Maximising
the
saliency
ratio of the synchronous reluctance motor
D.A.
taton
T.J.E.
Miller
S.E.
ood
Indexing terms: Saliency ratio, Synchronous reluctance motor
Abstract:
Recent interest in the synchronous reluctance motor has increased in the context of possible applications in field oriented AC drives. The absence of rotor slip losses, and the apparent simplicity of the control, suggest the possibility of performance and cost advantages over the induc tion motor. With field oriented control, and con tinuous shaftposition feedback, the synchronous reluctance motor does not need a starting cage and can be designed for maximum saliency ratio
(LJL,
ratio). This ratio is by far the most import ant parameter for achieving high power factor, torque/ampere, and constantpower speed range. This paper analyses the various known forms of the synchronous reluctance motor, to determine the maximum achievable saliency ratio and iden tify the parameters on which it depends. The main srcinality is the analysis of the effect of the number of flux guides/barriers. It is shown that a minimum number is required for the performance to surpass that of the induction motor. The analysis also reveals the optimum ratio of flux guide/flux barrier thicknesses and the effects of the tooth/slot geometry and stator saturation. Test results are included from three motors ranging from
50
W at
2000
rpm to 7.5 kW at
1500
rpm, covering both axially laminated and transversely laminated types.
1
Introduction
1.
A
revival
of
interest in the synchronous reluctance motor
This paper explores the performance limits of the syn chronous reluctance motor when operated from a current controlled PWM inverter (i.e. with ‘field oriented’ control), and focuses on the saliency ratio
(Ld/Lq)
s the key design parameter. Line start synchronous reluctance motors have been used for many years, but their design is compromised by the need for a cage winding for starting and stable operation. The vector controlled motor needs no starting cage, and its electromagnetic design can be optimised for maximum saliency ratio.
EE,
1993 Paper 9344B (Pl), received 1st September 1992 D.A. Staton and T.J.E. Miller are with the Department
of
Electronics and Electrical Engineering, University
of
Glasgow, Glasgow G12
SLT,
United Kingdom
S.E.
Wood is at 3 Bowling Green Court, Stainland, Halifax, West York shire HX4 9QQ, United Kingdom
IEE PROCEEDINGSB,
Vol.
140, NO. 4, JULY 1993
The synchronous reluctance motor is seen
as
a pos sible replacement for ‘vector controlled’ induction motors, or at least as an extension to a range of induc tion motors, in which the controller could be simplified by taking advantage of the absence of slip. While the induction motor is gaining in popularity for adjustable speed drives, it has inherent limitations (e.g. limited torque at low speed and complex control algorithms). At low speed, the losses in the synchronous reluctance motor might be low enough to relieve the need for an external fan. For certain applications (e.g. high tem perature applications) the absence of magnets may be an advantage. Recent work has established the feasibility of field oriented control, with a certain flexibility in control char acteristics [19,
203
covering a wide speed range. Imple mentation in a PWM inverter has been shown to be relatively straightforward. The synchronous reluctance motor shares many
of
the advantages claimed for switched reluctance motors
[2],
but
it
uses
a
standard AC induction motor stator and a standard PWM inverter circuit. Like the induction motor, it is robust and brushless, and since it operates with a rotating magnetic field
it
is inherently smooth and quiet in operation. Its inertia is lower than that of the equivalent induction motor.
1.2
Development history
Almost all of the important performance parameters of the synchronous reluctance motor depend on the syn chronous inductance ratio or saliency ratio,
5
=
L,/L,.
The main classes of rotor design aimed at maximising
5
are shown in Fig.
1.
In all cases, the objective is to achieve a high
Ld
by providing, essentially, flux guides
for
daxis flux; and a low
L,
by providing flux barriers to qaxis flux. Since attention is restricted to inverter fed machines with field oriented control and shaft position feedback,
it
is assumed that a high saliency ratio can be pursued without concern for the stability problems that may arise in line start motors
[SI.
Several of the key papers published in the
1960s
and 1970s, on line start reluctance motors, provide reviews of early work and discuss the geometry needed to achieve a high saliency ratio [7,
9,
101.
Some early workers recog nised the ultimate potential of the reluctance motor, but This work was supported by the
UK
Science and Engineering Research Council, the SPEED Con sortium, Brook Crompton Parkinson (Small Industrial Motors Division), and Lucas Advanced Engineering Research Centre.
249
could not achieve it in practice because they did not have field oriented controllers [ll, 121. A brief discussion
of
alternative rotor geometries is helpful. It is convenient to distinguish between salient pole designs, Figs.
la,
b, single barrier designs, Fig. IC, d and multiple barrier designs, Figs. le,$ The socalled seg quotes a calculated value of 25.6, concluding that the maximum torque is 80% of that of an ‘average’ induction motor (1923 vintage ) of the same size. Kostko also rec ognised that the effect
of
slot leakage flux (which adds to both
Ld
and
Lq)
could be decreased by having a large number of thin barriers, and states that even with only
Fig.
1
Main classes
of
synchronous reluctance rotor design
mental rotor design [lo] is of the multiple barrier type, but with a small number of ‘barriers’ (typically 23). The rotor in Fig. la is obtained by removal of material from a conventional induction motor rotor, either by a milling operation after casting the cage,
or
by punching before casting the cage. Rotors of this type (‘synchronous induction motors’) have simple construction, but the saliency ratio is too small to give competitive per formance. Fig. lb shows the salient pole construction, like a con ventional salient pole synchronous motor with the wind ings removed. This geometry was used by Lee [3] in a lowspeed sealed rotor motor, but he used a hermetic can around the rotor, increasing the airgap and decreasing the daxis inductance. More recently, Chiba and Fukao [4] described a twopole rotor, of similar type, using amorphous iron laminations in a high speed application. They reported an unsaturated inductance ratio
of
about 3, decreasing to about 2.5 under load. Hassan and Osheiba [5] considered several variants of this geometry, but reported no value of saliency ratio higher than 3.8. The development
of
more specialised rotors seems to have followed two distinct routes.
As
early as 1923, Kostko [6] analysed a rotor of the form of Fig. le embodying several features of both the main schools of later development, including the use of multiple flux bar riers, ‘segmental’ geometry, and a qaxis channel. Kostko points out the essential limitation of the salient pole design, namely, that
if
the interpolar cutout is widened to decrease the qaxis inductance, the pole arc is thereby narrowed, producing an unwanted reduction in
Ld.
He concludes, in effect, that the multiple barrier
or
seg mented arrangement is the natural way
to
make a synchronous reluctance motor because
it
involves no sac rifice of pole arc in the daxis. He calculates the unsatu rated saliency ratio for a rotor with
‘four
segments’, and ‘four segments’ the saliency ratio is ‘several times as great’ as with the salient pole design. Subsequent workers, generally aware of Kostko’s work, developed the geometry along two main lines: the segmental geometry
[
03 and the axially laminated geometry. In line start motors, the segmental rotor reached a high state of development in the work of Law renson [lo]. (See also Honsinger [13, 141.) The highest value quoted for
5
is that of Fong [7], who reported a value of 10.7 at no load and 5.3 under load. Lawrenson
[lo]
and Honsinger [13, 141 reported saturated values only slightly lower than Fong’s, all of the reported motors being in the range 110 hp. The power factors of these motors were generally in the range 0.550.7, but it is difficult to make a meaningful summary of the effi ciencies because of the variety of sizes and designs. All these workers recognised the improvements in per formance with increasing size, but very little
has
been published on larger motors. The literature consistently shows that, in its line start form, the axially laminated rotor produces a saliency ratio no higher than that of the segmental type. For example, Cruickshank
er
al.
reported a value
of
5.2
for
a
2.25
hp four pole motor. Rao [16] reported a full load value
of
6.8, but his motor was larger than the others discussed here. His 15 hp, fourpole line start motor achieved a power factor of
0.8
and an efficiency of 86% at full load. When the starting cage is removed, higher values of
5
are encountered. For example, Fratta
er
al.
[17] report a saturated value of 9.2 in a 20 kW motor. Lip0 [18] quotes performance figures for a sixpole motor which imply a saliency ratio of about 7. The cageless rotor in Fig.
Id
is distantly related to the segmental rotor. It is derived from the socalled interior magnet
PM
synchronous motor
[lZ,
151 by removing the
250
IEE PROCEEDINGSB,
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JULY 1993
magnets. The highest value oft reported for this design is
4.7
in a
6
kW motor
[l].
A figure of
4
was also achieved in a very small
(50
W) motor
[12].
What is surprising about all the reported saliency ratios is how far they fall short of Kostko's prediction of
25,
even for cageless designs. In the following Sections, this theoretical figure is redeveloped from a slightly dif ferent (but equally simple) basis, and it will be shown by finite element analysis why it cannot be achieved in prac tice with a fully loaded motor.
2
Basictheory
2.
Torque per ampere
The electromagnetic torque is the classical reluctance torque of the conventional synchronous machine, eqn.
1,
where
Id
and
I
are components of the RMS phase current
I
resolved along the d and qaxes of the phasor diagram, Fig.
2;
they correspond to the space
qaxis
I,%
I
PH
IPH
daxis
Fig.
2
Synchronous reluctance motor phasor diagram
vector components of stator MMF along the
d
and qaxes of the rotor. The torque is given by
rn
2
=
rnplJI,(LJ

L,)
=
lgH
sin
2y(Ld

L,)
(1)
Here,
rn
is the number of phases,
p
is the number of pole pairs, and
Ld
and
L,
are the direct and quadrature axis synchronous inductances, respectively. Note that
Xd
=
hfLd
and
X,
=
2nfL,,
where
f
is the frequency. The convention adopted here, in which the daxis is the high inductance axis, is the same as that used in the literature on the line start reluctance motor'. For maximum torque per ampere, the inductance difference
(Ld

L,)
should be maximised within constraints set by manufacturability, and the current angle
y
made equal to
45 .
Saturation in the daxis causes the maximum torque per ampere to occur at a value of
y
greater than
45 ,
and this value increases with increasing phase current (Section
6).
The inductance difference
(Ld

L,)
takes no account of the voltage requirements of the motor. The saliency ratio
(5
=
L,,/L,)
provides a more general guide to the overall performance, because the power factor, the speed range at constant power, and several aspects of the dynamic response, are all directly related to
[19,
203.
In
In References
1
and 12, the opposite convention was used, with the qaxis the high inductance axis, because the particular motors in those papers were related to the interior magnet hybrid motor in which the magnet axis
is
the low inductance direct axis.
general, the performance is improved as
t
is increased. In this paper, attention is focused on power factor: the effect of on the other parameters is discussed in References
19
and
20.
2.2
Power factor
The synchronous reluctance motor is intended to operate with sinewave currents, and therefore the fundamental
(or
'displacement') power factor cos
4
is used. It is related to the saliency ratio by the equation in 2y 2(tan
y
+
5
cot
y)
cos
4
=
(5

1)
in which
y
is the phase angle between the current and the daxis (Fig. 2). The inverter rating is closely related to the power factor and to the fundamental kVA requirement of the motor. Eqn.
2
assumes zero phase resistance
(RPH).
While this simplification is valid for motors with integral horsepower and larger rating, it is not valid when the resistance is comparable with
X,
,
as is the case in smaller motors. Neglecting
R,,,
the power factor has a maximum value of
51
cos
( J
=

with tan
y
=
,,/ )
(3)
Fig.
3
shows the variation in power factor with for
y
=
45 ,
and with
y
=
tan',,/((). To achieve a power factor greater than
0.8,
must exceed
9,
and
y
will have a value in excess of
71.6'.
Even with
=
9,
a power factor of only
0.625
is achievable when
y
=
45 .
r
B
6 01
t;
Bt
.5
L
i3 1
y=450
1.5
t
01
I
I
I
I
I
2
Ld/Lq
x
1.0el
Fig.
3
Variation in powerfactor with saliency ratio
3.1
Physical factors
For a fourpole motor with sinusoidally distributed wind ings,
if
the rotor is removed, the rotating magnetic field has the form of Fig.
4a.
By suitable choice of time srcin, the daxis can be aligned with the reference axis of the flux,
so
that all the flux is daxis flux, and the qaxis flux is zero. The saliency implied by this flux pattern is infin ite. The ideal rotor is one which is infinitely permeable along the flux lines in Fig.
4a,
and completely imperme able across them. This would require an hypothetical anisotropic material whose permeability was not only
Theoretical limits to the saliency ratio
IEE PROCEEDINGSE, Vol.
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1993
251
directional, but which also followed a pattern corres ponding to the natural shape of the flux lines. The axially laminated rotor approximates this arrangement. It has
daxis
/
\\
qaxis
/’
/’
Fig. 4
L
ideal rotor (current
sheet)
b
ideal rotor
(36
slots)
c
single barrier rotor
d
IOlayer rotor
e
24layer
rotor
J
axially laminated rotor
0132 synchronous reluctance
motor.flux
plots
laminations shaped to follow the daxis flux, and flux barriers which inhibit the qaxis flux. The achievable saliency ratio is limited by two factors that are immediately obvious:
(i)
the qaxis permeance cannot be zero; and (ii) the laminations are subject to saturation in the daxis.
A
third limiting factor, less obvious, is that (iii) if the laminations are too thick they can short circuit the stator slot openings; (as recognised by Kostko), effectively increasing the stator slot leakage inductance which adds
to
both
Ld
and
L,.
A
fourth limiting factor is (iv) end turn and other leakage inductances which add a ‘swamping term’ to both
Ld
and
L,
.
252
Two methods have been used to estimate the theoretical limits to saliency: a simple calculation based on the ideal flux paths, and a wide ranging study using finite element analysis.
3.2
Simple estimate
of
maximum saliency ratio
Assume that the laminations and flux barriers are every where very thin, and let
t
be the average ratio of flux barrier thickness to the combined thickness of lamination and flux barrier. Then
1/ 1

)
is a measure of the flux concentration that occurs in the laminations owing to the
loss
of effective daxis pole arc to the flux barriers. For a peak airgap flux density of
0.8
T and a saturation density of around 1.7 T,
t
must be limited to the order of
0.5.
Now the synchronous reactance
xd
is inversely pro portional to the airgap length
g,
and, by the methods of Reference 2, it can be shown that
X,
is inversely pro portional to the sum of
g
and the combined thickness of the flux barriers, which is of the order of
tR,
where
R
is the rotor radius. Therefore the saliency ratio is given approximately by
4)
=A=
tR
+
9)

R
,
x
9 9
With
t
=
0.5
and
R/g
typically 120, this indicates a maximum unsaturated saliency ratio of about
60,
which is even larger than Kostko’s prediction of 25. This simple theory explains the limitation due to the finite qaxis per meance (factor 1 above), but the limitations due to the other two factors are more difficult to estimate, and require finite element analysis in the context of the whole design of the motor. Nevertheless, the unsaturated figure of
60
represents a yardstick against which practical designs can be evaluated.
3.3
Finite element analysis
of
maximum saliency ratio
Theoretical limits on
L,
and
Ld
can be defined using a fictional motor model which approximates the proper ties of the ideal anisotropic material discussed in Section
3.1.
The daxis flux distribution is computed with a solid rotor having a normal
B/H
characteristic. The qaxis flux distribution is computed with the rotor removed alto gether. The ideals of infinite permability in the daxis and zero permeability in the qaxis are thus relaxed to what might be achievable with real materials.
A
further ideal isation is to represent the stator winding as an infinitely thin current sheet located on a smooth bore. This will give a benchmark against which the effects of slotting can be assessed. The qaxis and daxis flux plots for the ideal motor (in a D132 frame size) are shown in Fig.
4a
while the saliency ratios at two levels of phase current are given in the first row of Table 1. Saturation is minimal in this ideal machine, even at the maximum current of 15 A, and the saliency ratio of about
60
corresponds quite closely to the simple estimate in Section 3.2.
Table
1
:
D132
motor saliency ratios
(y
=
45”)
Design Unsaturated Saturated Ideal rotor
+
current sheet Ideal rotor
+
36 slot stator Single barrier
+
36 slots 3layer
+
36 slots 10layer
+
36 slots 24layer
+
36 slots Axial lamination
+
36 slots Ideal rotor
+
24 slot stator 24laver
+
24 slots
I
=
1 amp 61.70 30.76 1.72 6.68 10.09 11.21 11.63 26.53 9.57
I
=
15 amp 57.56 20.53 4.66 5.43 8.1 6 8.73 8.69 17.50 6.89
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PROCEEDINGSB,
Vol. 140,
No.
4,
JULY
1993