hed Reluctance
Motor
2.1
Introduction
Switched reluctance motor (SRM) drives are simpler in construction compared
to induction and synchronous machines. Their combination with power elec-
tronic controllers may yield an economical solution [Bos 04]. The structure of
the motor is simple with concentrated coils on the stator and neither windings
nor brushes on the rotor. This apparent simplicity of its construction is decep-
tive [Ste 95]. The Switched Reluctance Motor drives present several advantages
as high eciency, maximum operating speed, good performance of the motor
in terms of torque/inertia ratio together with four-quadrant operation, mak-
ing it an attractive solution for variable speed applications [Giu 91]. The very
wide size, power and speed range together with the economical aspects of its
construction, will give the SRM place in the drives family.
The performances of switched reluctance motor strongly depend on the
applied control. Figure 2.1 shows the principal parts of a switched reluctance
drive. Three main parts can be identied: the motor itself, which can have var-
ious topologies as explained in the next section, the power electronic converter
and the controller. The drive system, comprising signal processing, power con-
verter and motor must be designed as a whole for a specic application.
There is one converter unit per phase. A battery or a rectier supplies the dc
power. The basic principle is simple: each phase is supplied with dc voltage by
its power-electronic converter unit as dictated by the control unit, developing
a torque, which tends to move the rotor poles in line with the energized stator
poles in order to maximize the inductance of the excited coils. An important
fact is that the torque production is independent of the direction of current,
13 14
Principle of Operation
ß
U
DC
Converter
Controller
Phase current
SRM
Rotor position
Figure 2.1: Switched reluctance drive system.
which contributes to the reduction of the number of switches per phase.
This chapter presents the main topologies of switched reluctance motors,
the energy ows and control variables.
The electromagnetic principles are
described along classical lines. The machine operations in all of its four quad-
rants, the torque versus speed characteristics, and the mathematical model of
the equivalent circuit are formulated. The magnetically linear model is used
to provide a structure for understanding the SRM control. The chapter pro-
vides the description of a four-phase 8/6 SRM motor and its control scheme.
The simulated annealing method is proposed to nd the optimal speed con-
troller gains. The simulations carried out and their most important results are
discussed.
2.2
Machine Topologies
As any other motor, the structure of the switched reluctance motor consists
of a stator and a rotor. Both stator and rotor are laminated. Stacking the
laminations punched from steel lamination with high magnetic quality yields
the rotor cores. The stator is formed from punched laminations too bonded
into a core, and the coils are placed on each of the stator poles.
Each stator pole carries an excitation coil, and opposite coils are connected
to form one phase. There are no windings on the rotor. The number of stator
and rotor poles are chosen using a series of criteria developed in Chapter IV.
In this chapter it is supposed that the number of rotor poles N
r
, and stator
poles N
s
are known without discussing the criteria for their choice.
Switched reluctance machines can oer a wide variety of aspect ratios and
salient pole topologies without aecting performance too much. This means
that each application is likely to be better suited for a specic SR topology.
Single Phase Motor
These are the simplest SR motors having the advantage of fewest connections
between machine and power electronics. However, the very high torque ripple 2.3. Basic SRM Principles
15
and inability to start at all angular positions represents a drawback. They can
present interest only for very high-speed applications.
Two Phase Motor
The use of a stepping the air-gap can avoid the starting problems. For a two
phase SRM the high torque ripple is an important drawback.
Three Phase Motor
The most popular topology of a three-phase SRM is the 6/4 form (N
s
= 6
and N
r
= 4). It represents a good compromise between starting and torque
ripple problems and number of phases. Alternative three-phase machines with
doubled-up pole numbers can oer a better solution for lower speed applica-
tions.
Four Phase Motor
The four-phase motor is known for reducing torque ripple. The large number
of power electronic devices and connections is a major drawback, limiting four-
phase motors to a specic application eld. A practical limitation to consider
larger phase numbers is the increase of the converter phase units, hence of the
total cost.
2.3
Basic SRM Principles
The switched reluctance motor with its passive rotor has a simple construction.
However, the solution of its mathematical model is relatively dicult due to its
dominant non-linear behaviour. The SRM is characterized by its geometrical
layout, the characteristic of the magnetic material and electrical parameters.
The cross sectional view of a four-phase SRM is shown in Figure 2.2.
The selection of the stator and rotor teeth number N
s
and N
r
is made with
the respect to several constraints as rotor deformation, capability of torque
production at all rotor positions and four-quadrant operation. The relation-
ships among all these constraints will be presented in Chapter IV. The number
of phases is identied from the stator and rotor pole numbers:
q =
N
s
|N
s
N
r
|
,q integer
2N
s
|N
s
N
r
|
,q non-integer
(2.1)
Once the number of poles is chosen, the next parameters are stator
s
and
rotor
r
pole arcs in order to minimize the inductance, maximize the inductance
ratio, avoid dead zones and allow four quadrant operation. The stator and rotor
pole tapering angles
s
and
r
are direct functions of the number of stator and
rotor teeth: 16
Principle of Operation
1
2
3
4
b
s
b
r
a
r
a
s
Figure 2.2: Cross sectional view of a four-phase SRM. s
= 2
N
s
rad
and r
= 2
N
r
rad
(2.2)
A torque is produced when one phase is energized and the magnetic circuit
tends to adopt a conguration of minimum reluctance, i.e. the rotor poles
aligned with the excited stator poles in order to maximize the phase inductance.
As the motor is symmetric, it means that the one phase inductance cycle is
comprised between the aligned and unaligned positions or vice versa (Figure
2.3).
Figure 2.3: Inductance prole of SRM. 2.3. Basic SRM Principles
17
The aligned position (L
a
)
Consider a pair of rotor and the stator poles to be aligned. Applying a cur-
rent to phase establishes a ux through stator and rotor poles. If the current
continues to ow through this phase, the rotor remains in this position, the
rotor pole being stuck face to face to the stator pole. This position is called
aligned position, and the phase inductance is at its maximum value (L
max
or
L
a
) as the magnetic reluctance of the ux path is at its minimum.
Intermediate rotor positions (L
int
)
At intermediate positions the rotor pole is between two stator poles. In this
case the induction is intermediate between the aligned and unaligned values. If
there is any overlap at all, the ux is diverted entirely to the closer rotor pole
and the leakage ux path starts to increase at the base of the stator pole on
one side.
The unaligned position (L
u
)
In the unaligned position, the magnetic reluctance of the ux path is at its
highest value as a result of the large air gap between stator and rotor. The
inductance is at its minimum (L
min
or L
u
). There is no torque production in
this position when the current is owing in one the adjacent phases. However,
the unaligned position is one of unstable equilibrium.
Mathematically, the inductance prole of phase j may be approximated by:
L()
j
= L
1
()

r
q (j 1)
(2.3)
Figure 2.3 shows the idealised inductance prole of one phase as a function of
the rotor position for a pair of stator poles. The number of cycles of inductance
variation per revolution is proportional to the number of rotor pole pairs, and
the length of the cycle is equal to the rotor pole pitch. In reality the rotor pole
arc
r
is always larger than the stator pole
s
if N
s
> N
r
. The value of the
interval
r

r
between the rotor teeth is larger than
s
in order to have the
minimum value of the inductance L
min
as low as possible. For the calculation,
the value of the air gap is considered to be constant in the interval where the
stator and rotor teeth are face to face.
The equation of the inductance prole can be rewritten as:
L() =

L
u
, 1
< < 0
L
u
+ k,
0

s
L
a
, s

r
L
u
+ k(

r

s
), r

r
+
s
(2.4)
where k is the slope of the prole in the zone of increasing inductance: 18
Principle of Operation
k = L
a
L
u s
(2.5)
The torque developed by a phase in which current ows tends to move the
rotor in such a direction as to increase the phase inductance, i.e. the aligned
position. This means that the motoring torque can be produced only in the
direction of the rising inductance. The instantaneous torque is obviously not
constant, as shown further, depending of the rotor position and the instanta-
neous phase current. Note that the torque is independent of the direction of
current ow, the motoring or braking torque production only depending of the
rotor position, suggesting the existence of the impact of switching angles of the
power electronic s