IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 10, OCTOBER 2013
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The Effect of the Electrical Steel Properties on the Temperature Distribution
in Direct-Drive PM Synchronous Generators for 5 MW Wind Turbines
Damian Kowal , Peter Sergeant
, Luc Dupré , and Lode Vandenbossche
Department of Electrical Energy, Systems, and Automation, Ghent University, B-9000 Ghent, Belgium
Department of Electrotechnology, Faculty of Applied Engineering Sciences, University College Ghent, B-9000 Ghent, Belgium
ArcelorMittal Global R&D Gent, B-9060 Zelzate, Belgium
The effect of the magnetic and thermal properties of four electrical steel grades were compared for a permanent magnet synchronous
generator (PMSG). The low loss grades are expected to have less iron loss in the stator laminations, but their thermal conductivity may
be lower. Therefore, the evacuation of the heat may be less effective. This has an influence on the temperature distribution, which is
crucial in case of PMSG. The investigated generator is a 5 MW, radial flux machine designed for direct-drive wind turbines. A thermal
finite-element model was used to simulate the temperature distribution in the generator. The influence of the steel grade on the thermal
distribution was compared for four geometries of PMSG with varying air-gap diameter and pole-pair number. In conclusion, the number
of pole pairs has a major influence on the importance of electrical and thermal properties of the steel grades applied.
Index Terms—Permanent magnet machines, steel, temperature, wind energy.
I. INTRODUCTION
T
HE thermal modeling became an important part of the
electrical machine design process. This is due to the increasing importance of energy efficiency, high power density, as
well as cost reduction. Moreover, market situations impose the
maximal exploitation of new topologies and materials. Therefore, to meet the requirements of new designs, deep insight in
the thermal behavior is necessary. Thermal analysis of electrical
machines can be divided into two groups: analytical lumped-circuit based methods and numerical methods.
The analytical thermal models are known to be fast for calculations; however, building an accurate model of the machine
requires a lot of knowledge and experience [1]–[3]. The lumpedcircuit theory defining the heat transfer network is analogous to
the electrical network theory. The main challenge is to correctly
define the conduction, convection, and radiation resistances for
the different parts of the modeled machine.
Numerical methods can be divided in two groups: thermal finite-element method (FEM) [4], [5] with boundary conditions
that represent convection, and combined FEM and computational fluid dynamics (CFD) [6], [7], where CFD describes convection.
FE simulations of thermal behavior give very good results for
solid components. For the calculation of convection and radiation, the analytical algorithms are adopted. Despite the possibility of easy modeling of any geometry, which is advantageous
compared with analytical methods, the same input data for the
materials and surfaces (heat transfer coefficients) are necessary.
With the FEM, it is also possible to achieve strong coupling
Manuscript received January 11, 2013; revised March 29, 2013; accepted April 13, 2013. Date of publication April 29, 2013; date of current
version September 20, 2013. Corresponding author: D. Kowal (e-mail:
damian.a.kowal@gmail.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/TMAG.2013.2260553
of thermal aspects with the electromagnetic analysis using the
same method [8]. The computation time is the biggest issue for
FEM simulations; however, for very specific and complex geometries, it may be the only solution.
CFD is designed to determine the coolant flow rate, velocity
and pressure in the air gap, in the cooling ducts and around the
machine. Using this tool requires from the engineer a proper
understanding of fluid flow in and around the machine. A disadvantage of CFD apart from computer hardware requirements
is a much higher computational effort [6].
In this paper, an investigation of the temperature distribution
is presented for a 5 MW direct-drive, ring-type, radial flux,
inner rotor permanent magnet synchronous generator (PMSG)
for large-scale wind energy application. The direct-drive concept for offshore wind farms seems to attract attention of both
academic world (see [9] and [10]) and industry. Recently,
leading companies in wind energy have introduced direct-drive
generators in a power range between 2.3 and 6 MW.
Considering the advantages and disadvantages of the
methods available for thermal modeling the decision was made
to use the FEM. In the low-speed radial-flux machine, it is
expected that most of the heat will be evacuated by conduction
through the solid parts of the machine (stator and rotor yoke).
The FEM, in particular, is suitable for this type of simulation.
Moreover, there is a possibility to apply boundary conditions
that take into account convection and radiation on the outer
surface of the modeled geometry.
At first, the magnetic analytical model of the generator [11],
combined with an optimization algorithm, is used to determine
several generator geometries for the thermal behavior comparison. The geometries differ with respect to the size of the air gap
diameter as well as the pole pairs number.
Finally, a thermal FEM is obtained and used to simulate the
temperature distribution in the generator. Four geometries of the
5 MW PMSG generator are used for the temperature distribution comparison. The comparison is performed for the generators with 50 pole pairs and three air-gap diameters: 4, 6, and
8 m. Moreover, two generators with 50 and 150 pole pairs are
compared for the 6 m air-gap diameter.
0018-9464 © 2013 IEEE
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 10, OCTOBER 2013
TABLE I
BASIC VARIABLES OF THE GENERATOR
Fig. 1. Typical magnetization characteristics for the four steel grades with lamination thickness (0.5 mm) and different specific loss values.
Prior to FEM simulations, the heat sources and heat coefficients were identified for the applied geometry and cooling
strategy. Simulations of temperature distribution in each of the
generators were repeated for four steel grades, the BH-characteristics of which are presented in Fig. 1. Lamination thickness
of the steel grades is 0.5 mm. Thermal conductivity of the compared steel grades varies between 23 and 37 W/mK.
II. GEOMETRY AND ELECTROMAGNETIC
PROPERTIES OF THE GENERATOR
A parameter study of the generator is performed using the
electromagnetic model presented in [11]. The model is combined with the genetic algorithm to enable a geometrical optimization. The objective of the optimization is to maximize the
annual efficiency of the generator. The annual efficiency is defined as the ratio between the annual electrical energy
of the
generator and the annual mechanical energy input
from the
turbine rotor to the generator system ((1)). The mechanical energy input
is constant and based on the choice of the wind
turbine and wind speed distribution function [11]. The electrical
energy output
is calculated by the electromagnetic model
and therefore variable with the geometry of the generator, as
follows:
(1)
The procedure of optimization is as follows. First, the choice
of the steel grade applied in the stator lamination is made.
Second, the choice is made concerning the discretely changing
values: air-gap diameter, active mass limit, and number of pole
pairs of the generator. The active mass of the generator consists
of the mass of copper, permanent magnet material (NdFeB),
and electrical steel. Finally, the genetic algorithm runs for each
of the selected set of parameters. The variables of the algorithm
with the corresponding geometry parameters are presented in
Table I.
Two generator parameters are of the main importance in this
study. This is the air-gap diameter and the number of pole pairs.
The former is of a high priority to the application where size of
the generator is crucial for constructional and transportational
Fig. 2. Relation between number of pole pairs, air-gap diameter, and the annual
efficiency of the 5 MW generator, as a result of geometrical optimization. The
optimization is performed for the M250-50A electrical steel grade. The dots
represent the generators that were used for temperature distribution comparison.
purposes. Thus, the lower limit considered for the air-gap diameter is set to 4 m, which is just below the common limit for
the inland transportation, given by the heights of bridges and
tunnels.
The number of pole pairs of the generator varies between 20
and 150, and the range is chosen in such a way to show a significant change in the frequency of the generator, and therefore the
influence on the losses and annual efficiency of the generator.
In Fig. 2 one can observe that the highest annual efficiency is
reached for the high number of pole pairs of the generator and
large air-gap diameter. As can be seen in the right bottom corner
of the graph, the annual efficiency drops suddenly; this is due to
the limitation of the minimum pole pitch length in the analytical model [12]. According to this limitation, it is impossible to
fit 150 pole pairs in the generator with 4 m air-gap diameter. A
similar situation is causing a drop in annual efficiency in the region with low number of pole pairs and high air-gap diameter.
This situation is caused due to the fixed active mass of the generator (35 tons [13], [14]). The analytical model assumes one slot
per pole per phase and full pitch winding, which results in long
end windings. Therefore, for the generator with low pole pair
number and large air-gap diameters, the majority of the allowed
active mass of the generator is consumed by the end windings
of the generator.
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TABLE II
PARAMETERS OF CONSIDERED GENERATORS
As already mentioned, the air-gap diameter is an important
factor in the design process of the generator for the given application. Despite the fact that, from a strictly magnetic point of
view, it is beneficial to have a large air-gap diameter, a decision
was made to limit diameters for the thermal analysis to the range
based on the market review of existing generators for wind energy application. As a result, a thermal comparison is performed
on three generators with 50 pole pairs and air-gap diameters
equal to 4, 6, and 8 m. The choice of number of pole pairs was
made based on the highest annual efficiency for the considered
air-gap diameter range (see Fig. 2). Moreover, a comparison of
thermal behavior is provided for two generators with 6 m air-gap
diameter, but with different number of pole pairs, namely 50 and
150. All the considered geometries are a result of the geometrical optimization where allowed active mass is restricted to 35
tons, and the electrical steel properties used are corresponding
with measurements on the grade M250-50A.
Table II presents parameters for the four optimized generator
geometries, compared with blue dots in Fig. 2. Two observations
can be done based on Table II. First is that, for the same active
mass limit and number of pole pairs, with increasing air-gap diameter the axial length of the machine is decreasing and thickness of magnets, rotor, and stator yoke is increasing. Second, for
the generators with the same air-gap diameter but an increasing
number of pole pairs, the axial length is increasing while the
thickness of magnet, rotor, and stator yoke is decreasing (see
Table II).
III. COOLING STRATEGY
Having the generator geometries defined, we can proceed
to the thermal analysis. A large variety of cooling systems for
the large-scale wind turbines exist, starting from the natural air
cooling systems applied for the Vensys turbine where wind can
blow through the air gap and finishing on the two-stage water
cooling system dependent on the power, which is installed for
the Siemens PMSGs for offshore. From the market overview,
it is clear that most of the leading manufacturers like Vestas,
Siemens, Alstom, and Areva are using water cooling for the
new, high power units.
The proposed cooling system for a 5 MW large-scale wind
turbine is a combination of water and air forced cooling. At the
outer surface of the stator, a water jacket cooling is applied (see
Fig. 3). The heat accumulated by the water flowing in the spiral
tubes around the stator is dissipated in the heat exchanger exposed to the flow of the ambient air. The rotor inner surface
Fig. 3. FEM geometry of thermal model. 1—rotor back iron, 2—air gap,
3—permanent magnet (NdFeB), 4—copper area cross section, 5—stator tooth,
6—stator yoke. The PM region has a surface layer used to describe the eddy
current loss in the PMs.
is cooled by the fan that blows air through the clearance of
the rotor. In the air gap of the machine, no air exchange is assumed. Due to the water cooling applied at the outer surface of
the stator, the main heat flux is assumed in the radial direction,
and therefore, for the further thermal analysis, the cooling in the
axial direction is neglected.
IV. HEAT SOURCES IDENTIFICATION.
CALCULATION PROCEDURE
Generator geometries for which the temperature distribution
is investigated are optimized based on the electromagnetic analytical model of the generator [11]. The same analytical model
is used to calculate the copper and iron losses for each geometry
of the generator and each of the electrical steel grades. The computation of iron losses is based on the loss separation theory of
Bertotti [15]. The theory relies on the principle of loss separation into hysteresis, classical, and excess losses. The following
is used for the power loss calculation, for which a sinusoidal
magnetic induction waveform is assumed:
(2)
where
is the iron mass of the considered element of stator
core,
is the corresponding peak value of the induction level
in the lamination, is the electric frequency, and ,
, ,
, and are loss parameters fitted starting from iron loss
measurements [11]. The first term on the right-hand side of
(2) represents hysteresis losses. Since for each of the considered electrical steel grades the quasi-static losses were measured, it was possible to fit parameters and separately from
the parameters for dynamic losses (
, , and ). The model
takes into account a temperature dependence of the parameter
related with the classical losses in the electrical steel (see
Section V).
Copper losses are calculated based on the following equation:
(3)
where is the number of phases of the machine, is the (rms)
phase current, and
is the single-phase resistance. The
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 10, OCTOBER 2013
later defined FE model also takes into account the temperature
dependence of the copper resistance.
The magnet losses are computed using an electromagnetic
2D FE model, simulating the losses caused by the reluctance
effect of the slots as well as the space harmonics caused by the
nonsinusoidal magnetomotive force (MMF)-distribution of the
windings with only one slot per pole per phase. As the load of
the generator is assumed to take sinusoidal currents, the time
harmonics of the current were assumed to have negligible effect
on the magnet losses. The calculated magnet loss value in W/m
is then used for all the geometries and all the steel grades. The
same FE model calculates resistive heating in the rotor back iron
which is the result of eddy currents. The calculated heat source
is relatively small due to the large size of the air gap and the
shielding effect of the permanent magnets.
V. THERMAL FEM
The FEM model consists of one pole pair as presented in
Fig. 3. Due to the shape of the generator (ring type), the air-gap
diameters (4–8 m), and the number of pole pairs (50–150), a
model of one pole pair is considered as part of a linear machine,
compared with Fig. 4.
The heat equation of the software (Comsol) for conduction is
as follows:
(4)
where
is a time-scaling coefficient;
is the material density kg/m ;
is the specific heat capacity of the material [J/kgK];
is the thermal conductivity tensor [W/mK];
is the heat source (or sink) W/m .
1) Boundary Conditions: At the outer boundary of the stator
and rotor yoke [left and right boundaries of the model (Fig. 3)],
the heat flux boundary condition was used. The heat flux is described with:
(5)
where
represents a heat flux that enters a domain W/m ;
is the convection heat transfer coefficient W/m K ;
is the boundary temperature [K];
represents the ambient bulk temperature [K];
is the temperature of the surrounding radiation environment [K];
is the surface emissivity (dimensionless);
is Stefan–Boltzmann constant W/m K .
For the case of the inner rotor back iron surface, a forced air
cooling was applied. The convective heat transfer coefficient
Fig. 4. Schematic diagram of the multipole, radial flux, ring type, inner rotor
generator. In reality, the number of pole pairs can be higher than shown (ten
pole pairs in the figure).
was calculated for the air velocity of 10 m/s. The coefficient
values were estimated at 28.0, 32.4, and 35.3 W/m K via the
method described in [16] for the generator with 4, 6, and 8 m
air-gap diameter respectively (50 pole pairs). Moreover, the coefficient for the generator with 150 pole pairs and 6 m air-gap
diameter was estimated at 29.4 W/m K. The radiation in case
of the inner surface of the rotor was neglected due to the low
temperature gradient. for the rotor inner boundary is 0.
Most of the heat in the generator is produced in the stator, due
to the iron and copper losses. It was assumed that the easy way
for the heat evacuation from the stator would be in radial direction of the generator. This is due to the direction of lamination of
the electrical steel sheets in the stator core, which is laminated
axially. The decision was made to apply water jacket cooling
on the outer surface of the stator to deal with large amount of
heat produced in the stator. The heat transfer coefficient for the
water cooling of the stator outer surface was estimated by using
a simplified FE model
136.2 W/m K .
for the
stator outer boundary is 0.
On the top and bottom boundary of the model, the thermal
insulation/symmetry condition was applied. The thermal symmetry condition is described by the following equation:
(6)
Due to the shielding effect of the magnets, losses in the rotor
back iron occur mostly in between magnets; therefore, to those
boundaries of the rotor—see the bold lines in Fig. 3—heat
source was applied as a line source. represents the losses
in the rotor back iron, which are calculated by the electromagnetic FE model.
2) Subdomain Settings: For the subdomains of the modeled generator (Fig. 3), the material properties used are presented in Table III. Thermal conductivity of the stator and rotor
yoke depends on the chemical composition of the steel grade
KOWAL et al.: THE EFFECT OF THE ELECTRICAL STEEL PROPERTIES ON THE TEMPERATURE DISTRIBUTION IN DIRECT-DRIVE PMSGs
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temperature of the rotor and stator. To include the convection in
the air gap in the radial direction, a proper calculation was performed to convert the convection heat transfer coefficient into
an equivalent thermal conduction coefficient [1].
The convection in the air gap depends on the ruggedness of
the rotor and stator surfaces and the angular speed of the rotor.
Based on [1], the Nusselt number
for the air gap was estimated. The thermal resistance between rotor and stator can be
calculated as
TABLE III
PROPERTIES OF THE MATERIALS IN THE PMSG
(8)
used. In [17], the thermal conductivity was measured for different steel grades, and the relation between thermal conductivity and chemical composition was determined empirically.
Then, for the grades under study in this paper, the thermal conductivity values are calculated based on this empirical relation,
with typical chemical composition as input. Other values used in
Table III are typical values from literature in the subject. Heat
sources were assigned to the domains where heat is produced
due to losses. For these domains, it was assumed that the distribution of losses over the surface of the domain is uniform.
To assign more accurately the loss density in the stator, it is divided into the teeth and yoke domain (see Fig. 3). This is because the machines teeth are often characterized by higher induction levels and therefore higher losses.
The loss density values for the soft magnetic material regions
are computed by (2). The value of parameter in the thermal
model takes into account a temperature dependence of the electrical conductivity of the steel grades. It was assumed that the
electrical conductivity of the electrical steel is changing linearly
for the considered temperature range.
The copper regions represented in Fig. 3 (region 4) contain
also a heat source. The loss density is obtained by dividing the
resistive loss value of a single phase winding by the total volume
of the single phase copper winding. The resistive loss value is
calculated with (3). As mentioned before, the heat source for
domains of copper windings was implemented in a way to take
into account the temperature dependence of a single-phase resistance
, as follows:
(7)
where
is a single-phase resistance at 20 C.
In the PM, eddy currents only occur at a small skin depth.
Therefore, heat sources in the PM should be located close to the
surface. For the heat modeling, the PM is divided in a part
with no heat source
and a part at the surface with a
heat source related to the eddy currents. The value of the losses
is calculated in a 2D FE model.
Heat flux in the air gap can be described in radial and axial
direction. In the considered case, no air flow in the axial direction is assumed. Heat transfer in the radial direction consists
of conduction, convection and radiation. However, radiation is
neglected due to the relatively small difference in the surface
where is the thermal conductivity of the air gap,
is the
hydraulic diameter of the air gap calculated as
,
and is the surface area, which in this case is the air-gap surface
in circumferential direction.
It has to be mentioned that this way of calculation of the convection in the air gap contains a proportion of the conduction.
Based on the
value, the convective heat transfer can be
identified. However, due to the limitations of the software used
for thermal computations, the value of the thermal resistance in
the air gap was used for identification of corresponding thermal
conductivity value:
(9)
VI. RESULTS
At first, an analysis and comparison of three generators with
50 pole pairs and different air-gap diameters is presented. Then,
the generator with 150 pole pairs and 6 m air-gap diameter is
presented and compared with the one with 50 pole pairs and 6
m air-gap diameter. The same cooling strategy was chosen for
all considered generators in order to allow a fair comparison of
temperatures. Keep in mind that the intensity of cooling was
designed to keep temperatures of the generator with 50 pole
pairs and 6 m air-gap diameter under reasonable limits. This
means that the considered cooling for other generator may either
be not enough or too efficient.
A. Effect of Diameter
Three generators compared in this section have 50 pole pairs
and different air-gap diameter. The magnet losses calculated for
the generators are equal to 39.9, 28.9, and 24.9 kW, for the
air-gap diameter of the generator set to 4, 6, and 8 m, respectively. The magnet losses are strongly dependent on the surface
of the air gap of the machine (compare with Table II). The total
copper loss value for the generators with increasing air-gap diameter is equal to 300, 178, and 141 kW, respectively. The decrease of the copper losses with the increase of the air gap of
the generator is related with decreasing phase resistance, which
is related with the increase of the area of the stator slots.
For the direct-drive machine with 50 pole pairs, the electric
frequency of the generator is low (10 Hz). The low-frequency
affects the scale of the dynamic losses in the steel lamination
((2)). As a result, the values of the total iron losses per machine
remain relatively small when compared with the value of copper
losses [see Fig. 6(a)–(c)]. Therefore, even though the iron losses
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 10, OCTOBER 2013
Fig. 5. Comparison of the temperature levels for the 4 m air-gap diameter generator using different steel grades. Generator with 50 pole pairs.
are increasing with the decreasing magnetic quality of the electrical steel grade, the temperatures of the generator in Fig. 5, 8,
and 9 are not increasing. In fact, the opposite can be observed.
The decrease in the generator temperature for the decreasing
magnetic quality of the steel grade is related with increasing
thermal conductivity of the steel lamination (see Fig. 7). This
increase is causing more efficient heat evacuation from the heat
sources to the heat sinks.
Moreover, while comparing temperature distributions for the
three presented generators, it can be easily observed that the
highest temperatures of the components are for the generator
with an air-gap diameter equal to 4 m. This is a result of the
lowest efficiency of this generator (see Table III) and of applying
the same intensity of cooling system for all three generators (in
particular water cooling of the stator outer surface).
In all three cases, no significant influence of the steel grade
choice on the magnets temperature has been observed. It is a
result of the relatively weak heat transfer from stator to rotor
through the air gap.
Fig. 6. Full load iron losses per machine for (a) 4 m air-gap diameter, 50 pole
pairs generator; (b) 6 m air-gap diameter, 50 pole pairs generator; (c) 8 m air-gap
diameter, 50 pole pairs generator; (d) 6 m air-gap diameter, 150 pole pairs generator for four considered steel grades (steel grades: 1—M250-50A; 2—M33050A; 3—M400-50A; 4—M600-50A).
Fig. 7. Thermal conductivity for four considered steel grades (steel grades:
1—M250-50A; 2—M330-50A; 3—M400-50A; 4—M600-50A).
B. Effect of Pole Pair Number
For the generator with 6 m air-gap diameter and 150 pole
pairs the total, full-load magnet losses are equal to 46.5 kW for
all the steel grades. The total copper losses is equal to 149.5
kW. The total iron losses depending on the steel grade used are
between 27.7 and 58.9 kW [see Fig. 6(d)]. With an increased
number of pole pairs, the electrical frequency of the generator
increased and the ratio between copper and iron losses in the
generator has increased as well. The iron losses became more
significant in the overall total losses of the machine; therefore,
it can be concluded that the magnetic properties of the electrical
steel grade are significant in this case. The difference in the magnetic properties of the presented steel grades is causing 31.2 kW
difference in total stator core losses. This corresponds with 0.6%
of the input power of the generator. An influence on the temperature distribution caused by the increase of the total iron losses
with decreasing magnetic quality of the electrical steel cannot
be neutralized by the increase of thermal conductivity (compare
Fig. 8. Comparison of the temperature levels for the 6 meter air gap diameter
generator using different steel grades. Generator with 50 pole pairs.
Figs. 6 and 7); this results in the increase of the temperature for
decreasing magnetic quality of the electrical steel (Fig. 10).
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erator, the thermal properties of the electrical steel grade have
greater influence on the temperature distribution.
Fig. 9. Comparison of the temperature levels for the 8 m air-gap diameter generator using different steel grades. Generator with 50 pole pairs.
Fig. 10. Comparison of the temperature levels for the 6 m air-gap diameter
generator using different steel grades. Generator with 150 pole pairs.
While comparing the temperature distribution for two generators with the same air-gap diameter (6 m), but different number
of pole pairs (50 and 150), several conclusions can be drawn.
First of all, despite the same air-gap diameter and active material mass, the difference in geometry is strongly influencing the
cooling of the machine. The generator with 150 pole pairs is almost 40% longer and has much larger surfaces exposed to water
jacket and forced air cooling in the stator and rotor respectively.
However, the longer axial length for the same air-gap diameter
means greater surface of magnets exposed to the time-dependent field distribution in the air gap; this results in higher magnet
losses in the case of the generator with 150 pole pairs compared
with the one with 50 pole pair. Second, the difference in electrical frequency of the generators, which is influencing the ratio
between total copper and iron losses, is defining the significance
of magnetic and thermal properties of the electrical steel on the
temperature distribution. For the 150 pole pair generator, the
ratio of total iron to copper losses is much higher than in the
case of 50 pole pair generator. This means that, in the first situation, magnetic properties of the steel have more influence on the
thermal distribution. On the other hand, for the 50 pole pair gen-
VII. CONCLUSION
A thermal model of the direct-drive PMSG generator for
wind energy application was presented. The model takes into
account temperature dependence of the electrical conductivity
of both copper and iron. Prior to thermal simulations, the heat
sources and heat transfer coefficients were identified for a
chosen cooling strategy. The influence of four different steel
grades on the temperature distribution of three configurations
of the generators was presented. In case of the 50 pole pair
generator, the thermal conductivity of the steel grade has a
major influence on the temperature distribution due to the low
electrical frequency, whereas, for the generator with 150 pole
pairs, the magnetic properties of the electrical steel grade have
dominant influence on the temperature distribution.
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