Download the control of switched reluctance drives

THE CONTROL OF SWITCHED RELUCTANCE DRIVES
ELEONORA DARIE 1, EMANUEL DARIE 2
Key words: Switched reluctance machines, Generator, Flywheel storage, Drive
control.
This work describes the aspects of the topology and control of a switched reluctance drive
are considered and compared with the topology and control of conventional AC drives.
The focus herein lies on the control of switched reluctance drives. The switched reluctance
drive is necessary for a flywheel energy storage system for use in for instance an UPS. It is
shown that for this application, switched reluctance drives have some essential advantages
compared to conventional AC drives.
1. INTRODUCTION
The switched reluctance machine drives have gained considerable
attention among researchers due to several reasons. First of all, the rotor
construction is simple and robust, as it consists of pure (laminated) steel with
neither permanent magnets, nor electrical windings, while the stator can be easily
manufactured as the windings are not distributed but concentrated around the
salient poles. Secondly, the machine is cost-effective in comparison with
induction machines, while it is claimed to have a comparable or even higher
efficiency and power to volume ratio. In this work, the main aspects of principal
operation, inverter topology and control of switched reluctance machines are
reviewed. Also, the use of the switched reluctance machine as a generator is
considered and for this purpose a short review of publications in this matter is
performed. Finally, the application in a flywheel energy storage system is
considered and it is shown that this application permits to exploit most of its
specific advantages. In a switched reluctance machine, only the stator presents
windings, while the rotor is made by steel laminations without conductors or
permanent magnets. The switched reluctance machine motion is produced by the
variable reluctance in the air grip between the rotor and the stator.
1
) Technical University of Civil Engineering, Bucharest, Pache Protopopescu 66, Sector 2, e-mail:
[email protected].
2
) Police Academy, Bucharest, Privighetorilor 1-2, Sector 1, e-mail: [email protected]
Rev. Roum. Sci. Techn.– Électrotechn. et Énerg., 49, 4, p.
, Bucarest, 2004
Eleonora Darie, Emanuel Darie
2. PRINCIPLE OPERATION OF SWITCHED RELUCTANCE MAHINES
Although switched reluctance machines are in fact synchronous machines,
their operation and control differs fundamentally from conventional rotating-field
AC machines, such as induction or permanent magnet synchronous machines.
2.1. TORQUE DEVELOPMENT
Torque production in reluctance machines is achieved by the tendency of
the rotor to move to a position where the inductance, and hence the magnetic
field energy, of the excited winding is minimized [1]. An example of a 6/4
switched reluctance machine is shown in fig. 1. This three-phase machine is
denoted 6/4 because it has six stator and four rotor poles. In the position shown,
the resulting torque tends to rotate the rotor in clockwise direction towards the
aligned position. If the rotor continues past the aligned position, due to its
inertia, the attractive force between the poles produces a braking torque. To
eliminate this negative torque, the current must be switched off while the poles are
separating. The ideal current waveform is therefore a series of pulses synchronized
with aligning rotor poles and stator poles. By exciting the stator windings of the
different phases each time two rotor poles approach the appropriate stator poles, a
continuous torque production and rotation of the rotor is achieved. In generator
mode, windings are excited during the separation of the respective poles,
yielding a braking attraction. The requirement for an optimized current shape
makes it impossible to run such a machine directly from the grid. A power
electronic inverter with a control based on feedback of the rotor position is a
necessity.
Fig. 1 – The 6/4 switched reluctance machine with one phase excited.
3
The control of switched reluctance drives
2.2. CIRCUIT EQUATIONS
The general voltage equation of an electrical coil with a resistance R and
with Ψ(t) representing the instantaneous flux coupled with this coil, can be
written as:
u = R ⋅ i (t ) +
d Ψ (t )
dt
(1)
while, in case of a switched reluctance machine the inductance L is a complex
function of position and (through the non-linear ferromagnetic hysteresis
phenomenon) current:
Ψ (t ) = L ⋅ (i (t ),θ (t )) ⋅ i (t ) ,
dθ
=ω m
dt
(2)
where θ is the mechanical angle of the rotor position and ω m is the rotational
speed.
Using (1) and (2), the dynamic phase voltage equation of a switched reluctance
machine with the rotor position θ and the rotational speed ω m , neglecting mutual
coupling effects, can be stated as follows:

∂L(i,θ )  d i
∂L(i, θ )

u ph = R ⋅ i (t ) +  L(t ) + i (t )
+ i (t ) ⋅
⋅ω m
∂i  d t
∂θ

(3)
The last term is the back electromotive force (emf) e of the switched reluctance
machine:
e =ω m ⋅ i ⋅
∂L(i, θ )
∂θ
(4)
Hence, the induced voltage contains information about the rotor position. This
property can be exploited for position feedback without a shaft sensor.
Eleonora Darie, Emanuel Darie
With constant current, (4) is linked to both increase in magnetic field energy
and produced mechanical power. In unsaturated conditions, both terms equal each
other, and torque can be expressed as:
T=
i 2 ∂ L (i , θ )
⋅
2
∂θ
(5)
∂L
> 0 the torque is positive and electrical power is converted into
∂θ
∂L
mechanical output (motoring), while when
< 0 the torque is negative and
∂θ
mechanical power is converted into electrical power (generating). Note that the
produced torque is independent of the direction of the current, since i 2 is always
positive. With the machine driven in saturation, although (5) being no longer valid,
these conclusions remain true.
When
3. INVERTER TOPOLOGY
As torque is independent of the direction of the current, the flux-linkage and
the current, as well as the topology of the inverter circuit, may be unipolar. This
mode of operation is preferred because it permits a simpler form of controller.
However, to be able to switch off the current while the poles are aligned (in
motoring mode), a negative voltage must be applied to enforce this fast current
change in the relatively large inductance of the pole winding. The half-bridge
phase can supply current in only one direction. This circuit is capable of operating
the machine as a motor and generator. Several other circuits are possible besides,
using less power electronic switches and employ various means to produce the
reversed voltage [2]-[6]. However, in general these circuits either compromise the
performance of the machine or require additional components, while the faulttolerant operation, more in particular the impossibility to have a shoot-through,
of the drive is destroyed.
4. CONTROL OF THE SWITCED RELUCTANCE MOTOR
The control of electrical machines is typically achieved through several
control loops. Fig. 2 shows the basic control scheme of a servo drive [1]. The
outer control loops are generally similar for all drive types, while the inner torque
loop differs in switched reluctance machines fundamentally from other electrical
The control of switched reluctance drives
5
machines. Much of the classical theory of torque control in electric drives is based
on the DC machine, in which torque is proportional to flux multiplied by
current. The flux and current are controlled independently, be it through
mathematical transformations in AC field-oriented control. Generally speaking, in
classical DC and AC machines, the flux is maintained constant while the current
is varied in response to the torque demand. In switched reluctance machines,
unfortunately, there is no straightforward equivalent of field-oriented control.
Pulses of phase current, synchronized with the rotor position, produce torque in the
switched reluctance machine. The flux in each phase must usually be built up from
zero and returned to zero each stroke. The inner torque loop consists of controlling
timing and regulation of these pulses. Usually there is no torque sensor and
therefore the torque control loop is not closed. Because the switched reluctance
motor drive cannot be characterized by a simple torque constant kT
(torque/ampere), smooth torque control must be achieved through feed-forward
torque control algorithms, incorporating some kind of motor model. The fact that
the machine inductance is not only dependent on the rotor position, but also on the
excitation current, complicates the development of control strategies for switched
reluctance machine drive systems. For all other electrical machines, control
strategies are derived based on the machine parameters being constant for most of
the excitation range [1], [4].
m*
+
Position
Control
_
m*
Velocity
Control
T
*
Torque
Control
Motor
+
Load
m
Motor velocity
Shaft position
Fig. 2 Servo drive control system
4.1. LOW-SPEED CONTROL: CHOPPING
At lower speeds, the current is regulated either by pulse width modulation
(PWM)-voltage or direct instantaneous current regulation (e.g. hysteresis band
current control). The phase voltage is switched between -UDC and +UDC (hardchopping) or between zero and +UDC (soft-chopping). As speed increases also the
firing or commutation angles (turn-on and turn-off angles) of the commutation
cycle are advanced. The turn-on angle must be advanced to be able to build up the
flux from zero to the desired value before the inductance starts rising (approaching
of poles).
Eleonora Darie, Emanuel Darie
4.2. HIGH-SPEED CONTROL: SINGLE-PULSE OPERATION
As speed increases, the back-emf e increases according to (4). The speed for
which e equals UDC is called base speed [3]. At speeds higher than this base speed,
there is insufficient voltage available to control the current. Timing of current
pulses can then only control the current. This control mode is called single-pulse
mode.
5. SWITCHED RELUCTANCE MACHINE AS A GENERATOR
5.1. CURRENT CONTROL
Current control of the switched reluctance machine in generating is identical
to motoring mode. The only difference is timing of current pulses. While in
motoring mode the windings are excited during rising inductance (approaching
of poles), in generating mode each winding is excited while the poles separate from
each other. The objective of the generator control is normally to keep the DC-link
voltage at the desired value. Unlike field-oriented AC machines, power generation
is not continuous but pulse-wise. A DC-link capacitor must be retained to
provide excitation power during the fluxing interval, more in particular
during the first part of each stroke. The ratio between excitation energy and
generated energy is called the excitation penalty:
ε=
Pin , elec.
Pout , elec.
(6)
The DC-link voltage decreases during the fluxing interval, and increases
during the de-fluxing interval. The variation or ripple in the DC-link voltage
depends on the energy needed to build up the flux each stroke and the DC-link
capacitance. The essence of its instability is the proportionality of the excitation
power to the back- electromotive force (emf). If the load is too small, the DC-link
voltage rises exponentially towards infinity, and if the load is too large, the DClink voltage falls towards zero. For this reason it is necessary to feedback the DClink voltage or to control the average output current independently of the DC-link
voltage. The controller must maintain the average DC-link voltage constant in
much the same way as it must maintain a constant average torque in motoring
mode. However, the DC-link capacitance has an integrating or smoothing effect
such that it requires a lower bandwidth to control the DC voltage than to control
the torque [1].
7
The control of switched reluctance drives
Although relatively little has been reported on the design of the switched
reluctance generator controller, there is a broad variety in the proposed controller
schemes [1]. At lower speeds, the current pulses are controlled by chopping the
voltage between zero and -UDC,, or between +UDC and -UDC with fixed commutation
angles. The control is similar to the current chopping control in motoring mode. At
higher speeds the generator is operated in single-pulse mode. Adapting the
commutation angles regulates the current. As the speed increases, also the
amplitude of the negative back emf increases and may become larger than the
negative supply voltage. In this case an uncontrollable rise of the phase current
occurs. To avoid over-current conditions and torque pulsations, the control angles
have to be retarded as a function of the DC-link voltage as well as of the speed.
Measuring the variation of the DC-link voltage is necessary to avoid unstable
operating conditions. It is shown that maximum energy conversion is obtained
when back-emf and UDC are in balance. This balance is achieved through adaptation
of the firing angles and variation of the DC-bus voltage in proportion to the
speed. The drawback of this method is the necessity of a step-down DC/DC
converter in order to achieve a constant output voltage.
5.2. START-UP
Since the switched reluctance machine is singly excited, like the induction
machine, a DC source is necessary during start-up from cold, i.e. with the machine
not magnetized and no voltage on the DC-link capacitor. Once started, the system
is self-sustaining in its reactive power and the DC source can be disconnected. The
efficiency of the switched reluctance generator is very similar to the efficiency of
the switched reluctance motor. The main difference is that the losses in the
converter can be reduced as in the generator, the bulk of the current flows
through the diodes having in general less conducting losses than the switching
devices.
6. APPLICATION IN FLYWHEEL ENERGY STORAGE
In flywheel energy storage, electrical energy is stored in the form of kinetic
energy. As the amount of stored energy is proportional to the square of the rotation
speed, a high-speed, low-loss operation is desired. In view of its application in for
instance an uninterruptible power supply system (UPS) or a dynamic voltage
restorer (DVR), reliability and immediate and fast energy transfer is key. Hence,
primary requirements for the motor/generator of a flywheel energy storage system
can be summarized as: high output power capability, fast response on sudden
energy demand (for example when a voltage dip occurs), ability of the rotor to
withstand high speeds, ability of the rotor to operate in vacuum with adequate
Eleonora Darie, Emanuel Darie
thermal management (that is little or no heat generation in rotor), negligible zerotorque spinning losses, high reliability, high efficiency and low cost.
Switched reluctance machines have the following advantages over
permanent magnet synchronous machines: there is no concern with
demagnetization; hence switched reluctance machines are inherently more reliable
than permanent magnet machines, there need not be an excitation field at zero
torque, thus eliminating electromagnetic spinning losses, switched reluctance
machine rotors are constructed entirely from high-strength low-cost
materials.
A comparison between induction machines and switched reluctance
machines is less simple: because of the absence of currents flowing in the rotor,
there are no Joule-losses in the rotor, on the other hand eddy current and hysteresis
losses might be higher, efficiency, speed-range, power density and cost are
comparable, but often in slight favor of the switched reluctance machine, the
inverter topology of a switched reluctance drive is inherently more fault-tolerant
because of the absence of shoot-through possibility. Disadvantages of the switched
reluctance machine drive are its rather complex control.
7. CONCLUSIONS
The basic operation of a switched reluctance machine is reviewed for the
motor as well the generator operation; thereby illustrating its advantages over
other types of standard AC drives. The four-quadrant operation is appropriate for
the operation as a flywheel energy storage. It is especially very useful for highspeed operation due to its mechanical properties and low losses.
REFERENCES
1.D. E. Cameron, J. H. Lang, The Control of High-Speed Variable-Reluctance Generators in Electric
Power Systems, IEEE Transaction on Industry Applications, 29, 6, pp. 1106-1109, (1993).
2. S. Vukosavic, V.R. Stefanovic, SRM Inverter Topologies: A Comparative Evaluation, IEEE
Transaction on Industry Applications, 27, 6, pp. 1034-47, (1991).
3. P. C. Kjaer, C. Cossar, Switched Reluctance Generator Control using an Inverse Machine
Model, International Conference on Electrical Machines, Proceedings, pp. 380-385 (1994).
4. T. Sawata, P. C. Kjaer, T. J. E. Miller, A Control Strategy for the Switched Reluctance
Generator, Conference on Electrical Machines, Proceedings, 3, pp. 2131-2136 (1998)
5. Eleonora Darie, E. Darie, Linear and non-linear Model Simulation of a Switched Reluctance Motor,
Buletinul Institutului Politehnic din Iaşi, Tomul L(LIV) Fasc. 5, pag. 1275-1279, (2004).
6.W. F. Ray, M. T. Ebrahim, A novel high speed switched reluctance generator, European Conference
on Power Electronics and Applications, Proceedings, 3, pp. 811-816 (1995).