SR Motor and Drive Design Options

34.9.4 SR Motor and Drive Design Options

drives will vary according to the inverter topology. A wide The main components of the drive system are shown in range of different SR drive circuits are available for SR drives,

Fig. 34.99. It is important to design the motor and drive and these are detailed below. Circuits with only one switch together in an integrated manner. The main criteria that need per phase are possible; however, these have various disadvan- to be considered in designing the components of the SR drive tages such as control restrictions, a need for extra windings, system will be discussed later. It will be seen that certain design or higher switch voltages. However, with two switches per choices, which may be advantageous for one component of phase, the motor is fully controllable in four quadrants and has the drive system, may bring about disadvantages in another completely independent motor phase control. Therefore, the component. This highlights the need for a careful, integrated maximum number of power switches required for the motor system approach to be taken when designing the drive system. operation is normally 2q, where q is the number of phases.

34.9.4.1 Number of Motor Phases

34.9.4.4 Inverter Topology Types for SR Motors

There are many possibilities in choosing the number of stator As was mentioned, the torque produced in the SR motor is phases and rotor poles in SR motors. The simplest SR motor independent of the direction of current flow in each motor may consist of only one phase; however, to operate the motor phase. This means the inverter is only required to supply uni- in four quadrants (motoring or generating in both forward directional currents into the stator windings. The three major or reverse directions), at least three phases are required. The circuit topology types that have been used for each winding most common configuration to date has been the four-phase of an SR motor drives are shown in Fig. 34.100. As indicated SR motor, which has eight rotor poles and six stator poles, as in this figure, these are commonly termed the bifilar, split dc was shown in Fig. 34.97.

supply, and two-switch type inverter circuits.

3 Phase Controlled or

Load AC Mains

Uncontrolled

DC link

Inverter

SR Motor

Rectifier

Measured Currents and Voltages

Input Commands

Controller Position Feedback

FIGURE 34.99 Main components of an SR drive.

976 M. F. Rahman et al.

FIGURE 34.100 Major SR inverter topology types: (a) bifilar type; (b) split dc supply type; and (c) two switch type.

In the circuits shown in Fig. 34.100, only one or two switch- Upon examination of the circuit, it can be seen that because ing components per phase are required. Other circuit topology of the split capacitor bank, only half the available dc voltage types that use shared components between the motor phases can be switched across the phase winding. Thus, for the same have limitations in control flexibility.

voltage across the motor phases that is supplied by the bifilar circuit described earlier, the dc supply voltage must be doubled

with respect to the bifilar circuit supply. This means that the

34.9.4.4.1 Bifilar Type Inverter Circuit

In Fig. 34.100a, a

drive circuit for a bifilar-wound SR motor is shown. The bifilar voltage rating of the devices would effectively be the same as

in the bifilar circuit.

windings are closely coupled, with one winding being con- This is inherently inefficient. The configuration also has the nected to a switching device while the other is connected to a need for balanced split capacitive components. In addition, it freewheeling diode. Current is increased in the winding when will be seen that the soft-chopping form of control described in the switching device closes. At turn-off, the current transfers Section 34.9.7 is not available in this drive. to the secondary winding through transformer action, and the

inductive energy flows back into the supply via the freewheel- ing diode. If perfect coupling is assumed, then the voltage 34.9.4.4.3 Two-switch Inverter Circuit The two-switch across the switching device will rise to twice the dc supply volt- inverter type circuit, which is shown in Fig. 34.100c, uses age during turn-off. However, in practice this would be higher. two switching devices and two diodes per phase. Unlike the This is because there will be some uncoupled inductance in the previous two circuits, three modes of operation are possible: primary that will cause high induced voltages when the cur- rent in the winding collapses to zero. Thus, snubbing circuits Mode 1: Positive phase voltage would almost certainly be required to protect the switching

A positive phase voltage can be applied by turning both switch- components from over-voltage.

ing devices on. This will cause the current to increase in the The advantage of the bifilar circuit is that it requires only phase winding.

one switching device per phase. However, with the advent of modern power electronic devices, which have both low cost Mode 2: Zero phase voltage and low losses, this advantage quickly disappears.

A zero-voltage loop can be imposed on the motor phases when one of the two switches is turned off while current is 34.9.4.4.2 Split DC Supply Inverter Circuit The split dc flowing through the phase winding. This results in current supply type inverter circuit is in Fig. 34.100b. As in the bifilar flow through a freewheeling loop consisting of one switch- circuit, this configuration also uses only one switching device ing device and one diode, with no energy being supplied by and one diode per phase. However, a center-tapped dc source or returned to the dc supply. The current will decay slowly is required. When the switching device is turned on, current because of the small resistance of the semiconductors and con- increases in the phase winding because of the positive capaci- nections, which leads to small conduction losses. This mode tor voltage being applied. At turn-off, the current is forced to of operation is used in soft-chopping control, as described in flow through the diode and thus decays to zero more quickly Section 34.9.7. because of the connection to the negative voltage. It is usual for the dc center tap to be implemented using a split capac- Mode 3: Negative phase voltage itor in the dc-link. The voltages across each capacitor must When both switches in a motor phase leg are turned off, the remain balanced, which means that there can be no significant third mode of operation occurs. In this mode, the motor phase power-flow difference between the two capacitors.

current will transfer to both of the freewheeling diodes and

34 Motor Drives 977 return energy to the supply. When both of the diodes in the thus the inductance of the stator winding will be at a maxi-

phase circuit are conducting, a negative voltage with amplitude mum. The opposite will occur in the fully unaligned position equal to the dc supply voltage level is imposed on the phase (when the rotor inter-pole axis is aligned with the stator pole). windings.

Thus, the inductance becomes a function of position only and In this circuit, the switching devices and diodes must be able is not related to the current level. If it is also assumed that to block the dc supply voltage amplitude when they are turned mutual inductance between the phases is zero, then a typical off, in addition to any switching transient voltages. However, inductance variation L(θ) with respect to the rotor position because the circuit contains two devices in series, the blocking similar to that shown in Fig. 34.102 arises. Although this is an voltage is essentially half the value seen in the previous two idealized inductance variation, it is helpful in the understand- circuit types for the same applied motor phase voltage ampli- ing of key operating principles of the machine. One should tude. Another advantage of the two-switch inverter circuit is note that in the idealized inductance variation there are sharp that it offers greater control flexibility with its three modes of corners, which can only arise if flux fringing is completely voltage control.

ignored.

A disadvantage of this inverter type, as compared to the bifi- Four distinct regions can be identified in the plot of the lar and split dc supply types, is that it contains twice as many linear inductance variation shown in Fig. 34.102. These distinct switching components per phase. However, with the current regions correspond to a ranges of rotor pole positions relative wide availability and economy of power semiconductors, in to the stator pole positions as described below: most applications, the advantages of the two-switch circuit outweigh the cost of an extra switching device per phase.

Region A

This region begins at rotor angle θ 1 , where the first edge of the rotor, with respect to the direction of rotation, just

34.9.5 Operating Theory of the

meets the first edge of the stator pole. The inductance will

Switched-reluctance Motor:

then rise in a linear fashion until the poles of the stator and

Linear Model

rotor are completely overlapped at angle θ 2 . At this point, the magnetic reluctance is at a minimum and the phase induc-

If a linear magnetic circuit is assumed, the flux linkage is pro- tance is at a maximum. These rotor positions are illustrated in portional to phase current for any rotor position θ. This is Figs. 34.103a and b, for example, four phase motor with rotor demonstrated in Fig. 34.101, where the magnetization curves pole 1 approaching the stator pole of phase A. for the linear SR motor for various rotor positions and cur- rents are shown. In this linear case, the inductance L at any Region B

position θ, which is the slope of these curves, is constant and This region spans from rotor positions θ 2 to θ 3 . In this region, independent of current.

the inductance remains constant because the rotor pole is com-

As the motor rotates, each stator phase undergoes a cyclic pletely overlapped by the stator pole (i.e. the overlap area of

variation of inductance. As can be seen in Fig. 34.101, in the the poles remains constant). At rotor angle θ 3 the edge of the fully aligned position (when a rotor pole axis is directly aligned rotor pole leaves the stator pole overlap region, and thus the with the stator pole axis) the reluctance of the magnetic circuit area of overlap will again begin to decrease. The position at through the stator and rotor poles will be at a minimum, and which this occurs is illustrated in Fig. 34.103c.

Aligned Positi on

Flux Linkage

Rotor Position

Y (Wb) q (degrees)

Unaligned Position

Current i (A) FIGURE 34.101 Magnetization characteristics of linear SR motor.

978 M. F. Rahman et al.

Torque T

T max

Constant current i

T min

FIGURE 34.102 Typical linear inductance variations and corresponding torque variations for constant phase current.

Region C in other words, the rotor experiences a torque opposite to the

When the rotor moves past θ 3 , the rotor pole leading edge direction of rotation.

begins to leave the pole overlap region, and region C begins. It should be noted that this reluctance-machine torque At this point, the inductance begins to linearly decrease, until always acts to decrease the reluctance. The direction of current at θ 4 , the rotor pole has completely left the stator pole face flowing into the stator winding is irrelevant. This signifies that overlap region. At this point, the inductance is at its minimum unidirectional current excitation is possible in the SR motor once more. The rotor position at which the rotor pole has drive. completely left the overlap is indicated in Fig. 34.103d.

The variation of torque with rotor angle for a constant phase winding current is as shown in Fig. 34.102. It can be seen

Region D that the torque is constant in the increasing and decreasing In this region, the rotor and stator have no overlap, and thus inductance regions, and is zero when the inductance remains

the inductance remains constant at the minimum level, until constant. region A is reached once again.

The preceding physical explanation of the developed torque It was mentioned earlier that when a stator phase is excited, is also given by the familiar torque Eq. (34.96) for a variable-

the rotor poles will tend to move toward the maximum- reluctance machine. inductance region. Thus, a motoring torque is produced when

1 2 dL(θ)

(34.96) angles when the inductance is rising (assuming motoring rota-

a stator phase is provided with a current pulse during the

2 dθ

tion is in the direction of increasing θ in Fig. 34.102). This From Eq. (34.96), it is evident that the magnitude of the means that if positive torque is desired, excitation should be instantaneous torque developed in the SR motor is propor- arranged such that the current flows between the appropriate tional to both i 2 and dL/dθ. If the inductance is increasing with rotor angles when the inductance is rising.

respect to the angle, and current flows in the phase winding, Conversely, if current flows during the decreasing induc- then the torque will be positive and the machine will operate tance region, a negative torque would result. This is because in motoring mode. Hence, from Eq. (34.96), it can be seen the rotor will be attracted to the stator pole in such a way that that when the motor phase is excited during a rising induc- it rotates in the opposite direction to the motoring rotation, or tance region, part of the energy from the supply is converted

34 Motor Drives 979

Direction of rotation

Direction of rotation

Direction of rotation

Direction of rotation

FIGURE 34.103 Rotor pole 1 positions: (a) meeting edge of stator pole A; (b) overlapped by stator pole A; (c) edge of rotor pole leaving overlap region; and (d) rotor pole completely leaving overlap region. (Note: Airgap space is exaggerated for clarity.)

to mechanical energy to produce the torque, and another part the magnitude of the torque was constant in the rising or is stored in the magnetic field. If the supply is turned off decreasing inductance regions. However, it was seen that the during this region, then any stored magnetic energy is partly torque changes from positive to negative according to the sign converted to mechanical energy and partly returned to the of dL/dθ. supply.

Hence, the ideal waveform for the production of motoring However, a negative, or braking torque will be developed by torque would be a square wave pulse of current (with magni- the motor if the inductance is decreasing with respect to the tude equal to the maximum possible supply current) flowing rotor angle and current flows in the phase winding. In this case only during the increasing inductance period (Fig. 34.104). energy flows back to the supply from both the stored magnetic This current waveform is illustrated in Fig. 34.104b. However, energy and the mechanical load, which acts as a generator.

in practice this type of current waveform is difficult to produce It can also be seen from Eq. (34.96) that the sign (or direc- in a motor phase. This is because the motor phase current is tion) of the torque is independent of the direction of the supplied from a finite dc voltage source, and thus inductance current and is only dependent on the sign of dL/dθ. This of the stator phase winding would delay the rise and fall of explains the torque waveforms that were seen in Fig. 34.102, current at the pulse edges. Instead, a more practical current where for constant current (and constant dL/dθ magnitude), waveform is normally used as is illustrated in Fig. 34.104c.

980 M. F. Rahman et al. L( θ)

chopping-mode control method in SR motor drives. During the

(a)

time of conduction (between the turn-on and turn-off angles), the current is maintained within the hysteresis band by the switching off and on of the phase voltage by the inverter when

the phase current reaches the maximum and minimum hys- i( θ)

teresis band. An example of the voltage waveform used for the hysteresis current control is shown Fig. 34.104d, where a con- stant inverter dc supply voltage of magnitude V s is used. It can

(b)

be seen that the switching frequency of the voltage waveform decreases as the angle increases. This is due to the fact that the phase inductance is linearly increasing with angle, which has

i( θ)

hysteresis band

(c)

the effect of increasing the current rise and fall time within the hysteresis band.

In the chopping-mode control method, the turn-on region is defined as the angle between the turn-on angle θ on and θ on

θ off θ q

the turn-off angle θ off , and is chosen to occur during the ris- ing inductance region for motoring torque. In the practical

V s chopping current waveform, the current turn-on angle θ on is V( θ)

placed somewhat before the rising-inductance region. This is to ensure that the current can quickly rise to the maximum

level in the minimum-inductance region before the rising- θ on

inductance, or torque-producing, region. Similarly the turn- off angle θ off is placed a little before the maximum-inductance region so that the current has time to decay before the negative-

torque, or decreasing-inductance, region. The angle at which

the current decays to zero after turn-off is labeled as θ q in ψ (θ)

−V

Fig. 34.104c.

(e)

34.9.5.2 High-speed Approximation to Square-pulse