Recent Advances in the Design, Modeling and Control of Multiphase Machines - Part 1

Abstract

Multiphase machines are well recognized as an attractive alternative to conventional three-phase ones in a number of applications where high overall system reliability and reduction in the total power per phase are required. The pace of developments in the field has accelerated in the last few years, and substantial knowledge has been recently generated. The main objective of the two parts’ survey named ‘Recent Advances in the Design, Modeling and Control of Multiphase Machines’ is to present relevant contributions to encourage and guide new advances and developments in the field. More specifically, the part 1 of the work analyzes the recent progress in the design, modelling and control, including healthy operation of multiphase motor drives, and discusses open challenges and future research directions in the area.

Full text

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
Abstract

Multiphase machines are well recognized as an
attractive alternative to conventional three-phase ones in a
number of applications where high overall system reliability
and reduction in the total power per phase are required. The
pace of developments in the field has accelerated in the last few
years, and substantial knowledge has been recently generated.
The main objective of the two parts’ survey named ‘Recent
Advances in the Design, Modeling and Control of Multiphase
Machines’ is to present relevant contributions to encourage and
guide new advances and developments in the field. More
specifically, the part 1 of the work analyzes the recent progress
in the design, modelling and control, including healthy
operation of multiphase motor drives, and discusses open
challenges and future research directions in the area.
Index Terms

Multiphase machines, design, modeling,
parameter estimation, motor drive control in normal operation
mode.
I. INTRODUCTION
HE research in the multiphase machine area has attained
significant proportions in the last decade. With the
number of conventional electrical machines continuously
growing, the interest in multiphase machines is also rising
due to intrinsic features like power splitting, better fault
tolerance or lower torque ripple than three-phase machines
[1,2]. While advances in multiphase power supply,
modulation techniques and some innovative uses of the
additional degrees of freedom are surveyed in a companion
paper, this part of the state of the art paper looks at the
progress in the design, modeling and motor control of
multiphase machines in healthy situation. The work is
complemented with a second part that analyzes the recent
developments in multiphase generation systems and in the
fault-tolerant control of multiphase drives.
Recent research works and developments support the
prospect of future more wide-spread applications of
multiphase machines. Electric vehicles and railway traction,
all-electric ships, more-electric aircraft, and wind power
generation systems are areas where this research activity has
Manuscript received December 4, 2014; revised February 10, 2015 and
April 13, 2015; accepted May 5, 2015.
Copyright (c) 2015 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
This work was supported by the Spanish Ministry of Science and
Innovation under Projects DPI2013-44278-R and ENE2014-52536-C2-1-R,
and the Junta de Andalucía under Project P11-TEP-7555.
F. Barrero is with the Electronic Engineering Department of the
University of Seville, Spain, e-mail: fbarrero@us.es.
M.J. Duran is with the Electrical Engineering Department of the
University of Malaga, Spain, e-mail: mjduran@uma.es.
taken place in recent times. For example, a recent overview
states that multiphase machines can be a favored choice for
general aerospace applications [3], and actual works detail a
six-phase linear permanent magnet machine for oil pumping
applications to increase the fault tolerant capability and
reduce the detent force of the system [4] or a nine-phase
permanent-magnet traction motor used in ultrahigh-speed
elevators [5]. Such examples of actual industrial drive
developments and applications are very encouraging.
However, the difficulties in extending the three-phase
control structures to multiphase systems, the limited work on
the multiphase machine design or estimation techniques, the
necessity of fault detection and management algorithms or
the recent interest in multiphase generation systems are areas
where substantial new developments are expected to appear.
This two parts’ survey disseminates and shares recent
advances in the design, modeling and control fields of
multiphase machines, serving as a compilation for the
research community.
Part 1 of this survey paper is organized as follows. Section
II examines the trends in machine design, where focus of
attention has moved from the stator winding arrangement
and disposition towards novel machine structures with
improved reliability and low weight. The design aspects of
induction and permanent magnet (PM) synchronous
multiphase machines are surveyed, and the application of the
superconducting technology to multiphase machines is
introduced. Section III deals next with modelling issues,
analyzing both the contributions related to new analytical
models and the identification of the electrical parameters,
which appears as a topic that has received only limited
attention so far. Finally, control strategies in healthy mode of
operation are described in section IV, where the progress and
evolution in the field oriented control (FOC) and direct
torque control (DTC) techniques are discussed. Other
alternative control methods, also examined in the section, are
mainly based on model predictive control (MPC) techniques.
II. DESIGN TENDENCIES
The attention with regard to the multiphase machine
design has been focused in recent times on the development
of low weight, high reliability and fault tolerant structures
that are primarily based on multiphase permanent magnet
machines. Nevertheless, new challenges using
superconducting technologies or advances in the induction
machine design have also been recorded, and the last ones
are surveyed first.
Recent Advances in the Design, Modeling and
Control of Multiphase Machines – Part 1
Federico Barrero, Senior Member, IEEE, Mario J. Duran
T

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
A. Induction Machines
The work on the design of multiphase induction machines
is focused on achieving higher torque density and optimized
air-gap magnetic fields through the injection of stator current
harmonic components [6,7]. The benefits obtainable by a
modular or fractional-slot concentrated-winding (FSCW)
design, in terms of short end-turns and flux-weakening
capabilities, have been also explored in conjunction with
five-phase squirrel-cage induction motor drives in [8], where
the inability of the FSCW design for producing high quality
magnetic travelling fields is also investigated to reduce the
effect of space harmonics. Then, design considerations such
us the number of rotor bars or the required skewing angle are
given to reduce the torque ripple and core losses by
decreasing undesired space harmonics. It is also stated that
the FSCW design can provide advantages in applications like
high frequency induction machines and manually wound
electrical submersible pump motors.
B. FSCW PM Machines
Modular design is predominantly being explored in
conjunction with PM machines [9-24]. The multiphase
FSCW surface and interior PM machines (SPM and IPM,
respectively) are becoming an interesting choice for
automotive applications owing to their advantages which
include high power density, high efficiency, short end-turns,
high slot fill factor, low cogging torque, flux-weakening
properties and inherent fault-tolerant capability [9,10]. Their
main drawback is the generation of excessive rotor losses,
particularly in high speed operation, due to large spatial
harmonic components [11]. Then, an appropriate
combination of the number of slots and the winding
distribution is used in a five-phase IPM to reduce the torque
pulsations of the motor in [12]. Three five-phase external-
rotor PM machines with different combinations of the
numbers of slots and poles (20 slots/14 poles, 20 slots/18
poles and 20 slots/22 poles) are compared in [13,14]. This
comparative analysis concludes that the efficiency and
density of the machine torque are enhanced by the increase
in the number of rotor poles. However, this is achieved at the
expense of an increase in the dc-link voltage requirement.
Better flux distribution and lower core losses are obtained
with the 20 slots/14 poles combination, while the 20 slots/18
poles combination gives a lower torque ripple in healthy and
faulty states.
The impact of the number of phases on the rotor losses
and the slots-per-pole combination is studied in [15], where
three-phase, five-phase and seven-phase FSCW PM
machines are compared. The main conclusion of the work is
that a reduction of the spatial harmonics is obtained with
multiphase machines, although the reduction is lower than
expected. A similar study is done in [16], where an analytical
model for comparison of magnet losses in PM machines with
concentrated windings is also presented.
The safety requirements in terms of fault-tolerant
capabilities of these electrical machines are studied in [17],
for a duplex three-phase SPM generator integrated inside the
aircraft main gas turbine engine, and in [18] for a five-phase
modular PM in-wheel motor. The multiphase modular PM
machine is chosen in [18] to produce the rated power in case
of a single fault, with deep enough stator slots to obtain large
phase inductances that limit short circuit currents. The
magnet layer is also optimized in these machines using PM
shaping methods to increase the torque density in [19,20] and
to reduce the pulsating torque in [21], where a five-phase
SPM is used. Dual three-phase 12-slot 10-pole PM machines
are tested in [22], where different rotor topologies (IPM and
SPM) and winding configurations are compared in terms of
average torque, torque ripple, mutual coupling among phases
and faulty condition behavior. The study concludes that the
SPM machine almost doubles the power and torque
densities, although the IPM machine offers lower short-
circuit current and braking torque. The work is
complemented in [23], where different pole and slot number
combinations are analyzed, focusing on both single and
double layer windings and non-overlapping coils, and in
[24], where the torque components and the sensorless
position detection capabilities of the IPM machine are
investigated in healthy and faulty states, supplying only one
of the two three-phase fractional-slot windings.
C. Other PM Machines
Industrial demand for electromechanical systems with
high torque density or high speed and low cost applications
is increasing, and other electrical PM topologies have been
lately considered together with the multiphase stator
technology.
This is the case with PM synchronous machines
(brushless PM or simply BPM), which guarantee the highest
torque density. So, two modular BPM multiphase machines
are designed in [25] to meet the performance requirements
of an electromechanical flight control surface actuator. High
energy magnets (NdFeB or SmCo types) are normally used
in the manufacturing process of BPM machines, and losing
energy due to thermal stress is a major drawback of this
technology. Then, a computational technique to evaluate the
influence of the finite axial length of the magnets on the rotor
eddy-current losses is the main contribution in [25], and
optimization strategies are applied in [26] in the design
process of a five-phase BPM with concentrated windings for
automotive applications, where stator current references
(fundamental and third harmonic components) are obtained
to minimize the total loss (iron and magnet losses included)
and to improve the performance of the machine in the flux-
weakening region (high speed at 16000 rpm).
The synchronous reluctance machine (REL) is also an
interesting PM solution due to its low cost. Then, a light
weight five-phase axial flux REL machine is designed and
prototyped for electric vehicle applications in [27] and a
special type of brushless machine with PMs located in the
stator (called Flux-Switching PM or FSPM machine) is
combined with multiphase windings in [28,29], claiming the

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
TABLE I
PROPOSED APPLICATIONS TIED TO TYPE OF MULTIPHASE
MACHINE*
Type of machine
Ref.
Application
Induction
Machine
[8]
Submersible 5-phase pump motor
FSCW PM
(SPM type)
[9,10]
[17]
Fault-tolerant 6- and 5-phase in-
wheel motor for electric vehicle
6-phase generator inside the
aircraft main gas turbine engine
FSCW PM
(IPM type)
[20]
2.1 MW 5-phase marine propeller
BPM
[25]
4- and 5-phase electromechanical
flight control surface actuator
REL
[27]
5-phase axial-flux configuration
for electric vehicles
BLDC
[30]
12 kW 5-phase electro hydrostatic
actuator for aerospace application
Superconducting
Machines
[34,35]
Design of 12 MW 9- and dual-3-
phase synchronous generators
* Prototype multiphase machines are also implemented in the provided
bibliography, but they are not included in this table for simplicity reasons.
advantages of both BPM and REL machines.
Further recent studies propose other multiphase PM
machines. For example, a five-phase brushless dc motor
(BLDC) for safety critical aerospace applications is designed
in [30], adding fault tolerant and high reliability
characteristics to the compact structure, low weight and
highest torque density capabilities. A 5-phase SPM
bearingless motor with a single set of half-coiled winding is
also described, analyzed and controlled in [31], combining
torque driving and self-levitation characteristics. Finally, a
five-phase permanent magnet assisted synchronous
reluctance machine is designed and studied in [32,33], where
it is suggested as an alternative to IPM and REL machines
for low output torque ripple applications.
D. Superconducting Machines
Electric energy production via wind power is accelerating
nowadays the development of superconducting generators.
Market problems are avoided, i.e. the rapid change in price
or unavailability of magnets, and more than 5 MW of power
generation per tower is allowed without prohibitively large
size and weight of the nacelle. This technological challenge
has been recently explored and multiphase superconducting
electrical generators are proposed for large-scale direct-drive
wind turbines in [34,35]. Two 12 MW nine-phase
superconducting synchronous generators with different
armature winding arrangements are designed and compared
in [34], and a 12 MW dual three-phase superconducting wind
generator with FSCW (using 24-slot/10-pole combination) is
presented in [35]. The interest in wind power generators for
off-shore applications, the unpredictable behavior of the rare
earth magnet market, and the superconducting technology
development may favor the roll-out of this technology in the
near future.
Table I shows some real applications mentioned in the
provided bibliography in relation to the design tendency of
multiphase machines. Such applications not only favor the
appearance of new types of multiphase machines but also the
study of new models, as it will be discussed next.
III. MULTIPHASE MACHINE MODELING
The modeling of multiphase machines was extensively
studied in the last century. Nevertheless, some interesting
new models have been developed in recent times taking into
account the effect of magnetic saturation in the machine,
which produces coupling between different planes (primary
and secondary ones).
A. Modified Machine Models
The influence of the magnetic circuit saturation on the
main air-gap flux density is studied in a dual-stator-winding
induction machine in [36], where a dynamic model of the
system including this saturation effect is presented. Novel
methods for modeling five-phase induction machines are
given in [37,38], where the effect of magnetic saturation is
also considered. While the method presented in [37] uses the
well-known conventional multiple d-q planes, the model
proposed in [38] extends the voltage-behind-reactance
(VBR) formulation, introduced originally for the three-phase
induction machine. It uses dependent voltage source in series
with passive (R-L) impedances and includes shunt
resistances to model the core losses, which also solves the
problem of algebraic loops that the VBR model introduces
in the simulation. One interesting contribution of this
modeling method is that it is suitable for open-phase faulty
conditions, unbalanced supply and star, pentagon or pentacle
connections. The method has also been recently extended to
a dual-three phase induction machine with an arbitrary
displacement between the stator windings in [39].
Last but not least, a modified method for the analysis of
an asymmetrical six-phase IPM machine is given in [40],
where a decoupled d-q model is introduced, and more
recently an analytical model using magnetic equivalent
circuits and including saturation effects is proposed in [41]
for split-phase multiphase REL machines. The aim in this
contribution is to avoid iterative optimization processes
based on time-consuming finite element analysis (FEA)
normally applied in the design of these machines, setting
forth an accurate and fast method to predict the performance
of the machine. FEA techniques are arduous and iterative
off-line methods. Moreover, multiphase machines are still
often obtained rewinding stators of conventional three-phase
machines, which means that the resulting machine is not
optimal and the electrical parameters are difficult to obtain
using FEA or similar computational techniques [42]. Since
models of multiphase machines require knowledge of
electrical parameters, procedures for their identification are
also becoming an interesting research area. Methods for the
identification of resistances and inductances in conventional
three-phase electrical machines are well-known but their
extension to the multiphase case is at present limited, as we

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
will see later, and more work is expected in the near future
because only a few recent works attempt to tackle the issue.
B. Identification of Electrical Parameters
Different off-line procedures are applied in [43,44] for the
estimation of the electrical parameters of a five-phase
induction machine in the frequency and time domains. Figs.
1 to 3 summarize the method proposed in [44], where
recursive least-square (RLS) algorithms are applied for the
estimation of the electrical parameters of a five-phase
induction motor. The five-phase induction machine is
operated in the standstill mode (Fig. 1), so different winding
arrangements are proposed for the estimation of the electrical
parameters without generating electrical torque (stator
voltage components in the α-axis are maximized in Fig. 2,
while the rest of stator voltage components are minimized to
concentrate the identification study on analyzing the current
response in the α-axis). The obtained parameters are tested
in high-performance five-phase induction motor drives to
corroborate the validity of the estimation technique. The
agreement between Bode frequency responses of the real
system and the analytical model using the estimated
electrical parameters is also presented (Fig. 3). While
multiphase machines with distributed windings are
considered in [43,44], multiphase machines with
concentrated windings are analyzed in [45], where the
magnetizing inductances of the fundamental and third-
harmonic components in a 15-phase induction machine are
estimated using a Fourier analysis of the air-gap flux density
distribution and a distributed magnetic circuit approach.
Similarly, different off-line identification methods have been
developed for the estimation of the electrical parameters of a
dual asymmetrical three-phase IPM machine in [46]. The
study is complemented with [47], where a recursive least-
square algorithm is applied for their estimation during
normal operation of the drive. Knowledge of the electrical
parameters is of key importance if a high efficiency
multiphase motor drive is required, being a fundamental
requirement of the control system as it will be stated in the
next section.
Fig. 1. Schematic diagram of the identification procedures proposed in [44].
0
1708.0
1708.1
0


s
y
ss dc
s
x
dc
s
vvv
Vv
Vv


Fig. 2. One of the winding arrangement proposed in [44] to concentrate the
identification study on analyzing the current response in the α-axis.
Fig. 3. Comparative analysis shown in [44] in the α-β plane to illustrate the
usefulness of the proposed estimation technique. Bode frequency responses
are plotted, using the analytical model of the 5-phase induction machine
with the estimated electrical parameters (blue trace) and the real system (red
trace).Similar results are obtained in the x-y plane.
IV. PROGRESS IN MULTIPHASE MOTOR DRIVE CONTROL
The research activity has in recent past shifted from the
basic extension of the field oriented and direct torque control
methods, used in the three-phase drives, towards more
sophisticated control solutions for multiphase drives.
Asymmetrical six-phase and five-phase induction machines
with sinusoidally distributed stator windings continue to be
the most analyzed multiphase solutions, but higher phase
order machines and concentrated winding machines with an
odd number of phases have also been considered to obtain
torque enhancement on prototype machines using stator
current harmonic injection.
A. Field-Oriented Control
The most common control strategy in the multiphase
drives is the well-known rotor-flux oriented control (RFOC)
method, based on multiple inner current control loops with a
superimposed outer speed controller. The recent progress
focusses on the current controllers, whose number is
governed by the number of independent 2D planes. In

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
principle, an n-phase drive with a single neutral point
requires (n1) current controllers in order to reduce the low-
order harmonic current content due to asymmetry and
inverter dead time, and to improve the balancing of current
sharing between windings [48-52]. Five-phase and dual
three-phase induction machines with sinusoidal MMF
distribution have been used to study current control aspects
[48-50], and the obtained results have been also extended to
permanent magnet synchronous machines [51,52].
Another interesting research activity is related to torque
enhancement, by improving the flux pattern using stator
current low-order harmonic injection. Additional degrees of
freedom of multiphase machines are used yielding a near
rectangular air-gap flux for better iron utilization and higher
torque density in concentrated winding machines with an
odd number of phases [53,54]. Indirect RFOC (IRFOC) is
normally used [55-59], and different synchronization
methods are applied to avoid misalignment between the
fundamental and harmonic fluxes for all mechanical loads.
Research was initially restricted to the five phase induction
machine (fundamental and third harmonic injection) [55],
but seven and eleven phases induction machines have been
also analyzed in [56-59]. It is concluded in [58] that injection
of up to the fifth stator current harmonic is advantageous and
that injections of harmonics above the fifth produce a
negligible increment of the torque density. The increment in
the generated electrical torque is not only limited by the rotor
losses but also by the power converter constraints in overload
conditions. This issue is analyzed in [59], where a seven-
phase induction motor is again considered. The seven-phase
inverter ratings and constraints are studied to maximize the
electrical torque, injecting a third-order stator current
component, depending on the operating conditions and
including the field-weakening operation of the drive.
According to the results, the improvement of the overload
torque due to the third-order harmonic injection can be up to
17% of the original nominal torque. Different research works
concerning this issue include the definition of a numerical
procedure for setting the controllers in multiphase drives
with third harmonic injection [60], or the application of a
model reference adaptive system for the estimation of the
rotor speed and the implementation of a sensorless IRFOC
[61].
An alternative to the inner current controllers in a
multiphase drive using RFOC techniques has been recently
introduced. It is based on the model predictive control
(MPC) method [62,63], which is used instead of the classical
PI current controllers. Two concepts, one based on the MPC
approach to current control and the other based on the PI
current control, are illustrated in Fig. 4. The MPC, as used in
the electric drives, is typically finite control set MPC (or just
FCS-MPC) because the number of available converter
switching states is a finite set. The problem encountered in
utilization of the MPC based current control is that the
objective function (related to the selection of the inverter
output voltage vector that can minimize the control
objectives) becomes more involved than in the three-phase
case. This is so since there is a need to minimize current
errors for all current components and there are, in principle,
(n1) of them rather than just two. Needless to say, the
number of possible inverter states that can be applied
increases with the phase number exponentially and is already
32 for the five-phase two-level inverter (in contrast to being
just 8 for a three-phase two-level inverter).
The viability of the MPC based current control is assessed
in [62,63] for an asymmetrical six-phase drive, assuming
quasi-balanced operation. A sinusoidal output stator voltage
is required, and a pseudo-optimum search criterion with a
reduced set of voltage vectors is used to overcome the
computational cost of the control technique. Then, the
applied output voltage vector is not necessarily the optimal
one because not all available switching states have been
considered at the objective function minimization stage (only
13 of 64 inverter states are used). Other predictive control
techniques have also been introduced based on [62,63], with
the main goal of reducing the computational cost of the
control method and minimizing the generated harmonic
content. This is the case of the method proposed in [64]
termed ‘restrained search predictive control method’ or
RSPC, where the number of considered inverter states in
every sampling period is 6, 11 or 16. A dynamic selection
criterion to minimize the number of commutations in the six-
phase power converter is applied in every control step. The
number of usable voltage vectors in the asymmetrical six-
phase drive is therefore reduced, as is the computational time
of the control technique.
Different predictive current control techniques are also
developed to reduce the generated harmonic content. For
example, the selected voltage vector is combined during the
control period with a zero vector in [65], resulting in a
predictive current control method termed OSPC or ‘one–step
modulation predictive current control’. The active vector that
minimizes the cost function is modulated, and the OSPC
applies a more appropriate voltage vector in terms of
achieving the control goals. The number of available voltage
vectors is the same as used in [62,63]. This idea is further
refined in [66,67] where a proper pulse width modulation
scheme is combined with the predictive current control
technique, and a voltage reference that ensures sinusoidal
output voltage and operation in the linear modulation region
is imposed, while avoiding over-modulation region.
The MPC method has been extended to the five-phase
induction motor drive in [68], where the common mode
voltage is also reduced, and in [69], where a detailed
comparison between MPC based current controllers and PI-
PWM current control techniques is provided across the full
inverter’s linear operating region under constant flux-torque
operation mode. The predictive controller designed in [69]
applies a quadratic cost function with torque (primary plane)
and non-torque (secondary plane) producing currents, using

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
a weighting factor for the currents of the secondary plane.
Table II and Fig. 5 summarize obtained results. It is
concluded that a better transient performance is obtained
using FCS-MPC, but steady-state performance is superior
with PI-PWM control. Guidelines for the best switching state
set and weighting factor selections are also provided.
B. Direct Torque Control
High performance control of multiphase drives using
DTC techniques is much more difficult to achieve than using
three-phase drives, due to the inherent nature of the control
technique. Its basic principle is to regulate only two
variables, the electrical torque and stator flux, using
hysteresis controllers. This is fine in three-phase drives,
since there are only two independent currents. But, in
multiphase machines, there are in principle (n1)
independent currents and hence using a single voltage vector
in each switching period, selected purely on the basis of flux
and torque requirements, may lead to excessive non-
flux/torque producing currents and low efficiency. Stator
voltage vector is typically obtained from an optimal
switching table (ST-DTC) or by imposing a direct mean
torque control approach and a constant switching frequency
(PWM-DTC). The efficiency of the controller decreases
when the number of phases and degrees of freedom increase.
The DTC technique has not been extended yet to any
phase number higher than six. However, some advances
have been recently achieved in the application of the ST-
DTC method to the multiphase drives. The focus is on the
definition of the switching table for five-phase and
asymmetrical six-phase induction machines and the
reduction of the stator voltage in the secondary plane(s) to
minimize the generated non-torque producing stator current
components [70-73]. The improvement of the obtained
performance at low-speed operation is also analyzed in [71].
Distributed winding machines are considered, and some
further work is expected in the area in the future like in [74],
where the ST-DTC method is extended and generalized for
n-phase induction machines and n is any odd number higher
than three.
C. Alternative Control Methods
A recent control proposal in the multiphase drive area is
predictive torque control (PTC) method, detailed in Fig. 6
and presented in [75] as a competitor of the DTC method for
a five-phase induction machine. The viability and
effectiveness of the PTC strategy is confirmed using
experimental results, which are compared with those
obtained using the modified DTC method of [70]. Fig. 7 and
8 summarize obtained results, where it can be deduced that
the PTC-based control technique is a viable alternative to the
DTC method, offering better torque dynamic performance,
quicker speed response and lower torque ripple, while the
overcurrent protection of the power converter and the
operation at a lower average switching frequency are
guaranteed (Fig. 7). From the computational point of view,
PTC requirements are about 2.5 times higher than DTC ones,
which is a clear disadvantage (Fig. 8).
A different control method that does not require the
application of coordinate transformations, based on the
brush-dc-machine operation principles, is applied in [76] to
a nine-phase cage-rotor induction machine. A model
reference adaptive speed controller based on artificial neural
networks is used in five-phase interior permanent magnet
motor drives in [77]. A modified V/f control technique has
been applied in [78] to a five-phase induction machine to
generate a trapezoidal air-gap flux, combining fundamental
and third harmonic stator voltages. Results obtained in [78]
prove that the torque/ampere ratio is increased, compared
with the conventional V/f control technique, if the machine
is under heavy load conditions (above 50% of the nominal
one). However, larger stator losses and currents are
generated in light load operation modes.
Finally, the effect of stator winding configuration is
studied as a mean to extend the operational range of
multiphase drives in [79,80]. The number of possible
alternatives for connecting the phases of an n-phase electric
machine is (n+1)/2, but most of the available research is
restricted to the star connection. When the speed goes up,
higher multiphase power converter ratings (voltages and
currents) are required, which limit the operational speed
range of the drive. A five-phase permanent magnet machine
is operated in [79] using three types of winding
configurations, star, pentagon and pentacle, and the
comparative performance of the drive is analyzed in terms of
torque-speed and efficiency. It is concluded that the
configurations with lower voltages are suitable for higher
torque and lower speed, while those with higher voltages are
appropriate for lower torque and higher speed. Then, a
winding changeover technique is applied for extending the
operational speed range of the drive, together with a
maximum torque per ampere control strategy. The star and
pentagon connections are also compared in [80], where a V/f
control method is used. Provided results show a superior
TABLE II
COMPARISON OBTAINED IN [69] BETWEEN PI-PWM AND FCS-
MPC USING 31 DIFFERENT VOLTAGE VECTORS (MPC-31)
Feature
MPC-31
PI-PWM control
Sampling freq.
10 kHz
2.5 kHz
Switching freq. (exp.)
1950-3700 Hz
2500 Hz
Dynamic decoupling
Internal
External
Machine parameter
requirements
All
All except stator
resistances
Control of the secondary
plane currents
Current error in the
cost function
Additional pair of PI
controllers
Computational cost
High, 82s
Low, 27s
Tuning
Easy, retuning is not
required
Difficult, retuning
required for different
operating points
Phase voltage/current spectra
and THD
Broad & continuous,
high THD
(10.8% - 12.6%)
Modulation type, low
THD
(6.4% - 6.9%)
Transient, 90% rise time
(see Fig. 16 in [69])
Consistently faster,
0.7ms
Slower, 4.5ms
Current control bandwidth
Larger
Smaller

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
Fig. 4. The current controller in the rotor flux oriented reference frame is compared in [69] for a five-phase induction motor using: (a) MPC based current
control with all 31 voltage vectors (MPC-31) involved in the objective function minimization stage, and (b) PI-PWM current controllers. Reproduced from
[69] with the permission of the authors.
Fig. 5. Experimental stator current and rotor speed responses obtained in [69] using the MPC-31 (left plots) and the PI-PWM (right plots) control methods.
The same stator current commands are applied for both controllers. Reproduced from [69] with the permission of the authors.
Fig. 6. General PTC control scheme proposed in [75] for a five-phase
induction motor drive.
Fig. 7. Experimental results obtained in [75] where the PTC method (left
plots) and the modified DTC technique detailed in [70] (right plots) are
compared.
abcd
dqdq
1122
isd *
1
isq1*
i=
sd2*0
i=
sq2*0ωre
QEP
si gnals
DSP Microcontroller-T MS32F28335
PI
θrf
Carrier-ba sed
PW M with mi n-
max inje ction
abcde
dqdq
1122
Five-
phas e IM PMDC
ia to id
Resol ver
DC-bus
Two-level
fi ve-phas e inverte r
Current s ensors
Swi tching
si gnals
Rot or flux
posi ti on
estimat ion
PI
PI
PI
Dec
vsd1*
vsq1*
vsd2*
vsq2*
Re sis tor bank
RDC
(i sola ted neut ral)
Cos t
mi nimi zation
Mode l-bas ed
predi ct ion
abcd
dqxy
Sl ip
spe ed/R otor
fl ux posi ti on
estimat ion
isd*,k+2
isq*,k+2
ixs,
k
*+2=0
isy*=0
,k+2
Set of
sw itching
st ates
θrf
ωre
ωsl
isd, k+2
isq, k+2
isx,k+2
isy,k+2
DSP Microcontroller-T MS32F28335 (b)
(a)
-4
-2
0
2
4(a)
Current [A]
-4
-2
0
2
4(b)
Current [A]
-4
-2
0
2
4(c)
Current [A]
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-600
-300
0
300
600 (d)
Time [s]
Speed [rpm]
is

isx
isq
isd


2=1018rpm


1=527rpm
-4
-2
0
2
4(a)
Current [A]
-4
-2
0
2
4(b)
Current [A]
-4
-2
0
2
4(c)
Current [A]
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
-600
-300
0
300
600 (d)
Time [s]
Speed [rpm]


2=1006rpm


1=545rpm
isq1
isd1
isx
is


IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
Fig. 8. Real time implementation details in a sampling period shown in [75],
where PTC and DTC methods are compared.
performance of the star connection in healthy operation
mode. The paper also analyzes the faulty mode of operation
(open-phase condition), concluding that the pentagon
connection offers better behavior. The ability to operate the
multiphase drive in faulty state requires however some
modifications in the models, current references and control
strategies, and the recent advances in the field are surveyed
in the second part of this state of the art paper.
V. CONCLUSIONS
The attention paid to multiphase machines and drives has
experienced a continuous growth in recent times and the
body of knowledge in the area has significantly increased in
the last few years. This two parts’ paper surveys some of the
aspects of multiphase machines/drives with emphasis placed
on developments since the publication of the first Special
Section on “Multiphase Machines and Drives” in the IEEE
Trans. on Industrial Electronics in May 2008 [2]. The topics
covered in this part include the design, modeling and control
areas in motoring and healthy state.
At first, some novel aspects of the multiphase machine
design have been covered, with an emphasis placed on
structures that reduce the cost and weight of the
electromechanical system while improving the obtained
power density and reliability and introducing the interest of
the superconducting technology in the design of multiphase
machines. Next, the latest advances in the multiphase
machine modeling have been surveyed, including the state-
of-the-art in off-line and on-line identification techniques of
the machines’ electrical parameters.
Finally, recent advances in control strategies for
multiphase machines in healthy operation are also reviewed.
A special attention has been paid to multi-frequency current
supply cases, where lower distortion and torque
enhancement are obtained. While FOC and DTC are still the
dominant control approaches when it comes to variable-
speed multiphase drives, it is interesting to note that an
entirely new area has appeared in recent years, namely model
predictive control. While MPC is a well-known control
approach for the three-phase drives, its use in multiphase
drive related research commenced well after the publication
of [2].
REFERENCES
[1] E. Levi, R. Bojoi, F. Profumo, H.A. Toliyat and S. Williamson,
“Multiphase induction motor drives - A technology status review,”
IET Electric Power Applications, vol. 1, no. 4, pp. 489-516, 2007.
[2] E. Levi, “Multiphase electric machines for variable-speed
applications,” IEEE Trans. on Ind. Electron., vol. 55, no. 5, pp. 1893-
1909, 2008.
[3] W. Cao, B.C. Mecrow, G.J. Atkinson, J.W. Bennett and D.J.
Atkinson, “Overview of electric motor technologies used for more
electric aircraft (MEA)” IEEE Trans. on Ind. Electron., vol. 59, no. 9,
pp. 3523-3531, 2012.
[4] J. Liu, L. Huang, H. Yu, C. Wen and W. Zhong, “Study on the
characteristics of a novel six-phase fault-torrent linear permanent
magnet machine for linear oil pumping,” IEEE Trans. Appl.
Supercond, vol. 24, no. 3, 2014.
[5] E. Jung, H. Yoo, S. Sul, H. Choi and Y. Choi, “A nine-phase
permanent-magnet motor drive system for an ultrahigh-speed
elevator,” IEEE Trans. Ind. Appl., vol. 48, no. 3, pp. 987-995, 2012.
[6] A. Abdelkhalik, M. Masoud and W. Barry, “Eleven-phase induction
machine: steady-state analysis and performance evaluation with
harmonic injection,” IET Electric Power Applications, vol. 4, no. 8,
pp. 670-685, 2010.
[7] L.A. Pereira, C.C. Scharlau, L.F.A. Pereira and S. Haffner, “Influence
of saturation on the airgap induction waveform of five-phase
induction machines,” IEEE Trans. Energy Convers., vol. 27, no. 1,
pp. 29-41, 2012.
[8] A.S. Abdel-khalik and S. Ahmed, “Performance evaluation of a five-
phase modular winding induction machine,” IEEE Trans. Ind.
Electron., vol. 59, no. 6, pp. 2654-2669, 2012.
[9] P. Zheng, F. Wu, Y. Lei, Y. Sui and B. Yu, “Investigation of a novel
24-slot/14-pole six-phase fault-tolerant modular permanent-magnet
in-wheel motor for electric vehicles,” Energies, vol. 6, pp. 4980-5002,
2013.
[10] Y. Sui, P. Zheng, F. Wu, B. Yu, P. Wang and J. Zhang, “Research on
a 20-slot/22-pole five-phase fault-tolerant PMSM used for four-
wheel-drive electric vehicles,” Energies, vol. 7, pp. 1265-1287, 2014.
[11] A. Boglietti, A.M. El-Refaie, O. Drubel, A.M. Omekanda, N. Bianchi,
E.B. Agamloh, M. Popescu, A. Di Gerlando and J.B. Bartolo,
“Electrical machine topologies. Hottest topics in the electrical
machine research community,” IEEE Ind. Electron. Mag., vol. 8, no.
2, pp. 18-30, 2014.
[12] L. Parsa, H.A. Toliyat and A. Goodarzi, “Five-phase interior
permanent-magnet motors with low torque pulsation,” IEEE Trans.
Ind. Appl., vol. 43, no. 1, pp. 40-46, 2007.
[13] A.S. Abdel-Khalik, “Five-phase modular external rotor PM machine
with different rotor poles: A comparative simulation study,”
Modelling and Simulation in Engineering, vol. 2012, article ID
487203, 2012.
[14] A.S. Abdel-Khalik and S. Ahmed, “Performance evaluation of a five-
phase modular external rotor PM machine with different rotor poles,”
Alexandria Engineering Journal, vol. 51, pp. 249-251, 2012.
[15] E. Fornasiero, N. Bianchi and S. Bolognani, “Slot harmonic impact
on rotor losses in fractional-slot permanent-magnet machines,” IEEE
Trans. Ind. Electron., vol. 59, no. 6, pp. 2557-2564, 2012.
[16] B. Aslan, E. Semail and J. Legranger, “General analytical model of
magnet average eddy-current volume losses for comparison of
multiphase PM machines with concentrated winding,” IEEE Trans.
Energy Convers., vol. 29, no. 1, pp. 72-83, 2014.
[17] A. Cavagnino, Z. Li, A. Tenconi and S. Vaschetto, “Integrated
generator for more electric engine: design and testing of a scaled-size
prototype,” IEEE Trans. Ind. Appl., vol. 49, no. 5, pp. 2034-2043,
2013.
[18] P. Zheng, Y. Sui, J. Zhao, C. Tong and T.A. Lipo, “Investigation of a
novel five-phase modular permanent-magnet in-wheel motor,” IEEE
Trans. Magn., vol. 47, no. 10, 2011.
[19] K. Wang, Z.Q. Zhu and G. Ombach, “Torque improvement of five-
phase surface-mounted permanent magnet machine using third-order
harmonic,” IEEE Trans. Energy Convers., vol. 29, no. 3, pp. 735-747,
2014.
[20] F. Scuiller, E. Semail, J.F. Charpentier and P. Letellier, “Multi-
criteria-based design approach of multi-phase permanent magnet low-

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
speed synchronous machines,” IET Electric Power Applications, vol.
3, no. 2, pp. 102-110, 2009.
[21] F. Scuiller, “Magnet shape optimization to reduce pulsating torque for
a five-phase permanent-magnet low-speed machine,” IEEE Trans.
Magn., vol. 50, no. 4, pp. 1-9, 2014.
[22] M. Barcaro, N. Bianchi and F. Magnussen, “Analysis and test of a
dual three-phase 12-slot 10-pole permanent-magnet motor,” IEEE
Trans. Ind. Appl., vol. 46, no. 6, pp. 2355-2362, 2010.
[23] M. Barcaro, N. Bianchi and F. Magnussen, “Six-phase supply
feasibility using a PM fractional-slot dual winding machine,” IEEE
Trans. Ind. Appl., vol. 47, no. 5, pp. 2042-2050, 2011.
[24] M. Barcaro, A. Faggion, N. Bianchi and S. Bolognani, “Sensorless
rotor position detection capability of a dual three-phase fractional-slot
IPM machine,” IEEE Trans. Ind. Appl., vol. 48, no. 6, pp. 2068-2078,
2012.
[25] J.D. Ede, K. Atallah, G.W. Jewell, J.B. Wang and D. Howe, “Effect
of axial segmentation of permanent magnets on rotor loss in modular
permanent-magnet brushless machines,” IEEE Trans. Ind. Appl., vol.
43, no. 5, pp. 1207-1213, 2007.
[26] J. Gong, B. Aslan, F. Gillon and E. Semail, “High-speed functionality
optimization of five-phase PM machine using third harmonic
current,” COMPEL: International Journal for Computation and
Mathematics in Electrical and Electronic Engineering, vol. 33, no. 3,
pp. 879-893, 2014.
[27] A. Labak and N.C. Kar, “Designing and prototyping a novel five-
phase pancake-shaped axial-flux SRM for electric vehicle application
through dynamic FEA incorporating flux-tube modeling,” IEEE
Trans. Ind. Appl., vol. 49, no. 3, pp. 1276-1288, 2013.
[28] Z.Q. Zhu, A.S. Thomas, J.T. Chen and G.W. Jewell, “Cogging torque
in flux-switching permanent magnet machines,” IEEE Trans. Magn.,
vol. 45, no. 10, pp. 4708-4711, 2009.
[29] X. Xue, W. Zhao, J. Zhu, G. Liu, X. Zhu and M. Cheng, “Design of
five-phase modular flux-switching permanent-magnet machines for
high reliability applications,” IEEE Trans. Magn., vol. 49, no. 7, pp.
3941-3944, 2013.
[30] X. Huang, A. Googman, C. Gerada, Y. Fang and Q. Lu, “Design of a
five-phase brushless DC motor for a safety critical aerospace
application,” IEEE Trans. Ind. Electron., vol. 59, no. 9, pp. 3532-
3541, 2012.
[31] J. Huang, B. Li, H. Jiang and M. Kang, “Analysis and control of
multiphase permanent-magnet bearingless motor with single set of
half-coiled winding,” IEEE Trans. Ind. Electron., vol. 61, no. 7, pp.
3137-3145, 2014.
[32] J. Baek, S.S.R. Bonthu, S. Kwak and S.Choi, “Optimal design of five-
phase permanent magnet assisted synchronous reluctance motor for
low output torque ripple,” in Proc. of the IEEE Energy Conversion &
Expo ECCE, Pittsburgh, EEUU, CD-ROM, 2014.
[33] S.S.R. Bonthu, J. Baek and S.Choi, “Comparison of optimized
permanent magnet assisted synchronous reluctance motors with three-
phase and five-phase systems,” in Proc. of the IEEE Energy
Conversion & Expo ECCE, Pittsburgh, EEUU, CD-ROM, 2014.
[34] J. Wang, R. Qu and Y. Liu, “Comparison study of superconducting
generators with multiphase armature windings for large-scale direct-
drive wind turbine,” IEEE Trans. Appl. Supercond., vol. 23, no. 3,
2013.
[35] J. Wang, R. Qu, Y. Liu and J. Li, “Study of multiphase
superconducting wind generators with fractional-slot concentrated
windings,” IEEE Trans. Appl. Supercond., vol. 24, no. 3, 2014.
[36] O. Ojo and Z. Wu, “Modeling of a dual-stator-winding induction
machine including the effect of main flux linkage magnetic
saturation,” IEEE Trans. Ind. Appl., vol. 44, no. 4, pp. 1099-1107,
2008.
[37] A.S. Abdel-Khalik, S. Ahmed and A.M. Massoud, “A five-phase
induction machine model using multiple dq planes considering the
effect of magnetic saturation,” in Proc. of the IEEE Energy
Conversion & Expo ECCE, Pittsburgh, EEUU, CD-ROM, 2014.
[38] A.S. Abdel-Khalik, S. Ahmed, A.A. Elserougi and A.M. Massoud, “A
voltage-behind-reactance model of five-phase induction machines
considering the effect of magnetic saturation,” IEEE Trans. Energy
Convers., vol. 28, no. 3, pp. 576-592, 2013.
[39] S. Gradev, D. Findeisen, T.L. Toennesen and H.G. Herzog, “A
voltage-behind-reactance model of a dual voltage six-phase induction
machine,” in Proc. of the 21st International Conference on Electrical
Machines ICEM, Berlin, Germany, CD-ROM, 2014.
[40] S. Kallio, M. Andriollo, A. Tortella and J. Karttunen, “Decoupled d-
q model of double-star interior permanent magnet synchronous
machines,” IEEE Trans. Ind. Electron., vol. 60, no. 6, pp. 2486-2494,
2013.
[41] A. Tessarolo, C. Bruzzese, M. Degano and L. Branz, “Analytical
modeling of split-phase synchronous reluctance machines,” in Proc.
IEEE Ind. Elec. Soc. Annual Conf. IECON, Dallas, Texas, EEUU, pp.
3190-3196, 2014.
[42] A. Tessarolo, “Accurate computation of multiphase synchronous
machine inductances based on winding function theory,” IEEE Trans.
Energy Convers., vol. 27, no. 4, pp. 895-904, 2012.
[43] A.G. Yepes, J.A. Riveros, J. Doval-Gandoy, F. Barrero, O. Lopez, B.
Bogado, M. Jones and E. Levi, “Parameter identification of
multiphase induction machines with distributed windings—Part 1:
sinusoidal excitation methods,” IEEE Trans. Energy Convers., vol.
27, no. 4, pp. 1056-1066, 2012.
[44] J.A. Riveros, A.G. Yepes, F. Barrero, J. Doval-Gandoy, B. Bogado,
O. Lopez, M. Jones and E. Levi, “Parameter identification of
multiphase induction machines with distributed windings—Part 2:
time-domain techniques,” IEEE Trans. Energy Convers., vol. 27, no.
4, pp. 1067-1077, 2012.
[45] D. Wang, X. Wu, J. Chen, Y. Guo and S. Cheng, “A distributed
magnetic circuit approach to analysis of multiphase induction
machines with nonsinusoidal supply,” IEEE Trans. Energy Convers.,
DOI: 10.1109/TEC.2014.2362193.
[46] S. Kallio, J. Karttunen, P. Peltoniemi and O. Pyehönen,
“Determination of the inductance parameters for the decoupled d-q
model of double-star permanent-magnet synchronous machines,” IET
Electric Power Applications, vol. 8, no. 2, pp. 39-49, 2013.
[47] S. Kallio, J. Karttunen, P. Peltoniemi and O. Pyehönen, “Online
estimation of double-star IPM machine parameters using RLS
algorithm,” IEEE Trans. Ind. Electron., vol. 61, no. 9, pp. 4519-4530,
2014.
[48] M. Jones, S.N. Vukosavic, D. Dujic and E. Levi, “A synchronous
current control scheme for multiphase induction motor drives,” IEEE
Trans. Energy Convers., vol. 24, no. 4, pp. 860-868, 2009.
[49] H.S. Che, E. Levi, M. Jones, W.P. Hew and N.A. Rahim, “Current
control methods for an asymmetrical six-phase induction motor
drive,” IEEE Trans. Power Electron., vol. 29, no. 1, pp. 407-417,
2014.
[50] A.G. Yepes, J. Malvar, A. Vidal, O. López and J. Doval-Gandoy,
“Current harmonic compensation based on multiresonant control in
synchronous frames for symmetrical n-phase machines,” IEEE Trans.
Ind. Electron., vol. 62, no. 5, pp. 2708-2720, 2015.
[51] Y. Hu, Z. Zhu and K. Liu, “Current control for dual three-phase
permanent magnet synchronous motors accounting for current
unbalance and harmonics,” IEEE Trans. Emerg. Sel. Topics Power
Electron., vol. 2, no. 2, pp. 272-284, 2014.
[52] J. Karttunen, S. Kallio and P. Peltoniemi, “Decoupled vector control
scheme for dual three-phase permanent magnet synchronous
machines,” IEEE Trans. Ind. Electron., vol. 61, no. 5, pp. 2185-2196,
2014.
[53] A.S. Abdel-Khalik, M.I. Masoud and B.W. Williams, “Eleven phase
induction machine: steady-state analysis and performance evaluation
with harmonic injection,” IET Electric Power Applications, vol. 4, no.
8, pp. 670-685, 2010.
[54] A.S. Abdel-Khalik, S.M. Gadoue, M.I. Masoud and B.W. Williams,
“Optimum flux distribution with harmonic injection for a multiphase
induction machine using genetic algorithms,” IEEE Trans. Energy
Convers., vol. 26, no. 2, pp. 501-512, 2011.
[55] Z. Libo, J.E. Fletcher, B.W. Williams and H. Xiangning,“Dual-plane
vector control of a five-phase induction machine for an improved flux
pattern,” IEEE Trans. Ind. Electron., vol. 55, no. 5, pp. 1996-2005,
2008.
[56] A.S. Abdel-Khalik, M.I. Masoud and B.W. Williams, “Improved flux
pattern with third harmonic injection for multiphase induction
machines,” IEEE Trans. Power Electron., vol. 27, no. 3, pp. 1563-
1578, 2012.
[57] A.S. Abdel-Khalik, M.I. Masoud and B.W. Williams, “Vector
controlled multiphase induction machine: harmonic injection using

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
optimized constant gains,” Electric Power Systems Research, vol. 89,
pp. 116-128, 2012.
[58] A.S. Abdel-Khalik, M.I. Masoud, S. Ahmed and B.W. Williams,
“Effect of current harmonic injection on constant rotor volume
multiphase induction machine stators: a comparative study,” IEEE
Trans. Ind. Appl., vol. 48, no. 6, pp. 2002-2013, 2012.
[59] M. Mengoni, L. Zarri, A. Tani, L. Parsa, G. Serra and D. Casadei,
“High-torque density control of multiphase induction motor drives
operating over a wide speed range,” IEEE Trans. Ind. Electron., DOI:
10.1109/TIE.2014.2334662.
[60] M.R. Arahal and M.J. Duran, “PI tuning of five-phase drives with
third harmonic injection,” Control Engineering Practice, vol. 17, pp.
787-797, 2009.
[61] M.R. Khan, A. Iqbal and M. Ahmad, “MRAS-based sensorless
control of a vector controlled five-phase induction motor drive,”
Electric Power System Research, vol. 78, pp. 1311-1321, 2008.
[62] F. Barrero, M.R. Arahal, R. Gregor, S. Toral and M.J. Duran, “A
proof of concept study of predictive current control for VSI driven
asymmetrical dual three-phase AC machines,” IEEE Trans. Ind.
Electron., vol. 56, no. 6, pp. 1937-1954, 2009.
[63] M.R. Arahal, F. Barrero, S. Toral, M.J. Duran and R. Gregor, “Multi-
phase current control using finite-state model-predictive control,”
Control Engineering Practice, vol. 17, no. 5, pp. 579-587, 2009.
[64] M.J. Duran, J. Prieto, F. Barrero and S. Toral, “Predictive current
control of dual three-phase drives using restrained search techniques,”
IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3253-3263, 2011.
[65] F. Barrero, M.R. Arahal, R. Gregor, S. Toral and M.J. Duran, “One-
step modulation predictive current control method for the
asymmetrical dual three-phase induction machine,” IEEE Trans. Ind.
Electron., vol. 56, no. 6, pp. 1974-1983, 2009.
[66] R. Gregor, F. Barrero, S. Toral, M.J. Duran, M.R. Arahal, J. Prieto
and J.L. Mora, “Predictive-SVPWM current control method for
asymmetrical dual three-phase induction motor drives,” IET Electric
Power Applications, vol. 4, no. 1, pp. 26-34, 2010.
[67] F. Barrero, J. Prieto, E. Levi, R. Gregor, S. Toral, M.J. Duran and M.
Jones, “An enhanced predictive current control method for
asymmetrical six-phase motor drives,” IEEE Trans. Ind. Electron.,
vol. 58, no. 8, pp. 3242-3252, 2011.
[68] M.J. Duran, J. Riveros, F. Barrero, H. Guzmán and J. Prieto,
“Reduction of common-mode voltage in five-phase induction motor
drives using predictive control techniques,” IEEE Trans. Ind. Appl.,
vol. 48, no. 6, pp. 2059-2067, 2012.
[69] C.S. Lim, E. Levi, M. Jones, N.A. Rahim and W.P. Hew, “FCS-MPC-
based current control of a five-phase induction motor and its
comparison with PI-PWM control,” IEEE Trans. Ind. Electron., vol.
61, no. 1, pp. 149-163, 2014.
[70] L. Zheng, J.E. Fletcher, B.W. Williams and X. He, “A novel direct
torque control scheme for a sensorless five-phase induction motor
drive,” IEEE Trans. Ind. Electron., vol. 58, no. 2, pp. 503-513, 2011.
[71] L. Gao, J.E. Fletcher and L. Zheng, “Low speed control
improvements for a 2-level 5-phase inverter-fed induction machine
using classic direct torque control,” IEEE Trans. Ind. Electron., vol.
58, no. 7, pp. 2744-2754, 2011.
[72] A. Taheri, A. Rahmati and S. Kaboli, “Comparison of efficiency for
different switching tables in six-phase induction motor DTC drives,”
Journal of Power Electronics, vol. 12, no. 1, pp. 128-135, 2012.
[73] A. Taheri, A. Rahmati and S. Kaboli, “Efficiency improvement in
DTC of six-phase induction machine by adaptive gradient descent of
flux,” IEEE Trans. Power Electron., vol. 27, no. 3, pp. 1552-1562,
2012.
[74] R. Karampuri, J. Prieto, F. Barrero and S. Jain, “Extension of the DTC
technique to multiphase induction motor drives using any odd number
of phases,” in Proc. of the Vehicle Power and Propulsion Conference
VPPC, Coimbra, Portugal, CD-ROM, 2014.
[75] J.A. Riveros, F. Barrero, E. Levi, M.J. Duran, S. Toral and M. Jones,
“Variable-speed five-phase induction motor drive based on predictive
torque control,” IEEE Trans. Ind. Electron., vol. 60, no. 8, pp. 2957-
2968, 2013.
[76] N. Gule and M.J. Kamper, “Multiphase cage-rotor induction-machine
drive with direct implementation of brush DC operation,” IEEE
Trans. Ind. Appl., vol. 48, no. 6, pp. 2014-2021, 2012.
[77] L. Guo and L. Parsa, “Model reference adaptive control of five-phase
IPM motors based on neural network,” IEEE Trans. Ind. Electron.,
vol. 59, no. 3, pp. 1500-1508, 2012.
[78] C.C. Scharlau, L.F.A. Pereira, L.A. Pereira and S. Haffner,
“Performance of a five-phase induction machine with optimized air
gap field under open loop V/f control,” IEEE Trans. Energy Convers.,
vol. 23, no. 4, pp. 1046-1056, 2008.
[79] S. Sadeghi, L. Guo, H.A. Toliyat and L. Parsa, “Wide operational
speed range of five-phase permanent magnet machines by using
different stator winding configurations,” IEEE Trans. Ind. Electron.,
vol. 59, no. 6, pp. 2621-2631, 2012.
[80] A.S. Abdel-Khalik, A.S. Morsy, S. Ahmed and A.M. Massoud,
“Effect of stator winding connection on performance of five-phase
induction machines,” IEEE Trans. Ind. Electron., vol. 61, no. 1, pp.
3-19, 2014.
Federico Barrero (M 04; SM 05) received the MSc
and PhD degrees in Electrical and Electronic
Engineering from the University of Seville, Spain, in
1992 and 1998, respectively. In 1992, he joined the
Electronic Engineering Department at the University
of Seville, where he is currently an Associate
Professor. He received the Best Paper Awards from
the IEEE Transactions on Industrial Electronics for
2009 and from the IET Electric Power Applications
for 2010-2011.
Mario J. Duran was born in Málaga, Spain, in 1975.
He received the M.Sc. and Ph.D. degrees in Electrical
Engineering from the University of Málaga Spain, in
1999 and 2003, respectively. He is currently an
Associate Professor with the Department of Electrical
Engineering at the University of Málaga. His research
interests include modeling and control of multiphase
drives and renewable energies conversion systems.