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Franck SCUILLER, Hussein ZAHR, Eric SEMAIL - A bi-harmonic five-phase SPM machine with
low ripple torque for marine propulsion - In: 2017 IEEE International Electric Machines and Drives
Conference (IEMDC), Etats-Unis, 21-05-20 - A bi-harmonic five-phase SPM machine with low
ripple torque for marine propulsion - 2017
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c
2017 IEEE.
A bi-harmonic five-phase SPM machine with low
ripple torque for marine propulsion
Franck Scuiller
1
, Hussein Zahr
2
, Eric Semail
2
1
Ecole Navale; Naval Academy Research Institute, Brest, France, franck.scuiller@ecole-navale.fr
2
Ecole Nationale Sup
´
erieure d’Arts et M
´
etiers; Laboratory of Electrical Engineering and Power Electronics, Lille, France
Abstract—This paper addresses the design of a bi-harmonic
five-phase Surface-mounted Permanent Magnet (SPM) machine
for marine propulsion. The bi-harmonic characteristic results
from the particular 20 slots-8 poles configuration that makes
possible high value of third harmonic current injection. Thus
the machine performance can be improved in terms of average
torque, speed range, losses control and torque quality, this last
feature being the scope of the paper. As low ripple torques are
wanted at low speed, the magnet layer is defined to reduce the
cogging torque and to make third harmonic current injection
increasing average torque and reducing pulsating torque in the
same time. According to a selection procedure based on the
numerical simulations of a high number of machines, it appears
that designing the rotor with two identical radially magnetized
magnet that cover two-third the pole arc allows to reach this
goal. Referring to an equivalent three-phase machine, the torque
ripple level of the bi-harmonic five-phase machine is more than
three times lower, thus being obtained with a simple control
strategy that aims at achieving constant currents in the rotating
frames. The time simulations of the drive confirm the significant
reduction of the speed oscillation, especially at low speed.
I. INTRODUCTION
Multi-phase motors are widely used in electrical marine
propulsion for reasons such as reliability, smooth torque and
distribution of power [1]. For low power propulsion system
(less than 10kW), the power partition constraint results from
the low DC voltage (less than 60V) that supplies the drive.
Hence increasing the phase number enables to limit the rating
of the power electronic components. In addition, compactness
objective can be more easily achieved if the phase number is
considered as a design parameter. For instance, with five-phase
machine, third harmonic current injection can be performed
to boost the torque [2], [3]. Regarding the rotor, Permanent
Magnet (PM) structure contributes to enhance the power den-
sity [4], [5]. Furthermore, Surface-mounted Permanent Magnet
(SPM) rotor facilitates the ripple torque mitigation that is of
critical importance at low speed. If fractional-slot windings
facilitate the reduction of cogging torque for SPM machine [6],
they also generate magnetomotive force harmonics that could
result in excessive magnet losses. Machine with 0.5 slots per
phase and per pole (s
pp
=0.5) are known to limit this effect
[7]. In addition, the slot filling can also be improved with this
solution [8]. Therefore the machine here considered is a five-
phase machine with 20 slots and 8 poles (20-8-5 configuration)
for a marine propeller.
Three-phase machine with 12 slots (12-8-3 configuration)
could be chosen but this solution does not provide fault
tolerant ability. Furthermore, in [9] where 20-8-5 and 12-8-
3 machines are compared for the same design specifications
(rated torque, power and external diameters are identical) and
the same volume of magnetic materials (magnet, copper and
iron), it is shown that the 5-phase configuration makes possible
a significant reduction of the magnet losses, according to
numerical computations.
20-8-5 configuration is a particular winding distribution in
so far as the third harmonic factor (0.98) is higher than the
fundamental one (0.57). A machine equipped with this wind-
ing can be considered as a bi-harmonic five-phase machine
since it inherently offers an electronic pole changing effect
[10]. With this characteristic, the efficiency of the machine
can be improved for the whole speed range: the possibility
of limiting the magnet losses at high speed is shown in [9],
[10]. The speed range can be enlarged: this is true for SPM
machine [11] but also for Interior PM machine [12].
This paper focuses on a characteristic not yet described
for 20-8-5 SPM machine. In [13], it is shown that, for five-
phase SPM machine, a quite simple third harmonic current
injection can be used to virtually eliminate the pulsating
torque. The trouble is, except in case of particular design,
the smoother torque is obtained for a lower average torque.
The present study shows that, with a proper but quite simple
design of the rotor magnet layer, it is possible to inject third
harmonic to increase the average torque and to reduce the
ripple torque in the same time, which is particularly useful
at low speed. The paper will be divided into three parts.
The first part introduces the multi-machine decomposition for
five-phase SPM machine in order to determine bi-harmonic
(first and third) current control strategies. The second part
addresses the design of the 20-8-5 machine. A high number of
machines are simulated with Finite-Elements Analysis (FEA)
in order to select the best solution regarding the ripple torque
reduction. To demonstrate the improvement regarding three-
phase machines, 12-8-3 machines are also examined. The last
part focuses on the time simulation of the drive to preliminary
evaluate the possible influence of the current control on the
ripple torque and the rotating speed deviation.
II. M
ULTI-MACHINE DECOMPOSITION OF FIVE-PHASE
SPM MACHINE TO DETERMINE CONTROL STRATEGIES
A. Multi-machine decomposition of a five-phase machine
If the magnetic saturations and the demagnetization issue
are not considered, it can be shown that a star-connected five-
phase SPM machine behaves as two two-phase virtual ma-
chines that are magnetically independent but electrically and
mechanically coupled [14]. Furthermore, as the rotor saliency
can be neglected with SPM machines, the space harmonics
are distributed among the two virtual machines: the virtual
machine sensitive to the fundamental is called Main Machine
(MM) whereas the other sensitive to the third harmonic is
called Secondary Machine (SM). The space harmonics are
distributed according to the following law:
• MM is sensitive to 1
st
, 9
th
, (10k ± 1)
th
harmonics
• SM is sensitive to 3
rd
, 7
th
, (10k ± 3)
th
harmonics
Actually the virtual machine is a physical reading of the
mathematical subspace built on the linear application that
describes the phase-to-phase magnetic couplings: this two-
dimension subspace is usually represented with αβ-axis circuit
in stationary frame or with dq-axis circuit in rotating frame.
MM and SM are also characterized by their cyclic inductances
that will be of the same order with a tooth-concentrated
winding, thus making easier the current regulation of the two
virtual machines in case of PWM controlled voltage inverter.
B. Electromagnetic torque calculation
Therefore the five-phase machine electromagnetic torque T
is the sum of the torque produced by the Main Machine T
1
and
the Secondary Machine T
3
.Ifγ denotes the electrical angle,
the following expression is obtained:
T (γ)=T
1
(γ)+T
3
(γ) (1)
In case of first and third harmonic current control strategy,
MM and SM torques can be expressed as follows:
T
1
(γ)=
5
2
1
I
1
cos θ
1
+ t
1
(γ) (2)
T
3
(γ)=
5
2
3
I
3
cos θ
3
+ t
3
(γ) (3)
In (2) and (3),
1
and
3
are the first and third harmonics
of the no-load back-emf (at one rad/s speed), I
1
and I
3
are
the first and third harmonics of the current and θ
1
and θ
3
are the current-to-back-emf angles for first and third harmonic
respectively. t
1
and t
3
denote the pulsating torques. According
to the space harmonic distribution property, the MM pulsating
torque t
1
(γ) results from the interaction of the fundamental
of the current with particular back-emf harmonics (1
st
, 9
th
,
(10k ± 1)
th
) . The same applies for the SM pulsating torque
t
1
(γ) that results from the interaction of the 3rd harmonic of
current with particular back-emf harmonics (3
rd
, 7
th
, (10k ±
3)
th
).
C. Control strategy
At low speed, Maximum Torque Per Ampere (MTPA) con-
trol is wanted, thus meaning that, for both virtual machines,
back-emf and current should be aligned. Thus the current-to-
back-emf angles equal zero. Therefore, if r denotes I
3
rms
current to I
1
rms current ratio and I
b
the rated rms current of
the machine (that determines the copper losses), the control
strategy can be summarized as follows:
⎧
⎪
⎪
⎨
⎪
⎪
⎩
(I
1
,θ
1
)=
I
b
√
1+r
2
, 0
(I
3
,θ
3
)=
rI
b
√
1+r
2
, 0
(4)
MTPA is obtained if ratio r equals back-emf
3
to back-emf
1
ratio:
r
boost
=
3
1
(5)
With this approach, third harmonic current injection increases
the average torque. This strategy is called h1h3-boost. With
this strategy, the trouble is that the average torque enhancement
usually comes with more pulsating torque since the SM
pulsating torques t
3
add up to the MM ones t
1
.
In [13], a control strategy that aims at using the SM to
compensate the pulsating torque of the MM is introduced. This
control strategy is called h1h3-damp: it consists in choosing a
particular ratio r that depends of harmonics 7th, 9th, 11th and
13th of the back-emf, that is calculated in order to eliminate
the first harmonic of the pulsating torque.
r
damp
= −
11
−
9
13
−
7
(6)
The limitation of this strategy is that the SM operates as gener-
ator to absorb the pulsating torques of the MM, thus reducing
the average torque and the efficiency. The two introduced
controls (h1h3-boost and h1h3-damp) can be considered as
quite simple control in so far as they aim to regulate constant
currents in the dq-frames. In particular, h1h3-damp control
does not require a time varying d or q current components
to mitigate the ripple torques (as in [15]). Therefore the
implementation of the control with simple PI controllers can
be used since the necessary bandwidth of the controllers does
not relate to the frequency of the torque ripple.
III. M
ACHINE DESIGN
A. Objectives
The present section focuses on the 20-8-5 machine design to
make the two strategies h1h3-boost and h1h3-damp practically
similar. Hence third harmonic current injection will increase
the average torque and reduce the pulsating torque in the
same time. Due to its particular winding, the 20-8-5 machine
should be designed to be supplied with first and third harmonic
of current at low speed. Therefore the base idea consists in
designing the rotor such as third harmonic current injection
results in average torque increase (boost effect, see (5)) and
pulsating torque reduction (damp effect, see (6)) in the same
time. However attention must be drawn to the cogging torque
that can be very large for this kind of machine: magnet
segmentation is a solution to mitigate the cogging torque.
It should be mentioned that a quite simple design is aimed
for: simple magnet shape and no rotor or stator skewing.
Finally, in order to satisfy the pulsating and cogging torque
reduction constraints, solutions where the rotor consists in two
identical radially magnetized magnets are explored. As it can
be observed in Fig-1 that illustrates the electromagnetic circuit
of the machine over one pole pair, the magnet arc length τ
m
has to be chosen as a trade-off between cogging and pulsating
torque reduction.
τ
m
Fig. 1. Machine electromagnetic circuit (for τ
m
=1/3)
0.29 0.3 0.31 0.32 0.33 0.34 0.35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Magnet arc τ
m
to pole arc ratio
Δ T
h1h3−boost
/ Δ T
h1
1st harmonic
All harmonics
Fig. 2. Magnet arc τ
m
for which boost control reduces the pulsating torques
(referring to sinus control)
At the pre-design step, the influence of the magnet arc
length on the pulsating torque can be analyzed by using an
analytical two-dimensional field calculation that allows a quite
accurate estimation of the electromagnetic torque [16]. Thus
fig-2 shows the variation of the pulsating torque when using
boost control (denoted ΔT
h1h3−boost
, corresponding to (5))
out of the pulsating torque when using sinus control (denoted
ΔT
h1
, obtained by chosing r =0in (4)) according to the mag-
net arc length τ
m
. The dash line reports ΔT
h1h3−boost
/ΔT
h1
ratio change when only considering the first pulsating torque
harmonic whereas the solid line corresponds to the ratio
change when accounting the whole pulsating torque harmon-
ics. According to Fig-2, the boost control has damp effect if
the magnet arc length is chosen between 0.29 and 0.34 the
pole arc. The main machine parameters are listed in table I.
TABLE I
P
ARAMETERS FOR THE 5-PHASE MACHINE
Base point 9.5Nm @ 1000rpm
Pole pair number p =4
Slot number per phase per pole s
pp
=0.5
Effective length L
m
=0.050m
Stator Diameter 2R
s
=0.100m
Stator yoke thickness t
ys
=0.010m
Mechanical airgap g =0.001m
Rotor yoke thickness t
yr
=0.010m
Magnet layer thickness h
m
=3g
Remanent flux density B
r
=1.17T
Slot width (τ
s
, tooth pitch) 0.5τ
s
Slot width opening 0.25τ
s
Slot-closing thickness t
sc
=0.002m
Slot depth d
s
=0.0405m
B. Design exploration
In this part, the best design is found by using a numerical
two-dimensionnal field calculation (Finite Elements Analysis
FEA software FEMM, [17]). The advantages of the inves-
tigated 20-8-5 machine has to be discussed with regards to
an equivalent 12-8-3 machine (with the same rotor diameter,
magnet height and air gap).
Usually the rotor of 12-8-3 machine is made with a single
magnet per pole that covers two-third the pole pitch. For the
considered design specifications, according to FEA, such a
machine presents an excessive torque ripple: the peak cogging
torque is about 2.2Nm and the max-to-min full torque with
MTPA sinus control strategy is higher than 4.5Nm (that is
mostly 50% the rated torque). Consequently, skewing the rotor
or the stator would be necessary to mitigate the cogging torque,
thus making the manufacturing more complex. Controlling
the currents to mitigate the cogging torque is possible but
more complex and less robust than simply achieving constant
currents in the dq-frame. Finally, the investigated 20-8-5
machines with two magnets per pole is compared with an
equivalent 12-8-3 one, thus meaning that the equivalent 3-
phase machine is also equipped with a rotor made with two
identical radially magnetized magnets per pole.
Practically, by varying the pole arc to pole pitch ratio τ
m
from 0.25 to 0.49 by 0.01 step, 25 3-phase and 25 5-phase
machines are computed: for each of them, no-load and load
torques (9.5Nm) are calculated and recorded. Whatever the
magnet arc length is, the stator current is modified to make
the machine produce the rated average torque (the impact on
the thermal and inverter designs is not examined since the
goal is finding the less ripple torque solution). For the 3-phase
machine, sinus MTPA current control is supposed whereas, for
the 5-phase one, three current control strategies are computed:
• the MTPA h1h3-boost control introduced by eq.(5)
• the fundamental sinus current control (h1, all the torque
is produced by the MM, using the 4-pole polarity)
• the third harmonic current control (h3, all the torque is
produced the SM, using the 3×4-pole polarity).
Fig-3a represents the peak cogging torque change according
to the magnet arc length τ
m
. One can observe that the peak
cogging torque can be minimized by choosing τ
m
equal to
0.33 for the 5-phase machine and by choosing τ
m
equal
to 0.36 for the 3-phase one: nevertheless, according to the
FEA predictions, the minimum cogging torque for the 5-phase
machine is about two times lower than the 3-phase machine
one. This can be explained by lower slot openings for the
5-phase machine.
Fig-3b focuses on the pulsating torque change with magnet
arc length τ
m
for the 12-8-3 and 20-8-5 machines. The
pulsating torque can be reduced up to about 0.6Nm with the 3-
phase machine if the magnet arc length is 0.42 the pole pitch.
It can be observed that the possible pulsating torque reduction
is significantly better with the 5-phase machine: in case of
h1h3-boost control, a magnet arc length equal to 0.32 the
pole pitch corresponds to a pulsating torque of about 0.2Nm
(that is three times lower that the best 12-8-3 solution). For
20-8-5 machine, it is worth mentioning that the h1h3-boost
control reduces the pulsating torques referring to h1 control
if the magnet arc length is between 0.29 and 0.40 the pole
pitch, which is quite compliant with the analytical predictions
reported in Fig-2. Furthermore, with regards to h3 control, the
resulting pulsating torques are always reduced with the h1h3-
boost control if the magnet arc length is higher than 0.3 the
pole pitch. Finally, according to the numerical predictions, the
boost control has a damp effect if the magnet arc length is
between 0.3 and 0.4 the pole pitch.
Fig-3c reports the full ripple torque (cogging and pulsating)
for the 3-phase and 5-phase machines. As in Fig-3b, 5-phase
machine ripple torque is estimated for three current control
strategies: h1h3-boost, h1 and h3. First, one can observe that
the best torque ripple reduction is obtained for the 20-8-5
machine with h1h3-boost control: if the magnet pole arc is
0.33 the pole pitch, the max-to-min ripple torque is about
0.5Nm that is more than four times lower the value obtained
with the best 12-8-3 machine (about 2.2Nm, corresponding to
τ
m
=0.39). In addition, if the analysis is restricted on the 5-
phase machine, Fig-3c clearly shows that such a ripple torque
reduction can not be obtained with h1 or h3 controls. For these
two controls, the best result is obtained for h1 current control
applied to a machine with τ
m
=0.44: the ripple torque is then
about 1Nm, that is two times the best values (τ
m
=0.33 with
h1h3-boost control).
C. Results
The final design is the 20-8-5 machine with magnet length
equals one-third (0.33) the pole arc. The resulting electromag-
netic circuit is depicted in Fig.1. It is worth mentioning that
the final 5-phase machine has the same magnet volume as the
usual 12-8-3 one (with a single magnet per pole covering two-
third the pole pitch), examined at the beginning of subsection
III-B.
0.25 0.3 0.35 0.4 0.45 0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
Magnet Arc Length to Pole Pitch ratio τ
m
Max Cogging Torque (Nm)
12−8−3
20−8−5
(a) Peak cogging torque change with τ
m
0.25 0.3 0.35 0.4 0.45 0.5
0
1
2
3
4
5
6
7
Magnet Arc Length to Pole Pitch ratio τ
m
Max−to−min Em Torque (Nm)
12/8/3
20/8/5 (h1h3−boost)
20/8/5 (h1)
20/8/5 (h3)
(b) Max-to-min eletromagnetic torque change with τ
m
0.25 0.3 0.35 0.4 0.45 0.5
0
1
2
3
4
5
6
7
8
Magnet Arc Length to Pole Pitch ratio τ
m
Max−to−min Em Torque (Nm)
12/8/3
20/8/5 (h1h3−boost)
20/8/5 (h1)
20/8/5 (h3)
(c) Max-to-min full torque change with τ
m
Fig. 3. Magnet pole arc choice with regard to ripple torque