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1. IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005 1047
Theory and Operation of a Four-Quadrant Switched
Reluctance Motor Drive With a Single Controllable
Switch—The Lowest Cost Four-Quadrant
Brushless Motor Drive
R. Krishnan, Fellow, IEEE, Sung-Yeul Park, Student Member, IEEE, and Keunsoo Ha, Student Member, IEEE
Abstract—Low-cost motor drives are being sought for
high-volume energy-efficient home appliances. Key to the re-
alization of such low-cost motor drives is the reduction of the
power electronic converter to the barest in terms of its compo-
nents, particularly the active devices, finding the motor with the
least complexity for manufacturing and a controller that can
extract the desired performance from the machine and converter
combination. These and other factors such as self-starting, speed
control over a wide range, and, most of all, the crowning as-
pect of four-quadrant operation with a bare minimum number
of controllable switches remain as formidable challenges for
low-cost motor drive realization. An innovative four-quadrant
switched reluctance motor (SRM) drive with only one controllable
switch is realized in this paper, for the first time, in the opinion
of the authors. The motor drive is realized using a two-phase
machine and a single controllable switch converter. The theory
and operation of the proposed four-quadrant SRM drive with
the proposed control algorithm for its realization are described.
The motor drive is modeled, simulated, and analyzed to verify its
feasibility for self-starting, speed control, and for four-quadrant
operation, and the simulation results are presented. Experimental
results confirm the validity of the proposed control algorithm for
four-quadrant control of the SRM drive. The focus of the paper
is mainly directed toward the control algorithm for realizing the
four-quadrant operation of the two-phase SRM drive with a single
controllable switch converter.
Index Terms—Motor drives control, power electronics, switched
reluctance motor (SRM) drives.
I. PROPOSED MOTOR DRIVE FOR FOUR-QUADRANT OPERATION
FEDERAL regulations for some appliances in regard to
mandates on higher efficiency of the system to start with
have come into force and it is expected that they will also
spread to other categories of appliances. One way efficiency
can be increased is by introducing variable-speed operation
of the motor. Variable-speed operation increases the part load
Paper IPCSD-05-023, presented at the 2004 Industry Applications Society
Annual Meeting, Seattle, WA, October 3–7, and approved for publication in
the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Drives
Committee of the IEEE Industry Applications Society. Manuscript submitted
for review September 1, 2004 and released for publication April 15, 2005. This
work was supported by The Center for Innovative Technology, Reston, VA,
through the efforts of Panaphase Technologies.
The authors are with the Center for Rapid Transit Systems, The Bradley De-
partment of Electrical and Computer Engineering, Virginia Polytechnic Institute
and State University, Blacksburg, VA 24061 USA (e-mail: kramu@vt.edu; su-
park@vt.edu; ksha@vt.edu).
Digital Object Identifier 10.1109/TIA.2005.851019
efficiency as well as delivering higher efficiency over the
entire speed range and, hence, the interest in variable-speed
motor drives for applications that have traditionally remained
constant speed or with a few set speeds in home appliances.
While a variable-speed universal motor drive may become
acceptable in some appliances, the industry wants to move
away from brush and commutator-based machines for reasons
of reliability, safety, longevity of operation, acoustic noise, and
overload capability for longer durations. Hence, the search for
a simpler and lower cost four-quadrant brushless motor drive
has intensified with the prospective oncoming variable speed
applications in home appliances and hand tools contributed to
by both federal regulations and competition among appliance
manufacturers to introduce newer features and enhance system
efficiency.
Many solutions have been proposed for low-cost motor
drives and most of them revolve around the use of single-phase
switched reluctance motor (SRM) with parking permanent
magnets on the stator and two-switch-based asymmetric con-
verter, or two-phase SRM with three-switch-based converter
and single-phase permanent-magnet brushless dc motor drives
with four-controllable-switch-based converter, to mention a
few [1], and other variations in the literature too numerous to
mention here. Use of single-phase and three-phase induction
motors with four-controllable-switch-based inverters has been
attempted. Many of these solutions, though providing highly
desirable performance, are yet to be embraced as their cost is
as yet unacceptable in the appliance industries. The factors that
are widely cited in the industry for not embracing the formerly
proposed solutions are many. Some of these factors are given
below, and these served as a compass for the authors to steer
away from these concerns in seeking solutions to the low
cost motor drives in the competitive segment of the appliance
industries.
1) The cost of the machine is higher in almost all cases other
than the single-phase SRM.
2) The lowest cost machine, which is a single-phase SRM,
is not truly low cost as it involves permanent magnets
for parking the rotor at a desirable position for starting,
adding not only to the cost but complexity in manufac-
turing.
3) The cost of the converter and inverter has come down
significantly but not to the level where it can compete
0093-9994/$20.00 © 2005 IEEE

2. 1048 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005
with a one-controllable-switch universal motor drive for
one-quadrant application in many low-performance vari-
able-speed applications.
4) A two-controllable-switch-based converter (which seems
to have gained some traction) is still expensive as com-
pared to a one-controllable-switch-based brush dc or ac
universal motor drive system with limited one-quadrant
variable-speed application.
5) Though the proposed brushless and commutatorless so-
lutions as compared to brush-type machines in appliances
are welcome, being brushless alone is not the determining
factor in the selection of a motor or a motor drive in the
low-cost applications which is a key fact of life in this in-
dustry segment.
6) In high-speed ( 20 000 r/min) motor drives, the per-
manent-magnet brushless machines are believed not to
provide low-cost solutions even though there may be a
slight efficiency advantage in these machines, if not at
high speeds, but certainly at low and medium speeds.
In appliances, higher efficiency is desirable but cost-ef-
fective and high-efficiency solutions are much more
desirable and acceptable is a fact to be noted (as a few
point difference in percent efficiency is not a significant
factor).
7) Inmanyinstances,four-quadrantdriveoperationisnotnec-
essary but will be an important feature for future product
development of appliances. Some of the proposed conven-
tionalthree-phaseortwo-phaseacandSRMdrivessolutions
though provide a four-quadrant operation, the cost associ-
ated with the converter/inverter is high.
Anchored with these industry inputs, the authors have identi-
fied the following common features of low-cost motor drives
required for high-volume applications:
1) brushless motor (can be ac or permanent-magnet brush-
less dc or SRMs);
2) high-speed operational capability;
3) high-efficiency operability over a wide speed range;
4) four-quadrant operational capability;
5) minimum number of controllable switches (preferably
less than two) to reduce the cost of power electronic
circuit as well as to minimize the cost of the attendant
circuits such as gate drives and logic power supplies and
also to minimize the volume of heat sinks;
6) rotor position sensor-free operation;
7) smallest footprint for controller and converter layout to
reduce the volume, weight, and cost of the power elec-
tronics and controller.
To address these issues to the fullest possible level, some
solutions have already been proposed even though they have
not come into the literature. A single-controllable-switch-based
brushless motor drive solution is highly desirable for many of
the low-cost applications and such a set of solutions existed
[2], [3] prior to this publication for SRM drive systems. One of
the variations can be found in [4]. A number of single-quadrant
SRM drives with single-switch power converter topologies
have been under research and development for more than
four years at Virginia Polytechnic Institute and State Uni-
versity, Blacksburg. Power electronics and controller were
packed within 3 in 3 in 1.5 in with standard off-the-shelf
components for a 1-hp motor drive, though versions under
development are expected to have a volume reduction of 50%
in the packaging. While such packaging may be of critical
importance in commercial and industrial applications, this
will not be pursued in detail, as imparting four-quadrant op-
erational capability with this converter-based drive system
is considered much more important. It is highly significant
as it bestows for the first time a four-quadrant operation on
a brushless motor drive with only a one-controllable-switch
converter. This alters the current state of art, as there is no other
motor drive which can have a four-quadrant operation with
that bare minimum of controllable-switch-based converter. For
the first time, such a development points to the realization of
the lowest cost brushless motor drive that may be ideal for
many applications. Some of these applications have eluded
introduction of variable-speed and four-quadrant operation due
to the higher cost of the total motor drive package. Note that
a conventional four-quadrant SRM drive requires a minimum
of two or more controllable switches and, as well, so do brush
dc and ac universal motor drives. Therefore, the key aspect of
four-quadrant operability with a wide variable-speed control
will be the focus of this paper. It is believed with this fully
four-quadrant and variable-speed operation incorporated in
the single-controllable-switch-based SRM drive, a low-cost
brushless variable-speed motor drive has been realized for the
first time in the literature.
A two-phase SRM, one-controllable-switch converter, and a
digital signal processor (DSP) controller are the building blocks
ofthelow-costmotordriveconsideredinthispaper.Theproposed
control algorithms for starting, four-quadrant operation and
variable-speed control of an SRM drive with single controllable
switch are the key to the realization of the low-cost motor drive.
The proposed system is modeled, simulated, and analyzed for
validating the proposed control algorithms. Experimental results
fromalaboratoryprototypeconfirmthefeasibilityoftheproposed
low-cost motor drive four-quadrant control and operation.
Thispaperisorganizedasfollows.SectionIIdescribesthecon-
sideredSRManditsfeatures,andalsotheconverteranditsopera-
tionwiththeSRM.SectionIIIgivestherealizationofself-starting
of the motor drive without parking magnets. Section IV details
the control algorithm for the realization of a four-quadrant motor
drive. Based on these developments, the complete drive system,
itsmodeling,simulation,andanalysisarepresentedinSectionsV
and VI. Experimental results are presented both for self-starting
and for four-quadrant operation in Section VII. Conclusions are
drawn and presented in Section VIII.
II. CONSIDERED MACHINE AND POWER CONVERTER
Rationale for the selection of the electric machine and a
description of the one-controllable-switch-based converter are
given in this section.
A. Machine
The machine selection was based on factors such as the fol-
lowing [1], [10]:

3. KRISHNAN et al.: THEORY AND OPERATION OF A FOUR-QUADRANT SRM DRIVE 1049
1) free of brush and commutator;
2) easier manufacturability (and that, too, anywhere around
the world, and this factor excludes permanent-magnet
brushless dc machines);
3) preferably no permanent magnets on the rotor or stator
to reduce manufacturing complexity (this excludes all
permanent-magnet machines including brushless dc ma-
chines);
4) operability at speeds up to 40 000 r/min;
5) lowest cost (eliminates almost all other machines other
than SRMs);
6) operational capability with unidirectional current (this
eliminates induction and synchronous reluctance ma-
chines).
Given these factors, the choice narrows to switched reluctance
machines. With a minimum of winding insertion operation, a
two-phase SRM with concentric windings is considered for
further study. The machine is a two-phase SRM with one phase
forming the main phase and the other forming an auxiliary
phase. The torque is mainly extracted from the operation of the
main phase. The auxiliary phase is intended for commutation
of current in the main phase winding. Note that the auxiliary
winding also lends itself to sensing the rotor position by mon-
itoring its current and flux linkages or by other variables and
means. A number of opportunities which open up with this
kind of two-phase machines are to be noted. The number of
turns in the main and auxiliary windings need not be equal to
each other and, as well, their wire sizes also need not be equal.
The only requirement of the machine is that the phase windings
must be spatially (phase) shifted from each other. As the focus
of the paper is neither on design of such machines nor on the
requirement to optimize the drive system performance, further
treatment of the machine is not given for lack of space. The
machine used in this study is described with its characteristics
in [4]. Equally other types of machines such as those given
in [5]–[8] may also be sufficient for the proposed motor drive
system. While the constructional details and cost may vary
between these machines to some extent, a number of features
desirable in low-cost machines are preserved.
B. Power Converter
The power converter chosen to work with the two machine
phase windings is shown in Fig. 1. This is only one of the single-
controllable-switch-based converter topologies [2]. The power
converter obtains its dc link either from a single-phase (as shown
in figure) or from a three-phase ac through appropriate rectifiers
and an electrolytic capacitor. The machine-side converter con-
sists of a controllable switch Q , two diodes D and D , and a
capacitor C . The main winding is controlled with the control-
lable switch directly. When it is turned on (mode 1), the main
winding is applied with the dc-link voltage. If there is current in
the auxiliary winding, then it goes to charge the dc-link capac-
itor C , and closes the path through the capacitor C . When Q
is turned off, (mode 2) a path for the current is provided through
diode D and capacitor C and also through auxiliary winding
and D . Note that the capacitor C is very small compared to
the dc-link filter capacitor C almost by a factor of 100–200.
During the turn-off of the controllable switch, it is seen that the
Fig. 1. Considered motor and power converter schematic for four-quadrant
operation.
capacitor gets charged or the current is circulated through the
auxiliary winding and during both operations, the main winding
is involved. From this, it is seen that the current in the auxiliary
winding is also controlled by the controllable switch indirectly.
Alternately, one can perceive D and C as a snubber circuit for
transferring energy from the main winding during turn-off in-
stants of current control and commutation and also as an energy
source to force current through the auxiliary winding. More on
the converter operation, analysis, and design will be published
in the near future [3]. Diode D is optional it may be noted and
if it is used it need not be a fast acting type. With this, the circuit
becomes very compact and it is believed that it has the lowest
number of elements compared to other circuits in the literature.
III. SELF-STARTING
The single-switch converter creates a challenge in starting the
SRM. As the dc link is energized, note that the current flowing
in the main winding attracts the rotor poles to align with the
main stator poles. At this position, there is no torque production
capability for the main winding even if current is built in to the
main phase winding. As for the auxiliary winding, it requires
a current to produce a torque. This current can come from the
auxiliary (or snubber or auxiliary) capacitor C when the main
current decays and the auxiliary capacitor has enough charge
to initiate a current closing the current path through the dc-link
capacitor C . If the auxiliary current is insufficient to produce
a significant torque to move the rotor from its aligned position
with the main stator poles, then other options are built in for
self-starting. They are described in the following paragraph.
Key to the success of the four-quadrant operation of the con-
sidered motor drive is the ability to start at all rotor positions
in both directions. In order to start reliably, a starting scheme is
proposed in this paper. When the rotor poles are aligned to the
main stator poles, a start gate pulse signal of certain duration
is applied to the controllable switch. At this time, the rotor is at
standstill. This results in turn-on of the switch for a desirable du-
ration until the current is equal to a nominal or preset value and
then the switch is turned off. That provides a charge to the aux-
iliary capacitor C , as well as forcing a current in the auxiliary
winding. Thereby, the energy in the main winding is transferred
to the auxiliary winding and/or auxiliary capacitor due to the
flow of current from the main winding to the auxiliary winding

4. 1050 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005
and to the capacitor depending on the charge state of the capac-
itor. This results in the auxiliary winding producing a torque.
That torque may be enough to move the rotor poles away from
their aligned position with the main stator poles. When the main
winding current decays, note that the auxiliary capacitor sup-
plies the auxiliary winding with the current, resulting in some
positive torque production by the auxiliary phase winding.
However, the starting problem will persist if the rotor poles
align with the stator main poles exactly and the starting torque
produced by the auxiliary winding is insufficient to turn the rotor
poles away from the aligned position with the main poles. In that
case, multiple turn-on and turn-off of the controllable switch
builds a larger current in the main winding and, also, the auxil-
iary winding, resulting in starting of the machine. The number
of multiple turn-on and turn-off signals is determined by many
factors including the thermal capability of the machine as well
as by the way the two machine phases are arranged spatially with
respect to each other or how the rotor is constructed so that there
is an overlap of torque characteristics of phase windings over
the rotor position. Invariably, all these factors are influenced by
the intended application and its starting torque requirement. It is
critical to ensure that the desired direction of rotation is enforced
quickly when single-pulse or multiple-pulse starting is applied,
so that the rotor does not traverse noticeably over a significant
angular distance in the unintended direction.
IV. FOUR-QUADRANT CONTROL AND OPERATION OF THE
CONSIDERED SRM DRIVE
A large amount of literature [1], [11]–[14] exists on four-
quadrant control of conventional SRM drives with high degree
of freedom in the machine converter , and none exists for SRM
drives with a single-controllable-switch power converter. This
is due to the absence of the converter itself on the scene so far.
Significant features peculiar to this converter are limited direct
current control of the main phase and its heavy dependence on
the auxiliary phase winding and auxiliary capacitor state. Like-
wise, the auxiliary winding current control is dependent on the
duty cycle of the controllable switch, motor speed and load,
and state of the auxiliary capacitor. These constraints have to
be managed very tightly in order to implement a four-quadrant
variable-speed operation in this motor drive. It is discussed in
this section.
A. Clockwise (CW) Motoring and Regeneration
In order to achieve motoring in the forward direction, for ex-
ample, the CW direction, the stator winding should be excited
when the rotor is moving from the unaligned to the aligned posi-
tion. Assuming that the rotor poles reach the unaligned position
(almost in alignment with the auxiliary stator poles) of the main
phase winding and such a position is detected, the main phase
winding is energized. When the rotor poles have reached near
he aligned position with the main poles, the current in the main
phase is turned off. The machine spins then, for example, in the
CW direction and, during this time, the main winding is ener-
gized as the rotor poles move from the auxiliary stator poles to
the main stator poles. The regenerative braking, on the contrary,
is achieved by excitation of the stator windings when the rotor
moves from the aligned position toward the unaligned position.
During this time, the kinetic energy in the machine is transferred
to the dc-link source via the auxiliary winding. Note that the ma-
chine is still in the CW direction of rotation but its speed rapidly
decreases toward standstill.
B. Counter Clockwise (CCW) Direction Motoring and
Regeneration
When the speed reversal command is obtained, the control
goes into the CW regeneration mode as explained in the para-
graph above. That brings the rotor to the standstill position. In-
stead of waiting for the absolute standstill position, continuous
energization of the main phase is attempted during the time rotor
poles move from aligned to unaligned rotor positions. This not
only slows the rotor to standstill rapidly but also provides an op-
portunity for reversal if the rotor poles come to a stop between
the main and auxiliary poles. Therefore, there is the necessity for
determining the instant when the rotor of the machine is ideally
positioned for reversal. Hall-effect sensors are used to ascertain
the rotor position and speed and they are located at the main
winding and auxiliary winding. From the Hall sensor outputs,
it is determined whether the machine has reversed its direction.
Crucial to this is finding the aligned rotor position of the rotor
poles with the auxiliary poles. This is the ideal moment for en-
ergizing the main stator phase so that the machine can start mo-
toring in the CCW direction.
1) Delay Time: After sensing the unaligned position, the
pulsewidth-modulation (PWM) signal is cleared and a reversal
start pulse can be implemented. Sufficient time for the reversal
start pulse, which may be named the delay time, is required
due to the fact that the rotor does not move from its aligned
position with the stator main poles as it does not produce any
torque at this detent position. Best position to insert the start
pulse for reverse rotation is when the rotor poles are in between
the main stator poles and the auxiliary stator poles. The way to
get the rotor in to such a position is achieved by the procedure
described below.
The start pulse for reverse rotation consists of one turn-on
switch signal and one turn-off switch signal. When the turn-on
signal is given to the controllable switch, current flows into the
main winding. During turn-off of the controllable switch, cur-
rent in the main winding flows into the auxiliary winding after
charging the capacitor to a value equal to the dc-link voltage.
When the controllable switch is again turned on, the current in
the auxiliary winding goes to the dc-link source, resulting in
its prolongation. With the increase of auxiliary current by this
process of charging and discharging from the main winding,
the rotor starts moving from its aligned position. The energy
in the capacitor will increase the current through the auxiliary
winding, thus producing a torque moving the rotor poles toward
the stator auxiliary pole pair and eventually aligning the rotor
with the auxiliary poles and enabling rotation in the CCW di-
rection of rotation.
V. DRIVE SYSTEM CONTROL
With the understanding gained over the discussion of the
self-starting and four-quadrant control, the drive system control

5. KRISHNAN et al.: THEORY AND OPERATION OF A FOUR-QUADRANT SRM DRIVE 1051
Fig. 2. Proposed motor drive control system.
schematic is derived as in the following and shown in Fig. 2.
The drive system senses current and two discrete rotor posi-
tions, spaced 45 apart. A DSP accepts the Hall position signals
and the analog current signal. From the discrete rotor position
signals, rotor speed is estimated. The analog current signal is
filtered before it is fed to the DSP where it is digitized through
its analog-to-digital converter (ADC).
A startup signal is issued for the machine to activate its speed
command. Depending on the speed command, which consists of
themagnitudeanddirection,theoperationalmodecorresponding
to motoring or braking is evaluated. If it is motoring mode, the
speed error is found from the difference of the speed and its com-
mandwhichthenisprocessedbythespeedcontroller,inthiscasea
proportional plus integral (PI) controller. Then, the output of the
speed controller forms the current command. The current com-
mand is enforced by means of current feedback control having a
current controller which again is a PI type. The output of the cur-
rent controller is a control signal that is proportional to the duty
cycle of the controllable switch in the converter. This is updated
for every carrier period in the PWM control.
If speed command indicates regenerative braking has to be
performed then it takes a different route. If the rotor speed is
above a certain set low speed, only the PI current controller is in
force and nothing is tampered with. If the rotor speed is lower
than the set low-speed threshold, then the controller gives a re-
versal pulse to act upon directly and circumvents the PI current
controller during this period. Once the speed is reversed, then
automatically the controller goes into motoring mode in the op-
posite direction and the PI current controller comes into play
in dynamically determining and controlling the PWM signal
which serves as the gate control signal.
The software implementation of the control algorithm is
shown in Fig. 3 at macrolevel. With the explanations provided
in this and previous sections, this figure becomes self-explana-
tory. Note that SSSRM stands for single-switch SRM drive
system.
A. Four-Quadrant Control Algorithm
The flowchart for four-quadrant control implementation is
shown in Fig. 4. The purpose of the quadrant controller is to set

6. 1052 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005
Fig. 3. Flowchart for the software implementation of the proposed drive
system.
up the PWM sequence with respect to the quadrant command
and to generate the start pulse for reversal. After the rotor speed
reaches the desired speed, the starting signal for reversal will be
applied to the power converter. Fig. 4 shows the flowchart for
the four-quadrant control algorithm based on the descriptions
in Sections III–V.
The reason why the controller checks the unaligned position
for four-quadrant control is to easily obtain a huge negative
torque with short delay. The maximum negative torque can be
produced after the rotor passes the unaligned position (45 ) for
the machine under consideration. PWM off indicates the deac-
tivation of the PWM function resulting in no current flow to the
main winding. The “delay” is the time duration needed to move
the rotor to the maximum negative torque position.
The detailed flowchart for the DSP execution of the entire
proposed scheme is given in Fig. 5 and, in this case, the speed
command is given for 5000 r/min and the low-speed threshold
is kept at 250 r/min so that reversal is enforced. Similar to the
flowchart given in Fig. 3, this flowchart also is self-explanatory.
VI. MODELING, SIMULATION, AND ANALYSIS
OF THE DRIVE SYSTEM
In order to verify the feasibility of the proposed drive system,
the drive system was modeled, simulated, and analyzed. This
section gives a step-by-step derivation of the model of the drive
system from the algorithmic descriptions in Sections III–V. The
drive system block diagram for modeling is shown in Fig. 6.
The individual system equations for the motor and speed and
current controllers can be written from a standard modeling
procedure well known in the literature and one such is given
in [1] and the same is followed here. The integration of the
converter modes of operation with the machine and controller
is critical. In order to model the converter, the devices are
assumed to be ideal even though their voltage drops can be
Fig. 4. Flowchart for software implementation of the four-quadrant control
algorithm.
incorporated if required. Noting that the voltage drops of the
devices are small compared to the dc-link voltage, they are
treated as ideal devices.
Switching transients are ignored in this modeling as the elec-
trical and mechanical time constants are much greater than
the turn-on time and turn-off time of the devices. With these
assumptions, the converter–machine combination system equa-
tions can be derived based on the conduction or nonconduction
of the controllable switch given by modes 1 and 2, respectively.
Also, these equations are impacted based on the main and
auxiliary currents being greater than zero and on the state
of the auxiliary capacitor voltage. The system equations are
then assembled and integrated and solved for the variables of
interest.
The system equations are derived and given in the following.
Q1 ON
(1)
(2)

7. KRISHNAN et al.: THEORY AND OPERATION OF A FOUR-QUADRANT SRM DRIVE 1053
Fig. 5. Detailed flowchart for DSP implementation of the proposed
four-quadrant and variable-speed control system.
(3)
(4)
(5)
(6)
(7)
(8)
Q1 OFF
(9)
(10)
(11)
(12)
(13)
where are main phase, auxiliary phase, and aux-
iliary capacitor current, respectively, are phase
resistance of the main and auxiliary winding, respec-
tively, is the dc-link voltage, is the auxiliary ca-
pacitor voltage, are main and auxiliary winding
flux linkages, respectively, are main and auxil-
iary inductances, respectively, is the auxiliary capac-
itor value, and is the rotor position. The load dynamic
equation is
(14)
where is the electromagnetic torque obtained from
machine characteristic as a function of and is the
load torque, is the rotor speed, is the rotor and load
inertia, and is the friction coefficient of the motor and
the load.
A simulation result showing the four-quadrant operation of
the motor drive in normalized units is given in Fig. 7.
The machine is assumed to be in the unaligned position and
the starting is smooth. Even when the rotor is put in the aligned
position, the starting was delayed for a few hundred microsec-
onds, but the system started smoothly (not given for lack of
space here). Notice the smooth main phase current and its close
following of the reference. The simulation results demonstrate
the feasibility of the proposed control algorithms.
VII. PERFORMANCE OF THE PROPOSED MOTOR DRIVE SYSTEM
In order to validate the proposed four-quadrant operational
control of the considered motor drive system, comprehensive
sets of experiments were performed. Results relating to self-
starting at aligned and midpoint between aligned and aligned
positions, are shown in Figs. 8 and 9, respectively. There is
hardly any noticeable difference in the time taken to reach the
commanded 5000 r/min from both the starting positions with
the control.
Fig. 10 shows four-quadrant operation from standstill to
5000 r/min and then from there to 5000 r/min reversal and
then back to standstill. The speed and current are well behaved
in this four-quadrant operation. Results at speeds higher than
5000 r/min have been successfully achieved. Experimental
results validated the simulation results and the basic control
algorithms for this SSSRM drive.

8. 1054 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005
Fig. 6. Block diagram of the proposed motor drive system.
Fig. 7. Simulation of the four-quadrant operation of the proposed motor drive
system in normalized units.
Fig. 8. (a) Multiple pulses for self-starting from standstill at aligned position.
(b) PWM signals for motoring operation to 5 000 r/min (scale: motor speed =
2000 rpm/div, and time = 200 ms/div).
Fig. 9. Self-starting from standstill at midpoint between aligned and unaligned
position to 5 000 rpm (scale: motor speed = 2000 rpm/div, and time = 200
ms/div).
Fig. 10. Four-quadrant speed control performance of the drive system (scale:
speed and its command =5000 r/min/div; current =10 A/div; time =5 s/div).
VIII. CONCLUSION
For the first time, a two-phase SRM drive with a single con-
trollable switch was presented for four-quadrant operation and
control. The proposed system and its control structure for four-
quadrant operation is validated with simulation and proven with
experimental work. The invention is believed to be original.
The invention is fundamental as it changes the paradigm of
low-cost motor drives. The presented system is considered to
be the lowest cost four-quadrant motor drive system with the
self-starting feature. The position-sensorless control has been
incorporated in this motor drive for one-quadrant operation [9].
It has immense use in appliance applications.

9. KRISHNAN et al.: THEORY AND OPERATION OF A FOUR-QUADRANT SRM DRIVE 1055
ACKNOWLEDGMENT
The authors acknowledge with gratitude the following: L.
Whelchel, President and CEO of Panaphase Technologies for
granting permission to submit this paper for publication based
on the intellectual property of the company; C. Hudson for his
help in the development of the power electronics and DSP con-
troller package; A Staley for her help on machine details and
characteristics; and Prof. Holtz for suggestions to improve the
presentation of Figs. 8 and 9.
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R. Krishnan (S’81–M’82–SM’95–F’01) received
the Ph.D. degree in electrical engineering from
Concordia University, Montreal, QC, Canada.
He is a Professor of electrical and computer en-
gineering at Virginia Polytechnic Institute and State
University (Virgina Tech), Blacksburg. His research
interests are in electric motor drives and power elec-
tronics. He is the author of Electric Motor Drives
(Upper Saddle River, NJ: Prentice–Hall, 2001), its
Chinese translation (Taipei, Taiwan, R.O.C.: Pearson
Education Taiwan, 2002), Indian Edition (New Delhi,
India: Prentice-Hall of India, 2002 ), and International Edition (Upper Saddle
River, NJ: Prentice-Hall International, 2001) and Switched Reluctance Motor
Drives (Boca Raton, FL: CRC Press, 2003, 2nd ed.), and coeditor (with M. P.
Kazmierkowski and F. Blaabjerg) of Control in Power Electronics (New York:
Academic, 2002), the latter which won the Best Book Award from the Ministry
of Education and Sport, Poland, in 2003. His inventions constituted founding
technologies for two startup companies in the U.S. He directs the Center for
Rapid Transit Systems at Virgina Tech, pursuing unique, safe, high-speed, en-
ergy-efficient, and personal electric transit solutions. He has developed and de-
livered short courses for industry on vector-controlled induction motor drives
(with Prof. J. Holtz and Dr. V. R. Stefanovic), permanent-magnet synchronous
and brushless dc motor drives, and switched reluctance motor drives, and is cur-
rently developing linear electric motor drives with Prof. I. Boldea.
Prof. Krihnan has been a recipient of three Best Paper Awards from the In-
dustrial Drives Committee of the IEEE Industry Applications Society. In addi-
tion, he received the First Prize Paper Award from the IEEE TRANSACTIONS ON
INDUSTRY APPLICATIONS. He was awarded the IEEE Industrial Electronics So-
ciety’s Dr. Eugene Mittelmann Achievement Award for outstanding technical
contributions to the field of industrial electronics. He is a Distinguished Lec-
turer of the IEEE Industrial Electronics Society. He serves as the Vice President
(Publications) and Senior AdCom Member of the IEEE Industrial Electronics
Society. He served as the General Chair of the 2003 IEEE Industrial Electronics
Conference.
Sung-Yeul Park (S;05) was born in Seoul, Korea,
in 1973. He received the B.S. degree in control and
instrument engineering in 1998 from Hoseo Univer-
sity, Asan, Korea, and the M.S. degree in 2004 from
Virginia Polytechnic Institute and State University,
Blacksburg, where he is currently working toward the
Ph.D. degree.
His research interests include power electronics,
fuel-cell systems, and microcontroller application
systems.
Keunsoo Ha (S’04) was born in Seoul, Korea, in
1970. He received the B.S. and M.S. degrees in
electrical and control engineering from Hong-Ik
University, Seoul, Korea, in 1993 and 1995, respec-
tively. He is currently working toward the Ph.D.
degree at Virginia Polytechnic Institute and State
University, Blacksburg.
In 1995, he joined the Precision Machinery Re-
search Center, Korea Electronics Technology Insti-
tute, where he has been a Senior Researcher since
2000 and has conducted research on the development
of BLDCM drives for household air conditioners and refrigerator fans and step
motor controllers for car dashboards and linear motor drivers for machine tools.
His research interests include electric motor drives, power electronics, and sen-
sorless control.