor
core ducts in this case. In [23], a combined network and CFD
method is used to model the machine. Network analysis is used
to calculate conduction through the electromagnetic structure
while CFD is used for convection at the surface. The use of
CFD for prediction of convective heat transfer is expanded in
Section VI. Calibration with measured data is typically used to
calibrate thermal resistances that are influenced by the motor
manufacturing process [4], [6], [24]. An example is the thermal
interface resistance between stator lamination and housing,
which is influenced by the method used to insert the stator in
the frame.
II. T
HERMAL NETWORK BASED ON
LUMPED PARAMETERS
This section details the main concerns relating to lumped-
parameter thermal-network (LPTN) analysis. Analytical
thermal-network analysis can be subdivided into two main
calculation types: heat-transfer and flow-network analyses.
Heat-transfer analysis is the thermal counterpart to electrical-
network analysis with the following equivalences: temperature
to voltage, power to current, and thermal resistance to electrical
resistance. Flow-network analysis is the fluid mechanics
counterpart t o electrical-network analysis with the following
equivalences: pressure to voltage, volume flow rate to current,
and flow resistance to electrical resistance. In the heat-transfer
network, a thermal resistance circuit describes the main
paths for power flow, enabling the temperatures of the main
components within the machine to be predicted for a given loss
distribution.
As is well known, in a thermal network, it is possible to lump
together components that have similar temperatures and to rep-
resent each as a single node in the network. Nodes are separated
by thermal resistances that represent the heat transfer between
components. Inside the machine, a set of conduction thermal
resistances represents the main heat-transfer paths, such as
from the winding copper to the stator tooth and back iron (in
this case, the heat transfer is through the winding insulation
consisting of a combination of enamel, impregnation, and slot-
liner materials), from the tooth and stator back iron nodes to
the stator bore and housing interface, etc. In addition, internal
convection and radiation resistances are used for heat transfer
across the air gap and from the end windings to the endcaps and
housing. External convection and radiation resistances are used
for heat transfer from the outside of the machine to ambient.
In the past, due to limited computational capabilities, simple
thermal networks with few thermal resistances, capacitances,
and sources were adopted. Nowadays, much more detailed
thermal and flow networks can be quickly solved, including
a high number of thermal and flow elements. An example of
a detailed heat-transfer network is shown in Fig. 1. Detailed
information on this thermal network can be found in [35].
Lumped-circuit thermal models have been extensively uti-
lized and validated on numerous machine types and operating
points. Such a wide range of studies has increased confidence
in such thermal models.
As an example of this approach, the thermal model shown
in Fig. 1 has been used to analyze a 22.5-kVA synchronous
machine, shown in Fig. 2.
The model calculates both the air flow and heat transfer in the
machine. Air flow and temperature rise for all stator and rotor
nodes were within 10% of the measured values [25].
Analytical lumped-circuit techniques are also very useful in
determining the thermal model’s required discretization level.
This refers to the number of sections used to model the
electrical machine as a whole, or some of the more critical
components, both in the axial and radial directions. In [25],
studies have been performed to determine the required dis-
cretization level for a synchronous generator, with particular
attention being given to the winding area. Due to its low thermal
BOGLIETTI et al.: EVOLUTION AND MODERN APPROACHES FOR THERMAL ANALYSIS OF ELECTRICAL MACHINES 873
Fig. 1. Example of heat-transfer network for an electric motor.
Fig. 2. Radial and axial cross sections of the modeled alternator.
conductivity [2–3 W/(m ·
◦
C)], this area is of great thermal
significance and has to be analyzed with care.
In the real winding, the heat generation is distributed over the
section, and this paper highlights the impact upon accuracy of
specifying such a loss in the discrete nodes. A number of rotor
winding models were used, ranging from a “single-block” (1 ×
1) representation to a rotor winding represented by 100 smaller
sections (10 × 10). These two models are shown in Fig. 3.
In Fig. 4, the trend of the predicted averaged node tem-
peratures as a function of the number of network nodes per
section is shown. Concentrating all loss in one node in the
1 × 1 network results in an unrealistic gradient between the
wall and the winding center. Thus, a suitable formula must be
used to derive the average section temperature (20.2
◦
C) from
a single-node temperature and wall temperatures; otherwise,
it could be wrongly interpreted as the whole winding section
being at 60.5
◦
C. The winding discretization level of 10 ×
10 yields more accurate predictions (average 17.7
◦
C, peak
35.8
◦
C) without the need for the formula when compared
Fig. 3. Rotor winding models of (top) 1 × 1 and (bottom) 10 × 10.
with FEA results (average 17.0
◦
C, peak 37.2
◦
C). To sum
up, using lower levels of discretization reduces the accuracy of
the results, while increasing the node numbers unnecessarily
complicates the thermal model.
As previously reported, lumped thermal parameters analysis
involves the determination of thermal resistances. The main
methods used for the calculation of conduction, radiation, and
convection thermal resistances are hereafter summarized.
It is important to remark that these methods for the thermal
resistance determination have general validity and they are not
linked to the thermal-network complexity.
874 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 3, MARCH 2009
Fig. 4. Rotor winding discretization results up to 11 × 11.
A. Conduction Heat Transfer
Conduction thermal r esistances can be simply calculated
using the following:
R =
L
kA
(1)
where L (in meters) is the path length, A (in square meters) is
the path area, and k (in watt per meter degree Celsius) is the
thermal conductivity of the material. In most cases, L and A
can simply be gained from the components’ geometry. The only
complication is in assigning a correct value to L for thermal
resistances due to the interface gap between components. As
discussed in [24] and [26], experience factors are very impor-
tant for a correct prediction of this thermal resistance. Com-
mercial software packages typically provide details on various
types of material with different roughness and manufacturing
techniques to aid the user to set such interface gaps. Sensitivity
analysis with values between the minimum and maximum ex-
pected values is always useful to gain a thorough understanding
of the problem.
B. Radiation Heat Transfer
Radiation thermal resistances for a given surface can be
simply calculated using
R =
1
h
R
A
(2)
where A (in square meters) is the surface area and h
R
(in watt
per square meter degree Celsius) is the heat-transfer coefficient.
The surface area is easily calculated from the surface geom-
etry. The radiation-heat-transfer coefficient can be calculated
using the following:
h
R
= σεF
1−2
T
4
1
− T
4
2
(T
1
− T
2
)
(3)
where σ =5.669 × 10
−8
W/(m
2
· K
4
), ε is the emissivity of
the surface, F
1−2
is the view factor for dissipating surface 1 to
the absorbing surface 2 (the ambient temperature for external
radiation), and T
1
and T
2
are, respectively, the temperatures of
surfaces 1 and 2, in units of kelvin. The emissivity is a function
of the surface material and finish, for which data are given in
most engineering textbooks [7]–[12]. The view factor can easily
be calculated for simple geometric surfaces, such as cylinders
and flat plates; however, it is a little more difficult for complex
geometries, such as open-fin channels. In these cases, books
are available to help with the calculation of the view factor
[27], [28].
C. Convection Heat Transfer
Convection is the transfer process due to fluid motion. In
natural convection, the fluid motion is due entirely to buoyancy
forces arising from density variations in the fluid. In a forced
convection system, movement of fluid is by an external force,
e.g., fan, blower, or pump. If the fluid velocity is high, then
turbulence is induced. In such cases, the mixing of hot and cold
air is more efficient, and there is an increase in heat transfer. The
turbulent flow will, however, result in a larger pressure drop; as
a consequence, with a given fan/pump, the fluid volume flow
rate will be reduced. Convection thermal resistances for a given
surface can be simply calculated using
R =
1
h
C
A
. (4)
The previous equation is basically the same equation as
for radiation but with the radiation-heat-transfer coefficient
replaced by the convection-heat-transfer coefficient h
C
(in
watt per square meter degree Celsius). Proven empirical heat-
transfer correlations based on dimensionless analysis are used
to predict h
C
for all convection surfaces in the machine [3]–
[12], [24], [29].
D. Flow-Network Analysis
Forced convection heat transfer from a given surface is a
function of the local flow velocity. In order to predict the local
velocity, a flow-network analysis is performed to calculate the
fluid flow (air or liquid) through the machine. Empirical dimen-
sionless analysis formulations are used to predict pressure drops
for flow restrictions, such as vents, bends, contractions, and
expansions [24], [29]–[34]. The governing equation that relates
the pressure drop (P, in pascal, equivalent to an electrical
voltage) to the volume flow rate (Q, in cubic meters per second,
equivalent to electrical current) and fluid-dynamic resistance
(R, in kg/m
7
)is
P = RQ
2
. (5)
In (5), the formulation is in terms of Q
2
rather than Q due to the
turbulent nature of the flow. Two types of flow resistance exist.
The first exists where there is a change in the flow condition,
such as expansions, contractions and bends. The second is due
to fluid friction at the duct wall surface; in electrical machines,
this is usually negligible compared with the first resistance type
due to the comparatively short flow paths. The flow resistance
is calculated for all changes in the flow path using
R =
kρ
2A
2
(6)
