[01] Levi, E. -- Multiphase Electric Machines for Variable-Speed Applications

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

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Multiphase Electric Machines for Variable-Speed Applications Emil Levi, Senior Member, IEEE

Abstract—Although the concept of variable-speed drives, based on utilization of multiphase (n > 3) machines, dates back to the late 1960s, it was not until the mid- to late 1990s that multiphase drives became serious contenders for various applications. These include electric ship propulsion, locomotive traction, electric and hybrid electric vehicles, “more-electric” aircraft, and high-power industrial applications. As a consequence, there has been a substantial increase in the interest for such drive systems worldwide, resulting in a huge volume of work published during the last ten years. 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 reasons for potential use of multiphase rather than three-phase drives and the available approaches to multiphase machine designs, various control schemes are surveyed. This is followed by a discussion of the multiphase voltage source inverter control. Various possibilities for the use of additional degrees of freedom that exist in multiphase machines are further elaborated. Finally, multiphase machine applications in electric energy generation are addressed. Index Terms—Multiphase electric machines, multiphase variable-speed drives, multiphase voltage-source inverters (VSIs).

I. I NTRODUCTION

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ARIABLE-SPEED ac drives are nowadays invariably supplied from power electronic converters. Since the converter 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 sixstep mode of three-phase inverter operation, one particular problem at the time was the low frequency torque ripple. Since the lowest frequency torque ripple harmonic in an n-phase machine is caused by the time harmonics of the supply of the order 2n ± 1 (its frequency is 2n times higher than the supply 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 Research Council (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 Moores University, 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 fivephase 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 voltagesource 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 (per switch) 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 the already 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, control schemes in developed form, and experimentally obtained illustrations 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.

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TABLE I RELATIONSHIP BETWEEN DISCUSSED TOPICS AND REFERENCES

II. T YPES AND A DVANTAGES OF M ULTIPHASE M ACHINES FOR V ARIABLE -S PEED D RIVES The types of multiphase machines for variable-speed applications 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. Threephase machines are normally designed with a distributed stator winding that gives near-sinusoidal MMF distribution and is supplied with sinusoidal currents (the exception is the permanent 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. Nearsinusoidal MMF distribution requires use of more than one slot per pole per phase. As the number of phases increases it 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 appropriate 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 permanent magnet synchronous machine, then concentrated winding design yields a behavior similar to a BDCM [159]–[169]. A permanent 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 appropriate 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 in such a way that the spatial displacement between any two consecutive stator phases equals α = 2π/n, in which case a symmetrical 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 a subphases each (where n = a · k). Typically, a = 3 (although a = 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 an asymmetrical distribution of magnetic winding axes in the cross section of the machine (asymmetrical multiphase machines). In this multiphase machine type there are k neutral points and 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 all stator 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 the machine is with sinusoidal MMF distribution, is the independent 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 enhancing the torque production by stator current harmonic injection exists. Given the phase number n, all odd harmonics in between one and n can be used to couple with the corresponding spatial 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

LEVI: MULTIPHASE ELECTRIC MACHINES FOR VARIABLE-SPEED APPLICATIONS

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TABLE II POTENTIAL UTILIZATION OF ADDITIONAL DEGREES OF FREEDOM IN MULTIPHASE MACHINES

All multiphase variable-speed drives share a couple of common 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.

Fig. 1. Illustration of stator windings in multiphase machines: (a) sinusoidally distributed winding (two-pole, five-phase), (b) concentrated winding (two-pole, five-phase), and (c) modular design (four-phase; cross section 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 fundamental stator current component.

In summary, taking n as an odd prime number and assuming 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, realization 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 the stator 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 primarily 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 III OVERVIEW OF MAIN ADVANTAGES OF MULTIPHASE-MACHINE-BASED DRIVES

TABLE IV MULTIPHASE-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 loadcommutated 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 modular 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]. Individual H-bridge (single-phase) inverters are used for such drives. In these multiphase drive systems, the available additional degrees of freedom are normally used for achieving fault-tolerant operation of the drive. III. M ODELING OF M ULTIPHASE M ACHINES General tools for multiphase machine modeling have been developed in the first half of the 20th century [22]. The wellknown space vector and d−q models of three-phase machines are only particular cases of the universal n-phase machine

models. Since the phase-variable model of a physical multiphase machine gets transformed using a mathematical transformation, the number of variables before and after transformation must remain the same. This means that an n-phase machine will have n new stator current (stator voltage, stator flux) components after the transformation. If a machine is with sinusoidal-field distribution, standard modeling assumptions apply and only the first harmonic of inductance terms exists in the phase-variable model. Application of the decoupling (Clarke’s) transformation produces a set of n equations. The first, α−β, pair is identical to the corresponding 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 for n = even) pairs of rows which define (n − 3)/2 (or (n − 4)/2 for 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 for the zero-sequence component, meaning that the impedance for x−y stator current components is in essence the stator winding leakage 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 stator current x−y components. Corresponding decoupling transformation matrices are available 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 symmetrical six-phase induction machine are identical, as long as there is a single neutral point). In the special case when an n-phase winding is created using k individual a subphase windings with k isolated neutral points, the total number of equations and variables reduces to (n − k) after transformation, since zerosequence components cannot flow in any of the star-connected k windings. Since coupling between stator and rotor appears after decoupling transformation only in α−β equations of the multiphase 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 the common reference frame contains d−q and torque equations identical to those of a corresponding three-phase machine, zerosequence equations that are also the same, and, additionally, the x−y pair(s) of equations that, in form, correspond to zerosequence 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 terms in 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 transformation results now in (n − 1)/2 (or (n − 2)/2 for n = even) pairs


of equations (variables) that are again mutually decoupled but correspond, in form, to the α−β equations, since stator to rotor coupling 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 equation has now, in addition to the component due to the fundamental stator current, (n − 3)/2 new components, each of which is due to the interaction of a certain stator current harmonic and the corresponding spatial harmonic of the field. If an n-phase machine with sinusoidal winding distribution is 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 complete n-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 synchronous machines is concerned, it corresponds closely to the procedure described in conjunction with machines with sinusoidal 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. C ONTROL 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 vector control and DTC. As long as a symmetrical multiphase machine with sinusoidally 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 stator voltage) 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 can be controlled and here the standard ramp-comparison current

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Fig. 2. Basic rotor flux oriented control scheme for a multiphase machine with current control in the stationary reference frame.

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

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-phase induction or synchronous machine (permanent magnet or synchronous 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). For example, “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 the rotor 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 essentially has (n − 1) independent currents (or (n − k) in the case of the n-phase winding being formed of k identical a subphase windings 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 sharing 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 (as discussed 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 asymmetrical 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 references 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) current controllers. Vector control of concentrated winding machines is well-documented in literature for five-phase induction, permanent magnet synchronous, and synchronous reluctance machines, 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 sevenphase 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 fivephase machine, assuming again current control in the stationary reference frame, is shown in Fig. 3. The block “vector controller” 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 the desired 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. Alternatively, 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 machine’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 constant switching 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 manner as for a three-phase induction machine, dictates application of 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 harmonics, which excite x−y stator circuits and lead to large unwanted stator 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 sixphase and five-phase induction machines, respectively. V. M ULTIPHASE VSI C ONTROL By and large, the existing research related to PWM control of 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 zerosequence harmonic (or adding the offset) into leg voltage references. 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 the improvement in the dc bus utilization as a result of the zerosequence injection, for various odd phase numbers. Carrierbased PWM is also suitable for control of concentrated winding machines, where in addition to the fundamental and zerosequence 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 available number of inverter output voltage space vectors changes according to the law 2n , since there are 2n different switch-

Fig. 5. Basic building blocks for VSI supplied multiphase machines: (a) Leg of a two-level inverter; (b) leg of a three-level NPC inverter; and (c) H-bridge supply. For an n-phase machine, legs of the type shown in (a) or (b) are combined into an n-phase bridge inverter or n individual H-bridge inverters of (c) are used. TABLE V PERCENTAGE INCREASE IN THE FUNDAMENTAL OUTPUT VOLTAGE OBTAINABLE WITH 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 operation. 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 to α−β and x−y pairs of components. Harmonics of the order

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TABLE VI HARMONIC MAPPING INTO DIFFERENT PLANES FOR FIVE-PHASE AND SEVEN-PHASE SYSTEMS (j = 0, 1, 2, 3, . . .)

2jn ± 1(j = 0, 1, 2, . . .) map into the first, α−β plane, while all the other harmonics map into the other (n − 3)/2 planes. For example, for a five-phase VSI, harmonics of the order 10j ± 3(j = 0, 1, 2, . . .) map into the (single) x−y plane. An illustration of the harmonic mapping in five-phase and sevenphase systems is given in Table VI (harmonics in bold denote those that are available for average torque production in concentrated winding machines). Since machines with sinusoidal MMF distribution have very small impedance for x−y voltage components, 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 output desired sinusoidal voltages using space vector PWM, it is necessary to use in one switching period (n − 1) active vectors neighboring 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, sevenphase, 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 plane there will be nonzero reference voltage space vector(s) in other, x−y plane(s). These references are firmly tied to the reference in the α−β plane with regard to amplitude, frequency, and phase. 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 be synthesized 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 equations is required to calculate application times of the (n − 1) active vectors 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 single 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 spacevector 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 stator winding structure using VSIs of m and l levels at two winding ends, respectively.

stator current ripple minimization. The same kind of equivalence 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 achievable output voltage in the linear modulation region, does not minimize 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 inductionmotor 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-level inverter is used. Configurations considered in the existing literature 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 sixphase 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 supply 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. F AULT -T OLERANT O PERATION One of the most important properties of multiphase machines is their ability to continue to operate after the loss of one


(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 appropriate postfault operating strategy. Behavior of multiphase drives in faulted operation and development of postfault operating strategies, in conjunction with sinusoidal and concentrated winding 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 multiphase machine can continue to operate with a rotating field as long as no more than (n − 3) phases are faulted. How the strategies 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 phase fails, the complete a subphase winding, in which the fault has taken 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 the healthy 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 disconnected from the supply due to faults. Taking out of service the whole a subphase winding results, in these applications, in a simple 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 with k isolated neutral points. This is so since the single neutral point 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) taken out 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,

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TABLE VII IMPACT 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 speedindependent). Suppose that one phase is open-circuited. One possible criterion for postfault operation can be that the machine’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). This leads 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). This allows for an increase in the current magnitude in the remaining healthy phases by a factor of n/(n − 1), but simultaneously reduces 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 (software reconfiguration), can be combined with hardware reconfiguration 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 additional semiconductors (triacs) for this reconfiguration [131].

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VII. M ULTIMOTOR M ULTIPHASE V ARIABLE -S PEED D RIVES W ITH S INGLE I NVERTER S UPPLY As already emphasized, flux and torque control of a multiphase 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 development of postfault operating strategies, has been addressed in Sections IV and VI, respectively. An entirely different utilization 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 producing (d−q) currents of one machine appear as nonflux/torque producing (x−y) currents for all the other machines and vice versa. The idea has been floated for the first time in [180] in conjunction with two-motor five-phase series-connected twomotor drive and is shown in Fig. 7(a) at a conceptual level for an 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 although 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. Such multimotor drive systems are possible for symmetrical multiphase 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 numbers and w = (n − 1)/2 for odd supply phase numbers. Whether or not 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 asymmetrical six-phase supply enables series connection of either two asymmetrical six-phase machines or one asymmetrical sixphase 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 sixphase 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 threephase 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 sixphase machine is of a considerably higher rating than the threephase machine. In contrast to this, in five-phase and asymmetrical six-phase configurations, both machines are affected by the series connection 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 connection. First of all, the dc-link voltage in the series connection is split across machines connected in series, while in parallel 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 all inverter current components are directly controlled and therefore 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 components in 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. M ULTIPHASE M ACHINES IN E LECTRIC -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 industrial uptake of such solutions. Permanent-magnet synchronous


Fig. 7.

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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 solution for the direct-driven applications in wind-powered plants, while multiphase induction generators with multiple threephase windings may have a prospect for applications in standalone self-excited generating systems in rural areas [213] and low-power hydroelectric plants [214].

A somewhat specific use of machines with more than threephases 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] have strong magnetic coupling. However, since the outputs of the

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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. O THER M ULTIPHASE M OTOR D RIVE S OLUTIONS Multiphase variable-speed drives, discussed so far, are predominantly 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 synchronous 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 utilization of an asymmetrical six-phase synchronous motor. Highpower multiphase synchronous motors for such applications are usually supplied from current-source thyristor-based 12pulse LCIs [219], [220]. Typically, two three-phase windings are displaced by 30◦ and supplied by two independent threephase LCIs, which receive dc current from two three-phase rectifiers [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 the main categories. In majority of cases, the intended application is automotive [223]–[228]. Potential multiphase-machine-based solutions for integrated starter/alternator applications are elaborated in [226] and [227], while potential application of a sixphase induction motor for electric power steering is discussed in [228]. X. C ONCLUSION Variable-speed electric drives, based on utilization of multiphase machines, have been known for half a century. A substantial 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. Utilization 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 briefly addressed.

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Emil Levi (S’89–M’92–SM’99) received the M.Sc. and Ph.D. degrees from the University of Belgrade, Belgrade, Yugoslavia, in 1986 and 1990, respectively. From 1982 to 1992, he was with the Department of Electrical Engineering, University of Novi Sad, Novi Sad, Yugoslavia. In May 1992, he joined Liverpool John Moores University, Liverpool, U.K., where he has been a Professor of electric machines and drives since September 2000. Dr. Levi is an Associate Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and an Editor of the IEEE TRANSACTIONS ON ENERGY CONVERSION. He is a member of the Editorial Board of the IET Electric Power Applications.

[01] Levi, E. -- Multiphase Electric Machines for Variable-Speed Applications

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