Project 2

26
1. Introduction
Servo drives with permanent magnet (PM) motors fed from static inverters are finding
applications on an increasing scale. PM servo motors with continuous output power of up to
15 kW at 1500 rpm are common. Rare-earth PMs have also been recently used in large power
synchronous motors rated at more than 1 MW [1]. Synchronous motors operate at a constant
speed in absolute synchronism with the line frequency or can also be supplied from a frequency converter. Currently, synchronous electric motors with permanent magnets (PM) and
an external rotor are gradually applied in the drives of electric vehicles and are stored directly
in the wheel.
Hub motors, also called in-wheel motors, were first patented in the 1880s. In 1899 the Viennese firm of Lohner & Co. built a car powered by battery-driven hub motors. This car was
also unique as the world’s first front wheel drive system. A news report at the time described
the development of the first-ever transmissionless vehicle as a revolutionary innovation. The
electric motor in the hubs of the front wheels had an output of 1.8 kW at 120 rpm [2].
2. The synchronous motor with PM external rotor – model and simulation
This chapter presents results of the electro-magnetic proposal for a synchronous motor
with external rotor with permanent magnets, simulation of electromagnetic field motor and
its operating characteristics. Basic electrical characteristics have been developed on the basis
of operational requirements for the motor – these are shown in Table 1.
Table 1
The synchronous motor parameters
Parameter Value
Rated power 3 kW
Rated voltage 3 x 82 V (Y)
Rated current 27 A
Rated torque 38 Nm
Synchronous speed 750 rpm
The electromagnetic design of the motor was calculated and optimized in ANSYS/
RMxprt. Based on the required electrical parameters and the geometric dimensions resulting
from the motor mount, a 3D model of electromagnetic circuit of the motor was designed in
ANSYS/Maxwell (Fig. 1).
The following are simulation results of the synchronous electric motor with an external
rotor and PM. The simulation of the electromagnetic field of the synchronous motor with PM
is shown in Fig. 2. Figure 3 shows a simulation of the induced voltage in all three phases of
the synchronous machine.
The simulation of the motor and load torque is shown in Fig. 4. The speed of synchronous
motor was 750 rpm. The simulation of the motor speed and torque is shown in Fig. 5.
27
Fig. 1. The 3D model of synchronous motor with PM
Fig. 2. Magnetic field of synchronous motor with PM
Fig. 3. Induced voltage calculated by ANSYS/Maxwell 3D
28
Fig. 4. Simulation of the motor and load torque calculated by ANSYS/Maxwell 3D
Fig. 5. Simulation of the motor speed and torque calculated by ANSYS/Maxwell 3D
3. Structural design of synchronous motor
Fig. 6. 3D solid model of the synchronous motor
a) b)
29
The construction and external dimensions of the motor are designed so that the motor
can be easily positioned and mounted onto a traditional 14” steel rim wheel. The 3D solid
model of the stator synchronous motor was created based on the geometric dimensions of
the optimized simulation. Figure 6a) shows the general view of the 3D solid model of the
synchronous motor with permanent magnets and the inverse rotor. A cross-sectional view of
the synchronous motor is shown in Fig. 6b).
4. Measurement of synchronous motor prototype
Based on the structural design of the motor referred to in chapters 2 and 3, a functional
prototype was devised. The synchronous motor was used for practical measurements in the
laboratory, a photo of which is displayed in Figs. 7 and 8.
4.1. Measurement of generator operation
When measured in a no load generator, the waveforms were recorded with an oscilloscope showing the voltage induced in individual phases. Figure 9 shows waveforms of induced voltages in the phases of the generator at a speed of 750 rpm.
When load is exerted on the generator (resistive load), its terminal voltage drops. In this
measurement, the phase voltage reached 47.6 V (RMS) and the line-to-line voltage was 82.6 V
(RMS). The frequency analysis of phase voltages (no load generator) is shown in Table 2.
Table 2
Frequency analysis of phase voltages
Order U1[%H01] U2[%H01] U3[%H01]
1 100 100 100
3 2.2 2.2 2.3
5 1.4 1.4 1.5
7 - 0.1 -
Fig. 7. The synchronous motor
prototype
Fig. 8. Measurement of the synchronous motor
prototype in the laboratory
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Fig. 10. Measured quantities for loads on the generator
When a load is exerted on the generator (resistive load), its terminal voltage drops. A plot
of the terminal voltage and efficiency versus mechanical torque for a generator speed of
750 rpm is shown in Fig. 10. The measured quantities are indicated by crosses. Whilst the
average efficiency is 94%, the voltage drop is up to 19%.
Figure 11 shows waveforms of voltage in the first phase and of the load current. The generator is loaded with a constant current of 20 A (RMS). Frequency analysis of phase currents
(for load current of 20 A) is shown in Table 3.
Table 3
Frequency analysis of phase currents
Order I1[%H01] I2[%H01] I3[%H01]
1 100 100 100
3 – – 0.2
5 1.2 1.2 1.2
7 – 0.1 –
Fig. 9. The measured induced voltages
31
4.2. Measurement of load motor operation
When measuring the synchronous machine in load motor operation, the machine is connected to a rated supply voltage of 82 V (RMS), with a frequency of 50 Hz. During loading
of the motor, the supply voltage remains constant.
The synchronous motor was operating at a constant speed (750 rpm) and was loaded by
a torque. At a constant mechanical speed, the mechanical output power is equivalent to mechanical torque on the shaft. The plot of motor torque is shown in Fig. 12, the input power
and the mechanical power supplied to the rated voltage versus the phase current for a motor
speed of 750 rpm. The measured quantities are indicated by crosses.
Fig. 11. Measured waveforms of voltage and current
Fig. 12. Measured waveforms of torque and the powers
32
Fig. 13. Measured efficiency of synchronous motor
Figure 13 shows the plot of efficiency versus mechanical torque for synchronous motor
speed of 750 and rated supply voltage of 82 V (RMS). The measured quantities are indicated
by crosses. Figure 14 shows waveforms of supply voltage in the first phase and current of the
motor. The motor is loaded with a constant torque of 1 Nm.
If the motor is loaded with a small torque (T = 1 Nm), then the waveform of the motor
current contains higher harmonics and is very inharmonic. The motor operates under excitation.
Figure 15 shows waveforms of supply voltage in the first phase and current of the motor,
if the motor is loaded with a constant torque of 36.6 Nm and operates as over-excited. If the
motor is loaded with a rated torque, then the waveform of the motor current contains lower
values of the higher harmonics and is roughly sinusoidal. Frequency analysis of phase voltages (for load motor torque – 36.6 Nm) is shown in Table 4.
Fig. 14. Measured waveforms of supply voltage
and current – T = 1 Nm
Fig. 15. Measured waveforms of supply voltage
and current – T = 36.6 Nm
50
Design of three LSPMSM rotor topologies
2.1. Introduction
The second chapter begins with a discussion about analytical methods used for
LSPMSM transient d-q equivalent circuit. Further, the development of analytical models
considering asynchronous and steady -state operations of the LSPMSM will be
introduced. It will be discussed how to create a magnetic equivalent circuit for each of
three rotor configurations selected in Chapter 1: series, radial magnetized and V-type.
The obtained value of the air-gap flux will be used in the calculation of the flux linkage
and steady-state performances.
The characteristics of each LSPMSM rotor configuration are described with aid of an
analytical model which is verified by numerical software presented in a dedicated
paragraph.
Finally, a general definition of the optimization problem is discussed and the results in
the form of Pareto frontiers for two variants of rotor cage are shown.
2.2. Analytical method of LSPMSM designing
In Chapter 1 it was concluded, that the most appropriate solution for the replying to the
thesis objectives consists on the development of a multi-physical generic model is the
usage of an analytical model. In this thesis the analytical model is based on d-q
equivalent circuit.
The circuit based model is a good solution for evaluating and analyzing the transient
and steady state performances of the LSPMSM. In spite of having calculation time
extremely reduced, he analytical model have a comparatively low accuracy. For
consolidation of the analytical models the F.E. modelling will be done using finite
element models. In this thesis a specialized FEM software Ansoft/Maxwell is used for
this purpose.
2.2.1. Park transformation and transient d-q equivalent circuit of LSPMSM
In electrical engineering, Park’s transformation is a mathematical direct–quadrature–
zero (dq0) transformation that rotates the reference frame of three-phase systems in an
effort to simplify the analysis of three-phase circuits.
The dqo transformation in matrix form applied to any three-phase quantities (e.g.
voltages, currents, flux linkages, etc.) is given by eq. (2. 1)
51
(2. 1)
In three-phase machines we are typically concerned with three self-inductances and six
mutual inductances. In matrix form it can be expressed as follows in (2. 2)
[HENDERSHOT_10].
(2. 2)
Using the Clarke transformation the column vector of synchronous inductances is
(2. 3)
Where is
(2. 4)
where is in electrical degrees.
Applying the three-phase sinusoidal voltage source to the stator winding of LSPMSM
produces the rotational magnetic field in the air gap of the motor. The permanent
magnet poles fixed on the rotor try to align along this rotating field, yielding a
synchronous torque on the rotor. During starting, the damping winding (in our case it
may be a squirrel cage or an aluminum or copper can) on the rotor generates the
asynchronous starting torque, creating a self-starting capacity [MODEER_07],
[WANG_07].
The d,q-axis voltages of LSPMSM for are shown in set of equations (2. 5)
(2. 5)
Where , are the d-axis voltage of stator and rotor, , are the q-axis voltage of
stator and rotor, is the electrical angle speed and is rotor winding resistance
52
transferred to the stator and depending on the rotor speed. At steady state and
can be considered to be zero.
The magnetic flux equations are shown in set of equations (2. 6)
(2. 6)
By describing the permanent magnet as a current source, the flux linkage can be
defined as eq. (2. 7)
(2. 7)
In order to be able to simulate the electrical behavior of the LSPMSM in any electrical
circuit analysis program the motors equivalent circuit (see Fig.2. 1) is needed. By
transforming the drive voltage into d-q parameters and connecting it to its respective dq equivalent circuit, estimations of the models currents can be done.
The differential equation describing the shaft speed is given by eq. (2. 8)
(2. 8)
Where is the rotational inertia of the motor and load, is electromagnetic
torque developed by motor, is the load torque and p is the number of pole pairs.
Fig.2. 1 Transient d-q equivalent circuits
53
In [HONSINGER_80] a set of equations describing the transient behavior of LSPMSM is
presented below by eq. (2. 9)
(2. 9)
2.2.2. Study of LSPMSM asynchronous operation
When designing an LSPMSM there are two options available. The most popular one
found in literature is an IM rotor retooling [SOULARD_02]. Since an LSPMSM can
operate with the same stator and winding arrangement as an IM, the IM rotor can be
replaced with an LSPMSM rotor [HENDERSHOT_10], [PYRHONEN_08], [DING_11],
[HUNG_08], [TAKAHASHI_10]. The simplest way of the rotor modification is the
embedding of PMs into the rotor core or onto its surface. This option expels the
necessity of machine sizing from zero and permits to start the design process from a
well-developed IM sizing procedure. The second option is to do a complete machine
design like it has been demonstrated in [SORGDRAGER_14].
In order to reduce the number of discrete parameters and, hence, to limit the
computation time, the design algorithm implemented to the LSPMSM models is based
on the first method. Fig.2. 2 presents the LSPMSM design procedure proposed in this
thesis.
As it has already been mentioned above, for economic reasons, the stator and windings
of the LSPMPM are identical to the induction motor of the same power used at present
in the electrical applications [SOULARD_02]. As the air-gap flux density contains a large
third harmonic due to the rectangular magnet flux density shape the stator winding is
star-connected in order to avoid the presence of this third harmonic into the line
currents.
In the first step of designing, the data concerning the power (see Fig.2. 2) and the stator
of the motor is to be entered. In the same time a user has to choose a configuration of
the PMs into the rotor.
The second step is the IM sizing for the same power range. At this stage the same design
methodology as for an IM can be applied. This allows to define the stator and winding
geometry and the number of rotor bars and to choose a structure of the squirrel cage
for a first approximation that gives the value of the rotor cage resistance and the level of
saturation in rotor teeth.
As soon as the geometry of the rotor and PMs is known, the d- and q-axis reactances
and and the no-load EMF can be calculated either analytically or computed using
FEM. Thanks to these parameters and taking into account the braking torque induced
54
by the PMs, the start of the LSPMSM can be simulated. If the motor is not able to start,
the designer has to go back either to the Stage 2 in order to change the rotor squirrel
cage and, hence, to increase the starting torque or to the Stage 3 to resize the PMs and
to reduce the breaking torque.

After the successful start of the LSPMSM, performances and steady-state characteristics
are calculated and used for finding the optimal solution. Then, the design procedure
must be repeated starting from the Stage 2. Every stage of the diagram will be more
detailed below.
Algorithm of IM sizing
The LSPMSM contains both IM and PMSM component parts which can be designed
separately. As it has been discussed in the previous chapters, once both rotor designs
are done they can be combined into one rotor. According to Fig.2. 2, the first step for the
design procedure is the sizing of an IM of the same power range that it is required by
the specification. The slot number combinations follow the same concerns as in
induction motors. Besides, it is generally favorable to have the number of rotor slots
divisible by the number of poles, so that the poles are symmetric.
The workflow summarizing the procedure of IM sizing is outlined in Fig.2. 3. Complete
description of the analytical approach for IM and an example of calculations are
Fig.2. 2 Algorithm summarizing the design procedure
55
presented in Appendix B. This approach can be applied for the design of a quite large
range of IM. It was compiled using the methodologies proposed in [BOLDEA_10],
[KOPILOV_86], [PYRHONEN_08].
Results of the analytical design
The principal motor design parameters, obtained from the calculations represent in
Appendix B, are given in Table 2. 1.
Design parameter Value
Rotor diameter, D2, mm 148.7
Stator outer diameter, Da, mm 225
Airgap length, , mm 0.7
Number of stator slots, Z1 36
Number of stator slots, Z2 40
Core length, , mm 110
Fig.2. 3 Workflow summarizing the procedure of IM sizing
Table 2. 1 Principal motor design parameters of 4-pole, 7.5 kW IM
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Fig.2. 4 illustrates the stator topology and windings distribution defined on the basis of
the analytical approach. It gives an idea of the motor topology and its parameters in a
first approximation. This approach also permits the calculation of starting torque and
consequently, the determination of acceptable braking torque.
Fig.2. 5 shows electrical parameters of T-type equivalent circuit of IM for one
configuration: r1, x1 are the resistance and reactance of the stator, r2/s is the equivalent
resistance of the rotor, x2 is the reactance of the rotor, and x12 is the magnetic reactance.
Table 2. 2 summarizes performances characteristics of 4-pole 7.5 kW IM model
represented in Appendix B.
Fig.2. 4 Stator topology, windings distribution and approximate rotor configuration provided
for the designing LSPMSM 7.5kW (see Appendix B)
Fig.2. 5 Single-phase T-type equivalent circuit of IM
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Performances characteristics Value
Starting current ratio 5.4
Starting torque ratio 1.64
Breakdown torque 2.54
Fig.2. 6a illustrates the results of analytical modelling for 4-pole 7.5 kW IM. Points of the
model are obtained with both high-fidelity industrial simulator ANSYS Maxwell/RMxprt
[ZHOU_10] and the applied analytical model. The same approach is applied at the
designing the 4-pole 18.5 kW IM (Fig.2. 6b).
On the whole, Fig.2. 6 shows a rather good agreement (maximal deviation is about 5% in
the case of designing the 7.5 kW 4-pole IM and 3% in the case of designing the 18.5 kW
4-pole IM) between the results of the analytical calculations and those of the
commercial software confirms that the presented method is suitable for the preliminary
design and analysis of IM part in the LSPMSM design algorithm. The experimental
verification of the model will be done in Chapter 3.
a) b)
2.2.3. Steady-State Model for the LSPMSM design
In steady-state conditions the LSPMSM is normally analyzed in the same way as a PMSM
using a d-q model where the d-axis is aligned with the direction of permanent magnet
flux. In general, the stator winding has three phase quantities and it can be transformed
to rotor reference frame and vice versa by using Park’s transformation (2. 1)
[MODEER_07].
At a steady-state, the phasor diagram of LSPMSM can be depicted as shown in Fig.2. 7.
The no-load phase EMF is
Table 2. 2 Performances characteristics of 4-pole 7.5 kW IM (analytical model)
Fig.2. 6 Torque versus speed: (a) 7.5 kW 4-pole IM, (b) 18.5 kW 4-pole IM
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(2. 10)
where is the flux linkage due to the fundamental component of d-axis flux produced
by the permanent magnet. All the equations in this section are reorganized from the
references [STOIA_09], [GIERAS_10].
The voltage equation of LSPMSM motor is:
(2. 11)
Or
(2. 12)
Where is leakage reactance, and are d-axis and q-axis components of and
reactances.
Thanks to the set of equations (2. 11), (2. 12) a vector diagram of LSPMSM can be
plotted as shown in Fig.2. 7.
Correspondingly the vector diagram:
(2. 13)
(2. 14)
(2. 15)
(2. 16)
(2. 17)
(2. 18)
where is power angle.
The input voltage projections on the d-axis and q-axis are
(2. 19)
(2. 20)
where is internal angle of the synchronous motor.
Solving eqs. (2. 19), (2. 20) one can find the components of the currents
(2. 21)
(2. 22)
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As it can be seen from the vector diagram, the vector of the input current can be
decomposed in two components, namely the active component and the reactive
component .
(2. 23)
From (2. 21) - (2. 23) it can be deduced
(2.
24
)
By neglecting the armature resistance and the leakage reactance, the components
and of the input current are
Fig.2. 7 Vector diagram of line-start permanent magnet synchronous motor [STOIA_09]
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(2. 25)
(2. 26)
Electromagnetic torque
The vector diagram in Fig.2. 7 can also be used for determination of the input power:
(2. 27)
From (2. 24)-(2. 27) it follows that input power is
(2. 28)
Because of neglected stator core losses, the electromagnetic power given by the
terminal power lowered by the stator winding losses:
(2. 29)
(2. 30)
At steady-state synchronous operation, the resulting torque that rotates a LSPMSM
combines the permanent magnet alignment torque generated by the PMs and the
synchronous reluctance torque Tr. It was found that the synchronous loading capability
is deeply influenced by the back EMF and the q-axis current.
When the LSPMSM is designed with different d- and q-axis, an additional provided
reluctance torque appears. It is proportional to the difference between the d-axis and
the q-axis reactances .
Assume that there are no armature losses, and then the total output torque developed
by a salient-pole synchronous motor is
(2. 31)
The total output torque can be also expressed as
(2. 32)
Where Ω is the synchronous angular speed and is synchronous speed
(2. 33)
For the LSPMSM with a surface magnet rotor, is almost the same as , thus the
reluctance torque term is insignificant. In a LSPMSM using an embedded magnet rotor,
is lower than as the magnetic flux flowing along the d-axis has to cross through
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the magnet cavities in addition to the rotor air-gap, while the magnetic flux of the q-axis
only crosses the air-gap [HUANG_08].
Eq. (2. 31) shows that the period of the reluctance torque is one half of that of the PM
generated torque. Fig.2. 8 proves that an interior magnet type LSPMSM can achieve
higher torque than a surface mounted LSPMSM which does not have any reluctant
torque component. However, the appearance of the reluctance torque does not mean
that the interior magnet type can have higher power density than surface mounted
LSPMSM because the magnet flux linkage in LSIPMSM is not the same as that in the
surface mounted LSPMSM with the same magnet volume. Eq (2. 32) is another form of
the torque equation (2. 31) and suggested by [HENDERSHOT_10] and showing that the
total torque of a LSPMSM is increased due to the saliency of the rotor.
2.2.4. Analytical calculation of electromagnetic parameters
In Chapter 1 there was chosen 3 LSPMSM rotor configurations meeting the major part
of specification requirements and having a high product of power factor and efficiency
were preselected in Chapter 1(see Fig.2. 9).
a) b) c)
Fig.2. 8 Torque-angle characteristics of a LSPMSM
Fig.2. 9 LSPMSM rotor configurations under study: (a) rotor with radial magnetic circuit
structure, (b) rotor with series-type magnetic circuit structure, (c) rotor with V-type magnetic
circuit structure
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In this paragraph the three analytical models for each LSPMSM rotor topology are
developed with the aid of common electromagnetic laws and taking into account
geometry of each of motors. The magnetic equivalent circuit will be deduced for each
studied rotor shape.
After every section devoted to one of three rotor topologies, the results of analytical
models are compared with the results issued from a commercial software and providing
from a finite element modeling.
LSPMSM with radial magnetic circuit structure
As it has already been discussed in the previous paragraph, the flux linkage and
reluctance are the key parameters to determine the steady-state characteristics of a
LSPMSM. Using the magnetic equivalent circuit is the most common method for the
determination of these parameters [HENDERSHOT_10], [FODOREAN_09],
[HEIKKILA_02], [CARPENTER_12].
Fig.2. 10 shows a simplified one pole scheme of a LSPMSM with a radial magnetic circuit
structure.
By Gauss’s law and neglecting leakage and presence of rotor bar, the total flux from the
permanent magnet travels through a half part of the air-gap as shown in eq.(2. 34)
[FODOREAN_09], [GIERAS_10].
(2. 34)
Where is the rotor radius.
According to Ampere’s law
Fig.2. 10 Simplified structure of a LSIPMSM with tangential magnetization
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(2. 35)
The linearly approximated equation of demagnetization curve for PM is given by
(2. 36)
Where is PMs flux density, is magnetic field strength of PMs, is the
permeability of vacuum, is relative magnetic permeability. Substituting eq.(2. 36) in
eq.(2. 35):
(2. 37)
When combining (2. 34) and (2. 37), the air-gap flux density is
(2. 38)
Air-gap flux density (2. 38) can be obtained from the simplified equivalent magnetic
circuit (Fig.2. 11). As the magnetic flux from the rotor passes only a half part in the air
gap, the air-gap reluctance with one half width of the one pole would be two times of
the one pole air-gap reluctance , which is expressed by (2. 39).
(2. 39)
Where is the Carter factor which takes into account the increased reluctance due to
slotting, is the air gap thickness, is the active rotor length, is magnet length,
is magnet height. The Carter factor can be found according to the algorithm presented in
Appendix B.
The PM remanent flux and the PM reluctance are as follows
Fig.2. 11 Equivalent magnetic circuit of a LSIPMSM with tangential magnetization (leakage
through the bridges are not taken into account)
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(2. 40)
(2. 41)
Usually the bridges are fully saturated under nominal conditions and behave like the air.
Neglecting the leakage through the bridge of the rotor (Fig.2. 11) the air-gap flux density
is
(2. 42)
It has been talking above that the magnet fluxes and the EMF could be analytically
expressed as function of the studied machine geometry. The magnets produce a flux
which is divided into a “useful” component circulating through the stator and which
participates in the energy conversion, and a leakage component via the nonferromagnetic hub and the magnetic shaft, that does not participate in
electromechanical conversion. The flux lines are supposed to be purely radial in all air
gaps, whose lengths are considered constant. A principle scheme used for analytical
model in case of LSPMSM with radial magnet structure is represented in Fig.2. 12.
Several assumptions should be made in order to simplify analytical calculations. The
magnetic cores are regarded as not saturated, thus the surfaces of the pole pieces are
equipotential. Furthermore, the decrease of the magnetic flux density in front of the
magnets is considered linear. Besides despite of having the rotor bars the distribution of
the magnetic flux in the rotor during the steady state is stated as uniform [JANNOT_09].
Fig.2. 12 Flux line calculation scheme of magnetic flux density due to PM for a LSPMSM with
radial magnet structure [JANNOT_09].
65
Due to assumptions made above and using the flux line calculation scheme (Fig.2. 12)
the Ampere’s theorem is
(2. 43)
The flux conservation law is:
(2. 44)
Where the g, sh and m subscripts deal, respectively, with the air gap, shaft and magnet
quantities. Geometrical coefficients γ and β used in (2. 44) can be calculated as follows
in (2. 45):
(2. 45)
Where is magnet width, is magnet height, is external shift radius. It is
necessary to add material behavior laws (2. 46) to close the system of Eqs. (2. 43)-(2.
45).
(2. 46)
Where is remanent magnetization. Combining Eqs. (2. 43), (2. 44) and (2. 46) with
geometrical relations (2. 45), the flat-topped value of the flux density waveform, due to
magnets, is given in (2. 47) [JANNOT_10].
(2. 47)
Appling the fast Fourier transform (FFT) for Eq. (2. 47) the fundamental harmonic of
the flux density in the air gap is
(2. 48)
where α=2/π is the ratio of the average-to-maximum value of the normal component of
the air gap magnetic flux density.
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According to the trapezoidal waveform of the flux density and the expression of the top
plate Eq. (2. 47) the fundamental of the linkage flux through the stator is directly
derived from the set of equations (2. 46) and gives (2. 49).
(2. 49)
where is slot number, is global winding coefficient, is bore radius. To
finalize calculations one can apply the Boucherot’s formula, which is a special case of
Faraday’s law. As so the EMF expression is (2. 50).
(2. 50)
where - electric frequency. All the expressions derived in this sub-section incorporate
leakage flux in the hub.
In the motor with a such configuration, the resulting armature reaction flux is oriented
into the line with the d-axis when PMs are removed from their locus and replaced with
non-ferromagnetic material. The magnetic flux flows through the space dedicated to
magnets and also through the shaft. After some combinations, the synchronous
inductance can be expressed as a function of the machine geometry and winding
arrangement could be founded:
(2.
51
)
The same approach may be used for determination of the q-axis synchronous
inductance. Now the resulting armature reaction flux is completely oriented in line with
the q-axis. In this position, it is admitted that there is no flux leakage because the
magnetic field is almost always circulating in the iron parts of the rotor and the stator.
As for the d-axis, the q-axis synchronous inductance can be calculated as in eq.(2. 52),
for all the phases, and is a function of machine geometry and winding arrangement.
(2. 52)

67
Comparison of analytical model with results of commercial software and FE simulations
in the case of LSPMSM 7.5kW and 18.5kW with radial magnetic circuit structure
The estimation of the reactances for two LSPMSMs of 7.5kW and respectively
18.5kW with radial magnetic circuit structure has been done using the commercial
software ANSYS RMxprt (Fig.2. 13, Fig.2. 15) and by FE analysis accomplished by ANSYS
Maxwell software and its Electric Machines Design Toolkit/ D-Q Solution Calculation
Method [MAXWELL_16] (Fig.2. 14. Fig.2. 16). The comparison of the results is
summarized in Table 2. 3 and Table 2. 4.
LSPMSM 7.5kW with radial magnetic circuit structure
Fig.2. 13 reactances given by ANSYS RMxprt for LSPMSM 7.5kW with radial magnetic
circuit structure
Fig.2. 14 Mean value of reactances given by ANSYS Maxwell for LSPMSM 7.5kW with a
radial magnetic circuit structure
Xad
Xaq
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Parameter
Air gap, mm lm, mm hm, mm Xad, Ohm Xaq, Ohm
Analytical Model 0.7 13 26 7.2 30.9
ANSYS RMxprt 0.7 13 26 6.2 33.2
ANSYS Maxwell 0.7 13 26 6.6 27.3
LSPMSM 18.5kW with radial magnetic circuit structure
Table 2. 3 Comparison of the results. LSPMSM 7.5kW with a radial magnetic circuit structure
Fig.2. 15 reactances given by ANSYS RMxprt for LSPMSM 18.5kW with a radial
magnetic circuit structure
Fig.2. 16 Mean value of reactances given by ANSYS Maxwell for LSPMSM 18.5kW with a
radial magnetic circuit structure
Xaq
Xad
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Parameter
Air gap, mm lm, mm hm, mm Xad, Ohm Xaq, Ohm
Analytical Model 0.5 13 25 4.1 28.2
ANSYS RMxprt 0.5 13 25 4.4 29.9
ANSYS Maxwell 0.5 13 25 4.0 26.0

LSPMSM with series magnetic circuit structure
The analytical calculations of inductances values for a LSPMSM with series magnetic
circuit structure is based on the analytical expressions for the average air gap flux
density and the permeance coefficients. Fig.2. 17 shows a cross section of this topology
with one half of two magnets, the associated stator and rotor back iron. In this
configuration the buried magnets are magnetized across their shorter dimensions along
the d-axis.
The equivalent magnetic circuit is shown in Fig.2. 18, where and are the
reluctances of the rotor and stator back irons, respectively, is the reluctance of the
one-half of air gap with compensation for slotting, is the reluctance of the one-half
of a magnet, is the reluctance modelling the flux leakage through the air under the
bridge and is the reluctance modelling the flux leakage through the bridge
[HADEF_11], [HWANG_02].
Table 2. 4 Comparison of the results. LSPMSM 18.5kW with a radial magnetic circuit structure
Fig.2. 17 Magnetic flux distributions in the cross section of the LSPMSM with series magnetic
circuit structure
70
Taking as a hypothesis the stator and rotor steel are infinitely permeable everywhere
excepting in the bridge between the pole pieces. The flux drops along the stator and
rotor yokes can be neglected and the air gap flux is related to the remanent magnet
flux by eq. (2. 53).
(2. 53)
In this equation is the reluctance ratio, and are the
leakage flux ratios. The average air gap flux density is given by
(2. 54)
where is remeance of the magnet and is the flux concentration factor,
and are the cross-sectional areas per pole of the air gap and magnet, respectively.
The corresponding magnet flux density in the magnet is determined as
(2. 55)
The leakage flux through the bridge between pole pieces as is illustrated in Fig.2. 18 is
given in eq. (2. 56).
(2. 56)
From Eq. (2. 56) the average flux density within the bridge is
Fig.2. 18 Equivalent circuit of LSPMSM with the series magnetic circuit structure [HWANG_02]
71
(2. 57)
where denotes the cross-sectional area of the bridge and and are the
bridge width and the stack length respectively. From eq. (2. 57) λ can be expressed as
(2. 58)
If the level of leakage flux through the bridge is limited to the flux density saturation
level of , then
(2. 59)
The air-gap reluctance is expressed as
(2. 60)
Consider Fig.2. 18.
(2. 61)
The reluctance of the air flux barriers under bridge is approximated as follows from
(2. 62)
and hence
(2. 63)
(2. 64)
where , , α is the pole-arc to pole-pitch ratio.
The amplitude of the fundamental component of the air gap flux due to the magnet
acting alone is
(2. 65)
72
where k1=4/π sin(α π/2) . Hence the amplitude of the fundamental flux per pole is
(2. 66)
For a winding with series turns per phase and a winding factor , the open circuit
EMF per phase is
(2. 67)
The direct and quadrature synchronous reactances could be found as a function of the
machine geometry and winding arrangement:
(2. 68)
(2. 69)
Where the armature reactance is the same as for a cylindrical-rotor synchronous
machine, , are equivalent d- and q-axis air gap thicknesses, are
the factors of the armature reaction
(2. 70)
(2. 71)
(2. 72)
(2. 73)
(2. 74)
(2. 75)

73
Comparison of analytical model with results of commercial software and FE simulations
in the case of LSPMSM 7.5kW and 18.5kW with radial magnetic circuit structure
LSPMSM 7.5kW with series magnetic circuit structure
Parameter
Air gap, mm lm, mm hm, mm Xad, Ohm Xaq, Ohm
Analytical Model 0.6 55 9 6.1 36.4
ANSYS RMxprt 0.6 55 9 6.1 40.57
ANSYS Maxwell 0.6 55 9 6.0 31.2
Fig.2. 19 reactances given by ANSYS RMxprt for LSPMSM 7.5kW with series magnetic
circuit structure
Fig.2. 20 Mean value of reactances given by ANSYS Maxwell for LSPMSM 7.5kW with
series magnetic circuit structure
Table 2. 5 Comparison of the results. LSPMSM 7.5kW with series magnetic circuit structure
Xad
Xaq
74
LSPMSM 18.5kW with series magnetic circuit structure

Parameter
Air gap, mm lm, mm hm, mm Xad, Ohm Xaq, Ohm
Analytical Model
0.5 76 6 4.1 28.2
ANSYS RMxprt 0.5 76 6 3.8 29.9
ANSYS Maxwell
0.5 76 6 4.0 24.7

LSPMSM with V-type magnetic circuit
The analytical model of a LSPMSM with V-type magnetic circuit is more complicated in
comparison with two previous types. Fig.2. 23 shows one pole of rotor with V-type PM’s
Fig.2. 21 reactances given by ANSYS RMxprt for LSPMSM 18.5kW with series magnetic
circuit structure
Fig.2. 22 Mean value of reactances given by ANSYS Maxwell for LSPMSM 18.5kW with
series magnetic circuit structure
Table 2. 6 Comparison of the results. LSPMSM 18.5kW with series magnetic circuit structure
Xaq
Xad
75
structure. In order to calculate the flux density in the air gap the theory of “Equivalent
Magnetic Circuits” has been used in [HEIKKILA_02]. Magneto motive force (MMF) -
drops in the rotor and stator iron have been neglected, the rotor slots are assumed to be
shaped like a quadrilateral, the air gap flux density is assumed to be rectangular.
The permanent magnet can be considered as a constant MMF-source in series with a
constant internal reluctance. The magnitude and the reluctance of the MMF-source can
be found from eqns. (2. 41), (2. 42). If the rotor has more than one magnet per pole, e.g.
due to flux concentration, eqns. (2. 41) and (2. 42) will still be valid if all the magnets
have the same thickness (which normally is the case):
(2. 76)
In this case the magnet width will be the sum of different magnet widths under one
pole:
(2. 77)
Due to the tolerances required for inserting the magnets into the slots an extra air gap
will be added to the magnetic circuit, see Fig.2. 23. The reluctance of the extra air gap can
be expressed as done in (2. 78). The notion of flux barriers includes rotor bars, air-filled
slots, the air-filled space between the magnets etc. For simplification all the flux barriers
can be regarded as air. The resulting reluctance can be found by connecting all flux
barriers under one pole in parallel:
Fig.2. 23 Parameters definition for LSPMSM with V-type magnetic circuit for one pole
[HEIKKILA_02]
76
(2. 78)
where is the average length of the route, along which the stray flux has to travel,
is the average width of the route, along which the stray flux has to travel. Nonrectangular flux-barriers, for example, an aluminium rotor bar, might be approximated
with their average width and average length, see Fig.2. 23. In our case we have two pairs
of flux-barriers: at the base and the top of the magnets (Fig.2. 23). Provided that
and the total reluctance of the upper flux-barriers
(2. 79)
At the lower part of the magnets it is usually reasonable to use flux barriers in order to
avoid a large stray flux (see Fig.2. 23, Fig.2. 24), since then less magnetic material is
needed to produce the desired air-gap flux. The free space between the two barriers can
be regarded as the iron bridges. The iron bridges are mandatory to keep the rotor
together mechanically. At the same time they “short-circuit” some of the flux from the
magnets. Depending on the thickness and number of iron bridges the “lost” flux can be
quite significant. When the iron bridges are completely saturated they can be
considered as air.
The length of the saturated bridge increases and the width of the flux route
decreases [HEIKKILA_02]. Fig.2. 24 may be used in order to calculate the approximate
value of .
Fig.2. 24 Definition of parameters for leakage reluctance calculation for LSPMSM with V-type
magnetic circuit
77
(2. 80)
(2. 81)
(2. 82)
(2. 83)
Then the stray reluctance grows, which causes a decreasing of the stray flux .
The total reluctance due to the presence of two magnets:
(2. 84)
Likewise as it was shown shown before the reluctance of the air gap can be expressed
(2. 85)
Where is the true circumferential pole width on the rotor surface
(2. 86)
where is the rotor radius, α is the electrical angle (in degrees) of half the true pole
width on the rotor surface (see Fig.2. 23) and is the number of poles.
The equivalent magneto motive force of the rotor is the magneto motive force of the
permanent magnets minus the product of the saturation flux and the reluctance of
the permanent magnet with surrounding air-gaps [NEE_00], [THELIN_01].
(2. 87)
The simple equivalent reluctance circuit of one pole is shown in Fig.2. 25.
78
The equivalent reluctance circuit of the permanent magnet motor consists of the airgap, the permanent magnets and bridge reluctances and iron reluctances. The air-gap
flux produced by the permanent magnets is calculated by using the equivalent
reluctance circuit as follows in eq. (2. 89)
(2. 88)
The flat-topped value of the flux density in the air gap is
(2. 89)
Where is the axial length of the magnet, is the true circumferential pole width on
the rotor surface. The peak value of the fundamental harmonic of the flux density in
the air gap can be calculated as coefficients for the fundamental harmonic of Fourier
series.
(2. 90)
Calculation of the d- and q-axis armature reaction reactances is expressed with the aid
of form factors of the armature reaction and [MILLER_84], [GIERAS_10]:
(2. 91)
(2. 92)
Where the mutual reactance is the same as for a cylindrical-rotor synchronous
machine
(2. 93)
Fig.2. 25 Equivalent reluctance circuit for LSPMSM with V-type magnetic circuit
79
The form factors of the armature reaction are defined as the ratios of the first harmonic
amplitudes to the maximum values of normal components of normal components of
stator magnetic flux densities in the d-axis and q-axis, respectively:
(2. 94)
(2. 95)
The peak values of the fundamental harmonics and of the stator magnetic flux
density can be calculated as coefficients for the fundamental harmonic of Fourier series.
In the case of a LSPMSM with a V-type magnetic circuit structure we can apply the same
analytical formulation as for inset-type PM motor:
(2. 96)
(2. 97)
(2. 98)
Where is the depth of the slot for the PMs.
It should be noticed that there is an optimal value of equals to 140 degrees
[HUANG_13] that provides sufficient asynchronous torque while delivering high
efficiency at synchronous rotation.
Comparison of analytical model with results of commercial software and FE simulations
in the case of LSPMSM 7.5kW and 18.5kW with V-type magnetic circuit
LSPMSM 7.5kW with V-type magnetic circuit
Fig.2. 26 reactances given by ANSYS RMxprt for LSPMSM 7.5kW with V-type magnetic
circuit
80
Parameter
Air gap, mm lm, mm hm, mm Xad, Ohm Xaq, Ohm
Analytical Model 0.7 32.2*2 3 8.4 36,5
ANSYS RMxprt 0.7 32.2*2 3 7,5 36.3
ANSYS Maxwell 0.7 32.2*2 3 7.2 30.2
LSPMSM 18.5kW with V-type magnetic circuit
Fig.2. 27 Mean value of reactances given by ANSYS Maxwell for LSPMSM 7.5kW with Vtype magnetic circuit
Table 2. 7 Comparison of the results. LSPMSM 7.5kW with series magnetic circuit structure
Fig.2. 28 reactances given by ANSYS RMxprt for LSPMSM 18.5kW with series magnetic
circuit structure
Xad
Xaq
81
Parameter
Air gap, mm lm, mm hm, mm Xad, Ohm Xaq, Ohm
Analytical Model 0.5 38 3 6.3 28.2
ANSYS RMxprt 0.5 38 3 5.7 29.9
ANSYS Maxwell 0.5 38 3 5.5 27.5
As it is demonstrated above the analytical models developed for three LSPMSM
topologies show a rather good agreement proving the validity of the parameter
determination procedures. In the case of two power ratings: 7.5kW and 18.5kW
variations between analytically calculated and FE-determined inductances are limited
less than 18%. The model deviation can be explained by the fact that the developed
analytical models the same as ANSYS RMxprt don’t take into account the rotor
saturation and deal only with the first harmonics. Though the error is present, such
accuracy is considered satisfactory enough and the models can be implemented into the
optimization procedure when the medium power LSPMSM is treated.
2.3. Optimization of LSPMSM
The process of design is a complex procedure encompassing a set of factors affecting a
final result. For example, the experience of a designer, the technical means, the methods
to be used have a considerable impact on the quality of the final product. Therefore, a
range of efforts must be allocated for the formalization and synthesis of the existed
practices. For that reason optimization is viewed as a mean of aiding designer to make
the decisions. In these conditions, finding an appropriate way of resolving an
optimization problem is a first challenge being faced by engineers.
Fig.2. 29 Mean value of reactances given by ANSYS Maxwell for LSPMSM 18.5kW with
series magnetic circuit structure
Table 2. 8 Comparison of the results. LSPMSM 18.5kW with series magnetic circuit structure
Xaq
Xad
82
Due to manufacturing constraints all of the components of design vector X such as the
PM’s dimensions and the air gap are discontinuous and standardized. The discrete
optimization problem is the one for which at least one variable has a discrete finite set.
One of the objectives of this work consists in the research of mathematical methods for
the class of discrete optimization problems concerning techno-economic criteria and
constraints.
2.3.1. Organization of the design process
There are multiple ways of resolving the industrial optimization problems. Often, the
set of candidate (already existing) configurations could be used as a support set in the
optimization processes. Indeed, the presence of the range of standard configurations is
a widely-used measure to increase the customization and decrease the total time of
design [ERENS_96], [GOMEZ_08].
Fig.2.30 illustrates four different ways of the design process organization. The methods
(a) and (b) have the same core idea which consists in resolving a problem by optimizing
each standard configuration separately. In the first case, the procedure of optimization
is sequential, whereas in the second is carried out concurrently. Case (c) is different
from (a), (b) in the view that the whole standard range of configurations is used in the
optimization loop. One example of such workflow is presented in the work [LAN_04].
Case (d) is a common situation when the knowledge base does not contain any
configurations with the demanded performance parameters: an inverse problem is
resolved without any supporting configurations. In this work, the concept (a) is
presumed to be used.
2.3.2. Optimization Problem
The following mathematical optimization problem statement is used throughout this
thesis:
(2. 99)
Here the vector is the design vector, the functions
are the objective functions, the functions are
the inequality and equality constraints. In the following subsections, each item from this
definition is considered in more details.
1.3.1.1 Objective functions
Generally, for the problem of techno-economic optimization, two objective functions are
taken into account: total costs (in the given case the magnet volume that is the
dominant of the motor cost) and losses (1 –efficiency) of LSPMSM. Due to the
peculiarity of the thesis, there is one of the more objective function considering the
braking torque.
83
1.3.1.2 Parameters
Theoretically, all parameters of problem stay constant during the entire optimization
loop as they must be defined in the customer requirement form before the actual
optimization process is started.
1. Nominal power (mechanical power shaft delivered):
2. Pole number:
3. Rated torque:
4. Voltage LL:
5. Load inertia:
6. Ambient temperature:
7. Motor axis height :
1.3.1.3 Constraint functions
Generally, for the majority of engineering problems, the entire list of constraints can be
separated on two groups: explicit and implicit constraints. The first one unifies all the
constraints expressed in the requirement specification while the second consists from
the list of domain specific constraints. In this section, both classes are considered for the
optimization problem of LSPMSM.
Fig.2. 30 Multiple possible workflows of the design process [SAMARKANOV_12]
84
Explicit constraints
These classes of constraints are closely related to the operational characteristics for the
demanded motor. In the problem of optimal design of LSPMSM the list of explicit
constraints are defined in the requirement specification. For example:
1. The motor should be able to start under 0.9*Un
2. Starting current ratio:
3. Power factor:
4. Maximal temperature of isolation in the stator slot:
5. Overload conditions:
6. Load torque: linearly from zero to nominal speed, starting from 0.8 to
7. EMF at no-load
Implicit constraints
Often, they are closely related to the manufacturing conditions in which the demanded
mechanism is produced. As a general rule, customers are not acknowledged about this
type of constraints. For the considered problem, the list of implicit constraints is defined
in the following way:
1. , where is the braking torque, is the cage
torque
2. Ratio of the number of poles and number of circuits in parallel:
3. Ratio of stator coil pitch to number of stator slots:
4. , where is the number of stator slots
5.
6. , where is the stator slot width, and is the stator slot pitch
7. , where is the stator slot width, and is the rotor slot pitch
To sum up, the problem of optimal design of LSPMSM has 14 constraints, 7 for which
are explicitly defined by the customer and others are internal, proper for the
manufacturing process.
1.3.1.4 Variables
The design vector identifies the set of design variables. The design
variables can be freely varied by the designer to define a designed object
[SAMARKANOV_12]. The design vector of the studied problem is composed of 3 or 4
variables depending on the LSPMSM rotor topology: – length of the air gap; –
magnet height; – magnet width, -position of magnets over the motor shaft (see fig.
85
Fig.2. 31). According to analytical models developed below, these parameters directly
influence computation of the d- and q-axis reactances Xd and Xq and the back-EMF.
2.3.3. Optimization Technique
The model used in optimization process is analytical and the optimization method
applied for the considering problem (2. 99) is the exhaustive enumeration (EE)
[SAMARKANOV_12], [VENKAT_10]. It is an exact method with evaluations of all possible
combinations of the PM dimensions and the air gap length. The method doesn’t have
any heuristic rules at all.
Because of the presence of several objective functions, the aim of multi-objective
evolutionary algorithms is to find compromise solutions rather than a single optimal
point as in scalar optimization problems. These tradeoff solutions are usually called
Pareto optimal solutions. The EE was applied in order to obtain a genuine Pareto-Front.
The method is not pretended to be the best one in terms of total time of calculation, but
on the other hand, it gives reliable results [ELISTRATOVA_13].
Conflicting in their nature, objective functions make a designer to undertake the optimal
choice in presence of trade-offs. Pareto-front is the set of optimal configurations and
for any configuration belonging to the following statement can be used (see eq. (2.
100)).
(2. 100)
2.3.4. Functionality of software DEMO-LSPM
Thanks to analytical models developed for the three LSPMSM configurations studied in
this thesis, the problem (2. 99) could be treated with use of the design-specialized
software DEMO-LSPM developed as part of this thesis. The developed software provides
the pre-designing of the three LSPMSM rotor topologies (see Fig.2. 31) and for power
range 1.5-32 kW.
Fig.2. 31 Variable parameters related to configurations under study
86
DEMO-LSPM is a tool that helps a designer to make a right choice thought the procedure
of LSPMSM design taking into account the given datasheet and specification (see
Appendix C). The software is implemented on Matlab with a possibility to pass directly
to ANSYS Maxwell and use it as a graphical interface and at the same time as a tool of
FE analyzing and, thus, an instrument of validation.
Generally, DEMO-LSPM functionality can be described by the three main stages:
1. Treatment of the customer specification form;
2. Identification of a set of most promising (candidate) configurations in the form
of Pareto frontier for the submitted customer specification form;
3. Medialization of the chosen configurations on ANSYS RMxprt/Maxwell.
As a result, the application returns a set of optimized configurations and the technoeconomical parameters for each solution.
2.3.5. Results of optimization technique in the form of Pareto frontier for two
variants of rotor cage
Thanks to the use of DEMO-LSPM three preselected configurations (Fig.2. 31) of
LSPMSM 7.5kW were analyzed and all the combinations belonging to the feasible
domain and defined by optimization constraints were plotted in the form of Pareto
frontier. In Fig.2. 32 the feasible set of solutions using the EE in the form of Pareto
frontier is presented.
Fig.2. 32 LSPMSM 7.5kW with classical rotor cage. Pareto frontier of efficiency versus magnet
section area: feasible configurations for radial magnetic circuit structure - blue empty
points, Pareto frontier of optimal solutions for radial magnetic circuit structure – green
filled points, feasible configurations for series magnetic circuit structure - yellow
empty points, Pareto frontier of optimal solutions for series magnetic circuit structure
– purple filled points, feasible configurations for V-type magnetic circuit structure –
black empty points, Pareto frontier of optimal solutions for V-type magnetic circuit
structure – red filled points
2
87
After analyzing Fig.2. 32 it may be concluded than the higher is the magnet surface area
the less are the losses (1 –efficiency). Besides, it can be noticed that the V-type magnetic
circuit structure is more performant than the two first LSPMSM configurations: radial
magnetic circuit structure and series magnetic circuit structure.
On the other hand as may be seen on Fig.2. 33 the V-type configuration suffers from high
braking torque and hence the startup of this motor will be rather long and difficult or
even impossible.
2.3.6. Advantage of rotor bar reduction
As mentioned previously during the start the LSPMSM behaves as the IM. Fig.2. 32
indicates that there is a proportional relationship between the PM volume and motor
efficiency and, hence, it can be interesting to keep more space under PMs. Previous
studies on IM theory [BENECKE_11] shows that in the case of startup, e.g. at low
rotational speed of rotor which is connected with increased values of rotor current
frequency, the current in the rotor bars is cumulatively displaced in radial direction to
the air gap like it can be seen in Fig.2. 34.
Fig.2. 33 LSPMSM 7.5kW with classical rotor cage. Pareto frontier of efficiency versus braking
torque: feasible configurations for radial magnetic circuit structure - blue empty
points, Pareto frontier of optimal solutions for radial magnetic circuit structure – green
filled points, feasible configurations for series magnetic circuit structure - yellow
empty points, Pareto frontier of optimal solutions for series magnetic circuit structure
– purple filled points, feasible configurations for V-type magnetic circuit structure –
black empty points, Pareto frontier of optimal solutions for V-type magnetic circuit
structure – red filled points
88
Under nominal operating conditions the speed of the LSPMSM rotor equals the speed of
the stator field and so the current in the rotor bars and, hence, the rotor losses are zero
and the rotor cage is usless. This phenomenon allows reducing of rotor bar section (see
Fig.2. 35) and obtaining more space for PMs.
The finite element modeling of LSPMSM for two rotor cage types proves the hypothesis
made above and demonstrates almost the same evolution of current in one rotor bar
during first 100ms of motor startup. It can be noticed that in both cases rotor currents
reach their maximal value and at time t=9ms
(Fig.2. 36, Fig.2. 37).
Fig.2. 34 Principle of leakage field distribution in slots of a bar-wound rotor, with s — slip, n —
rotational speed, f — electrical frequency (index: 1 — stator, 2 — rotor), - rotor
current, Φσ — leakage flux [BENECKE_11]
Fig.2. 35 Example of rotor bar reduction
89
a) b)
a) b)
After reducing the rotor bars (Fig.2. 35, Fig.2. 37) the Pareto frontiers for three studied
configurations of LSPMSM 7.5kW (Fig.2. 31) has been plotted. One can notice that they
comply with the same trend as demonstrated in Fig.2. 32. At the same time, in terms of
efficiency the rotor bars reducing made the LSPMSM with V-type and series magnetic
circuit structures more beneficial in comparison with the LSPMSM with radial magnetic
circuit structure.
In addition, the reducing of rotor bars significantly improves motor efficiency
increasing it in average by 0.1 p.u (see Fig.2. 38). Besides, the space extending under the
rotor cage permits to enlarge the number of possible combinations to vary and, thus,
multiplying feasible set of solutions to reduce the braking torque created by permanent
magnets (Fig.2. 39).
Fig.2. 36 Distribution of current in classical rotor cage: (a) Current density in rotor bars at
t=9ms, (b) evolution of current in one rotor bar at t=9ms
Fig.2. 37 Distribution of current in classical rotor cage: (a) Current density in rotor bars at
t=9ms, (b) evolution of current in one rotor bar at t=9ms
90
Fig.2. 38 LSPMSM 7.5kW with reduced rotor cage. Pareto frontier of efficiency versus magnet
section area: feasible configurations for radial magnetic circuit structure - blue empty
points, Pareto frontier of optimal solutions for radial magnetic circuit structure – green
filled points, feasible configurations for series magnetic circuit structure - yellow
empty points, Pareto frontier of optimal solutions for series magnetic circuit structure
– purple filled points, feasible configurations for V-type magnetic circuit structure –
black empty points, Pareto frontier of optimal solutions for V-type magnetic circuit
structure – red filled points
Fig.2. 39 LSPMSM 7.5kW with reduced rotor cage. Pareto frontier of efficiency versus braking
torque: feasible configurations for radial magnetic circuit structure - blue empty
points, Pareto frontier of optimal solutions for radial magnetic circuit structure – green
filled points, feasible configurations for series magnetic circuit structure - yellow
empty points, Pareto frontier of optimal solutions for series magnetic circuit structure
– purple filled points, feasible configurations for V-type magnetic circuit structure –
black empty points, Pareto frontier of optimal solutions for V-type magnetic circuit
structure – red filled points
91
2.4. Conclusion
In Chapter 2 the analytical models for each of the three studied LSPMSM rotor
configurations are elaborated. Subsequently, the validation of every analytical model
with aid of numerical softwares ANSYS RMxprt and ANSYS Maxwell has been realized.
After that a general definition of the optimization problem is given and a study of the
constraints and objective functions are provided. Based on analytical models and
formulated optimization problem, the design-specialized software DEMO-LSPM was
developed and tested. The developed software provides the pre-designing of the three
LSPMSM rotor topologies and for power range 1.5-32 kW.
Finally, some results in the form of Pareto frontiers for two rotor cage variants, classical
and reduced, were introduced and it was proved that the rotor bars reducing made the
LSPMSM with V-type and series magnetic circuit structures more efficient in
comparison with the LSPMSM with radial magnetic circuit structure.
In Chapter 3 the results provided by DEMO-LSPM will be used for realization of
LSPMSMs prototypes.
92
2.5. References
[BENECKE_11] M. Benecke , R. Doebbelin , G. Griepentrog , and A. Lindemann, “Skin
Effect in Squirrel Cage Rotor Bars and Its Consideration in Simulation
of Non-steady-state Operation of Induction Machines”, Progress In
Electromagnetics Research Symposium Proceedings, Marrakesh,
Morocco, Mar. 20–23, 2011
[BOLDEA_10] I. Boldea, Electric machines, 1st ed. USA: CRC Press, 2010
[CARPENTER_12] D. Carpenter, S. Deleanu, "Parameter determination of synchrnous
machine with radial permanent magnets using analytical calculation
and standstill tests," Electrical & Computer Engineering (CCECE), 2012
25th IEEE Canadian Conference, vol., no., pp.1,6, April 29 2012-May 2
2012
[DING_11] T. Ding «Etude et optimisation de macines a aimants permanents a
demarrage direct sur le reseau», Dissertation. L'Université Henri
Poincaré, Nanci I, France, 2011
[ELISTRATOVA_13] V. Elistratova, M. Hecquet, P. Brochet, D. Vizireanu, M, Dessoude,
"Analytical approach for optimal design of a line-start internal
permanent magnet synchronous motor," Power Electronics and
Applications (EPE), 2013 15th European Conference on , vol., no.,
pp.1,7, 2-6 Sept. 2013
[ERENS_96] F.J. Erens, The synthesis of variety: developing product families, 1996
[FODOREAN_09] D. Fordorean, A. Miraoui, “Dimensionnement rapide des machines
synchrones à aimants permanents (MSAP)”, Techniques de l’ingénieur,
Nov. 10, 2009
[GIERAS_10] J.F. Gieras, «Permanent Magnet Motor Technology. Design and
Application » CRC Press; Third Edition, 2010
[GOMEZ_08] A. Gomez, Optimisation technico-économique multi objectif de
systèmes de conversion d'énergie: cogénération électricité-hydrogène
à partir d'un réacteur nucléaire de IVème génération, 2008
[HADEF_11] M. Hadef, M. R. Mekideche, A. Djerdir, and A. Miraoui, “An inverse
problem approach for parameter estimation of interior permanent
magnet synchronous motors,” Progress in Electromagnetics Research
B, vol. 31, no. 15, 2011
[HEIKKILA_02] T. Heikkila «Permanent magnet synchronous motor for industrial
inverter application. Analysis and design», Dissertation. Acta
Universitatis Lappeenrantaensis, Finland, 2002
[HENDERSHOT_10] J.R. Hendershot & T.J.E. Miller, «Design of Brushless Permanent Magnet
Machines», Motor Design Books LLC; Second Edition, 2010
[HUANG_13] P-W. Huang; M-C. Tsai, "Investigation of V-Shaped Line Start
Permanent Magnet Motors Based on Reactance Effect," Magnetics, IEEE
Transactions on, vol.49, no.5, pp.2311,2314, May 2013
[HUANG_08] P-W. Hung, S-H. Mao, and M C Tsai, "Investigation of line start
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and surface-magnet rotors," Electrical Machines and Systems, pp. 2888
- 2893, October 2008
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[HWANG_02] Hwang, C. C., S. M. Chang, C. T. Pan, and T. Y. Chang, “Estimation of
parameters of interior permanent magnet synchronous motors,”
Journal of Magnetism and Magnetic Materials, Vol. 239, 600–603, 2002
[JANNOT_09] X. Jannot, J.-C. Vannier, J. Saint-Michel, M. Gabsi, C. Marchand and D.
Sadarnac «An analytical model for interior permanent-magnet
synchronous machine with circumferential magnetization design»,
IEEE, 2009
[JANNOT_10] X. Jannot , «Modélisation et Optimisation d’un ensemble convertisseurmachine. Application aux systèmes d’entrainement à haute vitesse»,
Electric power. Supélec, 2010. French
[KOPILOV_86] I. Kopilov, «Electric machines», Energoatomizdat, Moscow, 1986
[LAN_04] Lan, H., Ding, Y., Hong, J., Huang, H. & Lu, B. (2004). A web-based
manufacturing service system for rapid product development.
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[MAXWELL_16] Electric Machines Design Toolkit. Customized Solutions, ANSYS, Inc.,
January 12, 2015
[MODEER_07] T. Modeer «Modeling and Testing of Line Start Permanent Magnet
Motors» Dissertation. School of Electrical Engineering, KTH, Sweden
2007
[MILLER_84] T.J.E. Miller «Synchronization Line-Start Permanent Magnet AC
Motors», IEEE Trans. On PAS, PAS-103, No.7, July 1984, pp.1822,1828
[NEE_00] H-P. Nee, L. Lefevre, P. Thelin, J. Soulard « Determination of d and q
reactances of permanent magnet synchronous motors without
measurements of the rotor position, » IEEE Trans. on Industry
Applications, Vol. 36, No. 5, 1330-1335, Sep.-Oct. 2000
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United Kingdom: John Wiley &Sons, Ltd, 2008
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[SORGDRAGER_14] A.J Sorgdrager, A.J Grobler, R-J Wang « Design procedure of a line-start
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permanent magnet synchronous motor,» In Proc. ICEM. 2002, Brugge,
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Synchronous Motors. Analysis And Design», EDPE 2009, October 12-14,
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95
Prototyping and experimental results
3.1. Introduction
The primary goal of the third chapter is the specification and manufacturing of two
LSPMSM prototypes providing verification of the analytical and numerical models
described in the second chapter.
The first part of the chapter concerns sizing of two LSPMSM prototypes, specification
and prediction of their performances at steady-state and during the motor start and
synchronization.
In the second part of the chapter, the experimental validation of asynchronous and
synchronous parts in the LSPMSM design methodology is presented. In order to validate
the asynchronous part of the LSPMSM design methodology, a commercial 7.5 kW 4-pole
squirrel cage induction motor has been purchased.
The second part of the chapter is also dedicated to experimental tests performed on the
designed prototypes and on the purchased commercial induction motor. The tests must
validate the developed FE models and make a techno-economic comparison between
the three studied motors. The study of thermal behavior of the prototypes is also
presented in this part and the results are compared with the thermal behavior of the
commercial IM.
3.2. LSPMSM prototyping
Previously, it was discussed the economic interest to proceed at the LSPMSM designing
from the already existing IM of the same power rating. To follow this strategy it was
decided to buy several commercial 7.5kW 4-pole IM (Fig.3. 24b) and rebuilt them for
this purpose. Due to limited available funds it has been decided to realize only two
prototypes possessing better performances.
In Chapter 3 three motor configurations (Fig.3. 1) were analyzed with the aid of the
developed pre-design software DEMO-LSPM (see Chapter 2, Appendix C) and
compared. On the basis of this comparison the two topologies of higher performances
are chosen. They are motor with series-type magnetic circuit structure rotor and motor
with V-type magnetic circuit structure rotor (see Fig.3. 1a, b).
96
a) b) c)
In order to build the selected prototypes, a parametric study taking into account the
manufacturing constraints has to be carried out. The study is led by the package
Optimetrics of ANSYS Maxwell_RMxprt.
As soon as the prototypes are specified it’s necessary to conduct the dynamic analysis in
order to be sure that the prototype of chosen configuration is capable to start and to
keep its performances under the most difficult conditions of the design specification.
3.3.1. Sizing of two LSPMSM rotors
In this paragraph the strategy of the rotor topology selection is demonstrated. For each
configuration the design vector consists of 3 or 4 variable parameters.
Mechanical constraints
In addition to specification requirements (Appendix A), there is also a set of mechanical
constraints imposed by the manufacturer of the prototypes. They are:
1. Minimal distance between two rotor bars is equal to the widest part of one
tooth, Rib=5mm
2. The distance between the slot of a PM and a rotor bar must be higher than
1.4 mm that fixes the diameter D1 =110 mm
3. Magnet thickness MT vary from 5mm to 6 mm
4. Minimal and maximal distances between the axis and the position of PM is 28
mm and 45mm relatively, and so the parameter O2 may vary from 7mm to
16mm
5. Magnet width MW varies from 44mm to 58mm
6. The rotor cage is made of copper instead of aluminum.
Fig.3. 1 LSPMSMs rotor configurations studied in Chapter 3: (a) Rotor with radial magnet
configuration, (b) Rotor with series magnetic circuit structure, (c) Rotor with V-type magnetic
circuit structure
97
Electrical constraints
The most important conditions sustaining the successfully startup and overcharged
capacity during its steady-state are the appropriate value of back electromotive force
(70% in the given case [SOULARD_02], [STOIA_09]) and the ratio (see
Appendix A).
Fig.3. 2 Rotor with series magnetic circuit structure under technical constraints imposed by
manufacturer
Fig.3. 3 Rotor with V-type magnetic circuit structure under technical constraints imposed by
manufacturer
98
A short air gap length maximizes the flux for a given thickness of PMs. On the other
hand, it requires more accurate mechanical tolerances and increases cogging torque
[HENDERSHOT_10]. Besides, a low air gap augments the braking torque and provokes
the magnet demagnetization incited by stator currents during the startup. After finding
the compromise between these considerations the air gap length is
[FODOREAN_09], [HEIKKILA_02], [STOIA_09].
3.3.2. Search of the optimal rotor configuration for the LSPMSM with V-type
magnetic circuit structure
Varying 3 design variables MT, MW and O2 being the arguments for functions of backEMF and maximal output power the following dependences are plotted (see Fig.3. 4).
From Fig.3. 4 one can see that the angle opening O2 has a very little influence on the
back-EMF and has a slight one on the maximal output power and efficiency. The
parameters which affect and the most are magnet thickness MT and magnet
width MW. According to Fig.3. 4, the LSPMSM rotor which satisfies the required values of
back-EMF and maximal output power has the following dimensions: MT=6mm,
MW=51mm, O2=10mm, optimal volume = 52000mm3.
With regard to efficiency, Fig.3. 5 shows that for all the combinations tested above the
maximal values of efficiency are located in the rather narrow interval
[0.9425÷0.947]p.u. For the configuration MT=6mm, MW=51mm, O2=10mm, optimal
volume = 52000mm3 the maximal value of efficiency is about 0.9455 p.u, that satisfys
the requirements of the specification (see Appendix A)
Fig.3. 4 Maximal output power and back-EMF in base units vs. magnet volume (mm3) at
U=0.9 Unom
99
The selected configuration has been tested with aide of FE modelling. It is found that
between the model analyzed by ANSYS Maxwell_RMxprt and FE model there is an error
of 9% as it follows from eq. (3. 1).
(a) (b)
(3. 1)
Taking into account the error and considering the FE simulation more precise, the
dimensions of new rotor configuration are: MT=6mm, MW=45mm, O2=10mm, volume
Fig.3. 5 Maximal efficiency in base units vs. magnet volume (mm3) at U=0.9∙Unom
Fig.3. 6 Comparison of simulation results: (a) RMS value of fundamental phase EMF according to
ANSYS Maxwell_RMxprt, (b) Amplitude values of harmonic components of phase EMF according
to FE simulation
O2=7
O2=7
O2=7
MT=5.5mm MT=6mm
MT=5mm
mm
O2=16
O2=16
O2=16
m1
100
= 45900mm3. Dynamic analysis of the designed LSPMSM with V-type magnetic circuit
structure
3.3.3. Dynamic analysis of the designed LSPMSM with V-type magnetic circuit
structure
In order to be sure that the motor of chosen configuration is capable to start, its finite
element model has been tested under the most difficult conditions: supply voltage
=90% ,the load torque evolves linearly from zero to nominal speed, starting
from 0.8 to , moment of load inertia 0.15 (Appendix A). In
accordance with IEC 60034-1 the capability of 50% overload at U=90% Unom for 15s in
steady-state. The starting characteristics are given in Fig.3. 8 and Fig.3. 9.
Fig.3. 7 FE model of LSPMSM with V-type magnetic circuit structure and PM surface 6x45 mm²
Fig.3. 8 Speed during the synchronization of LSPMSM with V-type magnetic circuit structure and
PM surface 6x45 mm²
101
The provided analysis of LSPMSM dynamic behavior proves the capability of the
prototype with V-type magnetic circuit structure to start-up under the most difficult
conditions of the designed specification and to pass an overload test.
3.3.4. Demagnetization of the permanent magnets
The FE model is tested under nominal voltage and nominal load. Fig.3. 11 and Fig.3. 12
show the evolution of average and minimal values of flux density and average and
maximal values of magnetic field strength on the PM surfaces during starting and
synchronization using the real characteristics of SmCo S30H PMs furnished by the
manufacturing company (see Appendix D).
Fig.3. 9 Torque during the synchronization of LSPMSM with V-type magnetic circuit structure
and PM surface 6x45 mm²
Fig.3. 10 Flux density distribution inside the PMs at time =0.266s
Zone of minimal flux density
102
In order to obtain the average value of flux density or magnetic field strength, the
surface integral over those scalar fields is found and divided by permanent magnet
surface area.
As follows from the figures shown above, even during the starting when the highest
winding current giving the largest flux opposing the magnet [DING_11], the minimal and
average values of flux density are 0.182T and 0.497T respectively. It means that even in
the worst case of the maximal electromagnetic field applied to the SmCo S30H PMs in
Fig.3. 11 Average values of flux density and magnetic field strength on the PM surfaces during
starting and synchronization
Fig.3. 12 Minimal values of flux density and maximal values of magnetic field strength on the PM
surfaces during starting and synchronization
103
the prototype the flux density doesn’t shift to the point of irreversible demagnetization
of BH curve (see Appendix D). When the synchronization reverts to the steady-state the
minimal and average values of flux density grow to 0.65T and 0.866T. Thus, the analysis
of FE simulation indicates that even at start the permanent magnets are sufficiently
robust in order to withstand the demagnetizing stator current.
3.3.5. Search of the optimal rotor configuration for the LSPMSM with series
magnetic circuit structure
The same approach has been applied to the search of optimal configuration in the case
of LSPMSM 7.5kW with series magnetic circuit structure. As can be seen from Fig.3. 13,
the LSPMSM rotor satisfies the required values of back-EMF and maximal output power
when having the following dimensions: MT=5mm, MW=51mm, optimal volume =
42500mm3.
Fig.3. 14 shows that for the possible combinations tested above maximal values of
efficiency are located in the interval [0.946÷0.953]p.u. For the configuration MT=5mm,
MW=51mm the maximal value of efficiency is about 0.9455 p.u, that satisfies the
requirements of the specification (see Appendix A).
Fig.3. 13 Maximal output power and back-EMF in base units vs. magnet volume (mm3) at
U=0.9 Unom
104
The selected configuration has been tested with aide of FE modelling and it is found that
between the model analyzed by ANSYS Maxwell_RMxprt and FE model there is an error
of 9% as it follows from eq. (3. 1).
(a) (b)
(3. 2)
As a result, the rotor with the following dimensions is chosen: MT=5mm, MW=46mm,
volume = 39100mm3.
Fig.3. 14 Maximal efficiency in base units vs. magnet volume (mm3) at U=0.9∙Unom
Fig.3. 15 Comparison of simulation results: (a) RMS value of fundamental phase EMF according
to ANSYS Maxwell_RMxprt, (b) Amplitude values of harmonic components of phase
EMF according to FE simulation
m1
MT=5.5mm
MT=6.0mm
MT=5.0mm
MT=4.5mm
MT=4.0mm
105
3.3.6. Dynamic analysis of the designed LSPMSM with series magnetic circuit
structure
The same validation procedure is applied to the LSPMSM with series magnetic circuit
structure in order to prove the capability of chosen configuration to start, its finite
element model (Fig.3. 16) has been tested under the most unfavorable conditions:
supply voltage =90% ,the load torque evolves linearly from zero to nominal
speed, starting from 0.8 to , moment of load inertia 0.15
(Appendix A). In accordance with IEC 60034-1 the capability of 50% overload at
=90% for 15s in steady-state. The starting characteristics are given in Fig.3. 17
and Fig.3. 18.
Fig.3. 16 FE model of LSPMSM with series magnetic circuit structure and PM surface 5x46 mm²
Fig.3. 17 Speed during the synchronization of LSPMSM with series magnetic circuit structure
and PM surface 5x46 mm²
106
The provided dynamic analysis of LSPMSM with series magnetic circuit structure
proves that the prototype is able to start-up under the most difficult conditions of the
imposed designed specification and to pass an overload test.
3.3.7. Demagnetization of the permanent magnets
Similarly to the study presented in paragraph 3.3.4, the analyzing of demagnetization of
LSPMSM with series magnetic circuit structure is based on the finite element
computation.
Fig.3. 18 Torque during the synchronization of LSPMSM with series magnetic circuit structure
and PM surface 6x45 mm²
Fig.3. 19 Average values of flux density and magnetic field strength on the PM surfaces during
starting and synchronization
107
As can be seen from Fig.3. 19 and Fig.3. 20, the minimal and average values of flux density
are 0.291T and 0.406T respectively and at steady-state 0.575T and 0.826T. The FE
model proves that even whan the maximal electromagnetic field is applied to the SmCo
S30H PMs the flux density doesn’t shift to the point of irreversible demagnetization of
BH curve (see Appendix D). The FE analysis shows that normally the start of the
LSPMSM doesn’t cause the PMs demagnetization.
3.3.8. Realization of the prototypes
As soon as the rotor geometry for the each of LSPMSMs was specified it was sent to
Novelté Système Company in its design office in Belfort, France for further realization.
As it was mentioned above, the stator and the motor frame of the prototypes are those
that belong to the purchased industrial 7.5kW 4-pole IMs. Fig.3. 21 provides a partially
dissembled view of two commercial IMs dismantling for the following prototyping.
Thus, there are only two principal geometry modifications: insertion of permanent
magnets into rotor core and modification (reduction) of rotor bars.
Fig.3. 20 Minimal values of flux density and maximal values of magnetic field strength on the PM
surfaces during starting and synchronization
108
Fig.3. 22 shows two shapes of rotor sheets used in the LSPMSM prototypes. Fig.3. 23
presents on example of the prototype with V-type magnetic circuit structure rotor the
process of PMs manual embedding into the rotor core slots and their retention with
help of special adhesive.
(a) (b)
Fig.3. 21 Two commercial IMs dismantling for the following prototyping
Fig.3. 22 Rotor sheets of two designed LSPMSM prototypes: (a) Rotor with series magnetic
circuit structure, (b) Rotor with V-type magnetic circuit structure
109
a) b)
3.3. Experimental results
3.3.1. Test strategy
The primary goal of the experiments is the verification of the analytical and FE models
of asynchronous and synchronous parts in LSPMSM design. In the first part, verification
of analytical and numerical models for asynchronous design in LSPMSM design
presented in Chapter 2 and Appendix B is made using the set of classical laboratory
tests (DC resistance test, blocked rotor test, no-load test).
In the second part concerning the synchronous parts in LSPMSM design, the test at noload is aimed at the estimating and comparing the fluxes produced by the PMs in the
realized LSPMSM prototypes with results of FE modeling. The test has to exclude the
possibility of the PMs damage and demagnetization during the motor manufacturing.
Next, the starting operation and steady state load tests will be realized in order to in
verify the starting capability of the designed prototype and the important parameters of
interest such as the electromagnetic torque, efficiency and power factor.
3.3.2. Validation of asynchronous part in LSPMSM design
In Chapter 2 an analytical approach for analyzing the asynchronous part of LSPMSM
design has been presented and validated using the commercial software ANSYS
Maxwell/RMxprt. In order to confirm the validity of the analytical and numerical
Fig.3. 23 Process of PMs embedding into the LSPMSM rotor core: (a) Filling up of a rotor slot
with special adhesive, (b) embedding of PM into rotor core
110
models, several experiments are carried out on the commercial 7.5 kW 4-pole squirrel
cage induction motor.

Comparison of the analytically designed IM and a commercial IM
Fig.3. 24 and Table 3. 1show the difference in main geometrical parameters and
material consumption of the analytically designed IM and a commercial IM.
(a) (b)
Analytically designed IM 7.5kW Commercial IM 7.5kW
Motor depth, mm 114 170
Outer stator diameter, mm 225 200
Outer rotor diameter, mm 150 125
Air gap, mm 0.35 0.35
Number of stator slots 36 48
Number of rotor slots 28 40
Armature copper weight, kg 4.8 6.1
Armature core steel
Consumption, kg
46 41.3
Fig.3. 24 Geometry comparison: (a) 7.5 kW 4-pole cage analytically designed IM, (b) 7.5 kW 4-
pole cage commercial IM
Table 3. 1 Geometry comparison between the analytically designed IM and the commercial IM
111
As it can be seen from the motor comparison, the designed methodology proposed in
Chapter 3 and Appendix B gives a motor geometry significantly different from the
commercial one. It can be explained by the fact that the commercial motor is designed
by the company with the use of its specific design methodology.
After three classic laboratory tests (DC resistance test, blocked rotor test, no-load test)
[BOYNOV_08], [DING_11], [ECE_09], [MODEER_07], the impedance parameters of the IM
equivalent schema have been determined and compared with those of the equivalent
schema of induction motor (Fig.3. 25) analytically designed in Appendix B.
Analytical model Tests on commercial IM
(a) (b)
The comparison of one-phase equivalent schema schemes represented on Fig.3. 25
shows a close similarity. The only parameter that is really different is the stator
resistance . This fact can be explained by disparity between two IM geometries such
as the motor depth and the number of stator and rotor slots (see ). Besides, there was
no information about the magnetic properties of the rotor and stator electrical
materials, thus information on the BH-curves used for analytical design is provided by a
reference book [KOPILOV_86].
Though, there is a difference in parameters between the analytically dimensioning
model and the real industrial motor, their performances show rather good correlation
(Fig.3. 26). So, the proposed approach may be successfully used when the IM is
designed. In addition, it can be applied for the dimensioning of the LSPMSM stator and
winding and its startup analyzing.
Fig.3. 25 One-phase equivalent schema of 7.5 kW 4-pole cage IM: (a) based on the analytical
model, (b) based on the experimental tests realized on a commercial IM
112
(a) (b)
Analytically designed
IM
Commercial IM |Divergence|, %
Starting torque, Nm
84.5 110 23.2
Nominal speed, rpm
1446 1470 1.6
Nominal current, A
15.5 14.9 4.0
Nominal efficiency, p.u
0.85 0.89 4.5
cos ( ), p.u
0.830 0.835 4.2
Average temperature rise
in stator winding, K 67.2 69.3 3.0
Separation of losses in three phase induction motor at no-load test
From IM theory the no load losses are the constant losses which include core loss ,
the Copper losses result from Joule heating and friction and windage loss
resulting in so-called mechanical loss as shown in eq. (3. 3)Erreur ! Source du
renvoi introuvable. [BOYNOV_08], [KOPILOV_86]. The separation between the two
losses can be carried out by the no-load test conducted from variable voltage at rated
frequency. When the voltage is decreased below the rated value, the core loss reduces
as square of voltage with the mechanical loss remaining constant (Fig.3. 27).
Fig.3. 26 Comparison of performance characteristics of the 7.5kW 4-pole IM (blue line –
numerical model, red line – analytical model, green line – tested commercial motor):
(a) Torque versus speed, (b) Efficiency versus speed
Table 3. 2 Nominal regime: Comparison between the analytically designed induction motor and
the commercial induction motor
113
(3. 3)
As it can bee seen from Fig.3. 27 the mechanical loss =36.4 W. Proceeding from the
fact that the stator of the designed LSPMSM protoypes is identical to this of the LeroySomer IM, the value of mechanical loss may be kept and reused in all the following
computations concering these prototypes.
3.3.3. Validation of synchronous part in LSPMSM design
Prototypes tested at no-load regime
Fig.3. 28 illustrates the experimental workbench setting to obtain the experimental
results at no-load for the two designed LSPMSM prototypes and one commercial
induction motor 7.5kW [MODEER_07].
Fig.3. 27 Losses versus square of applied voltage
114
The tested prototypes are driven by a DC motor without any load at synchronous speed
1500 rpm. The speed is measured by a speed sensor. The phase EMF is measured by an
oscilloscope (see Fig.3. 28).
LSPMSM with series magnetic circuit structure and permanent magnet
area 46x5 mm2 per pole at no-load
Comparison of two methods (see eqs. (3. 4), (3. 5)) shows that the simulations (Fig.3.
29b, Fig.3. 30a) provide a good agreement with the experimental results (Fig.3. 29a,
Fig.3. 30b). The amplitude of the first and the third harmonics is almost the same.

Fig.3. 28 Experimental workbench
Fig.3. 29 Phase back-EMF comparison: measurement vs 2D FE calculation
LSPMSM
prototype
DC motor
115
0 50 100 150 200 250 300 350 400 450 500
0
50
100
150
200
250
FFT on EMF of signal
Frequency (Hz)
|Y(f)|

(a) (b)
(3. 4)
(3. 5)
LSPMSM with V-type magnetic circuit structure and permanent magnet
area 45-6 mm2 per pole at no-load
Using the same analysis which was applied to the LSPMSM with series magnetic circuit
structure the performance comparison between the FE model and the tested prototype
is realized (see Fig.3. 31 and Fig.3. 32).

Fig.3. 30 FFT on one phase A of back-EMF: (a) Simulation results for 1st and 3rd harmonics,
(b) Experimental results for 1st and 3rd harmonics
Fig.3. 31 Phase back-EMF comparison: measurement vs 2D FE calculation
FF
T
on
E
M
F,
V
FF
T
on
E
M
F,
V
m1
m2
116
0 50 100 150 200 250 300 350 400 450 500
0
50
100
150
200
250 FFT on EMF of signal
Frequency (Hz)
|Y(f)|

(a) (b)
Comparison of two methods shows that the FE model (Fig.3. 32a) provides a good
agreement with the experimental results (Fig.3. 32b). The amplitudes of the first and the
third harmonics are almost the same.
(3. 6)
(3. 7)
Steady-state performances of the two designed prototypes and the commercial induction
motor
Fig.3. 33 and Fig.3. 34 present the steady-state performances of two constructed
prototypes and the commercial IM under different output power and their comparison
with the international norms and the commercial LSPMSM 7.5kW. The experimental
results are summarized in Table 3. 3.
Fig.3. 32 FFT on one phase A of back-EMF: (a) Simulation results for 1st and 3rd harmonics,
(b) Experimental results for 1st and 3rd harmonics
Fig.3. 33 Comparison of three tested motors (blue line – Induction motor, red line – LSPMSM
with series PMs, violet line – LSPMSM with V-type PMs): efficiency vs. input power
FF
T
on
E
M
F,
V
FF
T
on
E
M
F,
V
m1
m2
117

Induction motor LSPMSM with series PM LSPMSM with V-type PM
Poutput,
W
Efficiency,
p.u.
Cos phi,
p.u.
Poutput,
W
Efficiency,
p.u.
Cos phi,
p.u.
Poutput,
W
Efficiency,
p.u.
Cos phi,
p.u.
265,90 0,408 0,12 267,04 0,468 0,115 267,04 0,438 0,12
1259,82 0,759 0,32 1418,12 0,831 0,38 1352,55 0,805 0,39
2603,81 0,855 0,49 2644,70 0,897 0,6 2663,44 0,888 0,65
3702,44 0,882 0,64 3856,43 0,920 0,74 3831,52 0,912 0,775
5042,81 0,891 0,725 5157,60 0,929 0,83 5129,50 0,924 0,86
6012,42 0,897 0,78 6216,07 0,932 0,85 6191,05 0,928 0,88
6986,75 0,896 0,82 6975,92 0,932 0,88 7001,56 0,930 0,903
7850,44 0,875 0,847 8413,55 0,930 0,89 8408,16 0,928 0,905

From the above comparison it can be seen, that efficiency of the designed LSPMSMs is
about 4% higher than that of the commercial induction motor (Fig.3. 33, Table 3. 3) and
1.3% higher than that of commercial LSPMSM 7.5kW [TISON_14]. Besides, under
nominal load the tested LSPMSMs possess significantly higher power factor than that of
the commercial IM: 0.9p.u for the LSPMSM with V-type magnetic circuit structure,
0.88p.u for the LSPMSM with series magnetic circuit structure and 0.82p.u for the
commercial IM (see Table 3. 3). However, the power factor of the commercial LSPMSM
is 2.8% higher than that of the designed prototypes.
As it was mentioned before, the high power factor has a lot of techno-economic benefits,
besides its high value puts less strain on the electricity grid and so reduces its carbon
footprint. Thus, even though the actual price of the designed LSPMSM prototypes is
rather high, they are much more ecologically friendly than the standard IM. Moreover,
according to IEC 60034-30 [IEC600034-30_11] the efficiency level of the tested
Fig.3. 34 Comparison of three tested motors (blue line – Induction motor, red line – LSPMSM with
series PMs, violet line – LSPMSM with V-type PMs): power factor vs. input power
Table 3. 3 Comparison of performance characteristics of the three motors
118
prototypes corresponds to IE4 Super Premium Efficiency Class and so investments in
the LSPMSM prototypes may be already justified in the mid-term perspective.
3.4. Thermal study
In LSPMSMs the temperature of the magnets needs to be kept under control, in order to
avoid demagnetization. According to the imposed specification (Appendix A) the
average stator winding temperature rise shouldn’t overpass 80K (hot spot 90K).
Fig.3. 35 shows thermal test measurements applying to the commercial IM and the
LSPMSM prototype. The measurement of temperature was realized in two motor parts:
in the hottest point of motor frame and the hottest point of the stator winding. Table 3. 4
shows the comparison of experimental measurements with the results of analytical
thermal model presented in Appendix B [MEZANI_04], [KOPILOV_86].
Analytical model Experimental
Measurement |Divergence|, %
Stator winding temperature
rise in LSPMSM, K
37.8 40.8 7.3
Stator winding temperature
rise in IM, K
67.2 69.3 3
From Fig.3. 35 it can be seen that due to the absence of rotor losses the temperature rise
in the winding of the LSPMSM is significantly lower (about 41%) than that of the
commercial induction motor.
Fig.3. 35 Thermal test measurements applying to the commercial IM and the LSPMSM
Table 3. 4 Comparative results of experimental measurements and analytical model
119
The estimate of stator winding temperature rise in the LSPMSM prototype is based on
the thermal analytical model used for IM stator winding temperature rise prediction as
shown in Appendix B. To adapt the analytical model to the LSPMSM prototype the rotor
losses are not taken into account. As can be seen from Fig.3. 35 and Table 3. 4 the
analytical model shows a good agreement with experimental tests and can be used as a
part of multiphysical design model.
3.5. Conclusion
In the third chapter, two LSPMSM prototypes for two rotor structures previously
selected in Chapter 2 (rotor with V-type magnetic circuit structure and rotor with series
magnetic circuit structure) were sized. After that the prototypes were specified and,
according to the elaborated specification, manufactured in the design office of Novelté
Company.
The tests performed on the prototypes in the laboratory of Ecole Centrale de Lille
validated the synchronous part in the LSPMSM design methodology introduced in
Chapter 2 by FE and analytical models. The asynchronous part in the LSPMSM design
was confirmed by experimental measurement with aide of the commercial 7.5 kW 4-
pole squirrel cage induction motor specially purchased for this purpose.
The experimental results proved that a well-designed LSPMSM shows an absolute
superiority over a standard IM in terms of efficiency and power factor and answer the
requirements of such high International Efficiency Class as IE4.
In conclusion, the study of thermal behavior of the prototypes was presented and the
results were compared with the thermal behavior of the commercial IM. The
measurements confirmed that due to the absence of rotor losses the temperature rise of
a LSPMSM is significantly lower than that of the standard induction motor.
120
3.6. References
[BOYNOV_08] K. Boynov, “Efficiency and time-optimal control of fuel cell -
compressor - electrical drive systems”, Thesis, Technische Universiteit
Eindhoven, 2008
[ECE_09] Electrical and Computer Engineering, “Induction Motor Parameter
Measurement”, 2009, http://ece.mst.edu
[DING_11] T. Ding «Etude et optimisation de machines a aimants permanents a
demarrage direct sur le reseau», Dissertation. L'Université Henri
Poincaré, Nanci I, France, 2011
[FODOREAN_09] D. Fordorean, A. Miraoui, “Dimensionnement rapide des machines
synchrones à aimants permanents (MSAP)”, Techniques de l’ingénieur,
Nov. 10, 2009
[GIERAS_10] J.F. Gieras, «Permanent Magnet Motor Technology. Design and
Application » CRC Press; Third Edition, 2010
[HENDERSHOT_10] J.R. Hendershot & T.J.E. Miller, «Design of Brushless Permanent Magnet
Machines», Motor Design Books LLC; Second Edition, 2010
[HEIKKILA_02] T. Heikkila «Permanent magnet synchronous motor for industrial
inverter application. Analysis and design», Dissertation. Acta
Universitatis Lappeenrantaensis, Finland, 2002
[HUANG_13] P-W. Huang; M-C. Tsai, "Investigation of V-Shaped Line Start
Permanent Magnet Motors Based on Reactance Effect," Magnetics, IEEE
Transactions on, vol.49, no.5, pp.2311, 2314, May 2013
[IEC600034-30_11] Ed. 2, Draft, Nov. 2011, WG31/2CD: Rotating Electrical Machines—Part
30: Efficiency Classes of Single-Speed, Three-Phase, Cage-Induction
Motors (IE-Code), IEC Std. 600-34-30, Nov. 2011
[KOPILOV_86] I. Kopilov, «Electric machines», Energoatomizdat, Moscow, 1986
[MEZANI_04] S. Mezani «Modélisation électromagnétique et thermique des moteurs à
induction, en tenant compte des harmoniques d'espace», Dissertation.
L'Institut National Polytechnique de Lorraine, France, 2004
[MODEER_07] T. Modeer «Modeling and Testing of Line Start Permanent Magnet
Motors» Dissertation. School of Electrical Engineering, KTH, Sweden
2007
[SOULARD_02] F. Libert, J. Soulard, and J. Engstrom, «Design of a 4-pole line start
permanent magnet synchronous motor,» In Proc. ICEM. 2002, Brugge,
Belgium
[STOIA_09] D. Stoia, M. Cernat, K. Hameyer, D. Ban «Line-Start Permanent Magnet
Synchronous Motors. Analysis And Design», EDPE 2009, October 12-14,
2009, Dubrovnik, Croatia
[TISON_14] O. Tison «Rapport d'essais d'un moteur WEG synchrone à aimants
permanents à démarrage direct de 7,5 kW», EDF R&D, décembre 2014.
© 2010 ANSYS, Inc. All rights reserved. 2 ANSYS, Inc. Proprietary
Power Supply Inverter Actuator Mechanic Load
Digital Control Analog Control
 Automotive and railway systems, electric drives, home
appliances and other systems consist of a variety of
components. Each component may influence the behavior
of another component.
System Simulation:
Drive System Example
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Electromechanical (EM)
Components and Systems
• Component Analysis
– Look at component alone
– Motors, actuators, coils, ...
– Usually by field simulation or
analytical models
– Distributed parameters –
geometry, materials,
boundaries, sources
• System Analysis
• Look at interactions of components
• Drives, converters, ... composed of
motors, coils, resistors, diodes, ...
• Usually by system/circuit
simulation or analytical models
• Concentrated parameters –
behavioral component models
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Electrical Machine Technology:
Yesterday vs. Today
1980’s DC Machine for Military Aircraft 2004 Toyota Prius IPM Machine
1980 2004
Size in2 68.75 20.78
Weight lb 70 23
Rated Power kW 13 50
Rated Torque Nm 100 400
Smaller!
Lighter!
More Powerful!
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Modern Product Design Issues
To meet todays requirements:
• Include transients
• Previous: Static fields enough
• Latest: Consider eddy and core effects from nonsinusoidal excitations
and motion
• Far more than 50% of all machines produced today are inverter driven
• Include interactions between
• Different physical domains:
• Old: Cool by more steel New: Save steel!
• Different components:
• Old: Leave space between components
• New: Reduce size
• Component and system:
• Old: Leave reserves to account for additional coupling effects
(e.g. Induced Eddy Currents)
• New: Reduce reserves more and more
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Optimetrics/DX
Parametrics, Optimization,
Sensitivity, Statistical,
Tuning
RMxprt
Analytical Machine Design
Electrical Machines –
Design Suite
Maxwell 2D/3D
Electromagnetic Fields
Static, Dynamic (t, f), Motion, Circuits
MultiPhysics
Stresses, Heat, CFD
Simplorer
Multidomain Systems
Circuits, Blocks, States, VHDL-AMS
• State-of-the-Art
Design:
• RMxprt for analytical
machine design or
ECE
• Maxwell 2D/3D for
static or transient
electromagnetic FEA
• Simplorer for circuit
and system analysis
• ANSYS for thermal
and stress analysis
• Optimetrics or DX for
optimization, statistics,
sensitivity, ...
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Electrical Machines –
RMxprt Overview
Analytical design of rotating machines
– Calculate machine performance, make material
and size decisions
– Flexible design and optimization process
– Perform hundreds of "what if" analyses in a
matter of seconds
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Electrical Machines –
RMxprt Overview
Machine types
• Induction machines
• Three-Phase, Single-Phase
• Wound Rotor (new v13.0)
• Synchronous machines
• Line-Start PM, Adjustable Speed PM
• Salient Pole, Non-Salient Pole
• Brush commutated machines
• DC, Permanent Magnet DC
• Universal, Claw-Pole Alternator
• Electronically commutated
machines
• Brushless PM, Switched Reluctance
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RMxprt User Inputs
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Electrical Machines –
RMxprt Typical Results, Report
Performance curve for varying magnet size
TCog(je
)
T(n)
h(n)
I(n)
P(n)
e(je
)
Motor Performance curves of a BLDC
Original Optimized
Optimization of a synchronous generator
with damper
Customized reports possible ...
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Electrical Machines – RMxprt
Maxwell and Simplorer Links
• RMxprt:
– Find optimum initial design of electrical machine
– Quick model generation for subsequent finite element analysis
– Easy model parametrization for Simplorer machine
– Typical geometry, saturation, eddy current effects in system model
?
© 2010 ANSYS, Inc. All rights reserved. 12 ANSYS, Inc. Proprietary
0
0
LPhaseA
LPhaseB
LPhaseC
0.00801603ohm
RA
0.00801603ohm
RB
0.00801603ohm
RC
7.95824e-006H
LA
7.95824e-006H
LB
7.95824e-006H
LC LabelID=VIA LabelID=VIB LabelID=VIC
+ 0V
1V
LabelID=V14
+ 0V
1V
LabelID=V15
+ 0V
1V
LabelID=V16
+ 0V
1V
LabelID=V17
+ 0V
1V
LabelID=V18
+ 0V
1V
LabelID=V19 100ohm R20 100ohm R21 100ohm R22 100ohm R23 100ohm R24 100ohm R25 LabelID=IVc1 LabelID=IVc2 LabelID=IVc3 LabelID=IVc4 LabelID=IVc5 LabelID=IVc6
-
+ 100V
LabelID=V32
-
+
100V
LabelID=V33 D34 D35 D36 D37 D38 D39 D40 D41 D42 D43 D44 D45
V S_46
V S_47
V S_48
V S_49
V S_50
V S_51
Model
DModel1
Model V
SModel1
Maxwell Motor Model Generation
• From RMxprt
– Most powerful way
– Complete model setup
– External circuit created
– Ready to solve
• Draw using UDPs
– Complex machine cores
– Windings with end turns
• Draw using CAD modeler
– Full ACIS based 2D/3D CAD
modeler included
– Easy to use
• Import geometry
• Share geometry
Automatically setup
– Geometry
– Motion
– Boundaries
– Excitations
– Materials
– Mesh
Operations
– Solve Setup
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Maxwell Motor Model Generation
• From RMxprt
– Most powerful way
– Complete model setup
– External circuit created
– Ready to solve
• Draw using UDPs
– Complex machine cores
– Windings with end turns
• Draw using CAD modeler
– Full ACIS based 2D/3D CAD
modeler included
– Easy to use
• Import geometry
• Share geometry
© 2010 ANSYS, Inc. All rights reserved. 14 ANSYS, Inc. Proprietary
Electrical Machines – Maxwell
Motor Model Generation
• From RMxprt
– Most powerful way
– Complete model setup
– External circuit created
– Ready to solve
• Draw using UDPs
– Complex machine cores
– Windings with end turns
• Draw using CAD modeler
– Full ACIS based 2D/3D CAD
modeler included
– Easy to use
• Import geometry
• Share geometry
© 2010 ANSYS, Inc. All rights reserved. 15 ANSYS, Inc. Proprietary
Electrical Machines – Maxwell
Motor Model Generation
• From RMxprt
– Most powerful way
– Complete model setup
– External circuit created
– Ready to solve
• Draw using UDPs
– Complex machine cores
– Windings with end turns
• Draw using CAD modeler
– Full ACIS based 2D/3D CAD
modeler included
– Easy to use
• Import geometry
• Share geometry
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Maxwell – Transient 2D/3D FEA
with Large Motion
• Easy to use, autoadaptive meshing
• Functional or PE-switched excitation
(circuits)
• dB/dt transients – fully integrated solution
• Large motion induced dB/dt transients
• Virtual Force and Stress Tensor-based
Force calculation
• Various loss schemes
• Windings: Stranded losses
• Laminated steel: Core losses
• Solids and magnets: Eddy current losses
• Linear and nonlinear, isotropic and
anisotropic, and laminated materials
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Induced J in cage at t = 8 ms
B in stator and rotor, J in cage
Maxwell – Engineering Approach
master
slave
Engineer‘s business:
• Geometry
• Materials
• Sources and boundaries
• Understand results
Maxwell‘s business:
• Numerics
• Meshing
• Solution
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Maxwell –
2D/3D Transient Large Motion
• Transient motion along/about one dimension
• Rotation – cylindrical, disk type, limited (tilting) – full
cylindrical or ring type, rotor eccentricity
• Translation
• Inertia, mechanical damping, load torque/force
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Maxwell 2D/3D: Transient Motion
with External Circuits
0
0
LPhaseA
LPhaseB
LPhaseC
2.99132ohm
R A
2.99132ohm
R B
2.99132ohm
R C
0.000921945H
LA
0.000921945H
LB
0.000921945H
LC LabelID =VIA LabelID =VIB LabelID =VIC
+ 0V
1V
LabelID=V14
+ 0V
1V
LabelID=V15
+ 0V
1V
LabelID=V16
+ 0V
1V
LabelID=V17
+ 0V
1V
LabelID=V18
+ 0V
1V
LabelID=V19 100ohm R 20 100ohm R 21 100ohm R 22 100ohm R 23 100ohm R 24 100ohm R 25 LabelID =IVc1 LabelID =IVc2 LabelID =IVc3 LabelID =IVc4 LabelID =IVc5 LabelID =IVc6
-
+
110V
LabelID=V32
-
+
110V
LabelID=V33 D 34 D 35 D 36 D 37 D 38 D 39 D 40 D 41 D 42 D 43 D 44 D 45
V S_46
V S_47
V S_48
V S_49
V S_50
V S_51
Model
DModel1
Model V
SModel1
10.00 15.00
Time [ms]
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
NodeVoltage(IVa) [kV]
-150.00
-100.00
-50.00
0.00
50.00
100.00
150.00
-BranchCurrent(VIA) [A]
Ansoft LLC Phase Voltage / Current 4_Partial_Motor_TR_PWM
Loss Types:
• Steel
• Copper
• Magnet
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Electrical Machines –
Design Issues
• Inductance calculation
– Static
– Transient
• Cogging torque
– Magnetostatic with swept jm, or
– Transient with wm = 1 deg/s and
Rabc = 1 MW
• Back-EMF
– Transient, some constant wm and
iabc = 0
• Conditions at operating points
(idle, rated, peak, startup, ...)
– Transient with wm = wm OP and
some vabc(t) or iabc(t)
0.00 5.00 10.00 15.00 Time [s]
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00 Moving1.Torque [NewtonMeter] Ansoft Corporation Torque Maxwell2DDesign1
Curve Info Moving1.Torque Setup1 : Transient
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Electrical Machines –
Design Issues
• Space harmonics
– Evaluate fft( Bn
( Lairgap ) )
• Losses
– Transient with eddy currents enabled
– Core losses setup for laminated objects
• Field distributions
• Startup, load variations
– Mechanical transients
• Rotor eccentricity
0.00 0.20 0.40 0.60 0.80 1.00 NormalizedDistance
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20 Bradial Ansoft Corporation XY Plot 2 PMSM_CT
Curve Info Bradial Setup1 : Transient Time='0ns'
© 2010 ANSYS, Inc. All rights reserved. 22 ANSYS, Inc. Proprietary
Electromagnetic Actuators –
Maxwell
• dB/dt – motion and time induced effects
– Transient solver solves time-varying magnetic fields
– Fully Coupled FEA with external circuit and motion
– Includes time-induced effects such as:
• Eddy effects
• Proximity effects
• Time diffusion of magnetic fields
– Motion-induced eddy effects
• Nonlinear material effects
• Power electronic switching
© 2010 ANSYS, Inc. All rights reserved. 23 ANSYS, Inc. Proprietary
Actuators
0
0
LCoil
Model
V
SW_Inf o
V S_Sw itch 0.077ohm R ds_on
12ohm
R_Coil
-
+
12.5V
LabelID=VSource
LabelID=I_Pulse
+ 0V
5V
LabelID=V_Pulse 1000ohm R 28
Model
Zener_Inf o
D _Z ener
LabelID=IBatt LabelID=ISwitch
LabelID=VCoil
LabelID=VZener
200 ms 500 ms 1000 ms
0.00 0.20 0.40 0.60 0.80 1.00 Time [ms]
0.00
5.00
10.00
15.00
20.00
25.00 Current(Winding) [A]
-50.00
-40.00
-30.00
-20.00
-10.00
0.00
10.00
20.00
30.00
40.00
50.00 Y2 [V]
Ansoft Corporation XY Plot 1 Maxwell3DDesign3
Curve Info
Current(Winding) Setup1 : Transient
InducedVoltage(Winding) Setup1 : Transient
NodeVoltage(IVM_SRC) Setup1 : Transient
© 2010 ANSYS, Inc. All rights reserved. 24 ANSYS, Inc. Proprietary
Electromagnetic Actuators –
Maxwell
Optimization of Closing Time:
ArmStepHeight
Gap
• Vary geometric parameters
• Transient run
• Detect closing time
© 2010 ANSYS, Inc. All rights reserved. 25 ANSYS, Inc. Proprietary
FEA
PhaseA1
PhaseA2
PhaseB1
PhaseB2
PhaseC1
PhaseC2
Rotor1
Rotor2
w
+
ICA: LL:=237.56u
RA:=696.076m
B6U
D1 D3 D5
D2 D4 D6
2L3_GTOS
g_r1
g_r2
g_s1
g_s2
g_t1
g_t2
~
3PHAS
~
~
A * sin (2 * pi * f * t + PHI + phi_u)
PHI = 0°
PHI = -120°
PHI = -240°
LDUM:=100m
CDC:=10m
LDC:=10m
RDC:=10
VZENER:=650
AMPLITUDE := 800 V
FREQUENCY := 60 Hz
FREQ := 800 Hz
AMPL := 800
PHASE := 0 deg
AMPL := 500
PHASE := -315 deg
FREQ := 50 Hz
PHASE := -195 deg
PHASE := -75 deg
SA
SB
SC
+
V
FEA
PhaseA1
PhaseA2
plunger1
plunger2
Ideal
F
UPPER_LIM := 0.1 in
S0 := 0 in
0.004 kg
10u Ns/m -0.04 N
-32.68u m
6.25 Ohm 153 N/m
D3
RS := 10 Ohm
6.25 Ohm
12 V D1
RS := 10 Ohm
Blocks, states, functions,
differential equations
Electric circuits
Electric circuits
Mechanics
Mechanics
Maxwell 2D/3D
Transient+Motion
Maxwell 2D/3D
Transient+Motion
Electrical Machines and Actuators –
Simplorer-Maxwell 2D/3D Cosimulation
© 2010 ANSYS, Inc. All rights reserved. 26 ANSYS, Inc. Proprietary
Simplorer
Multidomain Systems
Circuits, Blocks, States, VHDL-AMS
Maxwell 2D/3D
Electromagnetic Fields
Dynamic (t, f), Motion, Circuits
Electrical Machines and Actuators –
Simplorer-Maxwell 2D/3D Cosimulation
© 2010 ANSYS, Inc. All rights reserved. 27 ANSYS, Inc. Proprietary
Maxwell – Multiphysics Integration
Thermal/Mechanical Load Transfer
• Maxwell – ANSYS Workbench:
– One-way thermal coupling
– Two-way thermal coupling
– One-Way Mechanical Coupling
– Two-Way Mechanical Coupling (planned for 2012)
EM Force
Temperature
EM Loss
Maxwell
Electromagnetic Fields
Static, Dynamic (t, f), Motion, Circuits
ANSYS Multiphysics
Stresses, Heat, CFD
Deformation
© 2010 ANSYS, Inc. All rights reserved. 28 ANSYS, Inc. Proprietary
ANSYS Workbench R13 Interface
Power
Temperature
Maxwell
B-Field, Losses
Ansys Thermal
Temperature
© 2010 ANSYS, Inc. All rights reserved. 29 ANSYS, Inc. Proprietary
Maxwell – Multiphysics Integration
Electrical Machine Stresses
• Thermo-mechanical simulation from the thermal solution
• See the (thermo-) deformation of the structure
Stator, rotor
temperature
Deformation due to temperature
© 2010 ANSYS, Inc. All rights reserved. 30 ANSYS, Inc. Proprietary
Maxwell – Multiphysics Integration
Electrical Machine Stresses
• Static coupling
• Electromagnetic force density
– Automatically calculated in Maxwell
– Using the Maxwell’s stress tensor
– Mapped to the ANSYS mesh
– See stator, rotor, coil deformation
Original coil
position
© 2010 ANSYS, Inc. All rights reserved. 31 ANSYS, Inc. Proprietary
Vibration Analysis
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00
Time [ms]
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00 Moving1.Torque [NewtonMeter]
Torque 02_DC-6step_IPM ANSOFT
Curve Info avg pk2pk
Moving1.Torque 4.7552 5.7332
© 2010 ANSYS, Inc. All rights reserved. 32 ANSYS, Inc. Proprietary
Machine Model in Maxwell
• Fields Calculator to create
Radial and Tangential Force
Expressions from
EdgeForceDensity
• Calculates Radial and
Tangential Force on Tooth Tips
• Allows only force on edge that
neighbors non ferrous objects
© 2010 ANSYS, Inc. All rights reserved. 33 ANSYS, Inc. Proprietary
Machine Model in Maxwell
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 Time [ms]
-250.00
-200.00
-150.00
-100.00
-50.00
-0.00
50.00
Force (Newtons)
Radial Force on Tooth Tips 02_DC-6step_IPM ANSOFT
Curve Info
ExprCache(ToothTipRadial_Full1)
ExprCache(ToothTipRadial_2)
ExprCache(ToothTipRadial_3)
ExprCache(ToothTipRadial_4)
ExprCache(ToothTipRadial_5)
ExprCache(ToothTipRadial_6)
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 Time [ms]
-30.00
-25.00
-20.00
-15.00
-10.00
-5.00
0.00
5.00
10.00
Force (Newtons)
Tangential Force on Tooth Tips 02_DC-6step_IPM ANSOFT
Curve Info
ExprCache(ToothTipTangent_Full1)
ExprCache(ToothTipTangent_2)
ExprCache(ToothTipTangent_3)
ExprCache(ToothTipTangent_4)
ExprCache(ToothTipTangent_5)
ExprCache(ToothTipTangent_6)
© 2010 ANSYS, Inc. All rights reserved. 34 ANSYS, Inc. Proprietary
Geometry in WB
• Pattern Geometry in DM to create complete geometry
from 1/4th sector
© 2010 ANSYS, Inc. All rights reserved. 35 ANSYS, Inc. Proprietary
• Plane Strain 2D Analysis of the Stator
• Generate Mesh
• Fixed support at the four bolted edges
• Apply the time varying forces obtained from Maxwell
on stator tooth tip
Workbench Setup
© 2010 ANSYS, Inc. All rights reserved. 36 ANSYS, Inc. Proprietary
Workbench Setup
Radial and Tangential forces in Mechanical
© 2010 ANSYS, Inc. All rights reserved. 37 ANSYS, Inc. Proprietary
Results - Equivalent stress
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Results - Deformation
• Radial and Tangential Directional Deformation
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Electrical Machine Cooling –
Maxwell-CFD: Heat-Up Analysis
• Maxwell solve
• Maxwell loss to CFD
• CFX solver used
• CFD temperature back to Maxwell
• Iterate as necessary
EM Loss
Temperature
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Electrical Machine Cooling –
Maxwell-CFD: Heat-Up Analysis
Model without water
Model with solid only
Full model
• Maxwell2D Transient
– Losses averaged
– Expanded to 3D, mapped to ...
• ANSYS CFD (Fluent) solver
– Steady state analysis
– Water cooled
– Airgap
© 2010 ANSYS, Inc. All rights reserved. 41 ANSYS, Inc. Proprietary
Experimentation
with Maxwell, Simplorer, ...
Experimentation
• Have a model with x input
parameters
• Experiment with x to make y
outputs as desired
• Experimentation Analyses:
– Parametrization
– Optimization
– Sensitivity
– Statistical
Experimentation
External tools via
scripting
Ansoft
Optimetrics
ANSYS
DesignExplorer DX
(calls Optimetrics)
© 2010 ANSYS, Inc. All rights reserved. 42 ANSYS, Inc. Proprietary
DX – IPM Torque Optimization
• Multiobjective optimization
– Maximize torque with fixed current
– Minimize magnet volume
– Maximize torque/volume ratio
– Obtain a maximum stator tooth flux
density of 1.9 T
• Vary parameters
– 20 < tN < 36 (Slot Height)
– 3 < bN < 11 (Slot Width)
– 5 < hM < 16 (Magnet Height)
– 25 < wM < 44 (Magnet Width)
© 2010 ANSYS, Inc. All rights reserved. 43 ANSYS, Inc. Proprietary
DX – IPM Torque Optimization
Maxwell runs a parametric solution given
x from DOE setup.
DX creates n-dimensional response
surface from this DOE table.
© 2010 ANSYS, Inc. All rights reserved. 44 ANSYS, Inc. Proprietary
DX – IPM Torque Optimization
• Response Surface Technique
– ANSYS DesignExplorer (DX)
– Various experimentations can be
applied (optimization, sensitivity, ...)
– Very fast (analytical) results
– Response Surfaces precalculated
from Design of Experiments (DoE)
– Reduces drastically the amount of
FEA calculations
[1]: Germishuizen, J. J.; Hädrich, O.; Stanton, S.; Tharp, J.: Torque Optimization for
Interior Permanent Magnet Machines (IPM). Proc. ACUM, Leipzig, 2009.
© 2010 ANSYS, Inc. All rights reserved. 45 ANSYS, Inc. Proprietary
DX – IPM Torque Optimization
TorquePerMagArea Bavg Tooth #5 Torque Magnet Area
Slot Width
Slot Height
Magnet Width
Magnet Height
Sensitivity chart (computed instantaneously from response surface)
© 2010 ANSYS, Inc. All rights reserved. 46 ANSYS, Inc. Proprietary
DX – IPM Torque Optimization Torque
T
Bavg Tooth #5
Pareto fronts shown, the best
to worst go from blue to red
respectively
© 2010 ANSYS, Inc. All rights reserved. 47 ANSYS, Inc. Proprietary
DX – IPM Torque Optimization
Probability density of output torque
© 2010 ANSYS, Inc. All rights reserved. 48 ANSYS, Inc. Proprietary
DX – IPM Torque Optimization
Flux density at
optimum design
parameters
© 2010 ANSYS, Inc. All rights reserved. 49 ANSYS, Inc. Proprietary
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