IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733
Recent Advances in the Design, Modeling and Control of Multiphase Machines – Part 1 Federico Barrero, Senior Member, IEEE, Mario J. Duran Abstract Multiphase machines are well recognized as an attractive alternative to conventional three-phase ones in a number of applications where high overall system reliability and reduction in the total power per phase are required. The pace of developments in the field has accelerated in the last few years, and substantial knowledge has been recently generated. The main objective of the two parts’ survey named ‘Recent Advances in the Design, Modeling and Control of Multiphase Machines’ is to present relevant contributions to encourage and guide new advances and developments in the field. More specifically, the part 1 of the work analyzes the recent progress in the design, modelling and control, including healthy operation of multiphase motor drives, and discusses open challenges and future research directions in the area. Index Terms Multiphase machines, design, modeling, parameter estimation, motor drive control in normal operation mode.
I. INTRODUCTION
T
HE research in the multiphase machine area has attained significant proportions in the last decade. With the number of conventional electrical machines continuously growing, the interest in multiphase machines is also rising due to intrinsic features like power splitting, better fault tolerance or lower torque ripple than three-phase machines [1,2]. While advances in multiphase power supply, modulation techniques and some innovative uses of the additional degrees of freedom are surveyed in a companion paper, this part of the state of the art paper looks at the progress in the design, modeling and motor control of multiphase machines in healthy situation. The work is complemented with a second part that analyzes the recent developments in multiphase generation systems and in the fault-tolerant control of multiphase drives. Recent research works and developments support the prospect of future more wide-spread applications of multiphase machines. Electric vehicles and railway traction, all-electric ships, more-electric aircraft, and wind power generation systems are areas where this research activity has Manuscript received December 4, 2014; revised February 10, 2015 and April 13, 2015; accepted May 5, 2015. Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to
[email protected]. This work was supported by the Spanish Ministry of Science and Innovation under Projects DPI2013-44278-R and ENE2014-52536-C2-1-R, and the Junta de Andalucía under Project P11-TEP-7555. F. Barrero is with the Electronic Engineering Department of the University of Seville, Spain, e-mail:
[email protected]. M.J. Duran is with the Electrical Engineering Department of the University of Malaga, Spain, e-mail:
[email protected].
taken place in recent times. For example, a recent overview states that multiphase machines can be a favored choice for general aerospace applications [3], and actual works detail a six-phase linear permanent magnet machine for oil pumping applications to increase the fault tolerant capability and reduce the detent force of the system [4] or a nine-phase permanent-magnet traction motor used in ultrahigh-speed elevators [5]. Such examples of actual industrial drive developments and applications are very encouraging. However, the difficulties in extending the three-phase control structures to multiphase systems, the limited work on the multiphase machine design or estimation techniques, the necessity of fault detection and management algorithms or the recent interest in multiphase generation systems are areas where substantial new developments are expected to appear. This two parts’ survey disseminates and shares recent advances in the design, modeling and control fields of multiphase machines, serving as a compilation for the research community. Part 1 of this survey paper is organized as follows. Section II examines the trends in machine design, where focus of attention has moved from the stator winding arrangement and disposition towards novel machine structures with improved reliability and low weight. The design aspects of induction and permanent magnet (PM) synchronous multiphase machines are surveyed, and the application of the superconducting technology to multiphase machines is introduced. Section III deals next with modelling issues, analyzing both the contributions related to new analytical models and the identification of the electrical parameters, which appears as a topic that has received only limited attention so far. Finally, control strategies in healthy mode of operation are described in section IV, where the progress and evolution in the field oriented control (FOC) and direct torque control (DTC) techniques are discussed. Other alternative control methods, also examined in the section, are mainly based on model predictive control (MPC) techniques. II. DESIGN TENDENCIES The attention with regard to the multiphase machine design has been focused in recent times on the development of low weight, high reliability and fault tolerant structures that are primarily based on multiphase permanent magnet machines. Nevertheless, new challenges using superconducting technologies or advances in the induction machine design have also been recorded, and the last ones are surveyed first.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733 A. Induction Machines The work on the design of multiphase induction machines is focused on achieving higher torque density and optimized air-gap magnetic fields through the injection of stator current harmonic components [6,7]. The benefits obtainable by a modular or fractional-slot concentrated-winding (FSCW) design, in terms of short end-turns and flux-weakening capabilities, have been also explored in conjunction with five-phase squirrel-cage induction motor drives in [8], where the inability of the FSCW design for producing high quality magnetic travelling fields is also investigated to reduce the effect of space harmonics. Then, design considerations such us the number of rotor bars or the required skewing angle are given to reduce the torque ripple and core losses by decreasing undesired space harmonics. It is also stated that the FSCW design can provide advantages in applications like high frequency induction machines and manually wound electrical submersible pump motors. B. FSCW PM Machines Modular design is predominantly being explored in conjunction with PM machines [9-24]. The multiphase FSCW surface and interior PM machines (SPM and IPM, respectively) are becoming an interesting choice for automotive applications owing to their advantages which include high power density, high efficiency, short end-turns, high slot fill factor, low cogging torque, flux-weakening properties and inherent fault-tolerant capability [9,10]. Their main drawback is the generation of excessive rotor losses, particularly in high speed operation, due to large spatial harmonic components [11]. Then, an appropriate combination of the number of slots and the winding distribution is used in a five-phase IPM to reduce the torque pulsations of the motor in [12]. Three five-phase externalrotor PM machines with different combinations of the numbers of slots and poles (20 slots/14 poles, 20 slots/18 poles and 20 slots/22 poles) are compared in [13,14]. This comparative analysis concludes that the efficiency and density of the machine torque are enhanced by the increase in the number of rotor poles. However, this is achieved at the expense of an increase in the dc-link voltage requirement. Better flux distribution and lower core losses are obtained with the 20 slots/14 poles combination, while the 20 slots/18 poles combination gives a lower torque ripple in healthy and faulty states. The impact of the number of phases on the rotor losses and the slots-per-pole combination is studied in [15], where three-phase, five-phase and seven-phase FSCW PM machines are compared. The main conclusion of the work is that a reduction of the spatial harmonics is obtained with multiphase machines, although the reduction is lower than expected. A similar study is done in [16], where an analytical model for comparison of magnet losses in PM machines with concentrated windings is also presented. The safety requirements in terms of fault-tolerant capabilities of these electrical machines are studied in [17],
for a duplex three-phase SPM generator integrated inside the aircraft main gas turbine engine, and in [18] for a five-phase modular PM in-wheel motor. The multiphase modular PM machine is chosen in [18] to produce the rated power in case of a single fault, with deep enough stator slots to obtain large phase inductances that limit short circuit currents. The magnet layer is also optimized in these machines using PM shaping methods to increase the torque density in [19,20] and to reduce the pulsating torque in [21], where a five-phase SPM is used. Dual three-phase 12-slot 10-pole PM machines are tested in [22], where different rotor topologies (IPM and SPM) and winding configurations are compared in terms of average torque, torque ripple, mutual coupling among phases and faulty condition behavior. The study concludes that the SPM machine almost doubles the power and torque densities, although the IPM machine offers lower shortcircuit current and braking torque. The work is complemented in [23], where different pole and slot number combinations are analyzed, focusing on both single and double layer windings and non-overlapping coils, and in [24], where the torque components and the sensorless position detection capabilities of the IPM machine are investigated in healthy and faulty states, supplying only one of the two three-phase fractional-slot windings. C. Other PM Machines Industrial demand for electromechanical systems with high torque density or high speed and low cost applications is increasing, and other electrical PM topologies have been lately considered together with the multiphase stator technology. This is the case with PM synchronous machines (brushless PM or simply BPM), which guarantee the highest torque density. So, two modular BPM multiphase machines are designed in [25] to meet the performance requirements of an electromechanical flight control surface actuator. High energy magnets (NdFeB or SmCo types) are normally used in the manufacturing process of BPM machines, and losing energy due to thermal stress is a major drawback of this technology. Then, a computational technique to evaluate the influence of the finite axial length of the magnets on the rotor eddy-current losses is the main contribution in [25], and optimization strategies are applied in [26] in the design process of a five-phase BPM with concentrated windings for automotive applications, where stator current references (fundamental and third harmonic components) are obtained to minimize the total loss (iron and magnet losses included) and to improve the performance of the machine in the fluxweakening region (high speed at 16000 rpm). The synchronous reluctance machine (REL) is also an interesting PM solution due to its low cost. Then, a light weight five-phase axial flux REL machine is designed and prototyped for electric vehicle applications in [27] and a special type of brushless machine with PMs located in the stator (called Flux-Switching PM or FSPM machine) is combined with multiphase windings in [28,29], claiming the
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733 TABLE I PROPOSED APPLICATIONS TIED TO TYPE OF MULTIPHASE MACHINE* Type of machine Ref. Application Induction [8] Submersible 5-phase pump motor Machine Fault-tolerant 6- and 5-phase in[9,10] FSCW PM wheel motor for electric vehicle (SPM type) 6-phase generator inside the [17] aircraft main gas turbine engine FSCW PM [20] 2.1 MW 5-phase marine propeller (IPM type) 4- and 5-phase electromechanical BPM [25] flight control surface actuator 5-phase axial-flux configuration REL [27] for electric vehicles 12 kW 5-phase electro hydrostatic BLDC [30] actuator for aerospace application Superconducting Design of 12 MW 9- and dual-3[34,35] Machines phase synchronous generators * Prototype multiphase machines are also implemented in the provided bibliography, but they are not included in this table for simplicity reasons.
advantages of both BPM and REL machines. Further recent studies propose other multiphase PM machines. For example, a five-phase brushless dc motor (BLDC) for safety critical aerospace applications is designed in [30], adding fault tolerant and high reliability characteristics to the compact structure, low weight and highest torque density capabilities. A 5-phase SPM bearingless motor with a single set of half-coiled winding is also described, analyzed and controlled in [31], combining torque driving and self-levitation characteristics. Finally, a five-phase permanent magnet assisted synchronous reluctance machine is designed and studied in [32,33], where it is suggested as an alternative to IPM and REL machines for low output torque ripple applications. D. Superconducting Machines Electric energy production via wind power is accelerating nowadays the development of superconducting generators. Market problems are avoided, i.e. the rapid change in price or unavailability of magnets, and more than 5 MW of power generation per tower is allowed without prohibitively large size and weight of the nacelle. This technological challenge has been recently explored and multiphase superconducting electrical generators are proposed for large-scale direct-drive wind turbines in [34,35]. Two 12 MW nine-phase superconducting synchronous generators with different armature winding arrangements are designed and compared in [34], and a 12 MW dual three-phase superconducting wind generator with FSCW (using 24-slot/10-pole combination) is presented in [35]. The interest in wind power generators for off-shore applications, the unpredictable behavior of the rare earth magnet market, and the superconducting technology development may favor the roll-out of this technology in the near future. Table I shows some real applications mentioned in the provided bibliography in relation to the design tendency of multiphase machines. Such applications not only favor the
appearance of new types of multiphase machines but also the study of new models, as it will be discussed next. III. MULTIPHASE MACHINE MODELING The modeling of multiphase machines was extensively studied in the last century. Nevertheless, some interesting new models have been developed in recent times taking into account the effect of magnetic saturation in the machine, which produces coupling between different planes (primary and secondary ones). A. Modified Machine Models The influence of the magnetic circuit saturation on the main air-gap flux density is studied in a dual-stator-winding induction machine in [36], where a dynamic model of the system including this saturation effect is presented. Novel methods for modeling five-phase induction machines are given in [37,38], where the effect of magnetic saturation is also considered. While the method presented in [37] uses the well-known conventional multiple d-q planes, the model proposed in [38] extends the voltage-behind-reactance (VBR) formulation, introduced originally for the three-phase induction machine. It uses dependent voltage source in series with passive (R-L) impedances and includes shunt resistances to model the core losses, which also solves the problem of algebraic loops that the VBR model introduces in the simulation. One interesting contribution of this modeling method is that it is suitable for open-phase faulty conditions, unbalanced supply and star, pentagon or pentacle connections. The method has also been recently extended to a dual-three phase induction machine with an arbitrary displacement between the stator windings in [39]. Last but not least, a modified method for the analysis of an asymmetrical six-phase IPM machine is given in [40], where a decoupled d-q model is introduced, and more recently an analytical model using magnetic equivalent circuits and including saturation effects is proposed in [41] for split-phase multiphase REL machines. The aim in this contribution is to avoid iterative optimization processes based on time-consuming finite element analysis (FEA) normally applied in the design of these machines, setting forth an accurate and fast method to predict the performance of the machine. FEA techniques are arduous and iterative off-line methods. Moreover, multiphase machines are still often obtained rewinding stators of conventional three-phase machines, which means that the resulting machine is not optimal and the electrical parameters are difficult to obtain using FEA or similar computational techniques [42]. Since models of multiphase machines require knowledge of electrical parameters, procedures for their identification are also becoming an interesting research area. Methods for the identification of resistances and inductances in conventional three-phase electrical machines are well-known but their extension to the multiphase case is at present limited, as we
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733 will see later, and more work is expected in the near future because only a few recent works attempt to tackle the issue. B. Identification of Electrical Parameters Different off-line procedures are applied in [43,44] for the estimation of the electrical parameters of a five-phase induction machine in the frequency and time domains. Figs. 1 to 3 summarize the method proposed in [44], where recursive least-square (RLS) algorithms are applied for the estimation of the electrical parameters of a five-phase induction motor. The five-phase induction machine is operated in the standstill mode (Fig. 1), so different winding arrangements are proposed for the estimation of the electrical parameters without generating electrical torque (stator voltage components in the α-axis are maximized in Fig. 2, while the rest of stator voltage components are minimized to concentrate the identification study on analyzing the current response in the α-axis). The obtained parameters are tested in high-performance five-phase induction motor drives to corroborate the validity of the estimation technique. The agreement between Bode frequency responses of the real system and the analytical model using the estimated electrical parameters is also presented (Fig. 3). While multiphase machines with distributed windings are considered in [43,44], multiphase machines with concentrated windings are analyzed in [45], where the magnetizing inductances of the fundamental and thirdharmonic components in a 15-phase induction machine are estimated using a Fourier analysis of the air-gap flux density distribution and a distributed magnetic circuit approach. Similarly, different off-line identification methods have been developed for the estimation of the electrical parameters of a dual asymmetrical three-phase IPM machine in [46]. The study is complemented with [47], where a recursive leastsquare algorithm is applied for their estimation during normal operation of the drive. Knowledge of the electrical parameters is of key importance if a high efficiency multiphase motor drive is required, being a fundamental requirement of the control system as it will be stated in the next section.
Fig. 1. Schematic diagram of the identification procedures proposed in [44].
vs 1.1708 Vdc v xs 0.1708 Vdc v0s v s v sy 0
Fig. 2. One of the winding arrangement proposed in [44] to concentrate the identification study on analyzing the current response in the α-axis.
Fig. 3. Comparative analysis shown in [44] in the α-β plane to illustrate the usefulness of the proposed estimation technique. Bode frequency responses are plotted, using the analytical model of the 5-phase induction machine with the estimated electrical parameters (blue trace) and the real system (red trace).Similar results are obtained in the x-y plane.
IV. PROGRESS IN MULTIPHASE MOTOR DRIVE CONTROL The research activity has in recent past shifted from the basic extension of the field oriented and direct torque control methods, used in the three-phase drives, towards more sophisticated control solutions for multiphase drives. Asymmetrical six-phase and five-phase induction machines with sinusoidally distributed stator windings continue to be the most analyzed multiphase solutions, but higher phase order machines and concentrated winding machines with an odd number of phases have also been considered to obtain torque enhancement on prototype machines using stator current harmonic injection. A. Field-Oriented Control The most common control strategy in the multiphase drives is the well-known rotor-flux oriented control (RFOC) method, based on multiple inner current control loops with a superimposed outer speed controller. The recent progress focusses on the current controllers, whose number is governed by the number of independent 2D planes. In
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733 principle, an n-phase drive with a single neutral point requires (n1) current controllers in order to reduce the loworder harmonic current content due to asymmetry and inverter dead time, and to improve the balancing of current sharing between windings [48-52]. Five-phase and dual three-phase induction machines with sinusoidal MMF distribution have been used to study current control aspects [48-50], and the obtained results have been also extended to permanent magnet synchronous machines [51,52]. Another interesting research activity is related to torque enhancement, by improving the flux pattern using stator current low-order harmonic injection. Additional degrees of freedom of multiphase machines are used yielding a near rectangular air-gap flux for better iron utilization and higher torque density in concentrated winding machines with an odd number of phases [53,54]. Indirect RFOC (IRFOC) is normally used [55-59], and different synchronization methods are applied to avoid misalignment between the fundamental and harmonic fluxes for all mechanical loads. Research was initially restricted to the five phase induction machine (fundamental and third harmonic injection) [55], but seven and eleven phases induction machines have been also analyzed in [56-59]. It is concluded in [58] that injection of up to the fifth stator current harmonic is advantageous and that injections of harmonics above the fifth produce a negligible increment of the torque density. The increment in the generated electrical torque is not only limited by the rotor losses but also by the power converter constraints in overload conditions. This issue is analyzed in [59], where a sevenphase induction motor is again considered. The seven-phase inverter ratings and constraints are studied to maximize the electrical torque, injecting a third-order stator current component, depending on the operating conditions and including the field-weakening operation of the drive. According to the results, the improvement of the overload torque due to the third-order harmonic injection can be up to 17% of the original nominal torque. Different research works concerning this issue include the definition of a numerical procedure for setting the controllers in multiphase drives with third harmonic injection [60], or the application of a model reference adaptive system for the estimation of the rotor speed and the implementation of a sensorless IRFOC [61]. An alternative to the inner current controllers in a multiphase drive using RFOC techniques has been recently introduced. It is based on the model predictive control (MPC) method [62,63], which is used instead of the classical PI current controllers. Two concepts, one based on the MPC approach to current control and the other based on the PI current control, are illustrated in Fig. 4. The MPC, as used in the electric drives, is typically finite control set MPC (or just FCS-MPC) because the number of available converter switching states is a finite set. The problem encountered in utilization of the MPC based current control is that the objective function (related to the selection of the inverter
output voltage vector that can minimize the control objectives) becomes more involved than in the three-phase case. This is so since there is a need to minimize current errors for all current components and there are, in principle, (n1) of them rather than just two. Needless to say, the number of possible inverter states that can be applied increases with the phase number exponentially and is already 32 for the five-phase two-level inverter (in contrast to being just 8 for a three-phase two-level inverter). The viability of the MPC based current control is assessed in [62,63] for an asymmetrical six-phase drive, assuming quasi-balanced operation. A sinusoidal output stator voltage is required, and a pseudo-optimum search criterion with a reduced set of voltage vectors is used to overcome the computational cost of the control technique. Then, the applied output voltage vector is not necessarily the optimal one because not all available switching states have been considered at the objective function minimization stage (only 13 of 64 inverter states are used). Other predictive control techniques have also been introduced based on [62,63], with the main goal of reducing the computational cost of the control method and minimizing the generated harmonic content. This is the case of the method proposed in [64] termed ‘restrained search predictive control method’ or RSPC, where the number of considered inverter states in every sampling period is 6, 11 or 16. A dynamic selection criterion to minimize the number of commutations in the sixphase power converter is applied in every control step. The number of usable voltage vectors in the asymmetrical sixphase drive is therefore reduced, as is the computational time of the control technique. Different predictive current control techniques are also developed to reduce the generated harmonic content. For example, the selected voltage vector is combined during the control period with a zero vector in [65], resulting in a predictive current control method termed OSPC or ‘one–step modulation predictive current control’. The active vector that minimizes the cost function is modulated, and the OSPC applies a more appropriate voltage vector in terms of achieving the control goals. The number of available voltage vectors is the same as used in [62,63]. This idea is further refined in [66,67] where a proper pulse width modulation scheme is combined with the predictive current control technique, and a voltage reference that ensures sinusoidal output voltage and operation in the linear modulation region is imposed, while avoiding over-modulation region. The MPC method has been extended to the five-phase induction motor drive in [68], where the common mode voltage is also reduced, and in [69], where a detailed comparison between MPC based current controllers and PIPWM current control techniques is provided across the full inverter’s linear operating region under constant flux-torque operation mode. The predictive controller designed in [69] applies a quadratic cost function with torque (primary plane) and non-torque (secondary plane) producing currents, using
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733 a weighting factor for the currents of the secondary plane. Table II and Fig. 5 summarize obtained results. It is concluded that a better transient performance is obtained using FCS-MPC, but steady-state performance is superior with PI-PWM control. Guidelines for the best switching state set and weighting factor selections are also provided. B. Direct Torque Control High performance control of multiphase drives using DTC techniques is much more difficult to achieve than using three-phase drives, due to the inherent nature of the control technique. Its basic principle is to regulate only two variables, the electrical torque and stator flux, using hysteresis controllers. This is fine in three-phase drives, since there are only two independent currents. But, in multiphase machines, there are in principle (n1) independent currents and hence using a single voltage vector in each switching period, selected purely on the basis of flux and torque requirements, may lead to excessive nonflux/torque producing currents and low efficiency. Stator voltage vector is typically obtained from an optimal switching table (ST-DTC) or by imposing a direct mean torque control approach and a constant switching frequency (PWM-DTC). The efficiency of the controller decreases when the number of phases and degrees of freedom increase. The DTC technique has not been extended yet to any phase number higher than six. However, some advances have been recently achieved in the application of the STDTC method to the multiphase drives. The focus is on the definition of the switching table for five-phase and asymmetrical six-phase induction machines and the reduction of the stator voltage in the secondary plane(s) to minimize the generated non-torque producing stator current components [70-73]. The improvement of the obtained performance at low-speed operation is also analyzed in [71]. Distributed winding machines are considered, and some further work is expected in the area in the future like in [74], where the ST-DTC method is extended and generalized for n-phase induction machines and n is any odd number higher than three. C. Alternative Control Methods A recent control proposal in the multiphase drive area is predictive torque control (PTC) method, detailed in Fig. 6 and presented in [75] as a competitor of the DTC method for a five-phase induction machine. The viability and effectiveness of the PTC strategy is confirmed using experimental results, which are compared with those obtained using the modified DTC method of [70]. Fig. 7 and 8 summarize obtained results, where it can be deduced that the PTC-based control technique is a viable alternative to the DTC method, offering better torque dynamic performance, quicker speed response and lower torque ripple, while the overcurrent protection of the power converter and the operation at a lower average switching frequency are guaranteed (Fig. 7). From the computational point of view,
PTC requirements are about 2.5 times higher than DTC ones, which is a clear disadvantage (Fig. 8). A different control method that does not require the application of coordinate transformations, based on the brush-dc-machine operation principles, is applied in [76] to a nine-phase cage-rotor induction machine. A model reference adaptive speed controller based on artificial neural networks is used in five-phase interior permanent magnet motor drives in [77]. A modified V/f control technique has been applied in [78] to a five-phase induction machine to generate a trapezoidal air-gap flux, combining fundamental and third harmonic stator voltages. Results obtained in [78] prove that the torque/ampere ratio is increased, compared with the conventional V/f control technique, if the machine is under heavy load conditions (above 50% of the nominal one). However, larger stator losses and currents are generated in light load operation modes. Finally, the effect of stator winding configuration is studied as a mean to extend the operational range of multiphase drives in [79,80]. The number of possible alternatives for connecting the phases of an n-phase electric machine is (n+1)/2, but most of the available research is restricted to the star connection. When the speed goes up, higher multiphase power converter ratings (voltages and currents) are required, which limit the operational speed range of the drive. A five-phase permanent magnet machine is operated in [79] using three types of winding configurations, star, pentagon and pentacle, and the comparative performance of the drive is analyzed in terms of torque-speed and efficiency. It is concluded that the configurations with lower voltages are suitable for higher torque and lower speed, while those with higher voltages are appropriate for lower torque and higher speed. Then, a winding changeover technique is applied for extending the operational speed range of the drive, together with a maximum torque per ampere control strategy. The star and pentagon connections are also compared in [80], where a V/f control method is used. Provided results show a superior TABLE II COMPARISON OBTAINED IN [69] BETWEEN PI-PWM AND FCSMPC USING 31 DIFFERENT VOLTAGE VECTORS (MPC-31) Feature MPC-31 PI-PWM control Sampling freq. 10 kHz 2.5 kHz Switching freq. (exp.) 1950-3700 Hz 2500 Hz Dynamic decoupling Internal External Machine parameter All except stator All requirements resistances Control of the secondary Current error in the Additional pair of PI plane currents cost function controllers Computational cost High, 82s Low, 27s Difficult, retuning Easy, retuning is not Tuning required for different required operating points Broad & continuous, Modulation type, low Phase voltage/current spectra high THD THD and THD (10.8% - 12.6%) (6.4% - 6.9%) Transient, 90% rise time Consistently faster, Slower, 4.5ms (see Fig. 16 in [69]) 0.7ms Current control bandwidth Larger Smaller
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733 DC-bus
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DSP Microcontroller-TMS32F28335 DSP Microcontroller-TMS32F28335 (a) (b) Fig. 4. The current controller in the rotor flux oriented reference frame is compared in [69] for a five-phase induction motor using: (a) MPC based current control with all 31 voltage vectors (MPC-31) involved in the objective function minimization stage, and (b) PI-PWM current controllers. Reproduced from [69] with the permission of the authors.
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Fig. 6. General PTC control scheme proposed in [75] for a five-phase induction motor drive.
Fig. 7. Experimental results obtained in [75] where the PTC method (left plots) and the modified DTC technique detailed in [70] (right plots) are compared.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS – DOI: 10.1109/TIE.2015.2447733 REFERENCES [1]
[2]
[3]
Fig. 8. Real time implementation details in a sampling period shown in [75], where PTC and DTC methods are compared.
performance of the star connection in healthy operation mode. The paper also analyzes the faulty mode of operation (open-phase condition), concluding that the pentagon connection offers better behavior. The ability to operate the multiphase drive in faulty state requires however some modifications in the models, current references and control strategies, and the recent advances in the field are surveyed in the second part of this state of the art paper. V. CONCLUSIONS The attention paid to multiphase machines and drives has experienced a continuous growth in recent times and the body of knowledge in the area has significantly increased in the last few years. This two parts’ paper surveys some of the aspects of multiphase machines/drives with emphasis placed on developments since the publication of the first Special Section on “Multiphase Machines and Drives” in the IEEE Trans. on Industrial Electronics in May 2008 [2]. The topics covered in this part include the design, modeling and control areas in motoring and healthy state. At first, some novel aspects of the multiphase machine design have been covered, with an emphasis placed on structures that reduce the cost and weight of the electromechanical system while improving the obtained power density and reliability and introducing the interest of the superconducting technology in the design of multiphase machines. Next, the latest advances in the multiphase machine modeling have been surveyed, including the stateof-the-art in off-line and on-line identification techniques of the machines’ electrical parameters. Finally, recent advances in control strategies for multiphase machines in healthy operation are also reviewed. A special attention has been paid to multi-frequency current supply cases, where lower distortion and torque enhancement are obtained. While FOC and DTC are still the dominant control approaches when it comes to variablespeed multiphase drives, it is interesting to note that an entirely new area has appeared in recent years, namely model predictive control. While MPC is a well-known control approach for the three-phase drives, its use in multiphase drive related research commenced well after the publication of [2].
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Federico Barrero (M 04; SM 05) received the MSc and PhD degrees in Electrical and Electronic Engineering from the University of Seville, Spain, in 1992 and 1998, respectively. In 1992, he joined the Electronic Engineering Department at the University of Seville, where he is currently an Associate Professor. He received the Best Paper Awards from the IEEE Transactions on Industrial Electronics for 2009 and from the IET Electric Power Applications for 2010-2011.
Mario J. Duran was born in Málaga, Spain, in 1975. He received the M.Sc. and Ph.D. degrees in Electrical Engineering from the University of Málaga Spain, in 1999 and 2003, respectively. He is currently an Associate Professor with the Department of Electrical Engineering at the University of Málaga. His research interests include modeling and control of multiphase drives and renewable energies conversion systems.
