Design of a 45 kW Permanent Magnet Synchronous Motor
DESIGN AND CONTROL OF A PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE FOR A
HYBRID ELECTRIC VEHICLE
S. Van Haute*, St. Henneberger*, K. Hameyer*, R. Belmans*
J. De Temmerman**, J. De Clercq**
* Katholieke Universiteit Leuven; Belgium
** Inverto N.V.; Belgium
Abstract The design and control of a 45 kW 6-pole permanent magnet synchronous motor (PMSM) with surface-inset
magnets for a hybrid electric vehicle is described. The advanced field weakening strategy takes advantage of the
additional reluctance torque. The influence of the saturation effects on the motor torque is considered by computing
the inductances Ld and Lq are for each operational point. The accurate prediction of the motor performance is essential
for the optimal control of the drive over a wide range of operation. The drive control is implemented on a DSP based,
MATLAB/SIMULINK programmable hardware system.
INTRODUCTION disadvantage for the motor control: the machine parameters are
dependent on the operating point due to saturation effects. As a real
Hybrid electric vehicles have the advantage to operate with zero time control strategy is essential to assure the continuous operation at
emission in the inner city while not being limited in the range for highest efficiency, those dependencies have to be known in advance.
intercity distances. Furthermore, the possibility of regenerating the The control algorithm then directly operates on the pre-calculated set
braking energy is offered. of performance characteristics in form of tables or polynomial
The main parts of the drive equipment are the energy sources, in this
study a Diesel generator connected in parallel to a rechargeable NiCd The design procedure takes advantage of analytical calculations as
traction battery, the traction motor with converter and controller, and well as static Finite Element Analysis (Chang et al , Slemon et al
the main controller unit. The drive module is connected to a main ) and thermal computations.
controller collecting the status information: acceleration, deceleration,
regenerating the braking energy, etc. (Fig. 1). The desired torque Td Apart from the feedforward torque control, several algorithms for
given by the driver of the vehicle is processed by the main controller. flux-weakening have been published recently, including current and
voltage limitation and compensation of cogging torque [6,i,j]. A
The heart of the drive consists of the permanent magnet excited general flux-weakening algorithm is adapted. to the designed motor,
synchronous machine. [PMSM]. The possibilities of such type of simulated and implemented on a DSP based hardware system using a
motors for road electric traction was already investigated in the early MATLAB/SIMULINK programmable control environment. The
eighties by Sneyers et al [a,b]. An electric vehicle motor design optimal negative direct axis current is determined for operating points
requires high efficiency, extended field weakening range, high both in constant torque region as in constant power region.
power/weight ratio and high reliability. Water cooling, high energy
density permanent magnets and special control strategies (], are The experimental setup further includes a modified standard inverter
applied in order to fulfil these requirements. for induction motors and a reduced scale prototype motor.
One of the main design goals for the studied drive system is the MOTOR DESIGN
continuous operation of the PMSM at high efficiency. Therefore, a
rotor geometry with Xq > Xd is chosen to benefit from an additional PMSMs are usually classified into surface mounted permanent
reluctance torque (Fig.1) (Jahns et al [d],]). The rotor design causes a magnet motors (SPMSM) and interior or buried permanent magnet
motors (IPMSM) [d,1]. The first can have sinusoidal back emf, but
have limited field weakening capabilities, due to relatively small
inductance values. The latter has higher inductances and thus an
extended constant power operation range. Moreover, because direct
and quadrature inductance are not equal, a reluctance torque
contributes to the total motor torque. However, the back emf is no
A motor design as shown in figure 2 can combine some advantages of
the above mentioned motor types. This motor is referred to as a
surface-inset PMSM (Sebastian and Slemon [e]). As in the IPMSM,
due to magnetically asymmetrical rotor design, the total torque has an
electromagnetic component and a reluctance component.
In order to achieve a high efficiency of the PMSM the losses have to
be kept low being contrary to a high power/weight ratio. Therefore,
the optimal choice of the desired low weight and acceptable iron
losses has to be made. In the same way, the contributing losses can be
reduced by using more winding copper, yielding in increasing costs
and additional weight. The thickness of the iron yoke is reduced by
applying a high number of poles. However, the number of poles is
limited by the frequency of the inverter, and furthermore, a wide
range of field weakening can only be achieved by a relatively small
Figure 1 Topology of the hybrid drive concept.
number of poles (Hadji Minaglou ). Iron losses are further efficiency 96,2 %
decreased by choosing thin low-loss lamination in the stack of the
stator. The power/weight ratio is further improved by applying an PMSM WITH EXTENDED FIELD WEAKENING
indirect water cooling system.
The motor operates in an advanced field weakening mode by
A high Ld value extends the field weakening range, however implementing a negative direct stator current in order to benefit from
increasing Ld by decreasing the thickness of the permanent magnets the reluctance torque. The motor can be operated in two modes. In
has limits. It enables their demagnetisation and reduces the reluctance the constant torque mode, the speed of the drive is increased by
torque by decreasing the ratio Lq/Ld. raising the stator frequency and voltage until rated speed is reached.
To increase speed further, power and voltage have to be maintained
constant while increasing the angle between stator current and field
d axis above 90º by additionally applying a negative direct stator
current component (Fig. 3). The required current is minimized and the
q Φ possibility of irreversibly demagnetizing the magnets is reduced. The
significant saliency of the motor, realized by constructing a rotor with
Θ surface-inset magnets (Fig. 2), is generating a reluctance torque.
-v1 u1 -w1 -w1 Direct and quadrature axis current components are calculated by
u1 -w1 Parks transformation and fed to the control algorithm (Figure 5). In d-
-v1 v1 q coordinates, the dynamic behaviour of a PMSM is described by the
following set of equations.
ud = R. i d − ωLq . i q + pLd id (3)
uq = R. i q + ωLd . i d + pLq iq + ωφ f (4)
Figure 2. Cross-sectional view of a 6-pole surface-inset PMSM.
The torque equation is a function of the angle Ψ = 90º-δ and can be
Another design aspect is the choice of the permanent magnet material. splitted into an electromagnetic component (1) and a reluctance
A high remanent flux density is needed, while a high coercivity is less component (2)
important as overloads do not occur. NdFeB permanent magnets offer m⋅p
a high energy density as well as a high remanence flux density. Te (Ψ ) = ⋅ E ⋅ Iq , (1)
Furthermore, the operating high temperatures are no longer a
drawback as the new generation of NdFeB magnets (VACODYM ( )
Tr (Ψ ) = m ⋅ p ⋅ I d ⋅ I q ⋅ Lq − Ld , (2)
411) retains its magnetic properties up to high temperatures of
120º C. where I d = I ⋅ sin (Ψ) , I q = I ⋅ cos ( Ψ) with m - the number of phases,
p - the number of poles, ω0 - the synchronous angular speed and E -
Using surface mounted magnet pieces, glued onto the rotor, instead of the fundamental e.m.f..
one magnet piece for one pole, reduces eddy current losses and
herewith the heating of the magnets.
r *I d jXq*Iq
The design procedure results in a motor design (Fig. 2) of which the
dimensions are summarised in table 1, fulfilling the performances jXd*Id r*Iq
listed in table 2. The torque/speed characteristic, showing the field
weakening range (Figure 3), is computed by calculating the operating
points of the equivalent circuit of the machine. The equivalent circuit E
is calculated as function of the rotor torque angle δ as well as the
terminal current, due to the fact that the inductances are dependent of
the current components Id and Iq. The mechanical torque is calculated
as function of the supplied voltage and the stator current. Figure 4
shows the terminal voltage, the stator current and the efficiency as ϕ I
function of the speed.
Tab. 1 Dimensions of the PMSM δ
Stack OD 299 mm Id
Stack ID 208 mm
Rotor length 130 mm
Figure 3. Phasor diagram of the PMSM in the advanced field
Overall mass 60.4 kg weakening mode.
Number of poles 6
The motor is controlled by adjusting the load angle to obtain the
Tab. 2 Performances of the PMSM maximum torque Tmax = Te+Tr which is expressed as a function of the
angle Ψ = 90º-δ by the equation
power/weight ratio 0.8 W/kg
weakening range nmax/nr 2.8
E E + 1 .
Ψopt = arcsin (3)
4I1ω Lq − Ld
( 4I ω L − L
1 q )
d ( )
The load angle, being a measure for the ratio of the current in the torque
direct axes versus the total current in the stator with I d = I ⋅ sin (Ψ) 100 I=1/2*Ir
is described as a function of the speed for different values of the T [Nm]
current in the stator: I=1/4*Ir
− e2 − xd 02 ⋅ i 2
sin( Ψ) = (4)
2 ⋅ e ⋅ xd 0 ⋅ i 0
0 10 20 30 40 50 60 70 80 90
Load angle Ψ [°]
Figure 5. Numerical computed overall torque as function of the load
Id/I angle at different stator currents.
-0.5 60 I=3/4*Ir
-0.6 Tr [Nm]
-1 0 0.5 1 1.5 2 2.5 3 3.5
0 10 20 30 40 50 60 70 80 90
Figure 4. Id/I for different arature currents as function of the speed .
Load angle Ψ [°]
Figure 6. Numerical computed reluctance torque as function of the
load angle at different stator currents.
Due to saturation effects in the stator teeth and the rotor iron in the
interpolar region, the inductances Ld and Lq are a function of the
The calculation of the inductances Ld and Lq as a function of the load
stator current and the load angle or, in other words of the current
angle δ1 is straightforward, applying a flux linkage method.
components Id and Iq. [d].They have to be known for each possible
Formulation (4) Henneberger et al  provides the general tool to
state of operation in order to accurately control the machine as well as
compute the inductance of a winding in two dimensions,
to simulate the dynamic behaviour of the machine. In the past, some
attempts were done to correct the classical mathematical model by
introducing cross-coupling terms [b],[c]. L = z ∫ A z ⋅ J dS
The application of the finite element analysis for the determination of
the lumped parameter model and the performance of the PMSM have
been discussed widely in the literature ,Nipp . As shown in ,
Az - the vector potential,
the FE analysis is suited for the calculation of the PMSM utilizing
l z- the stack length of the stator,
rotor geometry with Xq > Xd.
S - the surface of the cross section of the slots that carry the
current of the appropriate winding,
A high number of FE model evaluations is performed in order to have
i - the current per strand,
knowledge of the machine parameters in a variety of operating points.
J - the current density.
These data are used in off-line simulations, and can be used in simple,
parameter dependent real-time control schemes.
The number of windings is considered by the dependency of the
current density J from the current per strand i. One non-linear model
is solved for each studied load angle. In the post-process, the
appropriate distributions of J, conforming to Id or Iq, are generated. Ld
and Lq are extracted using (8). Due to the non-linear problem
definition, the saturation dependencies of the inductances are found.
0.5 a ∆L(δa)
0.4 Ld(Id) b
Figure 9: Thermal equivalent circuit of a water-cooled PMSM .
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Figure 7. Inductances Ld and Lq as function of the current components
Id and Iq for two different load angles at rated current.
In an application such as an electric vehicle, invertor and motor
160 efficiency should be as high as possible. With the rotor geometry as
described earlier, advantage can be taken of the reluctance torque [e]
as in the case of an interior PMSM [d], with this remark that the ratio
120 Ld/Lq is somewhat lower for the proposed inset permanent magnet
The drive control algorithm has to determine at any instant the
optimal torque per Ampere trajectory, regarding the additional
40 reluctance torque [d]. This means that also in the constant torque
region the id current (and thus the angle β) is varied. The required d-q
0 currents can be calculated from the command torque, resulting in a
2000 4000 6000 8000
n [rpm] simple feedforward torque control algorithm, as was proposed in [d].
Figure 8. Torque as function of the speed obtained by static The equations used to calculate id and iq command values rely on the
calculation of the equivalent circuit using Lq(I,δ) and Ld(I,δ). motor parameters.
To cover the whole operation range of the motor, the inductances Ld The torque command is normally the output of a PI controller. This
and Lq are computed for in the step of ∆δ=5º and ∆I=0.05*Ir. This output can also be considered as a stator current command and d-q
involves 380 FE solutions. The results for I=Ir are indicated in Fig. 5. components can be calculated according to (3).
The graph shows the difference ∆L = Lq-Ld for two selected load
angles δa and δb. ∆L rises if δ increases, due to the saturation of the d-
axis flux path.
The simple feedforward control does not take into account the
This predicts the variation of the inductances Lq(I,δ) and Ld(I,δ) can
operating limits of inverter driven PMSMs. In [f], the effect of the
be used in the control algorithm. Equation (3) becomes a differential
finite inverter dc bus voltage is extensively described and an
equation Ψopt(I,Ψ) and can be solved by using tables of the numerical
additional flux-weakening feedback scheme is presented. This work
computed values (Fig. 6,7). For real time control algorithms the
was further elaborated and a modified control is proposed in [g].
inductances are approximated by polynomial functions.
Figure xx illustrates these limits in the id-iq plane. Hyperbolas of
constant torque are shown, as wel as the voltage limit ellipses, the
maximum current circle and the optimal torque per ampere trajectory.
High performance for electric vehicle drives is obtained by allowing
the machine to carry a load exceeding its rated values for a short
period of time. The limit of such a overloading is described by the
maximum temperature rise. It is essential to predict the behaviour of
the machine for any time varying load. The temperature as function of
the time is determined by numerical integration of the differential
equations of the thermal equivalent circuit (Fig. 3). The elements of
Figure (torque hyperbola, voltage ellips and current circle)
the thermal equivalent circuit can be obtained by analytical methods
or the FEM and are implemented in the dynamic system of equations
The control has to cope with this varying voltage limitation, as well as
of the machine. The analytical calculated losses are verified by the
current limitation and saturation
FEM. Here, the motor model is taken from the FEM and the problem
The current has to follow the torque trajectory, until the voltage limit
definition is provided by the analytical calculation.
ellips is reached. As the torque command continues along the
trajectory, the maximum motor torque that can be delivered (at
constant speed) is realized by tracking the voltage limit ellips until
maximum current is reached.
The voltage limit ellips becomes smaller with increasing speed, but
depend also on the maximum stator voltage. Because of the presence i d* Ud*
of a varying dc bus voltage (battery voltage 240 V to 400V) in the accelerate Current 2 IGBT-
signal control and U * PWM Udc
vehicle applicaton, it is preferable to use a flux-weakening algorithm i q* q 3 inverter
that is based on the feedback of stator-voltage command, as in [h].
For the proposed drive, this control scheme is adapted to the motor brake Motor A/D
design and extended with the feedback of the measured dc bus voltage signal A/D
to decide on transition from constant torque to constant power region. A/D
In this way, flux-weakening starts automatically when any limit is PMSM
reached and the vehicle will have maximum available performance at
any dc bus voltage. θ
Figure? Simulation of transition into flux-weakening mode for the Serial
45 kW motor Communication
Hybrid drive magagement
The inverter for the designed vehicle motor will have the ratings listed
in Table xx. Its interface with the control board will be described in
the next section.
Figure 5: Control system for the PMSM.
In order to evaluate the electric vehicle motor design and control as
described above, a reduced scale prototype permanent magnet motor .
with surface-inset magnets was constructed and is tested in a
laboratory setup. Data of this motor are shown in table 3. To check
motor heating against the applied duty cycle, temperature sensors (Pt
100) are introduced only in the stator, because the rotor has no
winding and serious heating of the rotor is not expected.
The inverter used is a slightly modified standard VSI-PWM inverter
with IGBTs. Only an interface to galvanically isolate the control board Tab. 3 Data of the reduced power prototype surface-inset PMSM
from the inverter is added.
The motor control is implemented using a DSP based controller board ACKNOWLEDGEMENT
 with additional I/O features and an encoder interface. The
laboratory further consists of a host PC for the controller board, the The authors are grateful to the Belgium Ministry of Scientific
IGBT inverter, the 2.8 kW prototype motor, current sensors and an Research for granting the IUAP No. P4/20 on Coupled Problems in
incremental encoder. Electromagnetic Systems and the Council of the Belgian National
The heart of the controller board is a TMS320C31 Digital Signal
Processor. A slave processor is used to perform digital input and
output and generate PWM signals. The controller board can be REFERENCES
directly programmed using MATLAB/SIMULINK .
Motor currents are measured and fed to the control board by 16 bit 1. Nasar, S. A., Boldea, I., Unnewehr, L. E.: “Permanent Magnet,
AD converters and digitally filtered. Position is measured using an Reluctance, and Self-Synchronous Motors”. CRC Press, 1993,
incremental encoder, of which the signals can be directly connected to London Tokyo
the encoder interface on the controller board. This is sufficient for
laboratory testing. Because of the bit selectable I/O ports on the slave 2. L. Chang, G. E. Dawson, T. R. Eastham; “Permanent Magnet
processor, an absolute encoder or resolver can be used as well. Synchronous Motor Design: Finite Element and Analytical Methods”;
ICEM Conf. Proceedings, Cambridge, pp. 1082-1088, Aug. 1990.
The algorithm determines reference values for direct and quadrature
axis currents. The PWM generation scheme that is implemented in the 3. Slemon, G. R.: Xian, L.: “Modelling and Design Optimisation of
slave processor is based on phase voltage reference values. For this Permanent Magnet Motors”. Electric Machines and Power Systems,
reason, these reference values are determined using a decoupling vol. 20, no. 2, pp. 71-92, April 1992.
network and the inverse Park transformations. For an electric vehicle
application, the use of classical PI-controllers in the decoupling 4. Henneberger G., Hadji-Minaglou J.-R., Ciorba R. C. ; “Flux-
system is satisfying . Weakening Operations of Permanent Magnet Synchronous Motors for
Electric vehicle Operation”; Workshop on Electric and Magnetic
The dotted frame indicates the functions that are implemented on the Fields, Leuven, Conf. Proceedings, pp. 57-60, May 1994.
The current sample period has to be a multiple of the PWM period. 5. Hadji-Minaglou J.-R:“Antriebskonzepte mit permanent- erregten
Because the DSP can calculate the algorithm sufficiently fast, the Synchronmotoren für den einsatz im Elektrofahrzeug”, PhD-thesis
sample rate is chosen the same as the PWM frequency, i.e. 10 kHz. RWTH Aachen, jul. 1994.
 G. Henneberger, S. Domack and J. Berndt, "Comparison of
6. Nipp, E.: “Alternative to Field Weakening of Surface Mounted the Utilization of Brushless DC Servomotors with Different Rotor
Permanent Magnet Motors for Variable Speed Drives”. Proc. IAS’95, Length y 3D - Finite Element Analysis", IEEE Transactions on
pp. 191-198. Magnetics, vol. 30, no. 5, pp. 3675-3678, 1994
 D. Taghezout and P. Lombard, "Finite Element Prediction of
a Brushless DC Motor Dynamical Behaviour", 2nd EPE Chapter
Symposium on Electric Drive Design and Applications, Nancy,
France, June 4-6, 1996, Conf. Proc. pp. 47-52
Fig. 3: Torque as function of the motor speed
U [V] U I [A]
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