Electric Power Systems Research 61 (2002) 139– 147
www.elsevier.com/locate/epsr
Multi-phase induction machine drive research—a survey
G.K. Singh *
Department of Electrical Engineering, Indian Institute of Technology, Roorkee, Uttaranchal 247667, India
Received 19 July 2001; received in revised form 6 October 2001; accepted 20 December 2001
Abstract
Due to the potential benefits resulting from the use of a phase order higher than three in transmission, some interest has also
grown in the area of multi-phase machine. For machine drive applications, multi-phase system could potentially meet the demand
for high power electric drive systems, which are both rugged and energy-efficient. High phase number drives possess several
advantages over conventional three-phase drives such as: reducing the amplitude and increasing the frequency of torque pulsation,
reducing the rotor harmonic currents, reducing the current per phase without increasing the voltage per phase, lowering the dc
link current harmonics, higher reliability and increased power in the same frame. The high phase order drive is likely to remain
limited to specialized applications where high reliability is demanded such as electric/hybrid vehicles, aerospace applications, ship
propulsion, and high power application where a combination of several solid state devices form one leg of the drive. The research
has been underway for the last two decades to investigate the various issues related to the use of multi-phase machine as a
potential alternative to the conventional three-phase machine. This paper, therefore, reviews the progress made in multi-phase
induction machine drive research and development since its inception. Attempts are made to highlight the current and future
issues involved for the development of multi-phase induction machine drive technology for future application. © 2002 Elsevier
Science B.V. All rights reserved.
Keywords: Analysis; Drive; Induction motor; Multi-phase; Modeling; Stability
1. Introduction
High power electric machine drive systems have
found many applications such as pumps, fans, compressors, rolling mills, cement mills, mine hoists, to name a
few. At present, the most successful type of high power
drive systems is cycloconverter-fed electric machine
drives and synchronous machines fed by current source
thyristor inverters. Voltage source inverters, despite
their advantage of being able to use low cost induction
machines, are still limited to the lower end of the high
power range due to the limitations on gate-turn-off type
semiconductor power device ratings.
In the past decades, multi-level inverter fed electric
machine drive systems have emerged as a promising
* Fax: + 91-1332-73560.
E-mail address: gksngfee@iitr.ernet.in (G.K. Singh).
tool in achieving high power ratings with voltage limited devices. The typical structure of such systems is the
three-level inverter three-phase electric machine system
[1]. A three-level voltage source inverter is a series
switch type structure, which operates with split-voltage
dc bus. The voltage stress on each device is only half of
the total dc bus voltage and, thus, a doubled dc bus
voltage can be achieved. The parallel circuit dual to the
multilevel system is essentially the multi-phase inverter
fed electric machine drive system. In a multi-phase
machine drive system, more than three-phase windings
are housed in the same stator of the electric machine,
and the current per phase in the machine is, thereby
reduced. In the most common of such structures, two
sets of three-phase windings are spatially phase shifted
by 30° electrical. In such systems, each set of the
three-phase stator winding is excited by a three-phase
inverter, therefore, total power rating of the system is
theoretically doubled. In addition to enhancing power
0378-7796/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 7 7 9 6 ( 0 2 ) 0 0 0 0 7 - X
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G.K. Singh / Electric Power Systems Research 61 (2002) 139–147
rating, it is also believed that drive systems with such
multi-phase redundant structure will improve the reliability at the system level [2– 6]. In particular, unlike
in normal three-phase system, the loss of one phase in
multi-phase machine drive system does not prevent the
machine from starting and running. This paper deals
with a state-of-the-art discussion of multi-phase induction machine drive research and development, highlighting the analytical and technical considerations as
well as various issues addressed in the literature towards practical realization of this new technology.
2. Concept and benefits
2.1. Concept and feasibility studies
Ward and Harer [7], for first time in 1969 have
presented the preliminary investigation of an inverterfed five-phase induction motor and suggested that the
amplitude of torque pulsation can be reduced by increasing the number of stator phases. A very few
examples of multi-phase induction motors can be
found in the literature. Nelson and Krause [8] carried
out computer simulation on three types of six-phase
motors using an inverter source. They found that by
using a motor with 30° phase belts, the sixth harmonic
torque pulsation usually encountered in inverter driven
three-phase motors was eliminated, though the peak
stator currents were increased. Danzer has reported
the test results on five-phase motors [9– 11]. The reason given for using five phases was to reduce the
current such that it would match the rating of the
available thyristors, for inverter source. However, the
third harmonic current was found to be excessive
when it was supplied by the inverter. Motors with
many phases have been proposed for high degree of
reliability. These few attempts to develop multi-phase
induction motors show that they have some advantages over conventional three-phase induction motors.
2.2. Benefits
The potential benefits of a multi-phase induction
motor result from the 30° displacement angle between
the two three-phase sets of a six-phase motor, leading
to elimination of all the air gap flux harmonics of the
order (6m 9 1, m =1, 3, 5…). Consequently, all rotor
copper losses produced by these harmonics as well as
all the torque harmonics of the order (6m, m =1, 3,
5…) are eliminated. The most significant advantages
include: capability to start and run even on one or
two of its many stator phases open or short circuited,
lower current per phase without an increase in
voltage per phase, lower dc link current harmonics,
higher reliability and increased power in the same
frame.
3. Method of analysis
The analysis of standard symmetrical multi-phase
(more than three phases) induction machines is presented in several texts [12]. That, however, cannot be
directly applied to the machines with unsymmetrical
phase displacements between the multiple winding sets.
The derivation of the voltage equations in phase variables and the transformation to the d– q–o reference
frame of a multi-phase machine with unsymmetrical
phase displacement has been reported by Nelson and
Krause [8]. Analysis of six-phase machine with 0°
phase displacement between two winding sets has been
given by Singh et al. [13]. Abbas [14] and Lipo [15–17]
have reported a model for inverter fed dual threephase (spatially phase shifted by 30° electrical) induction machine drive system. The most commonly used
analytical tool for the analysis of unbalanced operation of electric machines has been the well-known
symmetrical component method. In this method, a
balanced structure is assumed after the machine loses
one or more of its phases. Although it has been used
successfully in the steady-state analysis of sinusoidal
excitation, however, as far as the dynamics of machine
is concerned, the method loses its utility due to the
fact that the interaction between the lost phases and
remainder of the machine windings no longer exists
and this drastically alters the dynamic behavior of the
machine. Two separate models have been used by
Zhao et.al. [16,17] to analyze the dynamic behavior of
machines for balanced, and unbalanced excitation due
to open circuit. These models are silent about the
analysis of unbalanced condition caused by the short
circuit at stator terminals. The two-axis (d–q) model
of the multi-phase machine in an arbitrary reference
frame was developed by the present author [5,6] and a
detailed analysis of the machine under balanced, and
unbalanced (open circuit and short circuit both) operating condition has been carried out. In this model,
the effect of mutual leakage reactance between the two
stator winding sets have also been included and is
valid for any angle of displacement between the two
three-phase winding sets.
4. Description of general nomenclature
A machine can have as many phases as coils per
pole pair. The number of phases for a machine is
assumed to be the same as number of stator terminals
or leads, excluding neutral. However, giving the number of phases is not always an adequate description
because two machine versions are possible based on
two possible values of the phase belt angle for a given
G.K. Singh / Electric Power Systems Research 61 (2002) 139–147
number of phases. Almost all the three-phase machines
have 60° phase belts but sometimes these machines are
wound with 120° phase belts, and have some different
characteristics from 60° version [18,19]. Table 1a and b
include the names and relate them to the phase belt
angle and the minimum number of stator leads required
[19].
5. Winding layouts
A six-phase machine can easily be constructed by
‘splitting’ the 60° phase belt into two portions each
spanning 30° [8]. This technique is illustrated in Table 2
for a simple machine having six poles and thirty-six
slots. The winding distribution factor increases from
0.965 for three-phase to 1.0 for six-phase for the split
phase belt connection. A ‘true’ six-phase distribution
that retains the same winding pitch and distribution
factor [15] is shown in Table 2. However, due to the
extra coil side insulation required, this ‘true’ six-phase
distribution is generally less desirable than the split
phase belt connection [15].
141
6. Space harmonics in multi-phase machine
The air gap distribution in cylindrical rotor machines
contains undesirable harmonics, and among these are
the phase belt harmonics. These as well as slot harmonics, produce cusps and dips in the torque curve for slip
near unity. They contribute to leakage reactance and
stray load loss. Stator coil pitch is normally chosen so
as to reduce lower order phase belt harmonics, which
are generally the largest. The phase belt harmonics that
can exist in the spatial distribution of flux are those, for
which, the harmonic order number k satisfies the
equation:
k= 2qi9 1
(6.1)
where, i is any integer.
The lowest order space harmonics are found by using
Eq. (6.1). When more phases are used, the order number for lowest harmonics is higher. For example, semi
12-phase machine can have no space harmonics below
the 11th. Therefore, the stator coil pitch need not be
chosen to reduce the fifth or seventh harmonics, as is
generally necessary for three-phase machines. This pos-
True Six-Phase Winding Distribution for 6 -Pole,
Phase (top layer)
a
a
Distribution (bottom layer)
−y x
a
−c
x
x
36 -slot machine
−c −c b
x
−z −z
−c b
b
−z −z y
b
y
For 6 -phase, 6 - pole, 36 -slot machine with split phase belts
Phase (top layer)
a
x
−c −z
Distribution (bottom layer)
x
−c −z b
05
b
b
−c
−c
For 3 -phase, 5 /6 pitch, 6 -pole, 36 -slot machine
Phase distribution (top layer)
a
a
Distribution (bottom layer)
a
−c
04
−c
b
03
01
02
Slot number
Table 2
Winding distribution
b
y
−a
y
y
−a
b
−a
06
−a
y
−a
−x
−a
−x
−a
−a
07
−a
−x
c
−x
−x
c
−a
c
08
c
−x
c
z
c
z
c
c
09
c
z
−b
z
z
−b
c
−b
10
−b
z
−b
−y
−b
−y
−b
−b
11
−b
−y
a
−y
−y
a
−b
a
12
a
−y
a
x
a
x
a
a
13
a
x
−c
x
x
−c
a
−c
14
−c
x
−c
−z
−c
−z
−c
−c
15
−c
−z
b
−z
−z
b
−c
b
16
b
−z
b
y
b
y
b
b
17
b
y
−a
y
y
−a
b
−a
18
−a
y
−a
−x
−a
−x
−a
−a
19
−a
−x
c
−x
−x
c
−a
c
20
c
−x
c
z
c
z
c
c
21
c
z
−b
z
z
−b
c
−b
22
−b
z
−b
−y
−b
−y
−b
−b
23
−b
−y
a
−y
−y
a
−b
a
24
a
−y
a
x
a
x
a
a
25
a
x
−c
x
x
−c
a
−c
26
−c
x
−c
−z
−c
−z
−c
−c
27
−c
−z
b
−z
−z
b
−c
b
28
b
−z
b
y
b
y
b
b
29
b
y
−a
y
y
−a
b
−a
30
−a
y
−a
−x
−a
−x
−a
−a
31
−a
−x
c
−x
−x
c
−a
c
32
c
−x
c
z
c
z
c
c
33
c
z
−b
z
z
−b
c
−b
34
−b
z
−b
−y
−b
−y
−b
−b
35
−b
−y
a
−y
−y
a
−b
a
36
142
G.K. Singh / Electric Power Systems Research 61 (2002) 139–147
G.K. Singh / Electric Power Systems Research 61 (2002) 139–147
143
8. Multi-phase induction machine in a phase-redundant
drive system
8.1. Phase-redundant dri6e system
Fig. 1. Equivalent circuit of induction machine with double stator
winding.
sibility of eliminating lower order harmonic is a clear
advantage of multi-phase machine. Klingshirn, in his
paper [19] has presented a detailed study about these
harmonics.
7. Equivalent circuit representations
Based on the equivalent circuit of a three winding
transformer, the equivalent circuit of the multi-phase
(six-phase) induction machine having a double stator
winding can be realized as shown in Fig. 1 [15]. The
common mutual leakage reactance, xlm, in the figure
represents the fact that the two sets of three-phase
stator windings occupy the same slots and are,
therefore, mutually coupled by a component of leakage
flux. Note that although the circuit is termed ‘per
phase’, in reality the circuit is drawn with two stator
circuits, one per three-phase group. The equivalent
circuit based on the generalized mathematical model
developed by Singh and Pant [5,6] is shown in Fig. 2.
The coil pitch affects the leakage reactance of the stator
winding. Lipo [15,18,20] has explained this in detail and
has given the technique for finding slot reactance.
Standard test procedures [21] are available to determine
the various machine parameters.
Fig. 2. The q- and d- axis equivalent circuit of a six-phase induction
machine in arbitrary reference frame.
Based on the general concept of parallel redundancy
[22,23], the phase redundancy technique [2] relies on
inherent capability of a general n-phase ac motor to
continue operation with (n−1) or less of its many stator
phases excited. Thorough evaluation of merits of this
technique demands that the number of motor stator
phases, n must be more than conventional three and an
ac machine potentially has as many phases as coils per
pole pair which is almost always greater than three. Thus,
the existing ac motors pose no problem for the designers;
existing coils are gathered into n-phase configuration for
n other than three at minimum additional expenses. Fig.
3 is the proposed drive configuration [6] in which, each
of the n-stator phases is either excited by an independent
single phase drive unit or in a group of three (each
displaced at 120°) by multiple independent three-phase
drive units with possible operational independence to
minimize the physical fault propagation from one unit to
others.
8.2. Fault analysis
Fault studies form an important step in the design of
adequate protective schemes for drive system. The various type of faults that can occur increases with the
increase in number of phase. The type of supply system
and the impedance across the unexcited winding terminals are the two parameters, which together determine
the basic drive configuration during fault. With regard
of type of source, the designer is left with a choice
between voltage and current source excitation. Since each
drive unit in a phase redundant system is provided with
as much operational independence as possible to prevent
the risk of physical fault propagation from one unit to
its neighbor, the basic drive configuration is reduced to
four discrete cases as follows:
(i) Voltage source excitation and the short circuit
occurring at the input stator phase terminal (VSSC);
(ii) Voltage source excitation and an open circuit
occurring at input stator phase terminal (VS-OC);
(iii) Current source excitation and short circuit occurring at input stator phase terminals (CS-SC);
(iv) Current source excitation and open circuit occurring at input stator phase terminal (CS-OC).
A detailed analysis of the machine under unbalanced
(caused by open circuit or short circuit) operating condition have been carried out to study the steady state,
transient and dynamic behavior of the machine with
different winding configuration (0, 30, and 60° displace-
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G.K. Singh / Electric Power Systems Research 61 (2002) 139–147
Fig. 3. Basic n-phase induction machine drive configuration using n-modular H-bridge PWM inverter.
ment) by a number of researchers [2,4– 6,17,24]. Based
on equivalent circuit representation, the motor torque
was calculated for different values of slip and for the
different number of phases for balanced as well as
unbalanced operating conditions under constant torque
operation for providing a common basis for performance comparison of the machine under unbalanced
condition [4,6]. The various studies [2,4– 6,8,25] made
on multi-phase induction reveal that,
“ Torque at any slip scales principally as [(n − 1)/n]2
and pulsating torque as [(n − 1)/n 2] under voltage
source short circuit and current source open circuit
condition.
“ Torque under voltage source open circuit and current source short circuit depends on the rotor slip.
“ Analysis has shown that transient responses are
qualitatively insensitive to the excitation frequency,
“ The machine torque characteristic for a 30° displacement between two winding sets is substantially improved. The amplitude of the pulsating component
of torque is reduced and the predominant frequency
is shifted from 6 to 12 times the supply frequency.
“ Rotor currents for the 30° case are more sinusoidal
due to the elimination of certain rotor harmonic
currents.
“ Higher peak currents in stator are observed for 30°
displacements.
9. Stability analysis
It was recognized first by Rogers [26] that an induction machine operating quite satisfactorily at normal
speed might display an oscillatory response that is
frequency dependent. The analysis was based on root
locus technique. Fallside and Wortley [27] have also
analyzed the instability of the induction motor fed by
variable frequency inverter, neglecting the effect of
harmonics. The effect of machine parameters on the
stability of the system was also reported.
Lipo and Krause [28] have performed the stability
study of a rectifier-inverter induction motor drive system neglecting stator voltage harmonics and using
Nyquist stability criterion. Cornell and Lipo [29] have
used transfer function techniques for the development
of controlled current induction motor drives and study
it’s stability. Macdonald et.al [30] have developed a
linearized small signal model of the current source
inverter–induction motor drive to study the stability of
the drive and provide a transfer function for different
control strategies. Tan et al. [31] have calculated the
eigenvalues of double-cage induction motor using decoupled boundary layer model.
In these works, only the fundamental component of
the inverter voltage has been taken into account neglecting the effect of harmonics. There is much evidence
G.K. Singh / Electric Power Systems Research 61 (2002) 139–147
in the historic literature [32– 35] dealing with the
transient analysis that the transient behavior predicted
using the conventional linearized model, although
agrees qualitatively, deviates from the actual
quantitatively. The cause of deviation may be due to
the assumption made in neglecting saturation effect,
skin effect, iron losses and mechanical damping etc.
However, the saturation effect has been suspected as a
prime cause for the disparity between the analytical and
experimental results. Some schemes [36,37] have
included the saturation effect in the induction motor
fed by variable frequency source. These models are
adaptive to digital simulation and time domain analysis
and successfully predict the instability region precisely.
Ahmed et al. [38] has analyzed the stability of linear
time invariant systems based on the Liapunov’s first
method using the placement of eigenvalues.
The stability studies have thus been carried out in
detail for three-phase machine. However, no such study
has been carried out for multi-phase (more than three
phase) induction machine, to the best knowledge of the
authors. A linearized model for 6-phase machine in d–q
variables of the machine in synchronously rotating
reference frame were developed by the present authors
on the lines of the three phase model developed by
Krause [39] and Hancock [40]. The resulting machine
model is of seventh order. The eigenvalues under
different operating conditions were calculated and
analyzed. The correlations between different machine
parameters and pairs of eigenvalues have been
established. The stability of the machine under
perturbation of any one variable was examined at a
time from the placement of the eigenvalues of the
machine. The system is said to be stable if all the
eigenvalues are located on the left half of the plane [25].
10. Performance analysis of multi-phase induction
machine
The characteristics of several high phase order induction motors were examined by Klingshirn [41]. A detailed performance analysis (no-load and load test) of
the six-phase induction machine have been presented by
Singh et al. [4,42]. This include the efficiency, power
factor, current, magnetization and no- load loss curve.
In another study, analytical and test results on a
scheme for power factor correction of an induction
machine using an auxiliary stator winding in conjuction
with a PWM voltage inverter and a single capacitor on
dc side have been presented by Tamrakar and Malik
[43]. In this study a criterian has been developed to
select the optimum value of the power factor for best
performance of the PWM inverter-fed induction motor
drives. The simulation and test results on a new type of
dual stator winding induction machine (DSIM) have
145
been presented by Lipo et al. [44]. The main advantage
of the drive is its improved capability to operate at low
and zero speeds, maintaining high stator frequencies. It
has been shown that this feature is particularly useful
for implementation of speed sensorless schemes and it
adds a new degree of flexibility to standard control
methods currently used in ac drives. Schouten et al. [10]
have studied the multiphase induction motors for integrated drives. Tests were carried out to compare the
performance of a three-phase PWM drive against threephase and six-phase square wave excited drives. It has
been shown that the high torque ripple present in the
three-phase square drives that leads noise and mechanical stress can be mitigated by using higher phase number motors with fully pitched windings, which are less
susceptible to voltage source harmonics. Toliyat et al.
[11] have presented the simulation and experimental
results for a novel direct torque control (DTC) method
for five phase induction machines. Test results demonstrate that DTC for five-phase induction motor can
achieve a more precise flux and torque control than
three-phase induction motor for the same commanded
inputs. It has been shown that the combination of DTC
with multi-phase induction machine can realize higher
performance.
11. Conclusions
The investigations spread over the last three decades
indicate the technical and economic viability of using a
number of phases higher than three in induction machine. The technology of multi-phase induction machine, once developed to the stage of practical
application, has many advantages to offer over conventional systems. Some of these advantages are:
“ Improved reliability as the machine continues running with one of its many phases open- or short-circuited and there is not much performance
degradation. This property of the multi-phase machine will be advantageous in nuclear power plants
for its circulation pumps and for other similar applications in process industries, which demand high
reliability.
“ Reduced iron loss leading to an improved overall
performance.
“ Lower current per phase without increase in per
phase voltage. This advantageous feature may be
useful for electric vehicles and similar applications
where lower, upper limit of voltage and current is
desirable.
“ The most advantageous feature is increase in power
rating of the machine on high phase order connection in the same frame. In other words, there is a
reduction in per phase power handling requirement
though with enhanced modularity and fault
tolerance.
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G.K. Singh / Electric Power Systems Research 61 (2002) 139–147
“
Increased torque per rms ampere for the same
volume machine.
Continuing advancement in the state-of-the-art of
CSI converter design will inevitably lead to high power
applications. With today’s devices, inverter drives in the
MW range can be readily achieved by use of machine
with multiple three-phase groups. With non-sinusoidal
voltage source, machines having more than three
phases have always less rotor I 2R loss and smaller
torque pulsations caused by harmonics. With non-sinusoidal current sources, there is always a reduction in
harmonic copper loss as compared with its three-phase
counterpart. Certain space harmonics are eliminated
from the air-gap flux in multi-phase machines thus
reducing stray load loss and eliminating some of the
cusps in the torque–speed characteristic. The coil pitch
does not have to be chosen to reduce such harmonics.
Substantial progress has been made in the multiphase induction motor drive research covering analysis,
simulation, hardware development and testing. However, many problems and issues, especially those related
to the development of protection schemes, efficient fault
analysis tools etc, still need to be addressed to brighten
the prospects for broad industrial application of this
new drive technology.
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