Abstract—This paper compares two motors as regard theirbehaviour during sensorless rotor position detection by means ofinjection of a high frequency signal. The motors are characterizedby the presence of a ring around each pole and by differentwindings: a distributed coil winding and a concentrated coilwinding. The effect of eddy currents in the magnets, due to thehigh frequency signal, is also considered. The effect of the slotopening is also taken in consideration. Finally, the comparisonwith two different PM rotor topologies, an interior PM motorand a INSET motor, is addressed.
I. INTRODUCTION
In the last years, the solution of tracking the rotor saliency
at low and/or zero speed [1], [2] has been largely adopted for
the electrical position estimation. To this purpose, the motor
has to present an anisotropic rotor characteristic. As far as
the Interior Permanent Magnet (IPM) synchronous machine is
concerned, it exhibits a different value of direct and quadrature
inductances, i.e. an anisotropic rotor, that makes simpler the
rotor position estimation [3], [4].
In the same way, the INSET motor offers a magnetic
saliency [5] in spite of its Surface Permanent Magnet Mounted
(SPM) rotor configuration. On the other hand, the presence
of cross–saturation between the d– and q–axis produces an
angular error in the rotor position detection [6].
In the case of the (SPM) synchronous machine, its isotropic
rotor characteristic does not allow the identification of the rotor
position. A possible solution is that to exploit the saturation
map due to the Permanent Magnets (PMs), but this is not
applicable for all motors.
There are some strategies to attain a different electromag-
netic behaviour along the d– and q–axis in the SPM motor. A
demonstrated valid solution is the insertion of short circuited
ring around each pole [4].
The resulting motor, called as ringed–pole SPM motor, is
shown in Fig. 1. The photo of the 6–pole rotor prototype is
reported in Fig. 2.
A different electromagnetic behaviours along the d– and the
q–axis is obtained at high frequency thanks to the presence of
the rotor rings.
The Ringed–Pole solution has been tested with a distributed
coil winding. The possibility to use this configuration with a
concentrated coil stator winding is investigated in this paper.
The feasibility of the solution, the effect of the saturated
iron and the influence of the permanent magnet currents is
discussed. A comparison with an IPM motor and a INSET
PM motor is also addressed.
Fig. 1. Scheme of the coil around the magnet of an SPM motor
Fig. 2. SPM rotor with short circuited rings around the poles
II. SENSORLESS CAPABILITY
Two kinds of motor are investigated: with distributed coil
winding (number of slots per pole per phase q = 1.5) and
concentrated–coil winding (q = 0.5). Finite Elements Method
(FEM) simulations have been carried out in the frequency
domain, with the aim to investigate the effect of a conductive
ring around the poles. As shown in [7] the effect of such a ring
is to create a high frequency rotor anisotropy. Since the PMs
are conductive, there is a slight effect on the rotor anisotropy
just due to that conductivity.
In the following FEM analysis, the effect of the ring is
separated from the effect of the PMs. During simulations, three
cases have been analyzed:
case 1 , where only the effect of the PMs (magnet con-
ductivity σPMs = 0.69 MS/m) is considered, i.e.
without the ring;
case 2 , with the effect of both the ring and the magnets;
case 3 , with only the effect of the ring (σPMs = 0).
The rotor iron conductivity is imposed to be zero (σIr = 0)
in the simulations, since the rotor is laminated. The frequency
range spans from 10 Hz to 8 kHz. Finally the ring conduc-
tivity is equal to σring = 40.
FEM simulations have been carried out with current in
both d and q axis. As reported in [8], in order to derive
the sensorless rotor position detection capability, a sinusoidal
current at different frequency is imposed in the stator winding.
2011 IEEE International Electric Machines & Drives Conference (IEMDC)
The rotor is placed in two different positions with respect the
stator field as shown in Fig. 3(b) and Fig. 3(a).
(a) Only d–axis current supplied (b) Only q–axis current supplied
Fig. 3. High frequency impedance measurement scheme
In Fig. 3(a), the magnetic field is along the q–axis and then
the q–axis impedance can be computed as the ratio between
the voltage and current. In the case reported in Fig.3(b),
the magnetic field is along the d–axis and then the d–axis
impedance can be computed. Such a procedure is applied
to investigate sensorless capability of both distributed and
concentrated coil windings.
Because of the short circuited rings, a saliency dependently
to the frequency can be defined as ratio of the q– and d–axis
impedance [8]:
ξ(ωh) =Zq
Zd
=Rr + jωhLr
Rr + jωhLrt
(1)
The terms Rr and Lr are the ring resistance and inductance
respectively. The term Lrt is the rotor transient inductance,
defined as:
Lrt = Lr −L2
M
Ld
(2)
where Ld is the d–axis inductance and LM is the mutual
inductance between the ring and the d–axis stator windings.
Using FEM simulations, the saliency ξ can be obtained from
the ratio λq/λd performed for each frequency.
III. DISTRIBUTED COIL WINDING
A motor with 27–slots 6–poles has been firstly investigated.
The motor is sketched in Fig. 4. Such configuration corre-
sponds to the motor prototype available in laboratory. The
tests on such machine and the comparison with the simulation
results [8].
Fig. 4. 27–slot 6–pole motor (distributed coil winding)
Fig. 5 shows the d–axis flux linkage versus the frequency
when the rotor is aligned as in Fig. 3(a). There is the maximum
coupling between the winding and the ring.
Comparing case 1 with case 2, one can note the effect of
the presence of the ring. The d–axis flux linkage decreases
as the frequency increases, and this effect is more evident for
case 2.
Assuming a zero PM conductivity, case 3, only the effect
of the ring is considered. Comparing case 2 with case 3 one
can see that the PMs yield a further reduction on the d–axis
flux linkage. Considering an injection frequency of 1 kHz, the
ring effect is necessary to obtain an appreciable high frequency
saliency for the rotor position estimation.
Fig. 6 shows the flux on q–axis versus the frequency when
the rotor is aligned with the stator field (Fig. 3(b)). In this case
the effect of the ring is not appreciable (case 2 and case 3)
(that is it has no effect on q–axis flux). On the contrary the
presence of the PMs yields an effect on the q flux (case 1 and
case 2).
0 2000 4000 6000 80001.5
2
2.5
3
frequency (Hz)d−
axis
flu
x lin
kage (m
Vs)
case 1
case 2
case 3
Fig. 5. d–axis flux versus frequency (stator field along the d–axis) withdistributed coil winding
Fig. 7 shows the saliency versus the frequency. At first, a
small saliency of about 1.07 can be noticed at low frequencies.
It is due to the slight rotor anisotropy of the rotor iron, since
the PMs are separated by a small iron tooth (see Fig. 4). If
only the ring is considered (case 3), the saliency spans from
1.07 to about 1.65. At the frequency of 1 kHz an appreciable
saliency value is found: with the ring the saliency increases
from 1.1 (case 1) to 1.3 (case 3). This value increases to 1.4considering also the PMs (case 2).
If the ring is removed (case 1), PMs yield a saliency
variation, but it appears at higher frequencies. Since the
frequency of interest is around 1 kHz or lower, no saliency
variation due to only PMs is achieved.
Fig. 8 shows the phase inductance versus the rotor electric
angle, achieved for a frequency of 1 kHz. The anisotropy
obtained by injecting a high frequency signal is significant
0 2000 4000 6000 80002
2.5
3
3.5
frequency (Hz)
q−
axis
flu
x lin
kage (
mV
s)
case 1
case 2
case 3
Fig. 6. q–axis flux versus frequency (stator field along the q–axis) withdistributed coil winding
594
only if a ring is present around the pole, and the effect of the
PMs conductivity is beneficial to improve the saliency.
101
102
103
104
105
1
1.5
2
frequency (Hz)
sa
lien
cy r
atio
(−
)
case 1
case 2
case 3
Fig. 7. Saliency versus frequency with distributed coil winding
0 50 100 1504.5
5
5.5
6
6.5
Electrical position, θme
(rad)
Inducta
nce, L (
mH
)
case 1
case 2
case 3
measurement
Fig. 8. Inductance versus rotor electric angle with distributed coil winding
In order to confirm the accuracy of the FEM motor model,
the stator inductance is derived by means of experimental tests.
Tests have been carried out moving the rotor with steps of
15 el.deg.. The measured stator inductances are reported in
Fig. 8 (square marker), compared with the FEM results (solid
line). There is a good agreement between the measurements
and predictions confirming the accuracy of the motor model.
IV. CONCENTRATED COIL WINDING
The aim of this section is to compare the sensorless rotor
position detection capability of a motor with non–overlapped
coil winding with those obtained from the previous motor.
The motor with 9–slots 6–poles sketched in Fig. 9 is
considered. The same rotor of the 27–slot 6–pole motor shown
in Fig. 4 is considered. Since the coil throw is unity, the motor
results with non–overlapped coils winding.
The motor with 9–slots and 6–poles has been modeled with
a different slot opening (see Fig. 10), with the aim to determine
which is its effect on the saliency.
Firstly, the motor model with a wide slot opening is consid-
ered. Figs. 11 and 12 show d– and q–axis flux linkages versus
frequency. Fig. 13 shows the saliency versus frequency and
Fig. 14 the inductance versus rotor electric angle at 1 kHz.
In the following, the motor model with a narrow slot
opening is considered. Figs. 15 and 16 show d– and q–axis flux
linkages versus frequency. Fig. 17 shows the saliency versus
frequency and Fig. 18 the inductance versus rotor electric
angle at 1 kHz.
The results are similar to those obtained from the previous
motor; the main differences are on the flux linkage amplitudes,
Fig. 9. 9–slot 6–pole motor (concentrated coil winding)
Fig. 10. 9–slot 6–pole motor (concentrated coil winding)
0 2000 4000 6000 80002
3
4
frequency (Hz)d−
axis
flu
x lin
kage (m
Vs)
case 1
case 2
case 3
Fig. 11. d–axis flux versus frequency (stator field along the d–axis) withconcentrated coil winding, wide slot opening
0 2000 4000 6000 80003
3.5
4
frequency (Hz)
q−
axis
flu
x lin
kage (
mV
s)
case 1
case 2
case 3
Fig. 12. q–axis flux versus frequency (stator field along the q–axis) withconcentrated coil winding, wide slot opening
but the behaviour under high frequency signal injection is
comparable. It can be concluded that also this motor is reliable
for position detection using high frequency signal injection.
The width of the slot opening influences the saliency at high
frequency, but the motor behaviour is unchanged, so that the
sensorless capability with injection of high frequency signals
remains still working.
V. EFFECT OF THE IRON SATURATION
With the aim to consider the effect of iron saturation on the
motor model, the mutual inductance between the ring and the
winding has been computed for different motor working point.
To this aim, some FE simulations have been carried out on a
wide range of Id Iq current.
595
101
102
103
104
105
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
frequency (Hz)
sa
lien
cy r
atio
(−
)
case 1
case 2
case 3
Fig. 13. Saliency versus frequency with concentrated coil winding, wide slotopening
0 50 100 1505.5
6
6.5
7
7.5
Electrical position, θme
(rad)
Inducta
nce, L (
mH
)
case 1
case 2
case 3
Fig. 14. Inductance versus rotor electric angle with concentrated coil winding,wide slot opening
0 2000 4000 6000 80004
5
6
frequency (Hz)d−
axis
flu
x lin
kage (m
Vs)
case 1
case 2
case 3
Fig. 15. Saliency versus frequency with concentrated coil winding, narrowslot opening
0 2000 4000 6000 8000
5.6
5.8
frequency (Hz)
q−
axis
flu
x lin
kage (
mV
s)
case 1
case 2
case 3
Fig. 16. Inductance versus rotor electric angle with concentrated coil winding,narrow slot opening
Figs. 19 and 20 show the mutual inductance LM in the
d− q current plane. As expected, the mutual inductance LM
depends on the Id current only, while it is almost independent
from Iq current. Along the MTPA trajectory LM is practically
constant, independently from the current magnitude.
101
102
103
104
105
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
frequency (Hz)
sa
lien
cy r
atio
(−
)
case 1
case 2
case 3
Fig. 17. Saliency versus frequency with concentrated coil winding, narrowslot opening
0 50 100 1509.5
10
10.5
11
11.5
12
Electrical position, θme
(rad)
Ind
ucta
nce
, L
(m
H)
case 1
case 2
case 3
Fig. 18. Inductance versus rotor electric angle with concentrated coil winding,narrow slot opening
−10 −5 0 5 100
1
2
3
4
5
6
7
8
9
10
Id (A)
Iq (
A)
37.5
37.5
38
38
38
38.5
38.5
38.5
39
39
39
39.5
39.5
39.5
40
40
40
40.5
40.5
40.5
41
41
41
41.5
41.5
41.5
42
42
42
42.5
42.5
42.5
Fig. 19. Map of LM (µH) with distributed coil winding
Substituting the LM values obtained in Figs. 19 and 20
in (1), the magnetic saliency at 1 kHz is equal to 1.3 with
the distributed coil winding and 1.15 with the concentrated
coil winding (narrow slot opening). These values are in
good agreement with the results reported in Figs. 7 and 17.
The saliency remains practically constant along the MTPA
trajectory for both the motors, since the saturation effect is
negligible. However, in all the d−q plane the saliency variation
is quite low, remaining around the aforementioned values.
596
−6 −4 −2 0 2 4 60
1
2
3
4
5
6
7
Id (A)
Iq (
A)
33
33
33
34
34
34
35
35
35
36
36
36
37
37
37
38
38
38
39
39
39
40
40
40
41
41
41
42
42
42
MTPA trajectory
Fig. 20. Map of LM (µH) with concentrated coil winding
VI. COMPARISON WITH OTHER MOTOR TOPOLOGIES
Two different PM motor topologies have been compared
with the ringed–pole motor solution. An interior PM (IPM)
motor, shown in Fig. 21(a), and an INSET motor, shown
in Fig. 21(b). Both motors present a magnetic saliency due
to the difference between the Ld and Lq inductances. Such
a magnetic saliency varies with the load, that is, with the
magnetic loading.
(a) 9–slot 6–pole IPM motor (b) 9–slot 6–pole INSET motor
Fig. 21. 9–slot 6–pole IPM and INSET motor with concentrated coil winding
These motors have been analyzed by means of FE simu-
lations. Their sensorless capability can be studied using the
small signal magnetic saliency [9]:
ξωh=
1 + b/f
1− b/f(3)
where b/f is the ratio between the amplitude of the backward
and forward sequence of the current signal, given by
b
f=
√
(Ld − Lq)2 + M2
dq
Ld + Lq
(4)
where Ld and Lq are respectively the d– and q–axis differen-
tially inductances and Mdq is the dq mutual inductance due
to the cross–saturation.
Figs. 22 and 23 show the anisotropy ratio given by (3) for
the IPM and the INSET motor respectively. In the same plane,
the trajectory of the Maximum Torque per Ampere (MTPA)
−15 −10 −5 0 5 10 150
2
4
6
8
10
12
14
16
Id (A)
Iq (
A)
1.1
1.2
1.3
1.3
1.4
1.4
1.4
1.5
1.5
1.5
1.5
1.5
2
2
2
22
2
2
3
3
3
3
3
3
3
4
4
4
4
45
5
5
5
6 6
6
Saliency
MTPA trajectory
Fig. 22. Magnetic saliency ξωhin the d–q plane, IPM motor
−15 −10 −5 0 5 10 150
2
4
6
8
10
12
14
16
Id (A)
Iq (
A)
1.3
1.3
1.4
1.4
1.4
1.4
1.4
1.4
1.5
1.5
1.5
2
2
2
3
3
Saliency
MTPA trajectory
Fig. 23. Magnetic saliency ξωhin the d–q plane, INSET motor
is reported (circle line), so as to highlight the operating points
of the motor. One can note that in both the cases the magnetic
saliency remains high in all the left–half plane and then there
is not a critical zone from the control point of view. However,
the mutual inductance due to the cross-saturation causes an
error in the estimated position. This error is given by [6]:
ǫ =1
2arctan
2Mdq
Ld − Lq
(5)
As regard the IPM machine, the estimated error increases
along the MTPA curve as shown in Fig. 24. The trajectory
Ld = Lq and Mdq = 0 are also shown. When the curve
Ld = Lq crosses the curve Mdq = 0 the sensorless detection
of the rotor position is not possible, since the saliency (3) is
unity, as highlighted in Fig.22.
As far as the INSET motor is concerned, Fig. 25, the
estimated error along the MTPA curve is lower than the IPM
case. This occurs because the curve Mdq = 0 is very close to
the MTPA curve. The limit Ld = Lq is not present since it is
out of the plot limits.
In the case of the ringed–pole motor, the high frequency
saliency is guaranteed from the ring effect in all the d–qplane. Moreover, being negligible the cross saturation effect,
(due to the rotor configuration with surface–mounted PMs) no
estimated error occurs. From the control point of view, this
is a significant advantage respect to both IPM and INSET
597
Fig. 24. Estimated error in the d–q plane, IPM motor.
−15 −10 −5 0 5 10 150
2
4
6
8
10
12
14
16
Id (A)
Iq (
A)
−30
−20
−2
0
−20
−20
−15
−15
−15
−15
−10
−10
−10
−10−5
−5
−5
−5
5
5
5
5
5
5
10
Mdq
=0
MTPA trajectory
Fig. 25. Estimated error in the d–q plane, INSET motor.
motors. In fact, any compensation estimated error has to be
implemented in the sensorless drive.
VII. CONCLUSIONS
Two ringed–pole SPM motors are compared according to
their behaviour in case of sensorless control at zero speed.
One has a distributed coil winding, the other a concentrated
coil winding. It is shown that a ring around each rotor pole
represent an effective method to create a high frequency
saliency, also when a fractional–slot winding is adopted.
The effect of eddy currents in the magnets due to the high
frequency injected signal is also investigated. It is shown
that eddy currents in the PMs give a useful contribution on
increasing the saliency, but they are not enough to create the
saliency without the ring.
Furthermore, the position detection by means of high fre-
quency signal injection has been used in two other PM motors:
an IPM motor and an INSET motor. It is shown they are
suitable for sensorless purpose, since they present an adequate
saliency. Nevertheless, a compensation algorithm is necessary,
since a position estimation error, due to the presence of the
mutual dq coupling, rises up. On the contrary, in the ringed–
pole solution, the mutual coupling is negligible. This leads to
have a negligible position estimation error, too.
REFERENCES
[1] L. Wang and R. Lorenz, “Rotor position estimation for permanentmagnet synchronous motor using saliency-tracking self-sensing method,”in Industry Applications Conference, 2000. Conference Record of the
2000 IEEE, 2000.[2] P. Jansen and R. Lorenz, “Transducerless position and velocity estimation
in induction and salient ac machines,” IEEE Transactions on Industry
Applications, vol. 31, no. 2, pp. 240 –247, 1995.[3] H. Kim and R. Lorenz, “Carrier signal injection based sensorless control
methods for ipm synchronous machine drives,” in Conference Record of
the 2004 IEEE Industry Applications Conference, 2004. 39th IAS Annual
Meeting., vol. 2, 2004, pp. 977 – 984 vol.2.[4] S. Bolognani, S. Calligaro, R. Petrella, and M. Tursini, “Sensorless control
of ipm motors in the low-speed range and at stand-still by hf-injectionand dft processing,” in IEEE International Electric Machines and Drives
Conference, 2009. IEMDC ’09., May 2009, pp. 1557 –1564.[5] N. Bianchi, S. Bolognani, J.-H. Jang, and S.-K. Sul, “Advantages of inset
pm machines for zero-speed sensorless position detection,” IEEE Trans.
on Industry Applications, vol. 44, no. 4, pp. 1190 –1198, 2008.[6] N. Bianchi, S. Bolognani, and A. Faggion, “Predicted and measured
errors in estimating rotor position by signal injection for salient-polepm synchronous motors,” in IEEE International Electric Machines and
Drives Conference, 2009. IEMDC ’09., May 2009, pp. 1565 –1572.[7] A. Faggion, S. Bolognani, and N. Bianchi, “Ringed-pole permanent
magnet synchronous motor for position sensorless drives,” in IEEE
Energy Conversion Congress and Exposition, 2009. ECCE 2009., 2009,pp. 3837 –3844.
[8] A. Faggion, N. Bianchi, and S. Bolognani, “A ringed–pole spm motorfor sensorless drives – electromagnetic analysis, prototyping and tests,”in IEEE International Symposium on Industrial Electronics, ISIE 2010,Bari, IT, Jul. 4–7, 2010.
[9] P. Guglielmi, M. Pastorelli, and A. Vagati, “Cross-saturation effects in ipmmotors and related impact on sensorless control,” Industry Applications,
IEEE Transactions on, vol. 42, no. 6, pp. 1516 –1522, 2006.
![Page 1: [IEEE Drives Conference (IEMDC) - Niagara Falls, ON, Canada (2011.05.15-2011.05.18)] 2011 IEEE International Electric Machines & Drives Conference (IEMDC) - Sensorless capability of](https://reader030.documents.pub/reader030/viewer/2022020212/57509f6f1a28abbf6b19ae77/html5/thumbnails/1.jpg)
![Page 2: [IEEE Drives Conference (IEMDC) - Niagara Falls, ON, Canada (2011.05.15-2011.05.18)] 2011 IEEE International Electric Machines & Drives Conference (IEMDC) - Sensorless capability of](https://reader030.documents.pub/reader030/viewer/2022020212/57509f6f1a28abbf6b19ae77/html5/thumbnails/2.jpg)
![Page 3: [IEEE Drives Conference (IEMDC) - Niagara Falls, ON, Canada (2011.05.15-2011.05.18)] 2011 IEEE International Electric Machines & Drives Conference (IEMDC) - Sensorless capability of](https://reader030.documents.pub/reader030/viewer/2022020212/57509f6f1a28abbf6b19ae77/html5/thumbnails/3.jpg)
![Page 4: [IEEE Drives Conference (IEMDC) - Niagara Falls, ON, Canada (2011.05.15-2011.05.18)] 2011 IEEE International Electric Machines & Drives Conference (IEMDC) - Sensorless capability of](https://reader030.documents.pub/reader030/viewer/2022020212/57509f6f1a28abbf6b19ae77/html5/thumbnails/4.jpg)
![Page 5: [IEEE Drives Conference (IEMDC) - Niagara Falls, ON, Canada (2011.05.15-2011.05.18)] 2011 IEEE International Electric Machines & Drives Conference (IEMDC) - Sensorless capability of](https://reader030.documents.pub/reader030/viewer/2022020212/57509f6f1a28abbf6b19ae77/html5/thumbnails/5.jpg)
![Page 6: [IEEE Drives Conference (IEMDC) - Niagara Falls, ON, Canada (2011.05.15-2011.05.18)] 2011 IEEE International Electric Machines & Drives Conference (IEMDC) - Sensorless capability of](https://reader030.documents.pub/reader030/viewer/2022020212/57509f6f1a28abbf6b19ae77/html5/thumbnails/6.jpg)
