Kaytto10 En

Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering 10.1

10. SYNCHRONOUS RELUCTANCE MACHINE .................................................................... 1 10.1 Operating Principle and Structure of a Synchronous Reluctance Machine ......................... 1 10.2 Model, Vector Diagram and Basic Characteristics of a Synchronous Reluctance Machine 4 10.3 Control of a Synchronous Reluctance Machine ................................................................. 12

10.3.1 Current Vector Control .............................................................................................. 12 10.3.2 Constant isd Control .................................................................................................... 13 10.3.3 Constant Angle Control .......................................................................................... 14 10.3.4 Combined Current-Voltage Vector Control ............................................................... 15 10.3.5 Direct Torque and Flux Linkage Control ................................................................... 16

10.4 Synchronous Reluctance Machine Operating as a Generator ............................................ 17

10. SYNCHRONOUS RELUCTANCE MACHINE An induction machine is the most inexpensive industrial motor; however, developing the machine any further is difficult. In the future, new motor types, such as permanent magnet synchronous machines and synchronous reluctance machines (SyRM), may gain ground thanks to some of the advantageous properties they have. An induction motor is less expensive than a permanent magnet synchronous machine, but the efficiency of an induction motor is, due to rotor losses, inferior to the efficiency of synchronous machines. Furthermore, the control of an induction machine is difficult at low speeds, if aiming at position sensorless drives. On the other hand, it is often necessary to set limits to the maximum torque of a permanent magnet machine, and temperature restrictions for the rotor to prevent demagnetization of the permanent magnets. Considering the operational principle, the simplest rotating-field machine is a synchronous reluctance machine, which is typically equipped with a simple, salient-pole laminated rotor without a winding. Thanks to its simple structure, the machine type is a favourable alternative for many purposes; however, a synchronous reluctance machine can seldom operate without a vector control. The synchronous reluctance machine has potential to overhaul the induction motor at least as a controlled drive. For direct-on-line start-up, a cage winding is required in the synchronous reluctance machine, which in turn, as the saliency ratio decreases, impairs the power factor and efficiency of the machine when compared with a synchronous reluctance machine with a cageless rotor. Furthermore, also the direct-on-line start-up may even be prevented, if the saliency ratio of the machine is very large. This is due to the asymmetric damper winding, which has a synchronous frequency at a half speed. Thus, an incorrectly designed machine may remain operating at a half speed.

10.1 Operating Principle and Structure of a Synchronous Reluctance Machine A synchronous reluctance machine is a salient-pole rotating-field synchronous machine, the rotor of which does not have excitation. Consequently, the load angle equation can be simplified to the form

2sin21

32sin2

3qs

d

q

2sv

qds

qd2sv L

LL

ULL

LLUP

. (10.1)


We can see that the difference of the direct-axis and quadrature-axis synchronous inductance Ld Lq should be as large as possible, and LdLq as small as possible in order for the SyR machine to yield a maximum power. In practice, the target is to maximize the direct-axis inductance and to minimize the quadrature-axis synchronous inductance. In principle, the machine can yield its maximum torque at the load angle = 45. Saturation and other phenomena may cause apparent deviation from this value. A damper winding belongs conventionally to the rotor of a SyR machine, when we desire the machine to start direct-on-line. In the stator, there is a poly-phase (e.g. three-phase) stator winding of an ordinary rotating-field machine. A synchronous reluctance machine is in principle a salient pole synchronous machine without field current. The simplest method to convert an induction machine to a SyR machine is to cut away equal segments from the opposite sides of the rotor. In practical applications however, the ferromagnetic rotor is shaped or laminated in such a way that the phase inductance variation with respect to the rotation of the rotor is as large as possible. The iron parts of the magnetic circuit of the SyR machine area not allowed to saturate magnetically under normal operating conditions, since the target is to keep the operating range of the machine linear. Typical applications of SyR machines are servo drives, pumps and conveyors, devices producing synthetic fibres, and packaging and wrapping machines. New fields of application are vehicle drives, robots, as well as generators of wind power plants and mini hydro power plants (Boldea 1996). The rotor of a synchronous reluctance machine should be constructed such that the ratio of the direct-axis inductance Ld and the quadrature-axis inductance Lq of the machine (saliency ratio) is as large as possible. Thus, the reluctance torque produced by the machine is also maximized. The ratio of the direct-axis Ld and the quadrature-axis inductance Lq of the rotor chiefly determines the characteristics of the SyR machine: what the peak torque of the machine is, how fast the machine responds to dynamic changes, and what power factor and efficiency can be reached by the machine. In order to be competitive with an induction motor of equal size, the saliency ratio of the SyR machine has to be at least ten. Next we consider further different rotor alternatives for a SyR machine, and the saliency ratios reached by these configurations. The simplest structure for a rotor of a SyR machine is obtained by removing teeth from the rotor of a conventional induction motor as shown in Figure 10.1. However, in the resulting rotor construction, the ratio of direct-axis and quadrature-axis inductance remains so low (Ld/Lq < 3) that the rotor is not a potential solution. The rotor of Figure 10.1d corresponds with the rotor of an ordinary salient-pole synchronous machine, from which the excitation windings have been removed. A salient-pole rotor can also be manufactured of notched segments made of solid iron. The saliency ratio of the conventional salient pole rotor remains nevertheless so low that a SyR machine with such a rotor cannot compete with an induction motor equipped with a similar stator. A typical saliency ratio for the rotor has been determined to be 34 (Staton et al. 1993). The so-called single-layer flux-barrier rotors illustrated in Figures 10.1b and 10.1e have been designed so that if desired, it is possible to mount permanent magnets in the insulation spacer intended to prevent the progression of the flux in q-axis direction; this way, the machine characteristics can be improved, and the size of the inverter required for the power supply can be reduced. As a matter of fact, the rotor structure of Figure 10.1e occurs in permanent magnet machines, in which the magnets are located inside the rotor. The rotor of Figure 10.1b is a sort of a mixture of a salient pole and a permanently excited rotor structure. The flux barrier is usually made


of a nonmagnetic material, such as aluminium, copper, slot insulation paper, or even plastics (Betz et al. 1993). A SyR machine equipped with the rotor of Figure 10.1b can at best be started direct-on-line, since the bars on the rotor surface comprise a cage winding. The quadrature-axis magnetizing inductance of a radially laminated rotor, in which the path of the magnetic flux is guided by flux barriers made of a nonmagnetic material and located below the bars of the cage winding, reduces rapidly with the increasing stator current aligned with q-axis. Furthermore, the leakage inductance of the rotor is low during the start-up. The cross-sections of the bars of the cage winding are left small in order to produce a high rotor resistance in the start-up, during which the start-up torque of the machine increases. The saliency ratio of this rotor type is of the scale 68 (Boldea 1996, Staton et al. 1993).

a)

q

d

b)

q

d

e)

q

d

d)

q

d

f)

d

q

q

d

c)

Figure 10.1 Four-pole rotors of a SyR machine. a) The simplest model, constructed of an ordinary rotor of an induction motor by removing certain teeth, b) a laminated flux-barrier cage rotor, c) an axially laminated rotor with alternating magnetic and nonmagnetic laminates. The shaded regions are pole holders made of nonmagnetic material; d) a salient-pole rotor with also a cage winding as a damper winding, e) a cageless flux-barrier rotor, f) a flux-barrier rotor produced by punching (Boldea 1996, Staton et al. 1993). The largest saliency ratios have been achieved by the axially laminated rotor of Figure 10.1c. Such results cannot be achieved by the multilayer flux-barrier rotor of Figure 10.1f due to the supports in the round laminates, since they reduce the reluctance of the quadrature axis. Ld/Lq values for the c-type rotors are normally above ten, and at their best even above 15 (Boldea 1996). In the f-type, we must content ourselves with the value ten for the saliency ratio Ld/Lq. In a multilayer flux-barrier rotor, several curved sections are cut away from the stator plate; when assembling the rotor stack, these sections can be filled with a desired nonmagnetic material by pressure casting. This way, the construction becomes mechanically stronger than it would be were the sections left unfilled. When employing a light material as the nonmagnetic material, also the inertia of the rotor can be kept low. The ratio of the thicknesses of the lamination layers, that is, the conductor and insulator layers has a significant impact in the saliency ratio of the machine. Figure 10.2 illustrates the dependence of the saliency ratio of a 6 kW SyR machine on the ratio of the thicknesses of the iron and insulator layers of the rotor wr/we. When the proportion of the iron


layer wr is increased in the lamination layer, the area of the cross-section of the magnetic circuit of the d-axis flux increases, and thus also Ld increases; however, as the insulator layer becomes thinner, its preventive effect on the progression of the flux reduces, and the quadrature inductance Lq increases. The figure shows that an optimum ratio is approximately one. The total number of insulator and conductor layers instead does not have a significant impact on the saliency ratio, if the number of layers is above ten (Staton et al. 1993; Matsuo and Lipo 1994). Figure 10.2 The saliency ratio Ld/Lq of a 6 kW synchronous reluctance machine. we is the thickness of the insulation layer, wr is the thickness of the iron layer. The number of layers (iron + insulator) is 24. The values of saliency ratios Ld/Lq are normalized with respect to the value corresponding to the thickness ratio one.

0

0,2

0,4

0,6

0,8

1

1,2

0 0,4 0,8 1,2 1,6

Ld/ L

q

wr/we

1,0

In addition to the structural factors of the rotor, the direct and quadrature inductances depend on the currents id and iq, the stator slotting, and the shape of the end windings. Considering the control of the machine, the sufficiently accurate determination of the saliency ratio is a complex task. Often it is necessary to resort to the estimation and determination of inductances by motor models.

10.2 Model, Vector Diagram and Basic Characteristics of a Synchronous Reluctance Machine A modern controllable electrical drive with its frequency converters allows the start-up of the electrical motor also without damper windings. This property makes the SyR machine a serious challenger for the induction motor, since the rotor of a SyR machine can be constructed without a cage winding, and thus the efficiency and power factor of the machine will be improved as the rotor losses are eliminated, and the rotor design will concentrate on maximizing the saliency ratio Ld / Lq and optimizing the synchronous operation. Simultaneously also the response times of the machine to the changes in torque decrease as the rotor becomes lighter. Therefore, we introduce next a mathematical model only for a synchronous reluctance machine without a damper winding. The model does not take into account the losses of the iron circuit. A synchronous reluctance machine can be considered to correspond to a non-excited salient pole machine, since in both machines, due to the rotor structure, the machine characteristics are different in direct and quadrature directions. The two-axis model equivalent circuit for a synchronous reluctance machine of Figure 10.3 is obtained from the corresponding model for a salient pole machine by omitting the components representing the excitation winding of the rotor.


ud

idRs

q

d

Ls

LmdiD

RD

id+iDLD

md uq

iq Rsd

q

Ls

Lmq

iQ

RQ

iq+iQLQmq

Figure 10.3 Equivalent circuit according to the two-axis model for a synchronous reluctance machine. The stator voltage and current components are indicated by the subscripts d and q. Damper windings are indicated by subscripts D and Q. The subscript refers to the leakage component. The iron losses are neglected. Voltage equations corresponding to the equivalent circuit by the notations of Fig. 10.3 are written as

u R itd s ssd

sq

dd

, (10.2)

u R itq s ssq

sd

dd

. (10.3) The flux linkage components in the equations are determined as

Dmddsmdddsd iLiLLiL , (10.4) Qmqqsmqqqsq iLiLLiL . (10.5)

The stator flux linkage of a SyR machine is comprised of the stator leakage flux linkage and the air gap flux linkage

s s m , (10.6) where s is the stator flux linkage, s is the stator leakage flux linkage, and m is the air gap flux linkage. The stator leakage flux linkage can be expressed by the stator leakage inductance as

s s s L i , (10.7) where is is the stator current. Figure 10.4 illustrates the vector diagram of the SyR motor. The vectors can be decomposed into direct-axis and quadrature-axis components.


md

Lsis = sis

us

iq

x

y

dq

r

idm

s

mqs

Figure 10.4 Vector diagram of a SyR machine at the nominal operating point. In the figure, is is the stator current vector and is the angle of current vector measured on the d-axis, s is the stator flux linkage vector, m is the air gap flux linkage vector, s is the stator leakage flux linkage vector, and us is the stator voltage vector. The angles s and m between the flux linkage vectors and d-axis are known as the pole angle of the stator flux linkage and the pole angle of the air gap flux linkage, respectively. The angle is the angle between the stator current vector and the d-axis of the rotor. The figure also shows the phase angle between the stator voltage us and the stator current is, which determines the power factor cos; the rotor angle r and the xy reference frame fixed to the stator. Note that the quadrature inductance has to be really low to prevent the stator flux linkage and air gap flux linkage from turning significantly away from the d-axis. Since the magnitude of the cross product of the vectors is proportional to the area of the parallelogram defined by these vectors, we may state that the torque produced by the machine is proportional to the triangle delimited by the vectors s, m, and s of Figure 10.4. Consequently, the function of the control can be considered to be the determination of the optimum triangle for the required torque according to the control method in question. On the other hand, during a transient, the function of the control is to implement the transition of the machine state from one triangle to another as rapidly as possible. The power angle producing the maximum torque for a SyR machine t,max is determined as follows

)cos(ssd , (10.7)

)sin(ssq , (10.8)

)cos(1 sd

sd Li , (10.9)

)sin(1 sq

sq Li . (10.10) The torque as a function of load angle, calculated with space vectors


)cos(1)sin()sin(1)cos(

23

23

ssd

sssq

ssse LLppT i

)cos()sin(1123

sdsq

2s

LLp , (10.11)

)2sin(21

23

dq

qd2s

LLLL

p .

The output power in pu values pout becomes

)2sin(22

3qd

qd2seout

llll

putp , (10.12)

when

b

ss U

u . (10.13) The maximum torque is obtained by the load angle = /4. Figure 10.5 depicts the torque production capacity of a SyR machine with the saliency ratio as a parameter. The quadrature inductance is kept constant at lq = 0.2.

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70 80 90

load angle

torq

ue

Ld/Lq= 5

Ld/Lq= 10

Ld/Lq= 50

Figure 10.5 Torque production capacity of a SyR machine at different saliency ratios; the quadrature inductance is constant lq = 0.2 [12]. In practice, the saliency ratio Ld/Lq = 50 cannot be reached, since the value 0.2 of the quadrature-axis synchronous inductance is almost impossible to reach, because the stator leakage alone comprises a half of this value. If the saliency ratio is 10, a per unit value of ld = 2 is required of the


direct-axis inductance; this value can well be achieved. In large induction machines, the direct-axis inductance is typically of the scale ld = 3.5; values above this are not easily achieved for the direct-axis synchronous inductance by a SyR machine either. A machine, the saliency ratio of which exceeds 10, can also provide the required breakdown torque. In the breakdown torque, however, the synchronous reluctance machine cannot challenge an induction machine. Not even an unrealistically high saliency ratio is capable of producing a 200 % breakdown torque. In asynchronous machines, the breakdown torque is typically above 300 %. Figure 10.6 illustrates also how the torque depends on the current angle in the voltage supply

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70 80 90Current angle with respect to rotor d-axis

Torq

ue. L d/L q= 10

L d/L q= 50

L d/L q= 5

Figure 10.6 Effect of the saliency ratio on the torque production capacity of a SyR machine and on the current angle in voltage supply. In the calculation, the rated current of the induction motor with a corresponding stator construction is used. The values are calculated for a 30 kW, four-pole 50 Hz machine (Haataja 2003). A large saliency ratio produces a large current angle, which is a prerequisite for a good power factor. When we neglect the effect of the stator resistance, we obtain for the power factor angle by employing Fig. 10.4

2 . (10.14)

At a maximum load angle, the power factor angle is approximately

2

maxt,max t, = 2

4 =

43 . (10.15)

The current angle remains always in the range

2,0 . (10.16)

At maximum power, the power factor of the SyR machine is thus always


4cosmaxt, = 0.707. (10.17)

Without the losses of the stator winding and the iron circuit, the power factor of the SyR machine is

cos 23

Tpu i

e

s s. (10.18)

is the electric angular speed of the rotor, us is the magnitude of the stator voltage vector, and is is the magnitude of the stator current vector. By applying the cross-field principle, the torque can be expressed as

T p L L i ie d q d q 32 (10.19) We may write for the magnitude of the flux linkage

s sd2 sq d d q q 2 2 2L i L i . (10.20) By substituting (10.18) to (10.19) and (10.20) and by using the following connections

us s , (10.21) i i is d

2q2 , (10.22)

we obtain the following equation for the power factor

cos

L L i i

L i L i i i

d q d q

d d q q d2

q22

2. (10.23)

By deriving Eq. (10.23) with respect to d/iq and by writing the obtained expression zero, we obtain the following condition for the maximum power factor

ii

LL

q

d

d

q . (10.24)

Hence, the power factor reaches its maximum at the current angle

q

darctanLL . (10.25)

The maximum power factor is thus


1

1cos

q

d

q

d

max

LLLL

. (10.26)

If Ld/Lq = 10, the current angle becomes = 72.5 and the maximum power factor will be cosmax = 0.81. A large saliency ratio leads to a small current angle and thus to a good power factor, Figure 10.7.

00.10.20.30.40.50.60.70.80.9

1

15 30 45 60 75 90

current angle [electric degrees]

pow

er fa

ctor L d/L q=50

L d/L q=10

L d/L q=5

Figure 10.7 The power factor of a SyR machine as a function of current angle at different saliency ratios. lq = 0.2 (Haataja 2003). Figure 10.8 illustrates the power factor of a SyR machine as a function of load angle.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 15 30 45 60 75 90

Load angle [electric degrees]

Pow

er fa

ctor

L d/L q= 50

L d/L q= 10

L d/L q= 5

Figure 10.8 The power factor of a SyR machine as a function of load angle at different saliency ratios. lq = 0.2 (Haataja 2003).


Figure 10.9 illustrates the power factor of a SyR machine as a function of shaft output power. The figure indicates clearly how essential a large saliency ratio is for the good machine characteristics.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2

Pow

er fa

ctor

L d/L q=50

L d/L q=10

L d/L q=5

Pow

er fa

ctor

Figure 10.9 The power factor of a SyR machine as a function of shaft output power at a rated speed (Haataja 2003). The efficiency of a synchronous reluctance machine can be investigated also at different values of the saliency ratio. The efficiency can be written in the form

LossOut

OutPP

P mekFes2se

e

PRImTT

. (10.22)

mekFes2sqdqd

2 's

qdqd2 '

s

)2sin()(

)2sin()(

PRImIILLUm

IILLUm

. (10.23)

The term PFe+Mech includes the no-load iron losses and the mechanical losses. Figure 10.10 depicts the idealized efficiencies of a 30 kW, four-pole SyR machine at different saliency ratios and pole angles. In reality, changing the saliency ratio requires also changes in the iron circuit and the air gap, and thus the motor parameters do not remain unchanged. The result of the illustration is thus fictitious.

80

82

84

86

88

90

92

94

96

0 20 40 60 80

Load angle

Effic

ienc

y

L d/L q=50

L d/L q=10

L d/L q=5

Figure 10.10 The calculated efficiency of a 30 kW machine as a function of load angle with the saliency ratio Ld/Lq as a parameter (Haataja 2003).


10.3 Control of a Synchronous Reluctance Machine Although the operation principle and the theory of the synchronous reluctance machine were documented already in the early 20th century, the poor torquecurrent ratio, a high torque ripple, a poor power factor and low efficiency prevented the SyR machine from becoming a serious competitor among controlled-speed electrical drives. An inverter drive allows an optimal design of a cageless rotor when considering an efficient synchronous operation. A cageless rotor enables a high saliency ratio, which improves the efficiency of the machine and reduces the inertia of the machine. A low inertia of the machine is favourable when considering the response time in transients. As the stator is identical with the asynchronous machine, and since the control system is comprised of similar components, yet the implementation of the system is somewhat simpler, the costs of a SyR machine drive remain below the costs of a corresponding induction machine drive or a permanent magnet synchronous machine drive. Since the control theories for the synchronous reluctance machine have in practice been developed already in the context of the control theories of other AC machines, only the most essential and relevant control principles are presented here. The control principles are based on the two-axis model of a SyR machine in the rotor reference frame. These control methods require the rotor angle information, and therefore a position or speed feedback is necessary. Characteristic of sensorless control methods is the use of different estimators, which requires large calculation capacity of the control system.

10.3.1 Current Vector Control In the current vector control, references idref and iqref are constructed for the direct and quadrature current components. Usually the references are formed directly from the torque reference Teref; however, in certain methods and cases, such as in field weakening, the current references are formed on the basis of the measured rotation speed or the torque reference given by the rotation speed controller (Luukko 1998). The torque control block produces the current references according to the selected control strategy. The strategies can be divided into two main categories: the constant angle control and the constant isd control. The latter is better adapted to the operation below rated speed (Vas 1998; Betz et al. 1992). The reference values for the phase currents are generated from the current references of the two-axis model by two-phase-to-three-phase (23) transformations. The current control is implemented with the measured stator phase currents and the phase current references for instance by a hysteresis controller. Figure 10.11 illustrates the block diagram of the operating principle of this kind of a control system.


TorquecontrolTeref

idref

iqref

ixref

iyref

isarefisbrefiscref

SYRM

isaisbiscr

sAsBsC

2 3 Current

controlrje

Figure 10.11 Block diagram of the current vector control system of a SyR machine.

10.3.2 Constant isd Control The torque equation for the SyR machine according to the cross-field principle is recapitulated here

T p L L i ie d q d q 32 . (10.24) Magnitude of the flux linkage

s sd2 sq d d q q 2 2 2L i L i . (10.25) By substituting iq solved from Eq.(10.25) to Eq. (10.24), the torque can be written in the form

T pL L L i L ie q d q d s2 d2 d2 32 , (10.26) when we solve Te/id = 0 from the above, we obtain

iLds

d2 . (10.27)

The maximum torque at a certain magnitude of the flux linkage is

T pL LL Lemaxd q

d qs2 3

4 . (10.28)


At speeds below the rated speed, isd is kept at a constant value, which is obtained with the torque reference from the equation

constant2 d

maxrefdref Li

, (10.29) where the maximum value for the reference flux linkage is obtained from the equation

maxref eref d qd q

43

T L Lp L L( )

. (10.30)

In the field weakening, the idref component is reduced along with the speed as follows

iLdref

maxref

d

n 2 . (10.31) The reference value iqref for the quadrature-axis stator current component is obtained from

iT

p L L iqreferef

d q dref

23 ( )

. (10.32)

Note that when isd varies, also Ld changes, and thus the torque is no longer directly proportional to the quadrature-axis current component isq. Now, more advanced methods have to be applied to; methods such as the self-tuning and model reference adaptive controllers are used to produce the current reference isqref [6, pp. 196197].

10.3.3 Constant Angle Control There are three methods based on keeping the angle constant between the stator current vector and the d-axis of the rotor:

1) the fastest torque control (gives the fastest torque response), 2) the maximum torque/current control, and 3) the maximum power factor control.

It can be shown that all the above three control strategies depend on the tan (Vas 1998). Let us first consider how the fastest torque response can be achieved. The solution of the extreme value problem (10.26) yields an equation for the quadrature current component

iLqs

q2 . (10.33)

By dividing the sides of Eq. (10.33) by Eq. (10.27) we obtain


ii

LL

LL

q

d

s q

s d

d

q

22

, (10.34)

which can be interpreted as tan (cf. Figure 10.4). The highest rate of torque change is thus obtained when the angle between the stator current vector and the d-axis is

arctan LL

d

q. (10.35)

The direct-axis current reference isdref is obtained by substituting the magnitude of the flux linkage solved from Eq. (10.27) to Eq. (10.28) and by substituting the real torque Temax by its reference

i Tp L Ldref erefd q3 2 tan . (10.36) The reference for quadrature-axis current is obtained from Eqs. (10.34) and (10.35)

ii T

qrefdref eref

tan sgn( ) . (10.37)

In the maximum torque/current control strategy, on grounds of the equation, it is obvious that the maximum value for the ratio is obtained when the angle between the current and the d-axis of the rotor is /4. Previously we showed that the maximum power angle is achieved when the angle of the stator current with respect to the d-axis is

arctan LL

d

q. (10.38)

The current references in the dq reference frame are obtained similarly as in the maximum torque/current control.

10.3.4 Combined Current-Voltage Vector Control The combined current-voltage vector control is adapted for instance for high rotation speeds; when using this control scheme, drawbacks resulting from the delays in the AC current references and saturation can be avoided (Vas 1998). The monitored rotor speed information is fed to the function generator, the output of which is the direct-axis stator flux reference sdref. During field weakening, the reference signal is a function of the rotor speed. The actual values of the stator flux linkage components or their estimates are obtained with the measured phase currents and the direct and quadrature-axis inductances in the stator flux linkage estimation circuit. The flux controller (a PI controller) produces a direct-axis stator current reference idref from the difference of the stator flux linkage component reference value and the actual value. The difference of the direct-axis stator current reference and the measured stator current component, fed to the current controller (PI


controller), yields the d-axis voltage component reference. Finally, the rotational voltage induced by the quadrature-axis stator flux linkage has to be subtracted from the voltage reference obtained with the current controller, as shown by the equivalent circuit of Figure 10.3. The torque reference Teref is implemented by a speed controller, usually also a PI controller. The quadrature-axis current reference is obtained by

iT i

sqreferef sq sd

sd , (10.39)

where Teref = 2Te/(3p). The reference obtained from the difference of isqref and isq (the error isq) is fed into the current controller (PI controller) similarly as in the case of the direct-axis component to obtain the quadrature-axis voltage component reference. The rotational voltage sd is added to the output signal, and thus the final usqref is obtained. By coordinate transformations and two-phase-to-three-phase transformations, phase voltage references are generated from the dq voltage references; the control of the PWM inverter is based on these obtained references. Figure 10.12 shows the block diagram of the control.

usdref

usqref

usxref

usyref

usArefusBrefusCref

rsd

sq-+

++

isd-+

isq

+

Fluxlinkagecontrol

isdref

isqref

sd-+

sdref

sd++

Te ref

sqisd

Functiongen.

-+

ref

isd

isq

isx

sy

isAisBisC

r

Ld

Lq

sdsq

1s

Currentcontr.

Currentcontr.

Soeedcontrol

-

2 3

irje

rje 2 3 inverter SYRM

Figure 10.12 Block diagram of the combined current-voltage vector control. The notation 1/s indicates integration with respect to time (Vas 1998)

10.3.5 Direct Torque and Flux Linkage Control The control scheme based on the direct torque and flux linkage control is in principle very well adapted for the synchronous reluctance machine as well as for other rotating-field machines. A control method applicable to a synchronous reluctance machine is obtained for the whole speed


range by employing a correction based on the current model similarly as in the case of a separately excited synchronous machine. When aiming at a position feedback system, in the case of the synchronous reluctance machine, the initial angle can be easily determined on grounds of the large difference between the direct-axis and quadrature-axis reluctance. In this case, the DTC should be supplemented with references inherent to this machine type for instance with respect to the power factor. Any of the previously discussed control schemes can be applied also to the case of a DTC inverter. Also a position-sensorless drive applying drift correction is adapted for the purpose. Also in this case, a very low quadrature-axis inductance may prove problematic for the DTC; the low inductance may result in an excessively high value of the quadrature-axis current ripple, or it may cause problems in measuring.

10.4 Synchronous Reluctance Machine Operating as a Generator A synchronous reluctance machine can be operated as a generator similarly as other electrical machines. It has been shown that reluctance generators are well adapted to low and medium-power applications, in which a low-loss rotor is a remarkable advantage when compared for instance with an asynchronous generator. Furthermore, the brushless and simple construction makes the synchronous reluctance machine a potential alternative for instance as a generator in small-scale hydropower plants or wind power plants. With a PWM inverter, the voltage of the generator can also be rectified, in which case the synchronous reluctance machine operates as a DC voltage generator. Similarly as in the motoring operation, the most important parameter in the SyR machine operating as a generator is the saliency ratio Ld/Lq, since the efficiency and the power factor of the generator are directly proportional to this ratio. However, at the present, large-scale research and development work is yet at the very beginning. Since the characteristics of a SyR machine can be improved only when the saliency ratio of the machine reaches a sufficiently high value, it can be easily shown that also in this case, constructing a machine with a very large number of poles is difficult, similarly as in the case of an induction machine. This is due to the fact that in machines with a very large number of poles, the stator flux leakage tends to increase to such a level that the characteristics of both an induction machine and a SyR machine are impaired. When constructing multi-pole machines, separately excited synchronous machines and permanent magnet synchronous machines are superior alternatives. A synchronous reluctance machine is best adapted for the pole pair number of p = 1 ... 3. References Betz, R.E. 1992. Theoretical aspects of control of synchronous reluctance machines. IEE Proceedings-B, Vol. 139, No. 4, pp. 355364. (4) Betz, R.E., Lagerquist, R., Jovanovic, M., Miller, T. J. E., and Middleton, R. H. 1993. Control of synchronous reluctance machines. IEEE Transactions on Industry Applications, Vol. 29, No. 6, pp. 11101122. (5) Boldea, I. 1996. Reluctance synchronous machines and drives. Oxford: Clarendon Press (1)


Boldea, I., Fu, Z. X., and Nasar, S. A. 1993. High-performance reluctance generator. IEE Proceedings-B, Vol. 140, No. 2, pp. 124130. (10) Haataja, J. 2003. A comparative performance study of four-pole induction motors and synchronous reluctance motors in variable speed drives. Acta Universitatis Lappeenrantaensis. Dissertation, Lappeenranta University of Technology. (12) Luukko, J. 1998. Kestomagneettitahtikoneiden vektoristperiaatteet. (Vector control principles of permanent magnet synchronous machines, in Finnish.) Lappeenranta University of Technology (unpublished). (7) Matsuo, T. and Lipo, T. A. 1994. Rotor design optimization of synchronous reluctance machine. IEEE Transactions on Energy Conversion, Vol. 9, No. 2, pp. 359365. (3) Reliance S-2000 Synchronous Reluctance B-2565 AC Motors. 2006. (Online). (Accessed 8 August 2006). Available at http://www.reliance.com/prodserv/motgen/b2565.html. (9) Pllnen, R. 1998. Shkvoimatekniikan kyttsovelluksia. (Practical applications in Electrical Power Engineering, in Finnish). Seminar paper, Lappeenranta University of Technology. (11) Salo, J., Pyrhnen, J. (ed.). 1997. Avonapareluktanssikoneet. (Salient pole reluctance machines, in Finnish.) Lecture Notes EN C-99. Lappeenranta University of Technology. (8) Staton, D. A., Miller, T. J. E., Wood, S. E. 1993. Maximising the saliency ratio of the synchronous reluctance motor. IEE Proceedings-B, Vol. 140, No. 4, pp. 249259. (2) Vas, P. 1998. Sensorless vector and direct torque control. Oxford: Oxford University Press 1998. 7 (6)

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