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Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering12.1

12. SWITCHED RELUCTANCE MACHINE .............................................................................. 1

12.1 Torque of a Switched Reluctance Machine ......................................................................... 3

12.2 Average Torque ................................................................................................................... 6

12.3 Control of a Switched Reluctance Machine ......................................................................... 8

12.3.1 Control Circuits ............................................................................................................ 8

12.3.2 Current Control ............................................................................................................ 9

12.4 Control of a Switched Reluctance Machine ....................................................................... 1112.4.1 General Controller Structure ...................................................................................... 11

12.4.2 Determination of the Rotor Position .......................................................................... 13

12.4.3 Current Profiling ........................................................................................................ 14

12.5 Position Sensorless Operation of an SR Machine.............................................................. 15

12.6 Conclusions ........................................................................................................................ 16

12. SWITCHED RELUCTANCE MACHINE

A switched reluctance machine (SRM) is an electrical machine, which in practice operates only

together with intelligently controlled power electronics. Reluctance machine has been applied for a

long time to stepper motor drives, which have not required a stepless torque control. Only the

development of power electronics and control systems has enabled the application of reluctance

machine in a reasonable power range, while previously the stepper motor applications operated in

the range of only a few hundred watts.

The principle of a switched reluctance motor with a mechanical chopper was introduced as early as

in 1838; however, a high-quality motor drive could not be implemented reasonably before an

advance in knowledge and components in power electronics. In 197172, electronic commutation

based on rotor position was patented, and thus the performance of the SR motor reached the level of

DC and AC drives. The structure and theory of the motor was quite well documented by the end of

the 1970s, and the development has been steady ever since. When discussing a salient polereluctance machine, we have to define whether we talk about a doubly salient switched reluctance

machine or a synchronous reluctance machine; a synchronous reluctance machine is a salient

rotating field machine, the rotor of which is not excited.

A switched reluctance motor refers to an electronically commuted motor type, the stator and rotor

of which are both salient-pole constructions. The poles of the machine are designed such that a

maximum saliency ratio (the ratio of the lowest and highest inductance at two different rotor angles)

is reached, however, with certain restrictions, in the motor phases. There is no winding in the rotor,

and the shaft excluded, the rotor is usually made of laminated iron. A damper winding is also

always out of question. An ideal switched reluctance machine is a fully undamped machine. The

stator is also made of laminated iron, in addition to which each stator pole has a winding coil of itsown. Figure 12.1 depicts some parts of the magnetic circuits of three-phase reluctance machines.

In English, the term Switched Reluctance Motor (SRM) is used of a doubly salient reluctance

motor; the term switched refers rather to the commutation method than the reluctance of the

machine. In the United States instead, the machine type is commonly known as Variable Reluctance

Motor(VRM), which is also a term for a certain stepper motor type. In German language, the term

isReluktanzmaschine mit beidseitig ausgeprgten Polen(a reluctance machine with doubly salient

poles).

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Figure 12.1 Stator and rotor laminations of 6/4-pole SR machines.

An SRM is an electrical machine, the torque of which is produced by the tendency of the rotor to

move into a position where the energy of the magnetic circuit is at lowest and the inductance of the

circuit is at highest. In practice, an even torque production is a demanding task, because the

inductance of the circuit changes non-linearly as the rotor rotates. The structure of a SRM is such

that the machine is, to some degree, applicable as a stepper motor. When employing a stepper motor

as a position servo, feedback of the rotor position is not necessarily required, as long as we ensure

that the stepped motion of the rotor is damped somehow. An SRM without feedback and with low

losses is only marginally stable as a stepper motor. It is difficult to drive at a very high speed, sincethe oscillation of the motor does not damp sufficiently between the control steps.

In an SRM position servo with rotor position feedback, the oscillation tendency can be avoided,

since the torque of the SRM can be set at every instant appropriate for the situation. Based on the

same reluctance variation, in addition to the position servo, a rotating SRM can also be made a

linear switched reluctance motor (LSRM). The force produced by the LSRM is based on the same

phenomenon as in a rotating machine, in other words, on the change in the inductance of the

magnetic circuit due to the change in the rotor position. In many cases, the linear motor is well

applicable as a position servo. An LSRM can be made more compact than a rotating SRM,

equipped with a converter of electric energy into linear motion.

Advantages of a servo drive implemented by an LSRM are

direct conversion of electric energy to linear motion (cf. a compressor or pump required by ahydraulic or pneumatic servo drive)

accurate positioning (no clearance, no notable friction) maintenance-free; does not include wearing parts high holding power is achieved at low losses applicable to hazardous environments

The large size of the LSRM servo drive compared to the achieved mechanical force can be

considered a drawback of the drive. However, the comparison is unfavourable only if we compare

the drive with a hydraulic cylinder, the power production capacity of which is superior to a

magnetic device. Figure 12.2 illustrates the structure of a cylindrical 4-phase LSRM.

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Figure 12.2 A 4-phase LSRM.

12.1 Torque of a Switched Reluctance Machine

The stator and rotor of a reluctance motor constitute a magnetic circuit, in which the stator winding

generates a magnetising current linkage, and further, the flux linkagepenetrating the rotor and airgap. Figure 12.3 illustrates the cross-section of a three-phase 6/4-pole SR motor, in which the coils

of the pole winding are connected in series. The inductance L of the magnetic circuit depends

strongly on the pole angle of the rotor. The magnetic force effects tend to minimize the magnetic

resistance of the magnetic circuit, that is, the reluctance, and the torque exerted to the rotor tends to

align the rotor poles with the stator poles.

i

Figure 12.3 A three-phase, 6/4-pole reluctance machine, in which iis the current of a single phase.

The easiest way to predict the torque of a SR motor is to apply d'Alemberts principle. Utilization of

the principle of virtual work presupposes that the hysteresis and eddy current losses are neglected,

in which case the energy Wof the investigated magnetic field or the coenergy W* can be expressed

with the rotor angle (reference to the phase of the motor is omitted):

constant

constant

0

0

d),(*

),(

d),(),(

i

ii

i

WiT

iW

T

i

(12.1)

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If the torque of an SRM was alternatively defined by numerical methods, the advantage to

employing the virtual work principle would be that simultaneously also the distribution of forces in

the SRM could be determined, similarly as the flux density distribution can be determined by the

finite element method. The advantage would be that in the design of the machine structure, both the

electromagnetic and mechanical stresses could be taken into account.

A general method to calculate the mechanical forces exerted by the magnetic field to an iron objectis to employ the Maxwell stress equations. Figure 12.4 shows the flux solution of the machine in the

case of overlapping poles.

Figure 12.4 The flux solution of a three-phase reluctance machine in the case of overlapping stator and rotor poles.

When the magnetic field strength vector His decomposed into the components orthogonal (n) and

tangential (t) to the surface

H n t n t H Hn t , 1 , (12.2)

the Maxwell stress equations can be written in the form (Carpenter 1959)

n n t

t n t

12

2 2H H

H H

,

. (12.3)

For instance, if the surface is selected to be a cylinder of the radius r, located in the air gap of the

stator and rotor of the SRM, the magnitude and direction of the total force exerted to the rotor can

be determined by integrating the equation

,d

d)(

221

n

tn2t

2n2

1

nH

tnF

HH

HHHH

(12.4)

the result of which should be zero, if the rotor is centred. Hence the magnitude of torque is obtained

from equation

nrHrnHT r ,d

, (12.5)

where ris a vector from the rotation axis of the rotor to the integration point of the surface . Eq.

(12.5) can be applied to, if either the magnetic field strength H, the flux density B, or the magnetic

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vector potential Ain the air gap of the motor has been determined in a numerical form for instance

by finite element method.

The operation of a reluctance machine is governed by the constant change in the machine

inductance as a function of the machine rotation angle. Furthermore, the machine saturates in the

region of pole edges, and therefore it is difficult to determine the inductances in different machine

positions and at different currents. The average torque of the machine is the higher, the larger is theinductance difference between the aligned and unaligned (direct and quadrature) positions.

Previously it was shown that the instantaneous torque of the machine could be computed from the

change in the coenergy of the machine as a function of rotation angle. In motoring operation, the

current of the machine is often kept constant with a switch-mode power supply, Figure 12.5.

If the magnetization curves of the machine are known at sufficiently many rotor angles, as well as

the phase current at these positions, the magnetic coenergy W* can be calculated at different rotor

positions; further its change with respect to the angle can be investigated with difference equations.

This way, it is possible to obtain approximations for the instantaneous torque.

In the special case in which the motor does not saturate, the magnetization curve is linear, and thus

the magnetic coenergy W*and the stored energy Weare equal

W W Li* e1

2

2 , (12.6)

and the instantaneous torque in the case of constant current is

T iL

1

2

2 d

d. (12.7)

Figure 12.5 The inductance

of a saturating reluctance

motor as a function of angle

with current as a parameter;

and the current pulses in

both motoring and

generating operation, when

the voltage of the

intermediate circuit remains

constant. In motoring

operation, the phase is

commutated with the angleC. The current of the motor

does not quite reach zero

before the aligned position is

reached. Now a slight

braking takes place as the

machine shifts away from

aligned position.

L

rotor angle

alignedunaligned

motoring generating

motor current

generator current

increasing current

C

In an unsaturated circuit, the inductance changes almost linearly, and thus its change with respect tothe angle is constant. Now the torque is proportional only to the square of current, and its regulation

is quite easy. In practice, it is not advisable to aim at an unsaturated structure, since it would require

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a large air gap. This would reduce the torque per the machine volume, since the inductance

difference between the direct and quadrature rotor position remains small. A large air gap would

also require an over-sized controller.

12.2 Average Torque

The instantaneous torque of a single phase does not remain constant when the rotor angle varies.Considering the electrical drive, it is important to determine the average torque of the machine. We

assume here that the angular speed of the machine remains constant.

When the supply voltage Ud and the phase resistance are constant, and the resistive voltage loss

remains low, there is a linear increase in the flux linkage as an integral of voltage after the

switching of the voltage d

1d dd RiUtRiUt . The current i increases first also

linearly as the inductance L remains low and almost constant in the vicinity of the unaligned

position. When the poles approach the aligned position, the inductance increases rapidly, and the

resulting back emf restricts the current. This phase is illustrated as the period 0C (Fig. 12.6a).With the rotor angle Cat point C, the phase in question is commutated. Now the energy brought to

the system is Wmt + Wfc (the bright + the shaded areas). Here Wfc is the energy stored in the

magnetic field, and Wmt is the energy converted into mechanical work when the transistor is

conducting. In this phase, the mechanical work is approximately equal to the energy stored in the

magnetic circuit. After the commutation, the polarity of the voltage is changed and the energy Wdis

returned through the diode to the voltage source, and the remaining energy Wmd is the obtained

mechanical work in the period C0, Fig. 12.6b. During the complete working stroke, the

mechanical work is thus Wmec= Wmt+ Wmdand the energy returning to the voltage source is WR=

Wd. The complete working stroke is illustrated in Fig. 12.6c. According to the example of the

figure, the proportion of the mechanical energy of the total energy is about 65 %.

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Wmt

C

Wmd

WdC

C

i

i

i

aligned

unaligned

a)

b)

c)

Wfc

Wmec

WR

Figure 12.6 a) Transistor conduction period, b) diode conduction period, c) energy conversion loop.

The rest of the energy is reactive energy of the reluctance machine that is stored either in the

electric field of the capacitor of the intermediate circuit or in the magnetic field of the magnetic

circuit of the machine.

Usually, an energy ratio is determined for an SR machine. This ratio expresses the energy that can

be converted into mechanical energy during the energy conversion loop

el

mec

Rmec

mec

W

W

WW

W

. (12.8)

The energy ratio is to some degree a quantity analogous to the power factor in AC machines. In the

example of Fig. 7.69, the energy ratio gets a value of approx.= 0.65. The average torque of a

reluctance machine can be determined when the number of strokes per revolution is known. In one

revolution, all poles Nr of the rotor must be worked on by all stator phases, and therefore, the

number of strokes per revolution is mNr. The average electromagnetic torque over one revolution

obtains thus the value

TmN

W r mek2. (12.9)

In practice, due to inaccuracies in manufacturing, the energy conversion loops for different phases

may differ slightly from each other, and thus cause differences in the torques of different phases.

The original energy Wel supplied by the power electronics to the machine can be expressed as a

fraction k of the product iCC, where C is the value of the flux linkage at the instant of

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commutation, and iCis the value of the current at respective moment. If the flux linkage increases

linearly during the flux formation period 0C as illustrated in Fig. 12.6, then

C d U/ . (12.10)

Here is the angle during which the power stage supplies power to the machine. We obtain now

Cdmecel

ikUWW

, (12.11)

and since iC is the peak value of the current yielded by the power electronics, the required power

processing ability of the output stage in a m-phase system is

S mU imW

k

T

N km d C

mek

r

2. (12.12)

The product of the torque and angular speed corresponds to the air gap power P, and the product

Nris constant, the maximum value of which is about /2 at the base rotation speed of the machine.The power processing ability of the power stage has to be thus

k

PS m

4 . (12.13)

The required power is thus independent of the phase number and the number of poles, and it is

inversely proportional to the energy conversion ratio and the utilization ratio k. Both and k

depend heavily on the static magnetizing curves of the machine, and on the curves of the aligned

and unaligned position in particular. These curves, however, are in practice highly dependent on thepole numberNr, which thus has a strong indirect effect on the dimensioning of the power bridge of

the machine. When the power processing ability of the power bridge is compared with the shaft

output power, we may approximate, assuming that k= 0.7 and = 0.6 that 10/m PS . This value

is typical of SR motor drives. Inverter power bridges of the same scale are required in induction

motor drives also (Miller 1993).

12.3 Control of a Switched Reluctance Machine

SR motors always require an individual control system, the performance of which decides the

overall characteristics of the machine. The control system is comprised of choppers and the controland measuring circuits controlling them. The direction of the torque of a reluctance motor does not

depend on the direction of the phase current, and therefore, unidirectional switches can be

employed in the chopper.

12.3.1 Control Circuits

In motoring operation, it is important to make the flux linkage increase maximally from zero as

rapidly as possible at the moment when the rotor pole approaches the stator pole of the respective

phase, and the inductance of the circuit increases strongly. This is done by switching the supply

voltage on at the rotor angle 0and by switching the voltage off at the commutation angle C. Figure12.7a illustrates an possible circuit for the control of a single phase of a reluctance motor. The

illustrated switches can be either bipolar power transistors, power FETs (Field Effect Transistors),

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or IGB (Insulated-Gate Bipolar) transistors. At low rotation speeds, the switches are controlled so

that the upper transistor T1 controls the magnitude of current, and the lower transistor T2 is

required for commutation. When the rotor angle reaches the position 0, both transistors are turned

to a conducting state, and the current passes through them and the phase winding. As the current has

reached the upper limit, the upper transistor T1 is brought to reverse state, while the current of the

phase winding passes through the transistor T2 and the diode D2 and converts the energy stored in

the winding into mechanical work. At the commutation angle C, also the lower transistor is broughtto reverse state, and the rest of the energy of the winding discharges through the diodes to the DC

voltage source or to the DC link capacitor, since the polarity of the voltage across the winding

changes. The flux linkage has to reduce to zero before the rotor passes the aligned position, or else

there occurs a negative, that is, a braking torque. Figure 12.7b illustrates the flux linkage and the

current under the control of a single control pulse (Miller 1993, pp. 5355).

At high rotation speeds, both transistors are usually controlled simultaneously. In this method, the

current ripple increases, and thus also the torque ripple and noise are increased. This method is

known as hard chopping, and it is chiefly used in braking the motor, that is, in the generating

operation (Carpenter 1959, p. 246).

12.3.2 Current Control

Figure 12.7b shows that a single DC pulse during the working stroke produces an indefinite current

waveform and thus also an uneven torque. The current increases first linearly, but then the back-emf

caused by the increasing inductance restricts the current. At the commutation point, the direction of

the voltage changes and causes a sudden decrease in the phase current. In the aligned position, the

direction of the back-emf changes as the inductance of the circuit starts to decrease, and the rate of

the fall of current decreases. In this period, there is danger that the back-emf exceeds the supply

voltage and the current starts to increase again. Therefore, in single-pulse operation, the

commutation angle must precede the aligned position by several degrees. As the speed increases,the commutation has to be advanced further; similarly, also the turn-on angle 0may be advanced

well ahead of the unaligned position (Miller 1993, p. 57).

Chopping of the supply voltage is necessary for controlling the current at low speed. The easiest

way is to leave the transistor T2 of Figure 12.7 conductive during the period 0 to C, and to switch

the transistor T1 on and off at a sufficiently high frequency. Instead of this soft chopping, also hard

chopping may be used, in which both transistors are switched together at high frequency. The

advantage of this pulse width modulation of voltage is the increased torque range, since the

commutation instant can be delayed due to the lower energy stored in the magnetic circuit. To

reduce acoustic noise, the switching frequency should be above 10 kHz; however, due to the

slowness of the large switches, the frequency remains below that.

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T1 and T2conducting

T2 and D2conducting

D1 and D2conducting

T1 D1

T2D2

a)

L(t)

u(t) +UDC

-UDC

(t)

i(t)

0 C

b)

Figure 12.7: a) The circuit controlling one phase of a reluctance motor and the current flow during the working stroke.

b) The current waveform in single-pulse operation in the case of idealized inductance (Miller 1993, p. 57).

If the switching frequency of the voltage remains the same during the whole working stroke of the

rotor, there occurs considerable ripple in the current, and therefore, the method is not recommended

for motoring operation. The ripple can be reduced by switching on and off the power transistorsaccording as the phase current is greater or less than a reference current. The waveforms of the

voltage, flux linkage and current obtained with a hysteresis-type current regulator are illustrated in

Figure 12.8. A simple hysteresis controller maintains the current waveform between the upper and

lower limit within the hysteresis band when the supply voltage is switched on. The switching

frequency decreases as the inductance of the magnetic circuit increases. In the case illustrated in

Figure 12.8, a hard shopping is applied; however, also soft chopping is possible; it decreases the

current ripple and noise and reduces the need for filtering in the DC link (Miller, pp. 6263).

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0 C

i

u

L

+U

-U

Figure 12.8 The current waveform, when the magnitude of current is controlled by switching on and off the voltage. In

the hysteresis control, soft chopping is used (Miller 1993, p. 63).

12.4 Control of a Switched Reluctance Machine

Digital control enables a versatile and reliable parameter setting and programming of operation

modes. The control design and implementation depend strongly on the requirements set by the load,and therefore, they have to be performed individually.

12.4.1 General Controller Structure

The servo drive of a reluctance motor sets extremely high requirements for low torque ripple and

rapid dynamic response; it also requires an ability to operate at zero speed and smooth reversing.

Even without these servo-quality requirements, the optimal operation in a simple variable-speed

drive requires continuous control of the firing angles. Four-quadrant operation, in other words, an

ability to operate in both rotation directions at a positive and negative torque, presupposes fast real-

time controllers that directly control the phase current and voltage. In the case of an SR motor, this

is difficult due to the fact that the ratios between torque, current, speed, and firing angles are often

nonlinear, and they vary as functions of speed and load. Figure 12.9 illustrates a general structure of

the controller of a switched reluctance machine. However, it is not capable of servo-quality

operation, since it does not include any dynamic control means for profiling the current waveform

in order to eliminate torque ripple, and no means for compensating the nonlinearities of the

magnetic circuit to produce a constant torque.

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SR motor

+

ControllerP

IT

s(JL+ JM)1

-+

LT

m

s1

Ign.

angle in

PWM

Ign.

angle in

Single pulse

C

0

Rotorposition

meas.

Speedmeas.

rpm

Braking

+ -

+

+

Currentlimit

i* m

ref

C0

C0

Figure 12.9 Structure of a controller capable of four-quadrant operation. Speed is controlled by feedback. i* is the

current demand signal, Tm is the torque of the motor and TL is the torque of the load, is the angular speed of the

motor, and ref its reference value.JmandJLare the moments of inertia of motor and load (Miller 1993, p. 106).

Figure 12.9 illustrates a reluctance motor and its power electronic control circuit as a simple control

block, the output of which is torque, and the inputs are the current demand signal i* and the turn on

and off angles (switching and commutation angles) 0 and C. The control block is assumed to

include a current regulator that can maintain the current within the desired limits, that is,approximately constant. The diagram also includes a notional conversion from torque to angular

speed and further to rotor angle. The difference of the torque Tmand the load torque TLis, according

to the Newtons second law of motion, a product of the common moment of inertia of the motor and

load (JM+JL) and the angular acceleration. The block after the error element thus integrates the

difference of the torques and divides it by the common moment of inertia; the result is the angular

speed m. The next block integrates the angular speed, and as a result, the rotor position angle is

obtained. In practice, the rotor position is sensed with an encoder, which generates a digital pulse

train. The speed is estimated from this pulse train by a suitable digital algorithm.

This digital speed estimate is compared with the reference speed ref. The error is applied to the PI

controller, which generates the current demand signal i*. If the speed error increases, that is, thespeed lags behind the reference, the proportional P-controller and the integral I-controller increase

the current reference; however, the current limiter sets a limit for the current to prevent damages for

the current circuit. If the speed exceeds the reference speed, the four-quadrant operation requires

that the motor produce a braking torque. In many ordinary variable-speed applications, this is not

necessary, since the load torque causes a sufficient deceleration whenever the motor torque

decreases below it. To produce a braking torque, current has to be fed to the circuit while the firing

angles are delayed. The magnitude of braking torque is a nonlinear function of the current and firing

angles, similarly as the motoring torque.

Figure 12.10 depicts the average torque of an SR motor as a function of rotation speed. From zero

speed to the base speed b, the motor current is kept constant by chopping the voltage in the

winding, and the motor operates at almost constant torque. As the speed increases further, the

switch is conducting during the whole working stroke, and the motor operates at maximum power.

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As the power remains constant at the maximum value, the rotation speed is controlled based on the

firing angles.

PWM increasesD constant

constantcurrent

constantpower

Tconstant

0 b

TD

TconstantT constant

Figure 12.10 The average torque of the motor as the angular speed varies.

12.4.2 Determination of the Rotor Position

A closed-loop control system controls the chopper switches based on the rotor position and the

rotation speed, as well as on grounds of the phase currents. Position can be measured either by

optical or magnetic positions sensors. An optical encoder consists of a slotted pulse disc rotating

with the rotor, a stationary reading mask, and a light detector connected to the logic unit. Figure

12.11 illustrates a simple SR motor drive with the LMB1008 control IC by National

Semiconductor. The drive includes three optical encoders for determining the rotor position. Since

the current waveform is at high speeds highly dependent on the firing angles, the switching

precision of 0.5or even 0.25is desirable (Miller 1993, pp. 99101; Carpenter 1959, p. 247).

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commutation

logic

Rotor

positionmeasuring

RotorSpeed

sensor

TACHO

PWM

generation

Compar-

ator

Currentlimiting

Speed reference

Ud

1 2 3

Figure 12.11 A simple SR motor drive with the LMB1008 control IC by National Semiconductor (Miller 1993, p. 100).

In the LMB1008 control, the error of the desired and real speed produced by the speed error

amplifier controls the chopping frequency of the external power transistors. As the speed error

increases, the chopping frequency is decreased. The control is thus pulse width modulation rather

than current regulation. The data obtained by current measurement is compared to the value of the

current limiter, and if the measured value exceeds the permitted value, the transistors are turned off.

The firing angles can be selected by the logic controller based on the data of the shaft sensors A, B,

and C.

Although the stepper motors operate well without a rotor position feedback, this open-loop control

method is not stable for a low-loss reluctance motor. Nevertheless, controllers have been developed

that operate without rotor position sensors. Reasons for this are cost reduction and improved

reliability particularly in extraordinary and difficult conditions.

12.4.3 Current Profiling

SR motors have conventionally been controlled similarly as stepper motors; constant voltage and

current pulses are fed to the phase windings of the stator by a frequency determined by the rotor

angle. The resulting large torque ripple has made the motors unsuitable for many applications.

Recently, however, control methods have been developed, in which the torque ripple has been

brought nearly or exactly to the level of the conventional electrical machines. These control

methods are based on experimental results, which determine an optimal duty type in different

operating situations. The advantage of a reluctance motor when compared with the conventional

applications is the large torque also at low speed, as well as the simple structure of the motor itself.

By regulating the current waveform, it is nowadays possible to reach a level of 510 % torqueripple. This, however, is possible only in the low-speed range. At high speed, limiting the torque

ripple is problematic. Increased application of reluctance motors will require new control and

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inverter solutions, when aiming at an even torque in wide rotation speed range. Figure 12.12

illustrates the control of a three-phase SR motor for constant torque production

0

0.2

0.4

0.6

0.8

1

1.2

0.5 1 1.5 2 2.5 3-400

-300

-200

-100

0

100

200

300

0.5 1 1.5 2 2.5 3

0

5

10

15

20

25

30

35

40

45

50

0.5 1 1.5 2 2.5 3-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.5 1 1.5 2 2.5 3

FLUX

LINKAG

ES[Vs]

PHASE 2

PHASE 3

ROTOR ANGLE

/12

/12

ROTOR ANGLEROTOR ANGLE

PHASECURRENTS[A]

TORQUEP.U.

PHASEVOLTAG

ES[V]

PHASE 3

PHASE 2

PHASE 3

PHASE 2

PHASE 2

PHASE 3

/12

/12

ROTOR ANGLE

Figure 12.12 A solution to produce constant torque at certain voltage limitation for profiling the currents in a three-

phase machine.

12.5 Position Sensorless Operation of an SR Machine

The control of an SR machine requires quite accurate information on the rotor position. This

information is obtained accurately only by an angle sensor; however, if the requirements of the

drive are not very strict, some position sensorless method may be applied to the determination of

the rotor position.

In literature, several authors have suggested the application of the currentless phases of the SR

machine in inductance measurements. This method, in which appropriate measurement signal is fedto the currentless phases, is best applicable to machines of a four-phase arrangement at minimum.

The results obtained by the method can be applied to some degree to the control of an SR motor;

however, the method is quite sensitive to disturbances.

If the machine is well known, it is possible to construct a flux linkageanglecurrent diagram as

shown in Figure 12.13; the diagram can be applied to the estimation of the rotor position. Since

there is also a voltage integral available for the flux estimation, and since the current can be

measured, the illustrated diagram can be employed to determine the position angle of the machine at

an instantaneous state. This is a kind of direct flux linkage control of an SR machine. In this case,

there are no problems of stator flux linkage drifting as in the DFLC of a rotating field machine,because the flux linkage of the phase increases at every stroke always from zero, and thus the

possible offset error can always be eliminated before the working stroke of the phase.

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current

rotor position

Figure 12.13 Flux linkageanglecurrent diagram of an SR motor, which can be employed in the determination of

machine position when the current has been measured and the flux linkage has been integrated from the voltage.

12.6 Conclusions

Advantages of a reluctance machine when compared with conventional electric drives are for

instance the following:

No winding is required in the rotor; the rotor construction is simple and easy tomanufacture.

The moment of inertia of the rotor is low; a fact that improves the dynamics of a controlledelectric drive.

The stator winding is easy to construct, and the losses of an end-winding are lower than in acorresponding induction machine.

Most of the losses occur in the stator, and therefore, cooling of the motor is easier, and ahigher load capacity is achieved. The large free spaces in the rotor enable efficient ventilation through the machine. The torque of the machine is independent of the direction of current, giving thus more

degrees of freedom in the inverter and control solutions.

The machine can produce a very high torque also at small rotation speeds and with a steadyrotor at low current.

The machine constant of an SR machine is higher than the machine constant of an inductionmotor.

The torque is independent of the direction of the phase current, and therefore, in certain

applications, it is possible to reduce the number of power switch components. In the event of a failure, the open-loop voltage and the short circuit current are low.

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In reluctance motor applications, the power electronic circuits do not have a so called shoot-through path, which eases the implementation of the control system.

Extremely high rotation speeds are possible.

A disadvantage of a reluctance motor is for instance a discontinuous torque that causes vibration in

the configuration as well as acoustic noise. In the low-speed range, the torque ripple can be

restricted to 510 %, which is comparable to induction motor drives. In the high-speed operationrange, the restriction of the torque ripple is impossible in practice. This is not a problem thanks to

mechanical filtering. Already at the present, the best drives produce a very low degree of torque

ripple at low speeds. The fact is that the smoothest torque is required just at low speeds, when the

loads are the most vulnerable to the harmful effects of the torque ripple. In small motors, the noise

can be damped at high speeds by selecting a switching frequency above the range of audibility.

In the torque control, the power is taken from the intermediate circuit in a pulsating manner, and

therefore, efficient filtering is necessary. In this sense, the drive does not differ considerably from

an inverter drive of an induction motor. A small air gap advantageous to the operation of the motor

increases the production costs. A small air gap is required to maximize the inductance ratio.

Despite notable advantages, the application of reluctance motors has so far been restricted by the

problems in the smooth torque production in a sufficiently wide rotation speed range. In order to

solve these problems, the operation principle of an SR machine requires new inverter and control

solutions. On the other hand, the present processor technology and power electronics allow control

algorithms of complicated electric drives also.

The design of an SR machine is based to a large extent on field calculation; in this calculation

process, the shape of the magnetic circuit of the machine and the inductances in different rotor

positions are determined. This is manually a demanding task due to the local saturation at salient

pole tips, which is typical of the operation of an SR machine. Due to the saturation, it is difficult toemploy an orthogonal field diagram. Therefore, field calculation software is required in the design

of an SR machine. The task becomes easier as the field solutions can usually be made in steady

states excluding the problems caused by eddy currents. However, the use of an SR machine is so far

so limited that no extensive calculation instructions can be found in literature.

Reluctance motors are nowadays manufactured in an extremely wide rotation speed and power

range, yet the wider utilization of the machine type has been delayed. One of the main reasons for

this delay is that a reluctance motor has so far always required a machine-specific electronic

chopper and control system.

Nowadays, high-torque, slow-operation motors of 30200 kW are employed in heavy four-quadrantdrives for instance in mining industry. General-purpose motors are manufactured for various

purposes, for instance to replace old DC and AC drives in applications that require accurate rotation

speed control.

Rotation speed control has become more common in pump and blower drives, improving their

efficiency. In the drives of this kind, SR motors are not yet competitive with frequency converter

drive induction motors for example due to their complicated control. The torque of an SR motor is

very high at low rotation speeds, and therefore, the motor type may become more popular in

applications in which a high torque is required.

The applicability of reluctance motors to electric tools has also been investigated. In these

applications, the size and the torque properties of reluctance motors are most beneficial. A

disadvantage of the mixed current motor, which is commonly used at the present, is wear of the

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mechanical commutator and the electromagnetic disturbances caused by the commutation. These

problems could be solved with an SR drive. Thanks to its durability and other favourable qualities,

a reluctance motor is also a suitable power source for electric vehicles.

References

Carpenter, C. 1959. Surface-Integral Methods of calculating forces on magnetized iron parts. IEE

Monograph, 1959, No 342.

Miller, T.J.E. 1993. Switched Reluctance Motors and their Control. Oxford: Magna Physics

Publications, Oxford University Press.

Tolsa, Kimmo. 1997. Licentiates thesis. Lappeenranta University of Technology.

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