SIXTH INTERNATIONAL SYMPOSIUM NIKOLA TESLA October 18 – 20, 2006, Belgrade, SASA, Serbia

Recent Developments in High Performance Variable-

Speed Multiphase Induction Motor Drives Emil Levi1

Abstract – Multiphase induction machines offer numerous advantages, when compared to their three-phase counterpart. As the number of machine’s phases is essentially unlimited when the motor is supplied from a power electronic converter, multiphase induction motor drives are nowadays considered as a potentially viable solution for numerous applications, such as for example electric ship propulsion, traction, electric and hybrid electric vehicles and the ‘more electric’ aircraft. The purpose of this paper is to provide a review of the recent developments in the area of multiphase induction motor control. Vector control and direct torque control (DTC) are addressed and utilisation of the additional degrees of freedom that exist in multiphase machines for differing purposes is described (higher stator current harmonic injection for torque enhancement and control of a group of series-connected multiphase motors supplied from a single multiphase VSI). Various pertinent topics are illustrated throughout the paper with experimental results, taken from a range of multiphase induction motor drive rigs.

Keywords – Multiphase induction machines. Vector and direct torque control. Multiphase voltage source inverters. Five-phase and six-phase induction machines.

I. INTRODUCTION

Variable-speed AC motor drives with more than three phases (multi-phase drives) have several advantages when compared to the standard three-phase realisations [1,2]: the current stress of the semiconductor devices decreases proportionally with the phase number, torque ripple is reduced, rotor harmonic currents are smaller, power per rms ampere ratio is higher for the same machine volume and harmonic content of the DC link current for VSI fed drives is reduced. Other advantages include an improvement in the noise characteristics [3] and a reduction in the stator copper loss, leading to improved efficiency [4]. Further advantages are related to the higher reliability at the system level, since a multi-phase drive can operate with an asymmetrical winding structure in the case of loss of one or more inverter legs/machine phases [5,6].

Applications of multi-phase induction motor drives are mainly related to the high-power/high-current applications, such as for example in electric ship propulsion [7,8], in -----------

1Emil Levi is with the Liverpool John Moores University, School of Engineering, Byrom St, Liverpool L3 3AF, UK, E-mail: e.levi@ljmu.ac.uk.

locomotive traction [9,10] and in electric/hybrid electric vehicles [11]. Other high-power applications, with multiphase induction motor drives, have also been reported. A vector-controlled 850 kW asymmetrical six-phase (dual three-phase) induction motor drive, used to drive a melt pump in a polyethylene plant, is presented in [12], while a 570 kW asymmetrical six-phase motor with PWM inverter supply is reported in [13]. Multiphase induction machines for the applications described above can be designed with distributed or concentrated stator windings. The windings can be full-pitch or short-pitch, depending on the machine design.

Another application area is related to the concept of ‘more-electric’ aircraft and aerospace in general [14-18]. In this case however a special machine design, so-called modular design, is employed with the idea of achieving as high as possible reliability of the drive. A phase winding is mounted in two adjacent slots and the individual phases of the machine are made with almost complete magnetic and thermal isolation. They are supplied from individual H-bridge single-phase inverters. Such multiphase drives are currently designed using permanent magnet synchronous machines and are therefore outside the scope of this paper.

Although multiphase induction motor drives have been around for more than 35 years [19], it is the last five years or so that have seen a tremendous increase in the volume of research related to these drive systems. As a consequence, the existing two surveys of these drive systems [20,21] have to a large extent become obsolete. The purpose of this paper is to provide an up-to-date review of the state of the art in the area of high performance variable-speed multiphase induction motor drive systems. Experimental results obtained from various multiphase induction motor drive rigs are provided throughout the paper.

II. CONTROL OF VARIABLE-SPEED MULTIPHASE INDUCTION MOTOR DRIVES

A. Introduction

Methods of speed control of multiphase induction machines are in principle the same as for three-phase induction machines. Constant V/f control was extensively studied in the early days of the multiphase variable-speed induction motor drive development in conjunction with voltage source

inverters operated in the 180° conduction mode [19,22,23] and current source inverters with quasi square-wave current output [24-26]. In recent times the emphasis has shifted to vector control and direct torque control (DTC) since the cost of implementing more sophisticated control algorithms is negligible compared to the cost of multiphase power electronics and the multiphase machine itself (since neither are readily available on the market). This section therefore provides a review of vector control and DTC schemes for multiphase induction machines. Since both rely on machine’s mathematical models, modelling of multiphase induction machines is addressed first.

B. Modelling of Multiphase Induction Machines

General theory of electric machines provides sufficient means for dealing with mathematical representation of an induction machine with an arbitrary number of phases on both stator and rotor. It can also effectively model machines with sinusoidally distributed windings and with concentrated windings, where one has to account for the higher spatial harmonics of the magneto-motive force. Probably the most comprehensive treatment of the modelling procedure at a general level is available in [27]. More recently, detailed modelling of an n-phase induction machine, including the higher spatial harmonics, has been reported in [28], while specific case of a five-phase induction machine has been investigated in detail in [29,30]. Transformations of the phase-variable model are performed using appropriate real or complex matrix transformations, resulting in corresponding real or space vector models of the multiphase machine.

A slightly different approach to the multiphase machine modelling is discussed in [31-33]. It is termed ‘vectorial modelling’ and it represents a kind of generalisation of the space vector theory, applicable to all types of ac machines. In principle, it leads to the same control schemes for multiphase machines as do the transformations of the general theory of electric machines. This modelling approach is therefore not discussed further on. In what follows, a brief summary of the modelling procedure based on the general theory of electric machines is provided.

To begin with, an n-phase symmetrical induction machine, such that the spatial displacement between any two consecutive stator phases equals α = 2π/n, is considered. Both stator and rotor windings are treated as n–phase and it is assumed that the windings are sinusoidally distributed, so that all higher spatial harmonics of the magneto-motive force can be neglected. The phase number n can be either odd or even. It is assumed that, regardless of the phase number, windings are connected in star with a single neutral point. The machine model in phase-variable form is transformed using decoupling (Clark’s) transformation matrix [27], which replaces the original sets of n variables with new sets of n variables. Decoupling transformation matrix for an arbitrary phase number n can be given in power invariant form with (1), where α = 2π/n.

The first two rows in (1) define stator current components that will lead to fundamental flux and torque production (α−β components; stator to rotor coupling appears only in the

equations for α−β components). The last two rows define the two zero sequence components and the last row of the transformation matrix (1) is omitted for all odd phase numbers n. In between, there are (n−4)/2 (or (n−3)/2 for n = odd) pairs of rows which define (n−4)/2 (or (n−3)/2 for n = odd) pairs of stator current components, termed further on x-y components.

Equations for pairs of x-y components are completely decoupled from all the other components and stator to rotor coupling does not appear either [27]. These components do not contribute to torque production when sinusoidal distribution of the flux is assumed. Zero sequence components will not exist in any star-connected multi-phase system without neutral conductor for odd phase numbers, while only 0_ component can exist if the phase number is even. Since rotor winding is short-circuited neither x-y nor zero-sequence components can exist and one only needs to consider further on α−β equations of the rotor winding.

As stator to rotor coupling takes place only in α−β equations, rotational transformation is applied only to these two pairs of equations. Its form is identical as for a three-phase machine. Assuming that the machine equations are transformed into an arbitrary frame of reference rotating at an angular speed aω , the model of an n-phase induction machine with sinusoidal winding distribution is given with

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where ( )MnLm 2= and M is the maximum value of the stator to rotor mutual inductances in the phase-variable model. Torque equation is given with

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Model equations for d−q components in (2)-(3) and the torque equation (4) are identical as for a three-phase induction machine. This means that, in principle, the same control schemes will apply to multiphase induction machines as for three-phase machines. However, existence of x−y equations means that utilisation of a voltage source that creates stator voltage x−y components will lead to a flow of potentially

large stator x−y current components, since these are restricted only by stator leakage impedance.

In essence, x−y components correspond to certain voltage and current harmonics, the order of which depends on the machine’s number of stator phases. Hence the inverter, used to supply a multiphase induction machine, must not create

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low-order voltage harmonics that will excite stator current low-order harmonic flow in x−y planes. This issue is of particular importance when realising inverter PWM control.

On the basis of (2)-(3) and assuming a single neutral point in stator winding it follows that after transformation of the model one has to deal with (n−1) equations, since 0+ component cannot be excited. However, if the stator winding of the machine is with n = a·k, (a = 3,4,5,6,7…, k =2,3,4,5…) number of phases, then it is possible to configure the complete winding as k windings with a phases each, with k isolated neutral points. This reduces the total number of equations after transformation to n−k, since in each star-connected winding zero-sequence cannot exist. For example, in a nine-phase machine with three three-phase windings shifted by 40° and with isolated neutrals there are only six equations instead of eight when there is a single neutral. This feature is often exploited in multiphase motor drives since it has advantages with regard to fault tolerance (if one phase fails the whole a−phase winding can be taken out of service and the machine can continue to operate with n’ = a (k−1) phases without problem, with a proportionally reduced output power). A 15-phase symmetrical induction machine of [34] is configured for this purpose with three five-phase stator windings, supplied from voltage source inverters connected to separate dc links. In case of failure of one or even two five-phase windings the machine can still continue to operate, offering therefore a significant improvement in fault tolerance compared to an equivalent three-phase machine.

An alternative configuration of stator windings is often utilised when the total number of stator winding phases is n = 3·k, k =2,3,4,5… Rather than placing the stator phases equidistantly along the circumference of the machine, one half of the angle α = 2π/n is used as the spatial shift between consecutive three-phase windings. This yields a six-phase machine with 30° displacement between two three-phase windings and a nine-phase machine with 20° displacement

between three three-phase windings. Machines designed in this manner are called here asymmetrical induction machines, since the schematic representation of the magnetic axes of the individual stator phases is asymmetrical. Modelling of asymmetrical induction machines will again result in the same model equations (2)-(4), provided that an appropriate decoupling transformation matrix is applied first. The decoupling transformation matrix for asymmetrical six-phase machine with two isolated neutral points is of the form [35,36]

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where the first three elements in each row are related to the first three-phase winding, while the remaining three elements apply to the second three-phase winding. Transformation matrix for asymmetrical multiphase machines with multiple three-phase windings is most easily formed using the vector space decomposition approach, detailed in [36]. For example, application of the vector space decomposition approach to an asymmetrical nine-phase machine model, assuming a single neutral point, yields the transformation matrix given in [37]. It is possible to derive in the same manner transformation matrices for asymmetrical machines with higher number of phases (12, 15, etc.).

In the case of induction machines with n = 3·k, k =2,3,4,…, an alternative approach to modelling [38,39] is also utilised. Since the machine’s stator winding consists of k three-phase star-connected windings with isolated neutral points, it is possible to formulate the transformation matrix in such a way that one obtains a pair of d−q equations for each three-phase winding, with the total torque determined as a sum of

individual contributions of each of the three-phase windings. This modelling approach therefore results in a model where each of the three-phase windings gets described with a pair of equations identical to the d−q pair in (2)-(3). For example, an asymmetrical six-phase machine with two isolated neutral points is fully described with the model containing two pairs of d−q voltage and flux linkage equations for both stator and rotor. Application of this modelling approach is currently restricted to multiphase machines with multiple three-phase windings and it therefore lacks the generality offered by the model (2)-(4). Nevertheless, ‘double d−q winding representation’ of asymmetrical six-phase machines is often utilised for development of vector control schemes for this particular machine type [11,12,40].

As the number of phases of an induction machine increases it becomes progressively difficult to achieve sinusoidal distribution of the magneto-motive force, due to the limited number of slots along the stator circumference. On the other hand, sinusoidal distribution is actually not even the desirable feature of a multiphase machine, since it prevents utilisation of one of the main advantages offered by such machines, torque enhancement by injection of higher stator current harmonics. If the stator winding is made as concentrated, then the magneto-motive force contains higher spatial harmonics [41,42]. By injecting stator current time harmonics of the order that coincides with the spatial harmonic order it becomes possible to develop an average torque with these harmonic currents that is in addition to the torque produced by the fundamental stator current. This possibility is brought into existence by the fact that control of flux and torque associated with any particular current harmonic requires only two stator currents. The fundamental flux and torque components are therefore controlled using the stator d−q current components, (2)-(4). Each of the additional pairs of x−y stator current components in (2)-(3) can be used to control an additional flux and torque component of the machine, caused by the injection of a certain stator current component. This possibility exists in not only multiphase induction machines with an odd phase number, but in all the other ac machine types (for example, synchronous reluctance machines [43,44] and permanent magnet synchronous motor drives [45]). However, the possibility of utilising higher stator current harmonic injection for torque enhancement is severely restricted in machines with an even phase number. The only known case where this is a possibility is the asymmetrical six-phase motor drive, where application of the stator current third harmonic current injection requires operation of the machine with single neutral point, which has to be connected to either mid-point of the capacitor bank in the dc link or to a separate (7th) inverter leg (induction motor drive [46-48] and permanent magnet synchronous motor drive [49]). In contrast to this, injection of the third stator current harmonic cannot be used for torque enhancement in a symmetrical six-phase drive.

From the modelling point of view injection of stator current harmonics modifies both the transformation matrices and the resulting model. Since now stator-to-rotor coupling takes place not only between stator and rotor d−q components but also between the other pairs of stator and rotor components, the pairs of axes after rotational transformation are usually

labelled d1−q1, d3−q3, d5−q5, etc. (rather than d−q, x1−y1, x2−y2, etc.) in accordance with the stator current harmonic order that appears as the torque enhancing in any particular pair of d−q components. Basically, voltage and flux equations for d3−q3, d5−q5, etc. components are of the same form as for d−q components in (2)-(3), with an appropriate scaling factor associated with the harmonic order, and the torque equation (4) contains additional components produced by higher order harmonics. In a five-phase induction machine the third stator current harmonic is used to enhance the torque production and hence the model contains coupled stator and rotor d1−q1 and d3−q3 equations, with the total torque given as a sum of the contributions of the fundamental and the third stator current harmonic [50,51]. In a seven-phase machine the 3rd and the 5th stator current component can be used for torque enhancement [52], while a nine-phase symmetrical stator winding enables torque enhancement by simultaneous injection of the 3rd, the 5th and the 7th stator current harmonics [44].

C. Vector Control of Multiphase Induction Machines

As long as a multiphase induction machine is symmetrical, with sinusoidally distributed stator winding, and the transformation is based on (1) the same vector control schemes as for a three-phase induction machine are directly applicable regardless of the number of phases (provided that there is perfect symmetry of machine’s and supply phases). 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. For current control in the stationary reference frame one utilises (n−1) current controllers (assuming stator winding with a single neutral point) and here the standard ramp-comparison current control method offers the same quality of performance as with three-phase induction motor drives. On the other hand, if current control in the rotating reference frame is used, there are only two current controllers, which appears as an advantage at the first sight. 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−phase windings with isolated neutrals), utilisation of the scheme with only two current controllers will suffice only if there are not any winding asymmetries within the n−phase stator winding and supply. Furthermore, application of the current control in rotating reference frame also requires an adequate method of inverter PWM control, in order to avoid creation of unwanted low order stator voltage harmonics that represent voltage x−y components in (2) and therefore lead to the flow of large stator current x−y current components. The problem of winding asymmetry is well documented for the asymmetrical six-phase induction machine (with two isolated neutral points) and it is in principal necessary to employ four (rather than two) current controllers. This applies to both the control scheme based on the ‘double d−q winding representation’ [11,12,40,53,54] and to the control based on model (2)-(4) where, in addition to the standard d−q stator

current controllers one needs to add a pair of x−y current controllers [55].

Although vast majority of control-related considerations in literature apply to either five-phase or asymmetrical six-phase induction machines, there are also reports related to other phase numbers. For example, indirect rotor flux oriented control of a symmetrical 15-phase induction machine is considered in [56], while [34] dealt with a 15-phase induction machine configured as three five-phase stator windings with independent inverter supply systems. Control of a 15-phase induction motor drive was also discussed in [57].

Provided that good quality of current control is achieved and/or an appropriate method of PWM for multiphase VSI is applied, the performance of a vector controlled multiphase induction machine will be very much the same as for its three-phase counterpart. As an example, Fig. 1 illustrates an experimental recording of a deceleration transient of the five-phase induction machine with indirect rotor flux oriented control. Phase current control is applied using ramp-comparison current control at 10 kHz inverter switching frequency [58]. Behaviour of the motor’s speed and torque is practically identical with what one would observe in an equivalent three-phase induction motor drive.

Asymmetrical six-phase machine is the most frequently considered multiphase induction motor drive for high power applications. The choice of asymmetrical (30° displacement between two three-phase windings) rather than symmetrical (60° displacement between two three-phase windings) six-phase configuration was in the early days of the multiphase induction motor drives (pre-PWM era) dictated by the need to eliminate the 6th harmonic of the torque ripple, caused by the 5th and the 7th harmonics of the stator current [38]. Utilisation of a proper PWM strategy, with sufficiently high switching frequency, for a six-phase VSI however leads to the performance of the asymmetrical and symmetrical six-phase machines that is practically the same [35, 59]. Performance of a symmetrical six-phase induction machine with rotor flux oriented control (using again ramp-comparison current control at 10 kHz switching frequency) is illustrated in Fig. 2 [60] (acceleration from standstill to 300 rpm). The transient behaviour is again commensurate with the one obtainable with a vector controlled three-phase induction motor drive.

Dynamics of an asymmetrical six-phase induction machine (with two isolated neutral points) are illustrated in Fig. 3. The machine is 10 kW, 50 Nm, 200 Hz, 40 V, 12-pole, for an electric vehicle application. This time stator current components in the stationary reference frame are controlled, using two pairs of current controllers for α−β and x−y stator current components [55]. This enables complete elimination of the undesirable effects caused by the asymmetry between the two three-phase windings [55]. The load rejection behaviour of the drive for rated speed and rated load conditions has been tested by imposing to the drive a start-up from standstill up to 2000 rpm (limit of the constant torque region), followed by step load torque transients of 50 Nm (Fig. 3a). The d−q current components of Fig. 3a are not used by the current control; they have been computed to show a correct position estimation of the synchronous reference frame since the flux-producing current component (along d-axis) is

practically invariant with the torque. To test the drive for high-speed conditions involving transition into deep field-weakening region, a 0-5500 rpm (≅ 550Hz) speed ramp response is examined. The results are shown in Fig. 3b (for this test the motor has not been connected to the DC machine due to its limited speed range).

D. Direct Torque Control

Two basic approaches to direct torque control (DTC) of three-phase induction machines can be identified. In the first approach hysteresis stator flux and torque controllers are utilised in conjunction with an optimum stator voltage vector selection table, leading to a variable switching frequency. In the second approach switching frequency is kept constant by applying an appropriate method of inverter PWM control (usually space vector PWM). In principle both approaches are also applicable to multiphase induction machines and the achievable dynamic performance is very much the same as for three-phase induction machines. However, there are some important differences, predominantly caused by the existence of additional x−y degrees of freedom in multiphase machines.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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of a five-phase induction motor from 800 to 0 rpm under no-load conditions (indirect vector control and phase current control).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

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Fig. 2. Indirect rotor flux oriented control of a symmetrical

six-phase induction motor drive using ramp comparison phase current control: acceleration from standstill to 300 rpm.

Assuming that the multiphase machine is with sinusoidal

magneto-motive force distribution, DTC scheme needs to apply sinusoidal voltages to the machine’s stator winding (neglecting PWM ripple), without any unwanted low order frequency components that would excite x−y circuits. If the constant switching frequency DTC is utilised, this problem can be solved relatively easily. It is only necessary to apply one of the PWM methods, which can provide inverter operation with sinusoidal (or at least near-sinusoidal) output voltages. For example, in the case of an asymmetrical six-phase machine supplied from two three-phase inverters one may apply standard carrier-based PWM with third harmonic injection for the control of each of the two inverters [61]. This will yield operation with near-sinusoidal inverter output, with negligible content of the 5th and the 7th stator voltage harmonics (which lead to the flow of x−y stator current components that are restricted only by stator winding leakage impedance, (2)-(3)). Hence constant switching frequency DTC of a multiphase induction machine can be realised without problem, by using an appropriate PWM method that ensures sinusoidal inverter output voltage. It appears that DTC scheme with higher stator current injection have not been developed so far for multiphase induction machines with concentrated windings. The only example of such a DTC scheme is the one of [62], where a five-phase permanent magnet synchronous machine was analysed.

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Fig. 3. Dynamics of the asymmetrical six-phase induction motor drive with direct rotor flux oriented control:

a. Drive start-up with inertial load up to 2000 rpm (1 pu) and step load transients of 50 Nm: (1) reference sped ω*

r (rpm); (2) actual speed ωr (rpm) ; (3) ids (A) (4) iqs (A); (5) Te (Nm).

b. Start-up of the drive from standstill up to 5500 rpm (≅550Hz): (1) rω (rpm); (2) *

rω (rpm); (3) dsi (A); (4) qsi (A).

It is a constant switching frequency DTC, where the overall

stator voltage reference is built on the basis of voltage requirements for the fundamental and the third harmonic. However, since the inverter output voltage space vector that is the nearest to the reference is applied, stator current is rich in unwanted low frequency harmonics (the 3rd and 7th harmonic).

Similar problem by default appears in hysteresis based DTC schemes. Here 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 [51,63,64]. These are normally selected as large vectors. However, each individual inverter output voltage space vector unfortunately leads to generation of unwanted low-order harmonics, which excite x−y stator circuits and lead to large stator current low order harmonics. To illustrate this problem, Fig. 4 shows experimentally recorded output phase voltage and its

spectrum, obtained at the output of a five-phase VSI when only large space vectors are utilised and the reference equals maximum achievable fundamental. As can be seen from Fig. 4, the 3rd harmonic is around 30% of the fundamental, while the 7th harmonic is just over 5%.

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Electrotek Concepts® TOP, The Output Processor®

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Frequency (H pu) Fig. 4. Output phase voltage of a five-phase VSI obtained using space vector PWM with large vectors only (maximum output

fundamental in the linear modulation region). It appears that this problem has not been solved so far for

any phase number higher than three, the exception being asymmetrical six-phase induction machine [65]. DTC scheme of [65] is, similar to [61], based on utilisation of two three-phase inverters for the two three-phase windings with isolated neutrals, shifted by 30 degrees. It is clearly shown in both [61] and [65] that utilisation of standard hysteresis stator flux and torque controllers in conjunction with an optimum switching table (where only twelve large vectors are utilised) leads to operation with substantial low order stator current harmonics (the 5th and the 7th). While the problem is circumvented in [61] by using constant switching frequency DTC with double zero-sequence injection, the solutions discussed in [65] are all based on modifications of the basic hysteresis based DTC. In principle, an additional hysteresis controller is introduced and the complexity of the control scheme is increased.

III. MULTIPHASE MULTI-MOTOR DRIVES WITH SINGLE INVERTER SUPPLY

Since independent flux and torque (vector) control of an ac machine, regardless of the number of phases, requires only

two currents, additional degrees of freedom that exist in multiphase machines can be used to enhance the torque production by stator harmonic current injection or to improve the fault tolerance. An alternative use of these additional degrees of freedom is to form a multi-motor drive system with single inverter supply. Stator windings of the machines are connected in series, using phase transposition, so that flux/torque producing (d−q) currents of one machine appear as non-flux/torque producing (x−y) currents for all the other machines and vector control is applied. This enables completely decoupled and independent control of the machines, although they are connected in series and a single VSI is used as the supply. The initial proposal was related to the five-phase series-connected two-motor drive [66]. However, the principle is applicable to any inverter phase number and it has been developed into considerable depth for all symmetrical multiphase VSIs with even phase numbers and with odd phase numbers in [67] and [68], respectively. The number of machines connectable in series is at most

2)2( −= nk for even supply phase numbers and 2)1( −= nk 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 [67,68]. The possibility of series connection exists also for asymmetrical machines. It has been developed in [69-71] for asymmetrical six-phase and in [37] for asymmetrical nine-phase case.

From the application point of view two potentially viable solutions appear to be two-motor series-connected five-phase and symmetrical six-phase induction motor drives. The connection schemes are illustrated in Fig. 5. In the 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 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 configuration 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 winder drives, [58]). More detailed considerations related to various aspects of six-phase and five-phase series-connected two-motor drives are available in [71,72] and [58,73,74], respectively. Transient behaviour of the five-phase two-motor drive is illustrated in Fig. 6. One machine operates with constant speed reference of 500 rpm, while the other machine is decelerated from 800 rpm to standstill. As can be observed from Fig. 6, the machine that runs at constant speed is not disturbed at all by the transient of the other machine, indicating full decoupling of control.

Implementation of the drive systems of Fig. 5 requires an appropriate method of inverter PWM control. Since the PWM scheme has to impress two fundamental sinusoidal waves at in general two different frequencies, the natural choice is a carrier-based PWM where modulating signals are composed of two sinusoidal signals of appropriate frequencies and

amplitudes (that are summed according to the connection diagrams in Fig. 5). An illustration of the line-to-line voltage generated in this manner for the five-phase two-motor drive is given in Fig. 7, where filtered waveform and its spectrum are shown. Two fundamentals can be clearly seen in the spectrum.

IV. CONCLUSION

Multiphase induction motor drives have attracted a substantial interest in the research community worldwide in recent times. An attempt is made in this paper to provide a review of the newest developments in this area. Available

A B C D E

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Fig. 5. Series-connected two-motor five-phase and six-phase

induction motor drives.

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Fig. 6. Series-connected five-phase two-motor drives: speed responses, stator q–axis current commands (peak), comparison of measured and reference current for one inverter phase, and current

references for one phase of the two machines: machine 2 (IM2) runs at 500 rpm, while machine 1 (IM1) decelerates from 800 to 0 rpm.

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Fig. 7. Five-phase VSI line-to-line voltage and its spectrum for

series-connected two-motor drive: carrier-based PWM with modulating signals composed of two sinusoidal components of

different frequency and amplitude.

control schemes are surveyed and the problems associated with PWM control of voltage source inverters are addressed. Operation of various multiphase induction motor drives is illustrated using experimental recordings.

ACKNOWLEDGEMENT

The author gratefully acknowledges support provided for the work on multiphase motor drives by the EPSRC and by Semikron Ltd – UK, MOOG – Italy and Verteco – Finland.

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