[01] levi, e. -- multiphase electric machines for variable-speed applications

8/18/2019 [01] Levi, E. -- Multiphase Electric Machines for Variable-Speed Applications

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 5, MAY 2008 1893

Multiphase Electric Machines forVariable-Speed Applications

Emil Levi, Senior Member, IEEE

Abstract—Although the concept of variable-speed drives, basedon utilization of multiphase (n > 3) machines, dates back to thelate 1960s, it was not until the mid- to late 1990s that multiphasedrives became serious contenders for various applications. Theseinclude electric ship propulsion, locomotive traction, electric andhybrid electric vehicles, “more-electric” aircraft, and high-powerindustrial applications. As a consequence, there has been a sub-stantial increase in the interest for such drive systems worldwide,resulting in a huge volume of work published during the last tenyears. An attempt is made in this paper to provide a brief review of the current state of the art in the area. After addressing the reasonsfor potential use of multiphase rather than three-phase drives and

the available approaches to multiphase machine designs, variouscontrol schemes are surveyed. This is followed by a discussionof the multiphase voltage source inverter control. Various possi-bilities for the use of additional degrees of freedom that exist inmultiphase machines are further elaborated. Finally, multiphasemachine applications in electric energy generation are addressed.

Index Terms—Multiphase electric machines, multiphasevariable-speed drives, multiphase voltage-source inverters (VSIs).

I. INTRODUCTION

VARIABLE-SPEED ac drives are nowadays invariably

supplied from power electronic converters. Since the con-

verter can be viewed as an interface that decouples three-phase

mains from the machine, the number of machine’s phases is not

limited to three any more. Nevertheless, three-phase machines

are customarily adopted for variable speed applications due

to the wide off-the-shelf availability of both machines and

converters. Such a situation is expected to persist in the future

and multiphase variable speed drive utilization is always likely

to remain restricted to specialized niche applications where for

one reason or the other, a three-phase drive does not satisfy the

specification or is not available off-the-shelf either.

The roots of multiphase variable speed drives can be traced

back to the late 1960s, the time when inverter-fed ac drives

were in the initial development stage [1]. Due to the six-

step mode of three-phase inverter operation, one particularproblem at the time was the low frequency torque ripple. Since

the lowest frequency torque ripple harmonic in an n-phasemachine is caused by the time harmonics of the supply of

the order 2n ± 1 (its frequency is 2n times higher than thesupply frequency), an increase in the number of phases of the

Manuscript received February 28, 2007; revised January 16, 2008. This work was supported in part by the Engineering and Physical Sciences ResearchCouncil (EPSRC) under Research Grant EP/C007395/1, in part by Semikron,U.K., in part by Moog, Italy, and in part by Verteco, Finland.

The author is with the School of Engineering, Liverpool John MooresUniversity, Liverpool, L3 3AF, U.K. (e-mail: [email protected]).

Digital Object Identifier 10.1109/TIE.2008.918488

machine appeared as the best solution to the problem. Hence,

significant efforts have been put into the development of five-

phase and six-phase variable-speed drives supplied from both

voltage source and current source inverters [2]–[6]. This is an

advantage of multiphase machines that is nowadays somewhat

less important since pulsewidth modulation (PWM) of voltage-

source inverters (VSIs) enables control of the inverter output

voltage harmonic content. The other main historical reasons for

early developments of multiphase drives, better fault tolerance

and the possibility of splitting the motor power (current) across

a higher number of phases and thus reducing the per-phase (perswitch) converter rating, are nowadays still as relevant as they

were in the early days.

Over the years, many other beneficial features of multiphase

machines and drives have become recognized. The pace of

research started accelerating in the second half of the 1990s,

predominantly due to the developments in the area of electric

ship propulsion, which remains nowadays one of the main

application areas for multiphase variable-speed drives [7]–[12].

A huge body of published work has appeared during the last

decade and an attempt is made in this paper to provide a brief

but up-to-date survey of the current situation, together with

an extensive bibliography. In writing this paper, every effort

has been put into making this review complementary to thealready existing surveys [13]–[16]. Reference [13] discusses

multiphase induction machines. It provides a treatment of the

stator winding layouts for various phase numbers, as well as

a discussion of space harmonics of the magnetomotive force

(MMF). Multiphase drive control schemes were reviewed in

[14] and a table, with reference classification according to the

machine type and phase number, has been provided. A survey

of control schemes for asymmetrical six-phase induction motor

drives and associated methods of VSI PWM control is given

in [15]. Finally, [16] covers multiphase induction machines and

drives in a considerable detail. It includes basic models, con-

trol schemes in developed form, and experimentally obtainedillustrations of performance for various multiphase induction

motor drives (asymmetrical and symmetrical six-phase, and

five-phase machines). It should be noted that all these survey

papers [13]–[16] contain at least some additional references,

when compared to the bibliography given here.

This paper addresses multiphase machines and drives of all

available types (induction and synchronous), with the exception

of switched reluctance machines. The references are grouped

in various subcategories, in accordance with what is perceived

to be their main contribution. Table I illustrates, for quick

reference, relationship between topics covered in this paper and

the references.

0278-0046/$25.00 © 2008 IEEE


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1894 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 5, MAY 2008

TABLE IRELATIONSHIP BETWEEN DISCUSSED TOPICS AND REFERENCES

II. TYPES AND A DVANTAGES OF M ULTIPHASE M ACHINES

FO R V ARIABLE-S PEED D RIVES

The types of multiphase machines for variable-speed applica-

tions are in principle the same as their three-phase counterparts.

There are induction and synchronous multiphase machines,

where a synchronous machine may be with permanent magnet

excitation, with field winding, or of reluctance type. Three-

phase machines are normally designed with a distributed stator

winding that gives near-sinusoidal MMF distribution and issupplied with sinusoidal currents (the exception is the per-

manent magnet synchronous machine with trapezoidal flux

distribution and rectangular stator current supply, known as

brushless dc machine, or simply BDCM). Nevertheless, spatial

MMF distribution is never perfectly sinusoidal and some spatial

harmonics are inevitably present.

Multiphase machines show more versatility in this respect. A

stator winding can be designed to yield either near-sinusoidal

or quasi-rectangular MMF distribution, by using distributed

or concentrated windings, for all ac machine types. Near-

sinusoidal MMF distribution requires use of more than one

slot per pole per phase. As the number of phases increasesit becomes progressively difficult to realize a near-sinusoidal

MMF distribution. For example, a five-phase four-pole machine

requires a minimum of 40 slots for this purpose, while in a

seven-phase four-pole machine at least 56 slots are needed (for

a three-phase four-pole machine the minimum number of slots

is only 24). Multiphase machines where an attempt is made to

realize near-sinusoidal MMF distribution by using an appropri-

ate number of slots are termed henceforth, for simplicity and

brevity, machines with sinusoidal MMF.

In both stator winding designs, there is a strong magnetic

coupling between the stator phases. If the machine is a perma-

nent magnet synchronous machine, then concentrated winding

design yields a behavior similar to a BDCM [159]–[169]. Apermanent magnet multiphase synchronous machine can also

be of so-called modular design where an attempt is made to

minimize the coupling between stator phases, for the reasons

detailed later on (a three-phase permanent magnet machine may

be designed in the same manner, but the most important benefit

of modular design, fault tolerance, is then not exploited to the

full extent). It should be noted that the spatial flux distribution in

permanent magnet synchronous machines (including BDCM)is determined by the shaping of the magnets. Stator current

supply should match the spatial flux distribution in terms of

torque-producing stator current components (harmonics), as ap-

propriate for a given phase number, for optimum performance.

An illustration of the possible stator winding arrangements in

multiphase machines is shown in Fig. 1.

Stator winding of an n-phase machine can be designed insuch a way that the spatial displacement between any two

consecutive stator phases equals α = 2π/n, in which case asymmetrical multiphase machine results. This will always be

the case if the number of phases is an odd prime number.

However, if the number of phases is an even number or an

odd number that is not a prime number, stator winding may

be realized in a different manner, as k windings having asubphases each (where n = a · k). Typically, a = 3 (althougha = 5 exists as well) and k = 2, 3, 4, 5, . . .. In such a case,the spatial displacement between the first phases of the two

consecutive a subphase windings is α = π/n, leading to anasymmetrical distribution of magnetic winding axes in the cross

section of the machine (asymmetrical multiphase machines).

In this multiphase machine type there are k neutral pointsand these are typically kept isolated, for the reasons discussed

later on.

Some of the advantages of multiphase machines, when

compared to their three-phase counterparts, are valid for allstator winding designs while the others are dependent on the

type of the stator winding. Machines with sinusoidal winding

distribution are characterized with [17]–[21] the following.

• Fundamental stator currents produce a field with a lower

space-harmonic content.

• The frequency of the lowest torque ripple component,

being proportional to 2n, increases with the number of phases.

• Since only two currents are required for the flux/torque

control of an ac machine, regardless of the number of

phases, the remaining degrees of freedom can be utilized

for other purposes. One such purpose, available only if themachine is with sinusoidal MMF distribution, is the inde-

pendent control of multimotor multiphase drive systems

with a single power electronic converter supply.

As a consequence of the improvement in the harmonic content

of the MMF, the noise emanated from a machine reduces and

the efficiency can be higher than in a three-phase machine.

In a concentrated winding machine, a possibility of enhanc-

ing the torque production by stator current harmonic injection

exists. Given the phase number n, all odd harmonics in betweenone and n can be used to couple with the correspondingspatial MMF harmonics to yield additional average torque

components. This possibility exists if the phase number is odd,while the only known case where the same is possible for an


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LEVI: MULTIPHASE ELECTRIC MACHINES FOR VARIABLE-SPEED APPLICATIONS 1895

Fig. 1. Illustration of stator windings in multiphase machines:(a) sinusoidally distributed winding (two-pole, five-phase), (b) concentratedwinding (two-pole, five-phase), and (c) modular design (four-phase; crosssection and an actual stator [170] are shown; photograph provided courtesy of B. C. Mecrow of University of Newcastle upon Tyne, U.K.).

even phase number is the asymmetrical six-phase machine with

a single neutral point. Torque enhancement by stator current

harmonic injection is one possible use of the additional degrees

of freedom, offered by the fact that only two currents are

required for flux and torque control due to the fundamentalstator current component.

TABLE IIPOTENTIAL UTILIZATION OF ADDITIONAL DEGREES OF

FREEDOM IN MULTIPHASE MACHINES

All multiphase variable-speed drives share a couple of com-

mon features.

• For the given machine’s output power, utilization of more

than three phases enables splitting of the power across

a larger number of inverter legs, thus enabling use of

semiconductor switches of lower rating.• Due to a larger number of phases, multiphase machines

are characterized with much better fault tolerance than the

three-phase machines. Independent flux and torque control

requires means for independent control of two currents.

This becomes impossible in a three-phase machine if one

phase becomes open-circuited, but is not a problem in

a multiphase machine as long as no more than (n − 3)phases are faulted.

In summary, taking n as an odd prime number and as-suming a single neutral point of the star connected stator

winding, there are (n − 3) additional degrees of freedom in

a multiphase machine that can be used for different purposes:torque enhancement in concentrated winding machines, real-

ization of multimotor drive systems with independent control

and single inverter supply with machines having sinusoidal

MMF distribution, and design of fault-tolerant strategies for

all multiphase machine types. However, the available degrees

of freedom can be used for only one purpose. Hence, if for

example a five-phase concentrated winding induction machine

operates with the third stator current harmonic injection and a

fault takes place, implementation of a fault-tolerant operating

strategy requires that the stator current harmonic injection is

dispensed with. Possible uses of additional degrees of freedom

in different types of multiphase machines (according to thestator winding design of Fig. 1) are summarized in Table II.

The main advantages of multiphase machines when compared

to their three-phase counterpart, discussed previously in this

section, are summarized in Table III.

The main driving forces behind the rapid development

of multiphase variable speed drives in recent times have

been some very specific application areas, in addition to the

aforementioned electric ship propulsion. These are primar-

ily locomotive traction, industrial high-power applications,

electric and hybrid-electric vehicles (propulsion, integrated

starter/alternator concept, and others), and the concept of the

“more-electric” aircraft. Table IV lists some of the applications

for which use of multiphase motor drives has been considered,together with associated references. The common features of


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TABLE IIIOVERVIEW OF MAI N ADVANTAGES OF

MULTIPHASE-MACHINE-BASED DRIVES

TABLE IVMULTIPHASE-MOTOR-DRIVE APPLICATIONS

most of the recent works related to these applications are that

typically high-performance motor control is utilized [vector

control or direct torque control (DTC)] and that the machine’s

supply is VSI based. Hence, this paper predominantly deals

with the review of topics pertinent to such solutions. The

exception is the material covered in Sections VIII (high power

compressors, where synchronous motors supplied from load-

commutated inverters (LCIs) are used) and IX, where other

possibilities are briefly addressed.

Drive systems, aimed at safety-critical applications such as

“more-electric” aircraft, are very specific and utilize the mod-

ular design of both the machine (which is always a permanent

magnet synchronous machine) and the supply system, so that

the stator phases are isolated and independent magnetically,

electrically, thermally and mechanically [170]–[179]. Individ-

ual H-bridge (single-phase) inverters are used for such drives.

In these multiphase drive systems, the available additional de-

grees of freedom are normally used for achieving fault-tolerant

operation of the drive.

III. MODELING OF M ULTIPHASE M ACHINES

General tools for multiphase machine modeling have been

developed in the first half of the 20th century [22]. The well-

known space vector and d−q models of three-phase machinesare only particular cases of the universal n-phase machine

models. Since the phase-variable model of a physical multi-

phase machine gets transformed using a mathematical transfor-

mation, the number of variables before and after transformation

must remain the same. This means that an n-phase machinewill have n new stator current (stator voltage, stator flux)components after the transformation.

If a machine is with sinusoidal-field distribution, standardmodeling assumptions apply and only the first harmonic of

inductance terms exists in the phase-variable model. Appli-

cation of the decoupling (Clarke’s) transformation produces

a set of n equations. The first, α−β , pair is identical to thecorresponding pair of equations for a three-phase machine.

The last equation (or the last two, for even phase numbers) is

the zero-sequence equation, again the same as for a three-phase

machine. In between, there are (n − 3)/2 (or (n − 4)/2 forn = even) pairs of rows which define (n − 3)/2 (or (n − 4)/2for n = even) pairs of equations, featuring the same number of new variables that are termed further on as x−y components.In principle, the form of x−y equations is the same as forthe zero-sequence component, meaning that the impedance for

x−y stator current components is in essence the stator windingleakage impedance. Provided that the machine is supplied

with purely sinusoidal voltages and the field is sinusoidal,

the x−y voltage components are zero and there are no statorcurrent x−y components.

Corresponding decoupling transformation matrices are avail-

able also for asymmetrical multiphase machines and the result

of the application of the decoupling transformation matrix is the

same as for symmetrical machines (for example, the models

obtained by applying appropriate decoupling transformation

matrices in conjunction with an asymmetrical and a symmet-

rical six-phase induction machine are identical, as long as thereis a single neutral point). In the special case when an n-phasewinding is created using k individual a subphase windings withk isolated neutral points, the total number of equations andvariables reduces to (n − k) after transformation, since zero-sequence components cannot flow in any of the star-connected

k windings.Since coupling between stator and rotor appears after de-

coupling transformation only in α−β equations of the mul-tiphase machine, it is only these equations that have to be

transformed further, using rotational transformation. The form

of this transformation is the same as for the corresponding

three-phase machine. The resulting final d−

q model in thecommon reference frame contains d−q and torque equationsidentical to those of a corresponding three-phase machine, zero-

sequence equations that are also the same, and, additionally,

the x−y pair(s) of equations that, in form, correspond to zero-sequence equations.

Modeling of multiphase machines has been and still is a

subject of considerable interest [23]–[36]. A great deal of effort

has been put into modeling of concentrated winding machines,

where both the starting physical-variable model and the final

d−q model are different. In principle, the inductance termsin the initial model have to include not only the fundamental

harmonic but also one (or more, as appropriate for the given

phase number) higher harmonics. Decoupling transformationresults now in (n − 1)/2 (or (n − 2)/2 for n = even) pairs


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of equations (variables) that are again mutually decoupled but

correspond, in form, to the α−β equations, since stator to rotorcoupling appears in all of them. Consequently, an appropriate

rotational transformation has now to be applied to all equations

(except for the zero-sequence components) and the final d−q model contains (n − 1)/2 pairs of equations of the form valid

for d−q equations of a three-phase machine. Torque equationhas now, in addition to the component due to the fundamental

stator current, (n − 3)/2 new components, each of which is dueto the interaction of a certain stator current harmonic and the

corresponding spatial harmonic of the field.

If an n-phase machine with sinusoidal winding distributionis formed by using k three-phase (a = 3) stator windings,then a rather different modeling approach can be used. It is

based on the observation that each three-phase winding can be

replaced with an equivalent d−q winding, so that the completen-phase machine model then contains k pairs of d−q equations.As a consequence, the torque equation is a sum of individual

contributions of each of the three-phase windings. Such a

modeling approach [31], [32] is widely used in conjunction

with asymmetrical six-phase machines in the development of

vector control schemes [15].

Basic transformation equations, as well as the resulting

mathematical models of multiphase induction machines with

sinusoidal winding distribution and with concentrated stator

winding are available in [16].

As far as modeling of modular permanent magnet synchro-

nous machines is concerned, it corresponds closely to the

procedure described in conjunction with machines with sinu-

soidal field distribution. The difference is in the absence of the

mutual inductance terms within the stator winding, since these

are deliberately eliminated by virtue of the machine’s design(basically, winding of one phase occupies two consecutive slots

[Fig. 1(c)] so that the phases are isolated).

IV. CONTROL OF M ULTIPHASE V ARIABLE-S PEED D RIVES

The methods of speed control of multiphase machines are

in principle the same as for three-phase machines. Constant

V/f control is nowadays of relatively little interest, since the

cost of implementing more sophisticated control algorithms is

negligible compared to the cost of multiphase power electronics

and the multiphase machine itself (neither are available on the

market). The emphasis is therefore placed further on vectorcontrol and DTC.

As long as a symmetrical multiphase machine with sinu-

soidally distributed stator winding is under consideration, the

same vector control schemes as for a three-phase machine are

directly applicable regardless of the number of phases [37]–

[51]. The only difference is that the coordinate transformation

has to produce an n-phase set of stator current (or statorvoltage) references, depending on whether current control is in

the stationary or in the synchronous rotating reference frame.

If current control is in the stationary reference frame, (n − 1)stationary current controllers (assuming stator winding with

a single neutral point) are required. Either phase currents or

phase current components in the stationary reference frame canbe controlled and here the standard ramp-comparison current

Fig. 2. Basic rotor fluxorientedcontrol schemefor a multiphase machine withcurrent control in the stationary reference frame.

Fig. 3. Basic rotor-flux-oriented control of a five-phase machine with con-centrated winding and with current control in the stationary reference frame(indexes 1 and 3 stand for the first and the third stator current harmonicreferences).

control method offers the same quality of performance as with

three-phase drives. Assuming that indirect vector control is

used, basic rotor-flux-oriented control scheme of an n-phaseinduction or synchronous machine (permanent magnet or syn-

chronous reluctance) with sinusoidal MMF distribution is of the

form shown in Fig. 2. The block “vector controller” is identical

to the one for the three-phase machine of the same type and

the value of the stator d-axis current reference depends on the

machine type (as does the transformation angle as well). Forexample, “vector controller” for a surface-mounted permanent

magnet synchronous machine is just a speed controller, stator

d-axis current reference is zero and transformation angle is therotor position angle. In the case of an induction machine, stator

d-axis current reference is the rated magnetizing current, while“vector controller” includes a speed controller, calculation of

the angular slip speed and calculation of the transformation

angle by summation of the slip angle and rotor position angle.

If current control is in the rotating reference frame, then it

would appear that only two current controllers are sufficient

since torque production is governed only by d−q stator current

components. However, since an n-phase machine essentiallyhas (n − 1) independent currents (or (n − k) in the case of the n-phase winding being formed of k identical a subphasewindings with isolated neutral points), utilization of only two

current controllers is in practice not sufficient, since winding

and/or supply asymmetries lead to the unbalanced load shar-

ing and effective flow of undesired x−y current components.Application of the current control in synchronous reference

frame also requires an adequate method of inverter PWM

control in order to avoid creation of unwanted low-order stator

voltage harmonics that map into voltage x−y components (asdiscussed in the next section) and therefore lead to the flow of

large stator current x−y current components. The problem of

winding/supply asymmetry is well documented for the asym-metrical six-phase induction machine (with two isolated neutral


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Fig. 4. Illustration of DTC schemes for multiphase machines: (a) Switching-table-based DTC and (b) constant switching frequency DTC.

points) and it is in principle necessary to employ four current

controllers rather than a single pair of d−q current controllers.If a concentrated winding machine is used, torque can be

enhanced using low-order stator current harmonic injection[52]–[54]. Hence, the vector control scheme has to be modified

accordingly [55]–[69]. The injected low-order stator current

harmonics are firmly tied to the fundamental in terms of

magnitude, frequency and phase and the major modification

of the vector control scheme consists in calculating the refer-

ences for these harmonics (on the basis of the fundamental)

and on utilization of the modified rotational transformation.

Vector control schemes have to utilize again (n − 1) currentcontrollers. Vector control of concentrated winding machines

is well-documented in literature for five-phase induction, per-

manent magnet synchronous, and synchronous reluctance ma-

chines, where torque enhancement is provided by the third

harmonic injection. Similarly, third harmonic injection can be

used in asymmetrical six-phase machines [58]–[61]. In a seven-

phase machine both the third and the fifth harmonic can be

used to improve torque per ampere characteristic [64], while

with a nine-phase machine injection of the third, the fifth,

and the seventh harmonic is possible [56]. A conceptual block

diagram of a rotor flux oriented control scheme for a five-

phase machine, assuming again current control in the stationary

reference frame, is shown in Fig. 3. The block “vector con-

troller” now additionally includes partitioning of the overall

torque reference (obtained at the output of the speed controller)

into the stator q -axis current references for the first and the

third stator current harmonic, as well as the calculation of the transformation angles for the first and the third harmonic.

Notice that the “rotational transformation” block in Fig. 3 is

different from the corresponding one in Fig. 2 (see [16]). The

outputs of this block are now four stator current components

(rather than just two as shown in Fig. 2), which reflect thedesired first and the third stator current harmonic.

There are two basic approaches to DTC of three-phase

machines. Hysteresis stator flux and torque controllers can be

used in conjunction with an optimum stator voltage vector

selection table, leading to a variable switching frequency. Alter-

natively, the inverter switching frequency can be kept constant

by applying an appropriate method of inverter PWM control

(usually space vector PWM). In principle, both approaches

are also applicable to multiphase machines [70]–[77] and are

shown in Fig. 4. However, there are some important differences,

predominantly caused by the existence of additional degrees

of freedom in multiphase machines (x−

y components). If a

multiphase machine is with sinusoidal MMF distribution, the

DTC scheme needs to apply sinusoidal voltages to the ma-

chine’s stator winding (neglecting PWM ripple), without any

unwanted low-order frequency components (since these excite

x−y circuits, as explained in the next section). With constantswitching frequency DTC, this problem can be solved relatively

easily. It is only necessary to apply one of the PWM methods

that will provide inverter operation with sinusoidal (or at least

near-sinusoidal) output voltages.

A problem that is encountered in hysteresis-based DTC

schemes for sinusoidal multiphase machines is that optimum

stator voltage vector selection table, designed in the same man-

ner as for a three-phase induction machine, dictates applicationof a single space vector in one (variable) switching period.


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However, each individual inverter output voltage space vector

inevitably leads to generation of unwanted low-order harmon-

ics, which excite x−y stator circuits and lead to large unwantedstator current low-order harmonics. This problem has so far

not been solved completely although a significant improvement

has been reported for an asymmetrical six-phase induction

machine in [74]. The solution is based on modifications of the basic hysteresis-based DTC and it requires introduction of

additional hysteresis controllers, thus increasing substantially

the complexity of the control scheme (and therefore negating

the main advantage of DTC when compared to vector control,

relative simplicity).

If the multiphase machine is with a concentrated stator

winding, hysteresis-based DTC can be utilized without any

modifications, using optimum stator voltage vector selection

table with large vectors only. This is so since in this case at

least some of the low-order harmonics actually lead to torque

enhancement by higher stator current harmonic injection. For

example, in a five-phase machine, utilization of only large

inverter vectors generates the third harmonic, causing flow of

the third stator current harmonic. However, since the winding is

concentrated, the third current harmonic couples with the third

field harmonic and produces an average torque, thus yielding an

automatic enhancement of the overall torque.

A more detailed description of the control schemes shown

in Figs. 2–4 and their detailed outlay for multiphase induction

motor drives is available in [15] and [16] for asymmetrical six-

phase and five-phase induction machines, respectively.

V. MULTIPHASE VSI CONTROL

By and large, the existing research related to PWM controlof multiphase inverters applies to two-level inverters [78]–

[117] [Fig. 5(a) and (c)]. The most straightforward approach

is undoubtedly utilization of the carrier-based PWM methods.

Similar to the carrier-based PWM with third harmonic injection

for a three-phase VSI, it is possible to improve the dc bus

utilization in multiphase VSIs by injecting the appropriate zero-

sequence harmonic (or adding the offset) into leg voltage ref-

erences. As the number of phases increases, the improvement

in the dc bus utilization by zero-sequence harmonic injection

rapidly reduces. The gain in the maximum fundamental in the

linear modulation region is only 5.15% for the five-phase VSI,

while it is 15.47% in a three-phase VSI. Table V illustrates theimprovement in the dc bus utilization as a result of the zero-

sequence injection, for various odd phase numbers. Carrier-

based PWM is also suitable for control of concentrated winding

machines, where in addition to the fundamental and zero-

sequence voltage, references also need to contain a certain

amount of specified low-order harmonic(s) aimed at providing

torque enhancement. In principle, carrier-based PWM can be

used without any problems for generation of multifrequency

output voltages with any number of components.

Space-vector PWM is undoubtedly the most popular method

as far as the three-phase inverters are concerned. However,

as the number of phases of the inverter increases, the avail-

able number of inverter output voltage space vectors changesaccording to the law 2n, since there are 2n different switch-

Fig. 5. Basic building blocks for VSI supplied multiphase machines: (a) Legof a two-level inverter; (b) leg of a three-level NPC inverter; and (c) H-bridgesupply. For an n-phase machine, legs of the type shown in (a) or (b) arecombined into an n-phase bridge inverter or n individual H-bridge invertersof (c) are used.

TABLE VPERCENTAGE INCREASE IN THE FUNDAMENTAL OUTPUT VOLTAGE

OBTAINABLE WIT H ZERO -SEQUENCE INJECTION

ing configurations. This means that, as the number of phases

increases, the problem of devising an adequate space vector

PWM scheme becomes more and more involved. On the other

hand, space-vector PWM offers a good insight into VSI op-

eration. The available 2n switching configurations define 2n

space vectors that map into (n − 1)/2 planes (n is taken as

an odd number in this section). These planes correspond toα−β and x−y pairs of components. Harmonics of the order


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TABLE VIHARMONIC MAPPING INTO DIFFERENT PLANES FOR FIV E-PHASE AND

SEVEN-PHASE SYSTEMS ( j = 0, 1, 2, 3, . . .)

2 jn ± 1( j = 0, 1, 2, . . .) map into the first, α−β plane, whileall the other harmonics map into the other (n − 3)/2 planes.For example, for a five-phase VSI, harmonics of the order

10 j ± 3( j = 0, 1, 2, . . .) map into the (single) x−y plane. Anillustration of the harmonic mapping in five-phase and seven-

phase systems is given in Table VI (harmonics in bold denote

those that are available for average torque production in con-

centrated winding machines). Since machines with sinusoidal

MMF distribution have very small impedance for x−y voltagecomponents, it is imperative that space vector PWM does

not generate such harmonics, since only the first harmonic is

available for the torque production.

If the goal is to generate purely sinusoidal voltages, then the

reference voltage space vector appears only in the α−β plane,while references in all x−y planes are zero. To get at the outputdesired sinusoidal voltages using space vector PWM, it is

necessary to use in one switching period (n − 1) active vectorsneighboring the reference. Duty cycles can be calculated using

either analytical expressions (similar to the well-known ones

for a three-phase VSI) or online solution of an appropriate

system of equations. Sinusoidal output voltage generation using

space vector PWM has been reported for five-phase, seven-phase, nine-phase, and six-phase VSIs. If the multiphase VSI

is used to supply a concentrated winding machine, then in

addition to the reference voltage space vector in the α−β planethere will be nonzero reference voltage space vector(s) in other,

x−y plane(s). These references are firmly tied to the referencein the α−β plane with regard to amplitude, frequency, andphase. Since the amplitude of the reference(s) in x−y plane(s)is considerably smaller than the amplitude of the reference

in the α−β plane, the desired reference voltages can still besynthesized by selecting the same set of active space vectors

as for the case of purely sinusoidal output voltage generation.

Typically, an online solution to the set of n algebraic equationsis required to calculate application times of the (n − 1) activevectors and the zero vector.

Selection of the active vectors according to the described

principle (i.e., by considering only the reference in the α−β plane) automatically restricts the achievable voltage in the

other, x−y planes. While this is not a problem when only a sin-gle multiphase machine (with either sinusoidal or concentrated

winding) is supplied, it means that it is not possible to generate

multifrequency output voltages required for normal operation

of multimotor multiphase drives with single inverter supply, of

the type discussed in Section VII.

Carrier-based PWM with zero-sequence injection and space-

vector PWM are exact equivalents in the three-phase case,which simultaneously enable both full dc bus utilization and

Fig. 6. Double-sided supply of an n-phase machine with an open-end sta-tor winding structure using VSIs of m and l levels at two winding ends,respectively.

stator current ripple minimization. The same kind of equiva-

lence exists in the PWM of multiphase VSIs. However, full

dc bus utilization is not possible if purely sinusoidal output

voltages are required. In addition, zero-sequence injection,

explicitly present in the carrier-based PWM and implicitly in

the space-vector PWM, although giving the maximum achiev-

able output voltage in the linear modulation region, does notminimize the current ripple [111], [112]. Stator current ripple

minimization requires a different approach to the selection of

the active space vectors, based on selecting the closest vectors

to the reference with due regard for the reference voltage

amplitude (rather than selection purely based on the reference

belonging to a given sector).

Multilevel inverters [Fig. 5(b)] for multiphase variable speed

drives appear to be a natural solution for high-power induction-

motor drives, such as those aimed at electric ship propulsion

[118]–[120] or locomotive traction [121]. A rather different

application, for microelectromechanical systems, is elaborated

in [122], where a six-phase machine supplied form five-levelinverter is used. Configurations considered in the existing lit-

erature are typically either H-bridge based or of neutral-point

clamped (NPC) inverter type [118]–[125]. Another approach to

realizing multilevel supply for a multiphase machine consists

of the use of an open-end stator winding machine, supplied

at both ends from a two-level VSI. Such an approach has so

far been considered only in conjunction with asymmetrical six-

phase machine [126], [127]. A set of four two-level three-phase

VSIs is used, configured into two six-phase VSIs, connected

at each side of the stator winding. Three-phase motor drives

with the open-end winding structure and double-sided sup-

ply are currently being investigated extensively as a potential

advanced solution for high-power applications. It is therefore

anticipated that more work will be done in conjunction with

the applicability of this supply arrangement for high-power

multiphase motor drives in the near future. In principle, two

inverter systems at the two sides of the open-end winding can be

of the same or different number of levels, which can be two or

more. The concept is shown in Fig. 6 for an n-phase machine.Two inverters are of bridge structure and can utilize inverter

legs, as shown in Fig. 5(a) and (b), as the basic building blocks.

VI. FAULT-T OLERANT O PERATION

One of the most important properties of multiphase machinesis their ability to continue to operate after the loss of one


9/17


(or more) phase(s) without problems, something that cannot

be achieved with three-phase machines. Under the faulted

phase(s) conditions, the available degrees of freedom that exist

in multiphase machines are effectively utilized for an appropri-

ate postfault operating strategy. Behavior of multiphase drives

in faulted operation and development of postfault operating

strategies, in conjunction with sinusoidal and concentratedwinding machines, is covered in [128]–[158], while similar

considerations related to the permanent-magnet machines of

modular design can be found in [170]–[179].

The analysis of the fault impact is most frequently based on

simulations using models of the type described in Section III.

Such relatively simple circuit modeling usually suffices for the

studies related to the design of postfault operating strategies. It

is also possible to use more complex machine representations

in fault studies, such as, the dynamic reluctance mesh model

[137], or generalized harmonic analysis [138].

The basic idea of all fault-tolerant strategies is that a mul-

tiphase machine can continue to operate with a rotating field

as long as no more than (n − 3) phases are faulted. How thestrategies are actually developed and implemented depends to

a large extent on the application of the multiphase drive. The

simplest case arises in multiphase machines with k windings of a subphases each, with k isolated neutral points. If one phasefails, the complete a subphase winding, in which the fault hastaken place, is taken out of service. For example, in the case

of a six-phase machine with two isolated neutrals, if one phase

fails the whole three-phase winding is taken out of service. The

machine can however continue to operate without any control

algorithm modification using the remaining healthy three-phase

winding, of course with the available torque reduced to one

half of the rating (assuming no increase in the current in thehealthy phases). This is a perfectly satisfactory solution in,

for example, traction applications [129], [130]. Similarly, the

15-phase induction machine for ship propulsion of [7] and [8],

configured with three five-phase stator windings, can continue

to operate with one or even two five-phase windings discon-

nected from the supply due to faults. Taking out of service the

whole a subphase winding results, in these applications, in asimple slowing down of a ship, train, or a vehicle.

Such a simple postfault operating strategy does not suffice for

safety-critical applications, such as for example fuel pump for

“more-electric” aircraft. Single neutral point now gives better

characteristics in postfault operation than the configuration withk isolated neutral points. This is so since the single neutralpoint enables utilization of all the remaining healthy phases

for postfault control, while in the case of the isolated neutral

points the complete faulty a subphase winding(s) is(are) takenout of service. In this case, the control algorithm of the drive has

typically to be reconfigured in the software, so that a new set of

current references is generated for the remaining healthy phases

after disconnection of the faulty phase(s). Since it is desirable

now to continue to operate with a rotating field although one (or

more) phase(s) is not available any more, the new set of currents

becomes inevitably asymmetrical, meaning that the available

degrees of freedom are used for postfault operation (i.e., the

x−y current components become of nonzero values). Hence,for example in a concentrated winding five-phase machine,

TABLE VIIIMPACT OF THE POSTFAULT STRATEGY ON MULTIPHASE INDUCTION

MOTOR DRIVE POSTFAULT OPERATION

torque enhancement by stator current harmonic injection is not

available any more for postfault operating conditions.

The impact of the postfault operating strategy on the drive

behavior depends on both the operating point and on the

characteristics of the load torque (speed-dependent or speed-

independent). Suppose that one phase is open-circuited. One

possible criterion for postfault operation can be that the ma-

chine’s torque remains of the same value as before the fault and

without any pulsations (strategy 1). While this is in principle

possible with multiphase machines, one inevitable consequence

is the increase of the current amplitude in the remaining healthy

phases over the prefault value, by a factor n/(n − 1). Thisleads to an increase in the stator winding loss and may cause

overheating if the operation is sustained for a prolonged period

of time. In addition, the semiconductor switches of the power

electronic converter must be able to withstand operation with

an increased current level. Alternatively, one may wish to keep

the stator winding losses at the prefault level (strategy 2). Thisallows for an increase in the current magnitude in the remaining

healthy phases by a factor of

n/(n − 1), but simultaneouslyreduces the available output torque at any given speed. Finally,

one may wish to continue to operate the machine without

any change of the currents in the remaining healthy phases

(strategy 3). This will lead to both stator winding loss reduction

and torque reduction.

A qualitative impact of these three strategies on postfault

operation is illustrated in Table VII for a multiphase induction

motor drive. It is assumed that one phase is open-circuited

and that the load torque is proportional to the speed squared

(corresponding quantitative data for prefault slip of 0.01,as a function of the machine’s phase number, are available

in [16]).

While by and large postfault operating strategies require

software reconfiguration only, meaning that the faulty phase(s)

is not supplied any more, control algorithm modification (soft-

ware reconfiguration), can be combined with hardware recon-

figuration if the reason for the loss of supply to a phase is not a

fault within the machine itself [131]. For example, in the case of

a fault of one inverter leg in a six-phase motor drive, the phase

that would be left without supply in postfault operation if only

software reconfiguration were applied gets connected to one of

the remaining healthy inverter legs (so that two motor phases

are now supplied form the same inverter leg) using additionalsemiconductors (triacs) for this reconfiguration [131].


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VII. MULTIMOTOR M ULTIPHASE V ARIABLE-S PEED

DRIVES W IT H S INGLE I NVERTER S UPPLY

As already emphasized, flux and torque control of a mul-

tiphase machine requires only two currents regardless of the

number of phases. How the remaining degrees of freedom can

be utilized for torque enhancement in concentrated winding

machines, using stator current harmonic injection, and for de-

velopment of postfault operating strategies, has been addressed

in Sections IV and VI, respectively. An entirely different utiliza-

tion of the remaining degrees of freedom is however possible

with multiphase machines having sinusoidal field distribution

(Table II). A certain number of machines can be connected in

series, using an appropriate transposition in the connection of

the machines’ phases, in such a manner that flux/torque pro-

ducing (d−q ) currents of one machine appear as nonflux/torqueproducing (x−y) currents for all the other machines and viceversa. The idea has been floated for the first time in [180] in

conjunction with two-motor five-phase series-connected two-

motor drive and is shown in Fig. 7(a) at a conceptual level foran n-phase supply. However, the origins can be traced back to[181], where a symmetrical six-phase machine was considered

and the phases were supplied with two current components.

One of these was generating flux and torque, while the second

one was creating forces required for bearing relief, without

impacting on the machine’s flux and torque production.

The concept of series connection using phase transposition

enables completely independent control of all the machines al-

though a single multiphase inverter is used as the supply. Vector

control is applied in conjunction with every machine in the

group and the inverter is required to generate a multifrequency

output voltage for the supply of the complete drive system. Suchmultimotor drive systems are possible for symmetrical multi-

phase machines with both an even and an odd supply phase

numbers and they have been investigated in a considerable

depth in [182]–[198]. The number of machines connectable in

series is at most w = (n − 2)/2 for even supply phase numbersand w = (n − 1)/2 for odd supply phase numbers. Whether ornot all the series-connected machines are of the same phase

number depends on the supply phase number. The possibility

of series connection exists also in the case of asymmetrical

machines and it has been so far developed for the asymmetrical

six-phase case and asymmetrical nine-phase case. The asym-

metrical six-phase supply enables series connection of either

two asymmetrical six-phase machines or one asymmetrical six-

phase machine and a two-phase machine. The latter possibility

has a drawback in that it requires the neutral of the drive system

to be connected either to the seventh inverter leg or to the

midpoint of the dc link. On the other hand, the properties of the

former are practically the same as for the two-motor five-phase

drive. The concept is independent of the machine type and has

been studied using induction, permanent-magnet synchronous,

and synchronous reluctance machines.

From the application point of view, two potentially viable

solutions appear to be two-motor series-connected five-phase

(or asymmetrical six-phase, comprising two asymmetrical six-

phase machines) and symmetrical six-phase two-motor drives.In the symmetrical six-phase configuration, the second machine

is three-phase and it is not in any way affected by the series

connection. Since flux/torque producing currents of the three-

phase machine flow through the six-phase machine’s stator

winding, impact of the series connection on the efficiency of

the six-phase machine will be negligible provided that the six-

phase machine is of a considerably higher rating than the three-

phase machine.In contrast to this, in five-phase and asymmetrical six-phase

configurations, both machines are affected by the series con-

nection since flux/torque producing currents of each machine

flow through both machines. Hence, the potential applicability

of this configuration is related to either two-motor drives where

the two machines never operate simultaneously or where the

operating conditions are at all times very different (for example,

two-motor center driven winder drives). However, the efficiency

of such a two-motor drive will always be lower than in a

corresponding two-motor drive with two independent VSIs as

the supply.

It is also possible to connect the multiphase machines in

parallel instead of in series [Fig. 7(b)]. Using the same idea of

phase transposition, independent control can again be achieved

[199], [200]. However, parallel connection can only be realized

when the system (VSI) number of phases is an odd prime

number. While parallel connection looks more attractive than

the series connection at first sight, it suffers from some serious

disadvantages that make it far inferior to the series connec-

tion. First of all, the dc-link voltage in the series connection

is split across machines connected in series, while in paral-

lel connection each of the machines is subjected to the full

dc-link voltage (dc-link voltage has to be increased by the same

amount, regardless of whether machines are connected in series

or in parallel). Even more importantly, in series connection allinverter current components are directly controlled and there-

fore known. In contrast to this, in parallel connection it is the

inverter voltage components that are directly controlled, leading

to essentially uncontrollable stator x−y current componentsin the machines of the group. The net result is that, although

fully decoupled dynamic control of all the machines of the

multimotor drive is possible using both series and parallel

connection, it is only the series connection that holds some

prospect for industrial applications.

VIII. MULTIPHASE M ACHINES IN

ELECTRIC-E NERGY G ENERATION

Potential utilization of multiphase (in essence, six-phase)

synchronous generators was considered extensively in the

1970s and 1980s [201]–[208]. The perceived applications

were related predominantly to uninterruptible-power-supply

systems. A similar but permanent-magnet-based synchronous

generator configuration has also been analyzed more recently

in conjunction with high-power high-speed systems for rectifier

load supply [209].

In recent times, interest in the use of multiphase generators

has reappeared, in conjunction with renewable electric-energy

generating sources [210]–[215]. It needs to be emphasized

though that there is no evidence at present of any indus-trial uptake of such solutions. Permanent-magnet synchronous


11/17


Fig. 7. Concept of multimotor multiphase drive systems with single inverter supply and independent control: (a) Series and (b) parallel connection.

multiphase generators [210]–[212] may become a viable solu-

tion for the direct-driven applications in wind-powered plants,

while multiphase induction generators with multiple three-

phase windings may have a prospect for applications in stand-

alone self-excited generating systems in rural areas [213] andlow-power hydroelectric plants [214].

A somewhat specific use of machines with more than three-

phases is met in Lundell alternators, aimed at the generation of

two independent dc voltages for automotive applications [216],

[217]. Typically, the machine is designed with two independent

three-phase windings which may [216] or may not [217] havestrong magnetic coupling. However, since the outputs of the


12/17


three-phase windings are kept independent and are individually

rectified, these machines are better described as “dual-stator”

machines than as multiphase machines (although the design of

the machine may be such that the stator winding is in essence a

six-phase winding).

IX. OTHER M ULTIPHASE M OTOR D RIVE S OLUTIONS

Multiphase variable-speed drives, discussed so far, are pre-

dominantly based on utilization of VSIs (as noted, current

source inverters were also considered in the early days of

the multiphase motor drive development [5], [6]). A different

solution is however used in conjunction with high-power syn-

chronous motors for pumps and compressors. Indeed, one of

the first actual applications of a multiphase electric drive was

aimed at such an application [218] and it was based on utiliza-

tion of an asymmetrical six-phase synchronous motor. High-

power multiphase synchronous motors for such applications

are usually supplied from current-source thyristor-based 12-

pulse LCIs [219], [220]. Typically, two three-phase windings

are displaced by 30◦ and supplied by two independent three-

phase LCIs, which receive dc current from two three-phase rec-

tifiers [219]. The rectifier input comes from a transformer with

star/delta connected dual secondary. Such multiphase drives are

of more than 10-MW rating and utilization of a multiphase

machine enables splitting of the power across more than three

phases, thus reducing the required rating of the semiconductor

components.

In addition to the mainstream trends in the development

of multiphase machines for variable-speed drive applications,

along which this paper has been organized, there are also some

very specific solutions [221]–[229] that do not fit any of themain categories. In majority of cases, the intended application is

automotive [223]–[228]. Potential multiphase-machine-based

solutions for integrated starter/alternator applications are elab-

orated in [226] and [227], while potential application of a six-

phase induction motor for electric power steering is discussed

in [228].

X. CONCLUSION

Variable-speed electric drives, based on utilization of multi-

phase machines, have been known for half a century. A sub-

stantial growth in this area has been witnessed during the last

decade, due to the developments in some specific application

areas. An attempt has been made in this paper to provide a brief

review of the state of the art in multiphase variable-speed drives,

as well as an up-to-date and exhaustive bibliography.

The main aspects of the multiphase variable-speed drives

have been surveyed. These have included, to start with, types

of multiphase machines, modeling, and control. Next, PWM

methods for multiphase VSI PWM have been reviewed. Uti-

lization of the additional degrees of freedom, available with

multiphase machines, for the design of postfault operating

strategies and for multimotor multiphase drives with single

inverter supply, has been further covered. Finally, the potential

of multiphase machines for electric-energy generation is brieflyaddressed.

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[01] levi, e. -- multiphase electric machines for variable-speed applications

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