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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 3, SEPTEMBER 2004
Operating Principles of a Novel Multiphase
Multimotor Vector-Controlled Drive
Emil Levi, Senior Member, IEEE, Martin Jones, Slobodan N. Vukosavic, Member, IEEE, and
Hamid A. Toliyat, Senior Member, IEEE
Abstract—Independent flux and torque control of an ac machine
can be achieved by means of vector control, utilizing only two
stator - current components. Consequently, in ac machines
with a phase number greater than three, there exist additional
degrees of freedom. Although they can be used to enhance the
torque production of a multiphase machine through injection of
higher stator current harmonics, an entirely different purpose is
possible as well. The additional degrees of freedom can be utilized
to control independently other machines within a multimotor
drive system. In order to do so, it is necessary to connect
stator windings of all the multiphase machines in series, with an
appropriate phase transposition, apply a vector control algorithm
to each machine separately, and supply the stator windings of the
multi-machine system from a single current controlled voltage
source inverter (VSI). Inverter current control is performed in
the stationary reference frame, using inverter phase currents.
The foundations of the concept are set forth in the paper, for an
arbitrary odd -phase case, using the general theory of electrical
machines. Further analysis is performed for all the theoretically
possible odd phase numbers and it is shown that the number
of machines connectable in series depends on the properties
of the phase number. Connection diagrams are illustrated next
for some selected phase numbers and vector control, including
the inverter reference current generation, is detailed for the
multimotor drive system. The main advantages and drawbacks
of the concept are discussed and verification is provided by
simulation of a nine-phase four-motor drive system.
Index Terms—Multimotor drives, multiphase machines, vector
control.
I. INTRODUCTION
A
PPLICATION of inverters in variable speed electric drives
enables to dispense with the standard three-phase configuration and use a multiphase ( -phase) configuration instead.
Ever since the inception of the first multiphase (five-phase) inverter-fed induction motor drive [1], the interest in multiphase
drive systems has been steadily increasing [2].
Major advantages of using a multiphase machine instead of a
three-phase machine are detailed in [3] and are higher torque
density, greater efficiency, reduced torque pulsations, greater
fault tolerance, and reduction in the required rating per inverter
leg (and therefore simpler and more reliable power conditioning
Manuscript received March 3, 2003. Paper no. TEC-00054-2003. This work
was supported in part by the Engineering and Physical Sciences Research
Council (EPSRC) under Grant GR/R64452/01, and in part by Semikron Ltd.
equipment). Additionally, noise characteristics of the drive improve as well [4]. Basic vector control scheme of a multiphase
machine, which utilizes only fundamental field component for
the torque creation, is essentially the same as for its three-phase
counterpart, regardless of whether the machine is five-phase,
nine-phase of fifteen-phase [3], [5]–[9].
Higher torque density in a multiphase machine is possible
since, apart from the fundamental spatial field harmonic, space
harmonic fields can be used to contribute to the total torque production [3], [5]–[8]. This advantage stems from the fact that
vector control of the machine’s flux and torque, produced by
the interaction of the fundamental field component and the fundamental stator current component, requires only two stator currents ( - current components). In a multiphase machine, with
at least five phases or more, there are therefore additional degrees of freedom, which can be utilized to enhance the torque
production through injection of higher order current harmonics.
In a five-phase machine third harmonic current injection can be
used [5], [6], [8], while in a nine-phase machine it is possible to
use injection of the third, the fifth and the seventh stator current
harmonics [7].
Since vector control of a multiphase machine requires only
two currents if only the fundamental of the field is utilized,
the remaining degrees of freedom can be used in an entirely
different manner, as the basis for a multimotor multiphase drive
system development. This constitutes the subject this paper
is discussed,
deals with. An -phase drive system
which can be composed of induction and/or permanent magnet
synchronous and/or synchronous reluctance motors. The supply
of the system comes from a single current controlled PWM VSI
and a vector control algorithm is applied in conjunction with
each machine in order to generate individual machine phase
current references. These are further summed in an appropriate
way and overall inverter phase current references are obtained.
It is shown that, by connecting the multiphase stator windings
of all the machines in series, with an appropriate phase transposition, it becomes possible to realize a completely independent
vector control of all the machines in the system although only
one inverter is used.
The roots of this idea can be found in [10], where the notion
of an -dimensional space for an -phase machine [11] was
applied in the analysis and a two-motor, five-phase system was
examined. The concept is investigated here using the general
theory of electrical machines [12] for an -phase multimotor
drive system with an arbitrary number of phases. All the possible
odd phase numbers are studied and it is shown that the maximum
number of connectable machines depends on the properties of
the system phase number. Rules for connecting the machines
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LEVI et al.: OPERATING PRINCIPLES OF A NOVEL MULTIPHASE MULTIMOTOR VECTOR-CONTROLLED DRIVE
in series are established by introducing so-called connectivity
matrix and connection diagrams are illustrated for some phase
numbers. Vector control algorithm and inverter phase current
reference generation are elaborated and the concept is verified
by simulating a nine-phase four-motor drive system. Major
benefits of the proposed multiphase multimotor drive system
are finally addressed.
II. MODELLING OF AN -PHASE MACHINE
A. General Remarks
An -phase machine, such that the spatial displacement beand is
tween any consecutive two stator phases is
an odd number, is considered. The type of the machine is irrelevant and the machine can be induction or synchronous (of any
type). It is assumed that the distribution of the mmf around the
air-gap is sinusoidal, since the intention is to control torque production due to fundamental field harmonic only. All the other
standard assumptions of the general theory of electrical machines apply.
509
number of phases will lead to the possibility of connecting at
most the same number of machines in series. Utilization of machines with an odd phase number is therefore advantageous and
this is the reason why the analysis is here restricted to odd phase
numbers.
Equations for pairs of - components are completely decoupled from all the other components and stator to rotor coupling
does not appear either. These components do not contribute
to torque production when sinusoidal distribution of the mmf
around the air-gap is assumed. Zero-sequence component will
not exist in any star-connected multiphase system. This means
machines (for an odd phase number)
that at most
can be connected in series. If the control is to be independent,
flux/torque producing currents of one machine must not produce flux and torque in all the other machines of the group.
This cannot be achieved by a simple direct series connection of
stator windings and an appropriate phase transposition is therefore required when connecting the windings in series, as discussed shortly.
C. Rotational Transformation
B. Decoupling Transformation
Decoupling transformation matrix for an arbitrary odd phase
number is, according to [12], given with the expression (1) at the
bottom of the page. Decoupling transformation substitutes the
original set of phase currents with a new set of transformed
currents. The first two rows in (1) define stator current components that will lead to fundamental flux and torque production
( - components; stator to rotor coupling appears only in the
equations for - components), while the last row defines the
pairs
zero-sequence component. In between, there are
pairs of stator current compoof rows, which define
nents, called further on - components. If the number of phases
is an even number, there is one additional zero-sequence component [12]. Hence the number of - pairs of current components
is the same for an odd number of phases and the subsequent
. As will be shown shortly, even number of phases
pairs of current components will be used in the series machine
connection for independent vector control. This immediately indicates that an odd number of phases and the subsequent even
Since stator-to-rotor coupling appears only in the equations
for - components regardless of the machine type, and since
the torque production due to fundamental field component is
entirely governed by - components only, rotational transformation is applied to - equations only [12]. Assuming
transformation into an arbitrary common reference frame
, the transformation matrix for stator is given
with
(2)
Application of (2) in conjunction with an appropriate model, obtained for the given machine type by utilizing (1), leads to the
transformation of the first two stator - equations into corresponding - equations. Equations for - components remain
unchanged and are for any pair of - components of the form
(1)
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 3, SEPTEMBER 2004
given for the first pair with (index stands for stator and all the
other symbols have the usual meaning)
(3)
Stator resistance and stator leakage inductance are the only machine parameters that appear in - equations.
The resulting - axis equations and the torque equation
are identical to those of a corresponding three-phase machine.
Hence the basic vector control scheme will remain the same as
for a three-phase machine of the same type.
III. SERIES CONNECTION OF MULTI-PHASE STATOR WINDINGS
- current components is
As only one pair of stator required for the flux and torque control in one machine, the repairs of stator maining degrees of freedom (
current components) can be used for control of other machines
connected in series with the first machine. If the control of the
machines is to be decoupled one from the other, flux/torque
producing currents of one machine must not produce flux and
torque in all the other machines in the group. This means that
multiphase
the connection of stator windings of
machines must be such that what one machine sees as the axis stator current components the other machines see as current components, and vice versa. It then becomes possible
to completely independently control the
machines
while supplying the drive system from a single current-controlled voltage source inverter. This can be achieved by introducing an appropriate phase transposition when connecting the
stator windings in series. The necessary phase transposition follows directly from the decoupling transformation matrix (1) and
is discussed shortly. In the general case a set of -phase stator
windings is supplied from a single -phase current-controlled
(CC) voltage source by connecting the stator windings in series
and using the phase transposition, as illustrated in Fig. 1. Phase
transposition means shift in connection of the phases
of one machine to the phases
of the second machine,
etc., where
is the flux/torque producing phase sequence of the given machine according to the spatial distribution of the phases within the stator winding.
The phase transposition is governed by the requirement that
flux/torque producing currents of one machine ( - or - currents) appear as currents that do not contribute to the flux and
torque production in all the other machines. Transformation matrix (1) provides an answer as to how this can be achieved. According to (1), phases ’1’ of all the machines will be connected
directly in series (the first column in (1)). The phase transposition for phase ’1’ is therefore 0 degrees and the phase step is
zero. However, phase ’2’ of the first machine will be connected
to phase ’3’ of the second machine, which will be further connected to phase ’4’ of the third machine and so on. The phase
transposition moving from one machine to the other is the spatial angle and the phase step is 1. This follows from the second
column of the transformation matrix. In a similar manner phase
’3’ of the first machine (the third element in the first row of (1)
0
Fig. 1. Supply of (n 1)=2 machine stator windings, connected in series, from
an n-phase current-controlled voltage source (odd phase number assumed).
with spatial displacement of ) is connected to the phase ’5’
of the second machine, which further gets connected to phase
’7’ of the third machine, and so on. The phase transposition is
, and the phase step is 2. This follows from the third column
of (1). Further, phase ’4’ of the first machine needs to be connected to the phase ’7’ of the second machine which gets connected to the phase ’10’ of the third machine and so on. Here the
phase step is 3 and the phases are transposed by . This corresponds to the fourth column in (1). For phase ’5’ of the first
machine the phase transposition equals
and phase step is 4,
and so on. This explanation enables construction of a connection
table, which is further called connectivity matrix. In the general
case of an -phase system connectivity matrix of Table I results. Flux/torque producing phase sequence for any particular
. rather
machine is denoted in Table I with symbols
than with numbers
(both notations are used further
on, depending on which one is more convenient for the given
purpose).
Double-line in Table I encircles the seven-phase case, while
the bold box applies to the five-phase case. Dashed line encircles
eleven-phase case, while solid line is the box for the thirteenphase case. If a number in the table, obtained by substituting
,
,
,
, etc., is greater than the number
of phases , resetting is performed by deducting
from the number so that the resulting number belongs
to the set
.
IV. CONNECTION DIAGRAMS AND CONNECTIVITY MATRICES
FOR SELECTED PHASE NUMBERS
Using the connectivity matrix and the connection diagram for
the general -phase case, given in Fig. 1 and Table I, corresponding diagrams and matrices are obtained for any specified
number of phases. A couple of cases are selected here, with the
aim of facilitating the discussion of the number of connectable
machines in Section V.
Connectivity matrix and the connection diagram for the
five-phase case are given in Table II and Fig. 2, respectively. It is
possible to use two machines connected in series and supply them
using five inverter legs, instead of six required in a customary
two-motor three-phase drive system. The seven-phase case is
illustrated in Table III and Fig. 3. Three machines can now
be controlled with a seven-phase inverter, enabling a saving
of two inverter legs with respect to the standard three-phase
three-motor system.
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TABLE I
CONNECTIVITY MATRIX FOR THE GENERAL n-PHASE CASE
Fig. 2. Connection diagram for two five-phase machines.
Connection diagram is shown in Fig. 4. It is important to note
that a re-ordering of the machines has to be done if series
connection comprises machines of different phase numbers,
as shown in Fig. 4. All the machines with the highest phase
number have to be connected at first in series to the source,
respecting the required phase transposition. They are followed
by all the machines with the second highest phase number, and
so on. The group is completed with the machine(s) having the
smallest phase number. This is so since, taking the nine-phase
case as the example, the three flux/torque producing currents
of a nine-phase machine which enter any given phase of the
three-phase machine sum to zero in any instant in time. This
simultaneously indicates that the three-phase machine will not
suffer any adverse effects due to the series connection with
three nine-phase machines.
V. MACHINE CONNECTIVITY
Fig. 3. Connection diagram for three seven-phase machines.
TABLE II
CONNECTIVITY MATRIX, FIVE-PHASE CASE
The number of connectable machines and their individual
phase numbers are governed by the system number of phases
. All the possible system phase numbers will belong to one of
the three categories detailed in what follows.
i) The number of phases is a prime number. In this case
the number of machines that can be connected in series
with phase transposition equals
(4)
TABLE III
CONNECTIVITY MATRIX, SEVEN-PHASE CASE
The two considered phase numbers are both prime numbers
and the situation is simple. If the number of the source phases
is not a prime number the situation becomes more interesting.
Connectivity matrix for the nine-phase case, obtained from
Table I, is shown in Table IV. As can be seen in Table IV, only
phases 1, 4 and 7 of machine M3 (encircled with a dotted
box) are utilized in the series connection. Since the spatial
displacement between these phases is 120 degrees, the machine
M3 is actually a three-phase rather than a nine-phase machine.
pairs of current components that
since there are
can be used for independent flux and torque control in
this multiphase machine set. All the machines are of the
same number of phases equal to . The phase numbers
, 5, 7, 11, 13, 17, 19,
belonging to this category are
etc.
ii) The number of phases is not a prime number, but it
satisfies the condition
(5)
The number of connectable machines is still given
. However, not all mawith (4), i.e.,
chines are now of the phase number equal to . For example, in the considered case of
a total of
machines can be connected in series:
there is one three-phase machine, and three nine-phase
the phase
machines. Hence for the general case of
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 3, SEPTEMBER 2004
Fig. 4. Connection diagram for the nine-phase case, comprising three nine-phase machines and one three-phase machine.
However, in general,
numbers equal to
the group will be composed of machines with the phase
and one of the prime numbers
numbers equal to
TABLE IV
CONNECTIVITY MATRIX, NINE-PHASE CASE
(8)
numbers of the machines that can be connected in series
are
(6)
Phase numbers in this category are:
, 25, 27, 49,
81, etc.
iii) System phase number is not a prime number and is not
equal to . However, is divisible by two or more prime
numbers. Let these prime numbers be denoted as , ,
, etc. The number of machines that can be connected
is now
(7)
Ordering rules require that all the -phase machines
are at first connected in series to the source, with phase
transposition. The machines with the largest prime
(say,
) follow
number value out of
next. This should be followed by connection of all the
machines with the second largest prime number, say
, etc. This rule has to be observed, since its violation
makes operation of a higher phase number machine, connected after a lower phase number machine, impossible.
phase machine
One thus reaches the stage where one
is to be connected to a machine with
phases. This is
is not an integer. An
not possible since the ratio
attempt to connect machines of phase numbers equal to
different prime numbers leads to the short-circuiting of
terminals.
Among these machines only a certain number will
be with phases. The other machines that should be
connectable in the multi-drive system will have phase
where
.
This class of odd phase numbers encompasses the situmay
ation where some of the numbers
be the same prime number, but there is at least one other
prime number in the sequence. That is,
,
. is included. The phase numbers
belonging to this category are 15, 21, 33, 35, 39, 45, 51,
55, 57, 63, 65, 69, 75, 77, etc.
Categories ii) and iii) can be regarded as sub-categories of
a more general case for which is not a prime number. Their
common feature is that two or more phase numbers appear in
the series connection with phase transposition of the multiphase
machines. However, the total number of connectable machines
is not the same, as given by (4) and (7).
A summary of all possible situations that can arise for odd
number of phases is given in Table V.
VI. VECTOR CONTROL OF AN -PHASE -MOTOR SYSTEM
A. Vector Control of an -Phase Machine
The simplest method of rotor flux oriented control of a current-fed ac machine is considered. The vector controller is in
principal the same as for a three-phase machine of the same
type. The only difference is in the coordinate transformation,
where phase current references are generated by means of (1)
and (2), instead of three. The vector controller is illustrated in
Fig. 5 for an -phase induction, permanent magnet synchronous
and synchronous reluctance motor. Operation in the base speed
(constant flux) region is considered.
B. Generation of Inverter Current References
Phase current references are built for each individual machine first, using Fig. 5. Taking the phase number as an odd
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513
TABLE V
POSSIBLE SITUATIONS WITH ODD PHASE NUMBERS
Inverter reference currents are further built, on the basis of
the connection diagram for the given number of inverter phases.
Taking as an example the nine-phase case of Fig. 4 and Table IV,
the inverter current references are built according to
(10)
Fig. 5. Indirect vector controller for an n-phase induction and an n-phase
synchronous motor (for permanent magnet machine with surface mounted
magnets i = 0; for synchronous reluctance machine, using constant current
along d-axis control, i = i
), respectively. Index n denotes rated values.
C. Inverter Output Phase Voltages
number and denoting with superscript
the machine under
consideration
, the phase current references for
any mutli-phase machine can be given with the expressions (9)
at the bottom of the page.
Since current control is applied in the stationary reference
frame using total inverter phase currents, inverter output phase
voltages will be of the form required to minimize the phase current errors. Inverter output phase voltages are governed with the
(9)
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 3, SEPTEMBER 2004
appropriate connection diagram. For the nine-phase case the inverter output phase voltages are
TABLE VI
APPLIED SPEED COMMANDS
(11)
VII. SIMULATION OF A NINE-PHASE FOUR-MOTOR DRIVE
The concept is verified by simulating the operation of the
nine-phase four-motor drive system of Fig. 4, using indirect
rotor flux oriented controllers of Fig. 5. The four machines
are all induction motors. Per-phase parameters and per-phase
ratings of the three-phase machine and the nine-phase machines
are the same and are given in Appendix. The current controlled
VSI is assumed to behave as an ideal current source, so that the
generated inverter current references of (10) are equal to the
inverter output currents. Closed-loop speed control is analyzed
and torque limit is set to twice the rated torque (30 Nm and
10 Nm for nine-phase and three-phase machines, respectively).
The excitation transient takes place first. Stator -axis current
reference is ramped to twice the rated value from 0 to 0.01 s. It
is kept at this value until 0.05 s and is then ramped down to the
rated value between 0.05 s and 0.06 s (since RMS value of the
rotor flux is the same for both three-phase and nine-phase machines, peak values after the transformation, to be shown in results, are different). After completion of the excitation transient,
speed commands, of different values, are applied to the four machines in different time instants (all with a ramp of 0.01 s). The
schedule is given in Table VI.
The first set of results, comprising rotor flux, torque response
and speed, is shown in Fig. 6. As can be seen from Fig. 6, forced
excitation takes place in all the four machines independently and
the rotor flux settles to the reference value. There are not any
rotor flux variations in any of the four machines during the subsequent acceleration transients, meaning that the flux and torque
control of each of the four machines is completely decoupled not
only one from the other but from the rest of the system (other
three machines) as well. Torque responses follow the reference
torques without any deviation due to the ideal current feeding
and the obtained speed responses are the fastest possible.
Fig. 7 illustrates stator phase ‘a’ current reference of the
first two machines and the inverter currents for the first two
phases. While current references are essentially sinusoidal
during acceleration and in final steady state, inverter currents
are, being an appropriate summation of the four machine
currents, highly distorted. Very much the same applies to the
stator phase voltages of the nine-phase machines, which are
illustrated in Fig. 8, together with the overall inverter output
phase voltages for the first two phases. Due to the series
connection of the stator windings, - voltage components
exist in the three nine-phase machines, leading to the distortion
of the waveforms. The worst level of distortion appears in
Fig. 6. Excitation and acceleration transients: rotor flux, torque response and
speed of the four machines.
machine 3, due to the lowest speed of rotation. It should however
be noted that the three-phase machine is not affected in any
adverse manner by the series connection of this four-motor
set, since all the torque and flux producing currents of the
nine-phase machines mutually cancel at the point of connection
with the three phase machine.
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515
Fig. 7. Stator phase ‘a’ current references of the first two machines and inverter
output currents for the first two phases.
VIII. DISCUSSION
Some advantages of a multiphase machine do not exist in
the proposed multimotor multiphase system. Torque production
cannot be enhanced by the stator current harmonic injection,
as the existing degrees of freedom are used to control other
machines in the group. Fault tolerance, an important feature
of multiphase single-motor drives, is substantially reduced for
the same reason. In principle, there remains only one degree
of freedom that can be used for this purpose if the number of
connected machines is the one of (4). If the number of connected machines is smaller than the maximum, there are more
remaining degrees of freedom for fault tolerant operation but the
reduction in the required number of inverter legs is smaller or
nonexistent. However, the situation is no worse than in any multimotor three-phase system. Therefore these features do not represent a drawback when compared to the existing technology.
The concept of the multiphase multimotor drive system,
developed in this paper, offers two important advantages when
compared to an equivalent three-phase multimotor system with
common dc link and a separate three-phase VSI for each
machine. The first one is the potential for saving in the number
of inverter legs. The saving exists for the five-phase system
and for all the phase numbers greater than or equal to seven. In
general, higher the phase number is, greater the saved number
of inverter legs is. For example, the analyzed nine-phase system
enables series connection of four machines, while asking for
nine inverter legs. An equivalent three-phase system would
require twelve legs, so that the net saving is three legs. Saving
in the number of inverter legs translates into application of a
Fig. 8. Stator phase ‘a’ voltages of the four machines (a.) and inverter output
phase voltages for the first two phases (b).
smaller number of semiconductors and associated components
(protection circuits, drivers, etc.). Due to the smaller overall
count of components, a multiphase multimotor drive system
will have a better reliability than the equivalent three-phase
system.
The second excellent feature of the proposed drive configuration is the easiness of the implementation of the vector control
algorithm for all the machines of the group within a single DSP.
If there are series connected machines the DSP needs to execute individual vector control algorithms in parallel, giving at
the output, after appropriate summation, the references for the
inverter phase currents.
The only drawback of the concept is an increase in the stator
winding losses due to the flow of the flux/torque producing
currents of all the machines through stator windings of the
other machines (the increase in stator core losses, caused by the
appearance of additional voltage drops in stator windings, is
negligible). This will decrease somewhat the efficiency of the
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 3, SEPTEMBER 2004
multimotor drive, when compared to an equivalent three-phase
counterpart. It is believed that the advantages outweigh this
shortcoming and that the proposed multiphase multimotor drives
will become a viable commercial solution in the future.
IX. CONCLUSION
The paper sets forth foundations of a novel concept for a multiphase multimotor drive system, which enables independent
vector control of all the machines within the group although
only a single current-controlled voltage source multiphase inverter is used. The stator multiphase windings have to be connected in series with an appropriate phase transposition, in order
to achieve the independent control of the individual machines
in the system. The concept is developed in a systematic manner,
using general theory of electrical machines, and is valid regardless of the type of the ac machine, so that different machine types
can be used within the same multimotor drive system. The necessary pre- requisite for the application of the concept in presented form is that the inverter current control is performed in
the stationary reference frame, using total inverter phase currents and an appropriate current control method. The concept is
in general applicable to any phase number greater than or equal
to five.
Classification of all the possible odd phase numbers is performed, with regard to the maximum number of machines that
can be connected in series and phase numbers of individual machines (the physical limitations with respect to the maximum
possible phase number are completely ignored throughout the
paper). A couple of characteristic phase numbers (
, 7 and
9) are illustrated with appropriate connection diagrams and a
vector control algorithm is presented for the general -phase
case. The concept is verified by simulating a nine-phase fourmotor drive system with indirect rotor flux oriented control. Finally, the main advantages of the concept are outlined, when
compared to an equivalent three-phase multimotor drive system.
APPENDIX
Per-phase equivalent circuit parameters of the 4-pole, 50 Hz
nine-phase and three-phase induction motors
Per-phase ratings of the nine-phase and three-phase motors:
220 V, 2.1 A, 1.667 Nm, rotor flux (rms) 0.5863 Wb. Inertia:
. Total rated torque is 15 Nm and 5 Nm for the
nine-phase and the three-phase machines, respectively.
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Emil Levi (S’89–M’92–SM’99) was born in 1958 in
Zrenjanin, Yugoslavia. He received the Dipl. Ing. degree from the University of Novi Sad, Novi Sad, Yugoslavia, and the M.Sc. and the Ph.D. degrees from
the University of Belgrade, Belgrade, Yugoslavia, in
1982, 1986, and 1990, respectively.
Currently, he is Professor of Electric Machines and
Drives at Liverpool John Moores University, Liverpool, U.K., where he has been since 1992. From 1982
to 1992, he was with the Department of Electrical
Engineering at the University of Novi Sad. He has
published many papers in major journals and is an Associate Editor of IEEE
TRANSACTIONS ON INDUSTRIAL ELECTRONICS.
Martin Jones was born in 1970 in Liverpool, U.K.
He received the B.Eng. degree (Hons.) from the
Liverpool John Moores University, Liverpool, U.K.,
in 2001, where he is currently pursuing the Ph.D.
degree.
His areas of research interest include vector control
of ac machines and power electronics.
Mr. Jones is a recipient of the IEE Robinson Research Scholarship for his Ph.D. studies.
Slobodan N. Vukosavic (M’93) was born in Sarajevo, Bosnia and Hercegovina, Yugoslavia, in 1962.
He received the B.S., M.S., and Ph.D. degrees from
the University of Belgrade, Belgrade, Yugoslavia, in
1985, 1987, and 1989, respectively.
Currently, he is a Professor at the Belgrade
University. He was with the Nikola Tesla Institute,
Belgrade, Yugoslavia, until 1988, when he joined the
ESCD Laboratory of Emerson Electric, St. Louis,
MO. Since 1991, he has been the project leader with
the Vickers Co., Milano, Italy. He has published
extensively and has completed more than 40 large R/D and industrial projects.
LEVI et al.: OPERATING PRINCIPLES OF A NOVEL MULTIPHASE MULTIMOTOR VECTOR-CONTROLLED DRIVE
Hamid A. Toliyat (S’87–M’91–SM’96) received the
Ph.D. degree in electrical engineering from the University of Wisconsin-Madison in 1991.
Currently, he is an Associate Professor in the
Department of Electrical Engineering at Texas
A&M University, College Station. He is an Editor of
IEEE TRANSACTIONS ON ENERGY CONVERSION, an
Associate Editor of IEEE TRANSACTIONS on POWER
ELECTRONICS, and a member of the Editorial Board
of Electric Power Components and Systems Journal.
His main research interests and experience include
multiphase variable speed drives, fault diagnosis of electric machinery, analysis
and design of electrical machines, and sensorless variable speed drives. He has
published many technical papers in these fields.
Dr. Toliyat received the Texas A&M Select Young Investigator Award in
1999, the Eugene Webb Faculty Fellow Award in 2000, NASA Space Act Award
in 1999, and the Schlumberger Foundation Technical Award in 2000 and 2001.
He is also Vice-Chairman of IEEE-IAS Electric Machines Committee, and is a
member of Sigma Xi. He is the recipient of the 1996 IEEE Power Engineering
Society Prize Paper Award.
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