Predictive current control in electrical drives: an illustrated review with case examples using a five-phase induction motor drive with distributed windings

Predictive current control in electrical drives: an illustrated review with case examples using a five-phase induction motor drive with distributed windings Mario Bermúdez1, Cristina Martín2, Ignacio González-Prieto3, Mario J. Durán3, Manuel R. Arahal4, Federico Barrero2,* 1 Electrical Engineering Department, University of Huelva, Avenida de las Fuerzas Armadas s/n, 21007, Huelva, Spain 2 Electronic Engineering Department, University of Sevilla, Camino de los Descubrimientos s/n, 41092, Sevilla, Spain 3 Electrical Engineering Department, University of Málaga, C/ Doctor Ortiz Ramos s/n, 29071, Málaga, Spain 4 Systems Engineering and Automation Department, University of Sevilla, Camino de los Descubrimientos s/n, 41092, Sevilla, Spain *[email protected] Abstract: The industrial application of electric machines in variable-speed drives has grown in the last decades thanks to the development of microprocessors and power converters. Although three-phase machines constitute the most common case, the interest of the research community has been recently focused on machines with more than three phases, known as multiphase machines. The principal reason lies in the exploitation of their advantages like reliability, better current distribution among phases or lower current harmonic production in the power converter than conventional three-phase ones, to name a few. Nevertheless, multiphase drives applications require the development of complex controllers to regulate the torque (or speed) and flux of the machine. In this regard, predictive current controllers have recently appeared as a viable alternative due to an easy formulation and a high flexibility to incorporate different control objectives. It is found however that these controllers face some peculiarities and limitations in their use that require attention. This work attempts to tackle the predictive current control technique as a viable alternative for the regulation of multiphase drives, paying special attention to the development of the control technique and the discussion of the benefits and limitations. Case examples with experimental results in a symmetrical five-phase induction machine with distributed windings in motoring mode of operation are used to this end. 1. Introduction It is expected that 80% of all the produced energy will be used by electric drives by 2030. Electric vehicles play a major role in this context, as they will account for almost 50% of the automotive market by that year [1]. Furthermore, electric drives are the basis of locomotive traction, electric ship propulsion, more-electric aircraft for various auxiliary functions (e.g., fuel pumps, starter/generator solutions, etc.), and renewable energy production. While conventional three-phase drives represent the principal choice for industrial applications, multiphase ones have recently awoken the interest of practitioners and researchers in the field. Any energy conversion system formed by a multiphase electric machine supplied from a multi-channel converter is termed multiphase drive. The first application of such a system was done in the late 60s in a five-phase drive [2], showing some of the advantages of multiphase systems over conventional three-phase ones. The main interest of this proposal was to highlight that the higher number of phases yields a torque ripple three-times lower with respect to the equivalent three-phase case. The better power distribution per phase helped in this way to mitigate one of the most reported problems in conventional drives by that time. However, it was not until the beginning of the 21st century that the interest of researchers in multiphase machines was renewed due to two main reasons. Firstly, the development of high-power high-frequency semiconductors using Pulse Wide Modulation (PWM) methods to control the ON/OFF states of these electronic devices. Secondly, the development of the microelectronic technology and the appearance of Digital Signal Processors (DSPs) and Field-Programmable Gate Arrays (FPGAs) with the ability to implement control algorithms in real time. Notwithstanding the foregoing, the crucial reasons for the renewed interest in multiphase drives can also be found in their intrinsic advantages together with the discovery of innovative and exclusive modes of operation. These benefits are based on the extra degrees of freedom provided by the higher number of phases, and are mainly the following: The fault-tolerant capability against a fault situation in the machine and/or the power converter, firstly presented in [3]. An n-phase machine can operate after one or several fault occurrences without any external equipment, as long as the number of healthy phases remains greater than or equal to three (assuming a single isolated neutral connection). Consequently, the system reliability is enhanced at the expense of a reduction in the post-fault electrical torque production. The capability to increase the power density in healthy operation by injecting specific current harmonics, firstly exposed in [4]. This is possible in certain multiphase machine configurations based on concentrated windings, where the lower current harmonic components can be used to increase the torque production. These advances and advantages underlie the adoption of multiphase machines for variable-speed drives in specific industry applications [5,6]. Electric propulsion of ships, traction in electric vehicles (hybrid/electric vehicles and locomotives), wind energy generation and low-power electric systems for more-electric aircraft are fields where the investigation in the last 20 years has been focused on [7,8]. The interest of multiphase machines in the cited applications, instead of their conventional three-phase counterparts, arises from the high torque/current and/or fault-tolerant requirements. Benchmark solutions adopted by important companies are the ultrahigh-speed elevator of Hyundai based on a 1.1 MW nine-phase electric drive [9] (see Fig. 1), the 5 MW twelvephase electric drives in the wind turbines of Gamesa for onshore and offshore plants, and the 20 MW fifteen-phase electric drive for ship propulsion introduced by the GE Power Conversion company in the Royal Navy [10]. (a) (b) Fig. 1. Example of an industrial multiphase drive: the ultrahigh-speed elevator developed by Hyundai, based on (a) multiple three-phase back-to- back converters and (b) a nine-phase permanent magnet synchronous machine with three isolated neutral points In order to create a body of knowledge, recent research works review the advances in the field of multiphase drives including their industrial applications, machine design and modeling, types of converters, modulation techniques, control strategies and innovative uses of the additional degrees of freedom (i.e., multimotor drives, battery chargers, post-fault control or dynamic breaking) [10,11-13]. In general terms, they show that: i) symmetrical five-phase and asymmetrical six-phase machines with isolated neutrals are the most popular multiphase machine types in the research community, and ii) an evolution in the control techniques has been necessary in order to optimally exploit their inherent advantages. In this regard, asymmetrical six-phase machines with isolated neutrals can be considered as two conventional three-phase machines coupled in a common case, while the five-phase drive can be considered the ideal case example to illustrate any study in the multiphase drive field. Previous state-of-the-art analyses on multiphase drives set the advances in the area in the last decades. However, they are mainly aimed at researchers and lack important information for practitioners and researchers starting in the field. Field Oriented and Direct Torque Controllers (FOC and DTC, respectively) have been usually considered as standard regulation strategies in conventional three-phase drives. However, Model Predictive Controllers (MPC) have recently appeared as a promising alternative. The simplicity and intuitive formulation of the control problem using predictive controllers applied to electric drives has boosted the interest of the research community [10,11-13]. This is particularly true in the multiphase drives field, where predictive controllers offer the possibility to perform multi-objective and multi-variable control, including non-linearities or constraints into the control process by just defining a proper cost function. Nevertheless, MPC faces some limitations that still require attention, being the most prominent one a high computational cost, which increases with the number of phases. This manuscript presents an up-to-date review of the most recent research in relation to the use of predictive current controllers for multiphase machines. The work goes beyond previous published papers, not only including the most recent applications of this technique found in literature, but also identifying some future research trends in the area. Furthermore, a detailed illustration using a particular five-phase induction motor drive as case example constitutes the basis of the review, with the aim of providing, all in all, a framework of analysis and guidelines for researchers and practitioners. After this introductory section, the paper is organized as follows. First, the five-phase induction motor drive system, which will be used as a case example along the work, is analyzed and modeled. Next, the control techniques recently used in multiphase drives are reviewed, focusing on the Predictive Current Control approach but in the context of control techniques that have been extended to multiphase drives in recent times. The key design and implementation features in predictive controllers, as well as the future prospect in the field are shown in Sections 4 and 5, respectively, and the conclusions are finally drawn in the last section of the manuscript. 2. Multiphase drives: the case of five-phase IM drives with distributed windings A common feature in most control techniques applied to multiphase drives, particularly MPC methods, is the necessity of a precise and complete knowledge of the system dynamics through a mathematical model. To obtain that model, different construction aspects of the multiphase machine and the power converter must be taken into account, beginning with the type of machine and converter. Depending on the rotor construction, multiphase machines can be divided into two main types, multiphase induction machines (IM) and multiphase synchronous machines, usually of the permanent magnet type (PMSM). Although both types present similar modeling approaches, IMs benefit from a simple and rugged construction with cheaper materials, low maintenance requirements, and well-proven technology, making them a usual election in industrial applications. Concerning the winding arrangement, the division is done between symmetrical or asymmetrical multiphase machines. First ones are constituted by consecutive phase windings equally displaced (being the number of phases), whereas the second ones are typically formed by independent sets of windings displaced . Another classification considers the number of phases, distinguishing between machines with an odd or an even number of phases, and machines with multiple sets of three-phase windings. Notice that the higher the number of phases, the more complex the model. Finally, multiphase machines can be constructed with either concentrated or distributed windings. The most relevant interest in the concentrated-windings type is the existence of higher-order spatial harmonics in the magneto-motive force (MMF) that contribute to the electrical torque enhancement. Conversely, these harmonics can be neglected in distributed-windings machines (with an appropriate stator winding design), resulting in near sinusoidal MMF. Regarding the power converter topology, the most widespread option is the back-to-back configuration, usually formed by a gridconnected three-phase rectifier electrically coupled to an n-phase inverter through a DC-link. This configuration permits the independent regulation of the inverter stage since it is decoupled from the distribution grid. Furthermore, it presents the capacity to generate an output with a wide range of frequencies and a small content of low-order harmonics by means of a suitable control algorithm (principally PWM-based techniques). The most used inverter type is the IGBT-based two-level voltage source inverter (VSI) that single-sided supplies the electric machine. However, depending on the application requirements, other types and converter topologies (multilevel VSI, matrix VSI or even current source inverters) can be found in the literature [14-16]. The model of the multiphase drive used as case example, composed by a five-phase two-level VSI that supplies a symmetrical five-phase IM with distributed windings, is introduced here. First, the physical model of the induction machine is presented, covering the one based on phase variables (or original model), and the additional transformations conventionally applied to reduce the complexity of the mathematical equations. These are the decoupled (Clarke) transformation and the rotational (Park) transformation. Finally, the model of the power converter is also presented. 2.1. Five-phase IM machine with distributed windings Any multiphase machine can be described as a set of differential equations in phase variables (currents, voltages and fluxes) using the general theory of electric machines [17]. However, the generalization from Fortescue and Clarke [18,19] laid the foundations for different mathematical transformations. Their main objective is the replacement of the original phase-variable model by equivalent equations using a reduced set of new (fictitious) variables, thus permitting the simplification of the machine model. These transformations are collected in what is usually named Vector Space Decomposition (VSD) approach [20,21], where matrix representation is conventionally adopted. This approach is slightly different depending on the winding arrangement of the machine (symmetrical or asymmetrical, and distributed or concentrated) and on the number of phases (multiple of three or not). Therefore, multiple works have been developed in the field of multiphase machines modeling, considering different topologies of both induction and synchronous machines [4,11,22-24]. The focus here is the symmetrical five-phase induction machine with distributed windings that are electrically displaced by . Since the rotor is squirrel-cage type, it can be treated as five windings equally displaced around the rotor circumference. A schematic representation of the machine is presented in Fig. 2, where to and to denote each phase of the stator and rotor windings, respectively. These windings are starconnected with an isolated neutral point. Additional simplifying assumptions are considered in the modeling: All phase windings in the stator/rotor are considered identical. The distribution of the MMF and, consequently, the flux around the air-gap can be regarded as sinusoidal, assuming symmetrical distributed windings. This means that all spatial harmonics can be neglected, except for the fundamental one. The magnetization characteristic of the ferromagnetic material is assumed to be linear. Therefore, the effects of magnetic field saturation are negligible and mutual inductances are constant. The air-gap is regarded as uniform by neglecting the impact of slotting. Stator and rotor resistances and leakage inductances are considered constant. Variations due to temperature and/or skin effect are neglected. Losses in the ferromagnetic material due to hysteresis and eddy currents are not considered. sa ra sb sc sd s e ωr rb rc rd re θr ϑ=2π/5 RsLls Ms (ϑ) Lsr (θr) Fig. 2. Scheme of the symmetrical and distributed-windings five-phase IM Taking into account the previous hypotheses and considering that the positive direction for the currents is from the supply source to the machine phases (motoring convention), the stator and rotor voltage equilibrium equations that describe each phase of the machine can be expressed in the following matrix form: (1) where and are the stator and rotor resistances. Stator and rotor currents ( ), voltages ( ) and fluxes ( ) are defined as (2) Since the studied induction machine has a squirrel-cage topology, rotor voltages are equal to zero. Additionally, it is important to remark that rotor variables and parameters in (1) and (2) are referred to the stator, this being a common procedure in three-phase machine modeling. Previous equations are completed with the definition of the stator and rotor fluxes in terms of stator and rotor currents (3), which represent the coupling between the stator and rotor. (3) Under the above considerations, stator and rotor inductance matrices, and , have constant coefficients that only depend on the stator and rotor leakage inductances and , the mutual inductance , and the winding electrical displacement as follows: .(4) On the other hand, mutual stator-to-rotor and rotor-to-stator inductance matrices in (3), which verify that , are not constant but dependent on the instantaneous value of the rotor position with respect to the stator, , through (5) where , with k = 1,2,...,5; and the rotor angle is obtained through the electrical rotor speed (6) Equations (1)-(6) describe the electrical part of the five-phase IM that is complemented with the mechanical equation (7) being the mechanical speed of the rotor shaft ( , with P the number of pole pairs), the load torque applied to the machine, the electromagnetic torque, the inertia of the rotating masses, and the friction coefficient. The electromagnetic torque is responsible for the electromechanical energy conversion, linking the electrical and mechanical subsystems. This torque is obtained with the following equation: (8) Taking into account that stator and rotor inductance matrices do not depend on the rotor position, the previous equation can be reduced to the one in (9), where it can be observed that the electromagnetic torque is entirely created from the interaction between the stator and rotor. (9) To summarize, the five-phase IM can be represented in the phase-variable domain through first-order differential equations, after the substitution of the flux expressions (3) into the voltage equilibrium equations (1), and the electromagnetic torque value (9) into the mechanical equation (7); plus 1 integral equation (6). Due to the time-dependence through the rotor position angle, these equations constitute a non-linear time-variant system. Even if the resolution of the phase-variable equations is possible with advanced computational devices, important simplifications can be done through the VSD approach. Thus, it is possible to represent the five-phase IM model in a stationary reference frame formed by a new set of five fictitious variables using the Clarke transformation. They are grouped into two two-dimensional orthogonal planes, named α-β and x-y, whose components are also orthogonal between them; plus an additional axis that contains the homopolar component, named z. The main characteristic of this new reference frame is that the different planes are completely decoupled due to the orthogonality, resulting in a simpler model that is more suitable for control purposes. In addition, the transformation of the phase variables into the new stationary reference frame provides better insight into the physical phenomena involved in the energy conversion process: the α-β plane becomes responsible for the torque production, while the x-y plane and the z-axis are only related to harmonic components and stator losses in the machine. Then, the relationship between the original phase variables and the new fictitious ones is obtained by applying the decoupled (Clarke) transformation matrix , defined in (11), to the stator and the rotor variables in the following way: (10) .(11) The coefficient in front of the transformation matrix is associated with the power of the machine after the transformation. The selected value keeps the original values of the electrical variables invariant after the transformation, but not the total power before and after the transformation, thus being commonly known as power-variant (or amplitude-invariant) transformation. However, it is also a common practice to use the coefficient instead, which keeps the total power of the machine before and after the transformation invariant (power-invariant transformation [5]). Substituting (3) into (1) and applying the decoupled transformation, the resultant stator and rotor equilibrium equations can be written as shown in (12) and (13) after some mathematical operations, where is the equivalent mutual inductance, and the stator and rotor inductances in the new reference frame are defined as and , respectively. The parameters that appear in these equations are, in essence, those of the well-known IM equivalent circuit in steady state. Consequently, they can be obtained from standard no-load and locked rotor tests [25,26]. . (12) (13) Again, rotor voltages are considered zero since the rotor is squirrel-cage type. It can be seen that stator variables are referred to the stationary reference frame α-β, whereas rotor ones are referred to a different reference frame α’-β’ that rotates at the rotor speed (see Fig. 3). This issue has been represented by the apostrophe in the rotor variables ( and ) only in the α-β equations because it is exclusively in this plane where the stator and rotor coupling takes place. As a consequence, the dependence on the rotor angle in some inductance terms still remains. In order to eliminate this dependence, it is necessary to apply an additional change of variables, which is β β′ α α′ ωr θr sa ra Fig. 3. Reference frames of stator (α-β) and rotor (α’-β’) variables equivalent to a rotational transformation of the rotor α’-β’ variables into the stationary α-β plane. This is done using the following rotational matrix [5,6]: (14) After the application of the rotational transformation to equations (12) and (13), the final electrical model of the machine in the stationary reference frame can be cast in the form [5,6] (15) (16) Notice that new expressions for the rotor and stator fluxes have been deduced: (17) The electromagnetic torque (9) can be expressed in the new stationary reference frame applying (11) and (14), and performing some calculations, giving rise to the following expression [5,6]: (18) It must be noted that the factor in this expression will not appear in the case of applying a power-invariant transformation. As expected, only variables in the α-β plane are involved in the electromechanical energy conversion process (remember that a distributed-winding machine is considered) or, in other words, in the fundamental torque and flux production. Some additional analyses must be done regarding the electrical model in (15) and (16). Since the coupling between the rotor and stator windings exclusively takes place in the α-β plane, from the rotor voltage equations it can de deduced that x-y and z rotor voltages can be discarded. Furthermore, the star connection of the stator windings with isolated neutral points avoids the flow of the homopolar current, so there is no need to take into account the z component equation. After all these simplifications, the final machine model in the stationary reference frame can be totally described by 6 differential equations plus the mechanical equation with the new torque expression, which implies a significant reduction of the model complexity in comparison with the original phase-variable model. However, the non-linear and time-variant properties of the differential equations remain. Note that the described transformation permits a detailed analysis of the voltage and current harmonic components, since some of them are mapped into certain planes. Therefore, in normal condition the fundamental frequency and harmonic components of order , with , map into the α-β plane contributing to the electromechanical energy conversion. Conversely, harmonics of order map into the x-y plane, only contributing to the losses in the machine. Finally, the DC component plus harmonics of order map into the homopolar axis, which cannot flow in the case study. Since α-β components are responsible for the torque/flux generation, they constitute the priority in the control process. However, these components present an oscillating nature, hence they are usually expressed in a rotating reference frame (termed d-q) to ease their regulation. Thus, after the rotational (Park) transformation, the d-q components of the electrical variables are constant in steady-state condition and variable during transients [27]. Regarding the x-y components, assuming an ideal symmetrical and balanced sinusoidal five-phase voltage supply, they are zero and consequently it is not necessary to rotate them. Nonetheless, they are also rotated in situations when the aforementioned assumption of ideal supply is no longer applicable (e.g., in fault conditions in the VSI legs [28]), leading to non-zero oscillating x-y currents. In this transformation, the new d-q reference frame is considered to rotate at an arbitrary speed and its instantaneous position with respect to the stator α-β reference frame is defined by the electrical angle (see Fig. 4), being both quantities mutually related through (19) Consequently, α-β stator variables can be referred to the new rotating reference frame with the following expressions and rotational matrix [5,6]: (20) (21) qd δ θ ω β β′ α α′ ωr θr sa ra Fig. 4. Rotating reference frame (d-q) In the case of rotor variables, expressed in the α’-β’ plane after the Clarke transformation, a different rotational matrix must be defined in order to refer both stator and rotor variables to the same d-q reference frame, eliminating the relative motion between stator and rotor windings. Following the representation in Fig. 4, the instantaneous position of the rotor reference frame α’-β’, which rotates at the rotor speed , with respect to the d-q reference frame, is given by the electrical angle . This angle can be obtained through (22) where is the relative speed between the rotating and the rotor reference frames, called slip speed. Hence, the rotor variables in the new rotating reference frame are obtained using the following equations and rotational matrix: (23) (24) Applying the rotational matrices (21) and (24) to the stator and rotor voltage equilibrium equations (12) and (13), the complete machine model in the rotating reference frame can be expressed as (25) (26) where the relationship between stator and rotor fluxes, and the stator and rotor currents in the rotating frame is the following: .(27) Notice that equations in the x-y plane stay unaltered since the rotation is only performed in the α-β plane. For simplification purposes, the stator and rotor z-axis components and the rotor x-y components are omitted following the previous reasoning. Proceeding in an analogous way, a new expression of the electromagnetic torque can be derived [5,6] (28) However, it is usual to find alternative expressions of this torque, such as the one shown in (29), where the correlation between stator and rotor fluxes and currents is implicitly considered. These alternative formulations are useful in some control strategies in order to reduce the number of calculations when the model is expressed in certain reference frames. Notice, again, that the coefficient would not appear if the power-invariant decoupling transformation is used instead of (11). (29) As a final remark, the speed of the rotating reference frame ( ) can be arbitrarily selected in the IM. However, depending on the control strategy, some selections are more favorable than others to reduce the machine model complexity. This is the case of the Rotor Field Oriented Control (RFOC), where is selected in such a way that the d-axis is fixed to the rotor flux and, consequently, the projection of this flux in the q-axis becomes null [6,29]. Another considered option consists in the alignment of the reference frame to the stator flux, which is typically used in the DTC technique [30,31]. 2.2. The power converter model The simplest configuration corresponds to a two-level five-phase VSI, formed by two IGBTs per leg with their corresponding antiparallel free-wheeling diodes, where the DC-link voltage ( ) is provided by an external low-impedance DC source. A schematic representation of this VSI is depicted in Fig. 5, where a balanced inductive load has been included to represent the machine stator windings when they are star-connected, being N the common neutral point. For this scheme, the state of each VSI leg can be defined as , with ; being when the upper IGBT is ON and the lower one is OFF, while the opposite occurs when . In this way, short circuits are avoided. In practice, a small dead-time should be introduced between the switching operation of the IGBTs aiming to avoid transient short circuits, but this is not reflected in the final VSI model for the sake of simplicity. Under these considerations, the voltage in the midpoint of the corresponding leg with respect to the negative bus of the DC-link can be defined in terms of the switching state of that leg using the following expression: (30) This voltage is related to the stator phase voltage, , through the voltage between the common point of the star connection and the negative bus of the DC-link, , in the following way: (31) Assuming a balanced load, the sum of the five stator phase voltages must be equal to zero. Thus, adding all stator phase voltages derived form (31) and combining the result with (30), the voltage can be defined as (32) Introducing this value in (31), an expression for the stator phase voltages in terms of the switching states of the VSI legs can be derived (33) Consequently, if the switching state of the VSI is defined as the vector , the above equation can be expressed in matrix form (34) For the case of the five-phase configuration, there are possible switching states that lead to phase voltage values equal to , , , and , according to (34). These states constitute different load conditions from the point of view of the VSI, characterized by the number of load windings connected to the positive and negative rails of the DC-link. The higher the number of phases of the VSI, the higher the number of voltage levels that the converter can generate. This leads to a decrease in the harmonic content and a better reconstruction of the sine wave that is generated by the power converter, as well as the reduction of the common-mode voltage [32]. Finally, the possible phase voltages can be mapped into VSD variables by applying the Clarke transformation matrix (11), producing voltage vectors represented in the α-β and x-y planes (z-axis component can be neglected in the star connection with isolated neutral point). Fig. 6 shows the projections of these vectors on each plane, where they have been numbered by the equivalent decimal number obtained from its corresponding switching state , being and the most and the least significant bits, respectively. It can be seen that there exist 2 null vectors and 30 active vectors, the last ones being classified in large ( ), medium ( ) and short ( ) vectors. Thus, the space is divided in ten sectors of the same size with a separation of between them. 2.3. Experimental test bench This illustrated review is based on a five-phase IM drive with distributed windings. Therefore, the contribution of the x-y plane to the electrical torque is neglected. Experimental results will be shown along the work to exemplify the performance of the system using different predictive current controllers. The experimental test bench depicted in Fig. 7 is used for this purpose. The test rig is composed by a three-phase IM rewound to have five phases with 30 slots and three pole pairs, whose electrical parameters are detailed in Table 1. The machine is supplied by two three-phase inverters from SEMIKRON that are connected to a DC-link voltage of 300 V from an independent DC power supply. The control algorithm is implemented in a TM320F28335 DSP placed on a MSK28335 Technosoft board. An external programmable load torque is also introduced in the system by means of an independently controlled DC motor. Finally, the rotor mechanical speed is measured using a GHM510296R/2500 encoder that is coupled to the shaft of the multiphase IM. isa vsa - + SbSc Sa abc N vsb - + vsc - + isb isc Sd d vsd - + isd Se e vse - + i se Vdc Se Sd Sc SaSb vN + - vj + - Fig. 5. Scheme of the five-phase two-level VSI with star-connected load 31 2 8 10 1 3 9 11 4 6 12 14 5 7 13 15 16 18 24 26 17 19 25 27 20 22 28 30 21 23 29 0 α β 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0x y Fig. 6. Space vector diagrams in the α-β and x-y subspaces Current Sensors DC MOTOR 5-PHASE IM a b DC MOTOR DRIVE RS232 Serial Ports 5-PHASE IM DRIVE Switching Signals Phase Currents CONTROL BOARD Speed Encoder (ωm) DC-LINK Vdc abde c POWER ELECTRONIC CONVERTERS (VSIs) Fig. 7. Graphic diagram of the experimental system Table 1. Electrical parameters of the machine Parameter Value Stator resistance 19.45 Ω Rotor resistance 6.77 Ω Stator leakage inductance 100.7 mH Rotor leakage inductance 38.6 mH Mutual inductance 656.5 mH Pole pairs 3 Stator rated current 2.5 A 3. Multiphase drives control techniques: the predictive current control approach With the increasing interest in multiphase drives, the need for high-performance controllers has led the research activity in the last years. Conventionally, they are a complex extension of those applied in the three-phase case, and their principal objective is the accurate and fast regulation of the speed and torque while fully exploiting the advantages of having more than three phases. The most widespread control technique applied to multiphase drives in the research literature and in industrial applications is the Vector Control (VC) or FOC. It is based on the use of Proportional-Integral (PI) regulators followed by a PWM stage that linearly provides the VSI switching combinations to be applied, hence it can be referred as a ‘linear’ controller. On the other hand, novel control strategies are appearing to simplify and enhance the multiphase control. These new techniques are based on ‘non-linear’ strategies, mostly known as ‘direct’ controllers, which do not include the PWM stage or other form of modulation. Conversely, they directly command the VSI forcing the controlled variables to rapidly follow their references. This is the case of the DTC method, which is the leading competitor of the FOC technique in three-phase drives; and the MPC technique, which has recently appeared as a promising alternative due to its flexibility and simple formulation. This section will be focused on the description of these methodologies and their most recent applications to multiphase drives, particularly to IM drives. 3.1. Field Oriented Control The basis of the FOC technique, founded at the beginning of the 70s [33], is the independent control of the flux and torque of the AC machine in a similar way as it is done in a DC machine. For that purpose, a proper transformation of the controlled variables to the dq plane is mandatory, where the d-axis is aligned with one of the flux components (air-gap, stator or rotor flux) in order to achieve the decoupling between flux and torque. Nowadays, the level of maturity of FOC for three-phase drives has permitted the total replacement of DC machines by AC ones in most industrial applications based on variable-speed drives. In the case of multiphase drives, the higher number of degrees of freedom increases the complexity of the controller extension, as it is shown in numerous research works mainly based on the Indirect Rotor FOC (IRFOC) [11,34-38]. In this particular version of the control technique, the d-current is aligned with the rotor flux through the proper selection of the rotating reference frame angle in the Park transformation ( in Fig. 4). In this way, the machine is fluxed by the d-current component while the electromagnetic torque is regulated by the q-component of the stator current. When applying the IRFOC to an IM, the orientation of the rotor flux in the required direction is done through the imposition of the slip speed in the following way: (35) where reference values of the flux- and torque-producing stator currents ( and ) are normally used in the calculation process. However, a good knowledge of some machine parameters in the previous equation is necessary for a good orientation. Other versions of the FOC technique can be encountered in the literature with different flux components aligned with the d-axis and various estimation methods in the flux angle calculation [24,33,39]. The general IRFOC control scheme for a five-phase IM with distributed windings is shown in Fig. 8. It has the same cascaded structure used for three-phase drives, with an outer speed controller and an inner current controller per current component. Both current and speed controllers are typically PI regulators. With this configuration, the speed controller establishes the q-current reference while the d-current reference is set as constant. Conventionally, its nominal value is selected if the reference speed is below the synchronization speed of the machine, or regulated to deflux the machine if the speed goes beyond the synchronization point (field weakening region). The outputs of the current controllers are the reference voltages that must be applied to the machine in order to follow the current references. In this process, compensations terms, and , are added to take into account the coupling of the d-q stator voltages equations and compensate in a feedforward manner the cross-coupling effect. These terms are highly dependent on the machine parameters. The difference of the control scheme with respect to the threephase case is the incorporation of additional PI regulators for the x- y currents. It should be emphasized that, although these currents can be theoretically zeroed in distributed-winding machines impressing zero x-y stator voltage components, this might not be the case in a real application if stator windings present some degree of asymmetry and/or if the impact of the VSI dead-time is not negligible [28,35]. Consequently, it is advantageous to regulate x-y currents to be zero. For the case of IMs without isolated neutral point, it is also necessary to include an additional controller for the homopolar current. From this, it is stated that the complexity of the control scheme increases with the number of phases, being necessary to add a higher number of PI regulators that should be independently tuned. Once the voltage references are given by the PI regulators in the d-q and x-y planes, they are transformed to phase variables using the inverse of the Park and Clarke transformations. After that, these phase voltages are modulated with some type of PWM strategy, conventionally Carrier-Based or Space Vector PWM (CBPWM and SVPWM, respectively) techniques, providing the switching pattern to be released to the VSI. Although these PWM techniques are well established in the three-phase case and the extension of the CBPWM to multiphase drives does not imply further complexity, the same does not apply to SVPWM, whose extension to the multiphase case has been recently investigated [10]. More recent research works in the field of FOC are centered on the full exploitation of the additional degrees of freedom in multiphase machines, like in the case of the torque enhancement through harmonic injection in concentrated-windings induction machines and in permanent magnet machines with different number 5φ IM VSI isa isc isb isd ise abcde dqxy ωm θ PWM isx PI isq ed eq λrd isd Sa Sc Sb Sd Se abcde dqxy PI PI PI isy PI ωm θ Position Estimator and Feedforward Terms ed eq isd isq isy isx θ Kflux ωm * * λrd * isq * isx * isy * vsd * vsq * vsx * vsy * isq * λrd Fig. 8. IRFOC technique for the distributed-windings five-phase IM drive of phases [40-44]. The extension of the FOC technique for the postfault operation of the drive has also been addressed, focusing on the case of open-phase faults (the most analyzed post-fault situation in the literature [12]). A mandatory control reconfiguration is usually required to obtain the desirable fault tolerance [28,45-52], where three different actions have historically been necessary: i) estimation of new reference values of the x-y currents [28,50,51]; ii) reconfiguration of x-y controllers [45,50,52]; and iii) derating of the drive [45,47]. 3.2. Direct Torque Control Another well-established control technique in three-phase drives is the DTC, whose origin took place in the mid-80s [53,54]. Since then, numerous studies have been developed in the three-phase drives case [55], being the industrial implementation initiated by ABB [56]. The extension of DTC to different multiphase drives topologies has also been proposed [5,11], being nowadays a competitor to FOC due to its advantageous characteristics of robustness against machine parameters variation and fast flux and torque responses [57]. In its standard form, the controller maintains the outer PI speed controller as in FOC, but the inner current controllers are replaced by hysteresis blocks that directly regulate the fluctuations in the flux and the torque with respect to their references. In this case, the PI speed controller provides the torque reference ( ) while the flux reference ( ) is again set constant or regulated to deflux the machine depending on the speed. Based on the output of these hysteresis blocks and an estimation of the flux position, the appropriate switching vector to be applied is selected through a predefined look-up table that takes into account all possible VSI states. The selected switching vector is directly released to the VSI without the intervention of a PWM stage. Continuing with the distributed-windings five-phase drive case example, the described scheme of the DTC is shown in Fig. 9. As it can be seen, the control structure is simpler than in FOC, since Park transformation is no longer necessary, and the number of controlled variables is reduced to two, theoretically decreasing the computational cost. However, it presents important disadvantages, such as higher torque ripple and variable switching frequency, which depends on the operating point and the bandwidth of the hysteresis controllers. In addition, the control performance is highly dependent on the drive topology [58]. In order to mitigate these disadvantages, some modifications in the DTC structure have been proposed in the literature, such as the inclusion of PWM strategies [59,60] that leads to constant switching frequency and reduces the harmonic content, particularly on the x-y plane. Most importantly, the extension of DTC to multiphase drives cannot completely regulate the x-y (and homopolar) currents with the basic control structure presented before, since only two variables (flux and torque) are controlled. As it occurs in FOC, these currents must be regulated to zero since they are only related to harmonic components and losses, except for the case of concentrated-windings machines. A recursive solution encountered in the literature is the definition of more elaborated look-up tables, or even the introduction of a second look-up table, in order to reduce the loworder harmonics and increase the efficiency [61-63]. Another solution just recently adopted is the use of virtual voltage vectors to nullify the average value of the x-y voltages and mitigate the x-y currents, while maintaining the original control scheme [30]. Most of the research works in the field of DTC are applied to five- and six-phase machines, but a recent work aims to extend the method to a higher number of phases [64,65]. Furthermore, the faulttolerant capability of the DTC has been recently addressed for a fivephase IM drive. The study presented in [66] extends the DTC method used in normal operation of five-phase IM drives to the open-phase fault procedure. The post-fault DTC controller is similar to the scheme presented in Fig. 9 for healthy situation, but switching tables and applied virtual voltage vectors must be redefined after the fault occurrence to continue the operation of the multiphase drive. The performances of DTC and FOC controllers are compared in [67], where the advantages and disadvantages of these techniques in healthy and open-phase faulty situations are shown, introducing a powerful tool for the controller selection when using multiphase drives in final applications. 3.3. Model Predictive Control A promising alternative to classical FOC and DTC methods, particularly in the multiphase drives field, is the model predictive control. This naming identifies a wide range of control techniques, whose functioning principle is based on the prediction of the future behavior of the system variables employing a mathematical model. The predictions are used to select the optimal control action to be applied according to a predefined cost function, which represents the control objectives [68]. The simplicity and intuitive formulation of the control problem has boosted the interest of the research community in the MPC strategy applied to electric drives [10,11]. Another reason has been the possibility to perform multi-objective and multi-variable control, or even to include non-linearities or constraints to the control process, just defining a proper cost function. This permits eliminating the classical cascaded structure in FOC, reducing the complexity of the controller and providing a fast dynamic response. Likewise, the high control flexibility of the MPC makes it a real alternative to DTC in the multiphase drive control area, since the main disadvantage of DTC is that it can manage the control of only two variables in its most conventional form. However, MPC faces the important limitation of the high computational cost required to solve the optimization problem for all the control actions, which increases as the number of phases grows. For that reason, although the concept of MPC was developed in the 70s, its use has been traditionally restricted to systems with slow dynamics that permit performing the required calculations. This is the case of the petrochemical industry, which has constituted one of its main application fields during a long time [68,69]. Only with the recent development of fast and powerful microprocessors, the use of MPC in power converters and electric drives has become affordable [70]. Since then, the research activity in the field has given rise to numerous control approaches, being quite difficult to develop a general classification for all MPC techniques. Conventionally, they are divided in two wide categories: Finite-Control-Set MPC (FCS-MPC) and Continuous-Control-Set MPC (CCS-MPC) [71-73]. In both cases, the control principle is the 5φ IM VSI isa isc isb isd ise abcde αβxy ωmLOOK-UP TABLE Sa Sc Sb Sd Se PI isα isβ isy isx Flux, Torque and Position Estimator θ dλ dT λs * λs Te Te * ωm *+1 -1 +2 -2 0 +1 -1 Fig. 9. DTC technique for the distributed-windings five-phase IM drive model that depends on predicted, measured and reference values of the controlled variables. Similar approaches can be found in [124,125], where proper PWM methods are applied and a fixed switching frequency is guaranteed. Finally, another strategy consists in the use of virtual voltage vectors in an MPC method (VV-MPC) instead of the conventional VSI switching vectors, in a similar way as it is done in DTC [126-128]. The obtained results have revealed the enhancement in the system efficiency by reducing the harmonic content, mainly in the x-y plane. Moreover, this technique presents a lower computational cost since reduced predicted models and cost functions are employed, even though it tends to provide higher switching frequencies than the conventional approach in some cases and reduces the available voltage limits. 5. Future prospects in the MPC field In the humble opinion of the authors, there are some recent research works in the application of MPC techniques to multiphase drives that go beyond the described control goals or try to alleviate aforementioned difficulties and seem to be interesting for future research. In particular, three main areas attract authors' attention. The first one is in relation to the inclusion of electrical limits in the control strategy of the multiphase drive. Optimal control techniques have appeared as a viable candidate to this end in classical three-phase drives [129], and many algorithms have been so far proposed in the scientific literature based on this industrial requirement [130]. For instance, the switching frequency and the current control limits are considered in [131] to avoid an excessive temperature increment in the critical components of the system. Optimal d-q current control vectors are estimated to maximize the drive efficiency and the speed-torque performance within the temperature and voltage constraints. The reference flux is also evaluated to guarantee the maximum torque capability over the entire speed range of induction [132-135] or permanent magnet [136] machines. More recently, different optimal controllers have been presented and experimentally compared in [137], where PMSM drives are again considered. Most of these scientific studies, if not all, focus on conventional three-phase drives, where one d-q reference subspace appears and an analytical expression of the optimal reference stator currents that respects the imposed constraints can be easily obtained. Indeed, the machine flux is usually weakened (the d-current component is reduced) to respect the imposed voltage limit, adjusting at the same time the q-current component with the aim of complying with the current limits. However, the situation becomes much more complex when a multiphase electromechanical drive is considered. Optimal controllers can enhance the benefits of using multiphase machines, but the appearance of multiple orthogonal d-q control subspaces involved in the torque production of the multiphase drive highly complicates the extraction of the maximum torque under electrical limits and constraints. The problem of applying an optimal controller in a multiphase drive is in relation with the difficulty to obtain analytical expressions for the electrical references in the orthogonal d-q sets from the electrical phase limits, where a dependency appears. In general terms, the peak value of the phase voltage (current) depends on the voltages (currents) in each d-q subspace, which are unrelated and have different frequencies, magnitudes and phase shifts. This dependency has recently been simplified using offline assumptions to force an analytical relation between the electrical references in the orthogonal d-q subspaces, obtaining a kind of suboptimal controller. This is the case in [42,138], where the worst-case scenario is considered, assuming that all d-q voltage (current) components reach their peak values at the same time instant. This gives in fact safety performance margins in the system, but the obtained results cannot be considered as optimal. An interesting alternative based on offline look-up tables appears in [139]. In this case, d-q reference currents are generated using a preliminary minimization technique that finds the minimum of a constrained nonlinear multivariable function. These values are then placed in reference tables to be used in the control strategy. A significant consequence is that steady-state reference values are found and used in look-up tables, and the defined controller has the ability to manage failure mechanisms and critical electrical limits. A potential alternative for the definition of optimal regulators can be the use of MPC techniques for solving the optimization and control problems. It is noteworthy that MPC techniques have been widely used to solve control problems in electrical applications with power converters, giving a high flexibility and including different control objectives and/or constraints, as stated along this work. However, electrical limits for multiphase drives have been first considered in [140,141] using a two-stage predictive controller (see Fig. 15). Firstly, a CCS-MPC stage produces optimal reference currents, taking into account programmed electrical and magnetic constraints. Secondly, an FCS-MPC controller regulates the stator currents of the system in order to track the optimal references. Therefore, optimal current controllers using MPC techniques are introduced, which allows the optimal utilization of the system torque capability under voltage, current and magnetic limitations. The obtained results should encourage the scientific community to work in this field, to overcome the obtained limitations, mostly in relation with the online implementation of the controller and the applied optimization algorithm. The second future prospect focuses on the use of predictive controllers with variable sampling time. Predictive controllers and multiphase drives have been developed hand in hand and most common findings show that the computational cost of the controller is a serious handicap for its implementation, and that high harmonic content is generated due to the fixed sampling-time nature and the absence of modulation methods in the control algorithm. Regarding the harmonic content, different methods have explored the possibility to reduce it, as in the case of including rotor current observers to create a more precise predictive model of the multiphase machine. However, a more natural way to face the harmonic problem consists in introducing the concept of nonuniform sampling time as a new degree of freedom in the FCS-MPC technique. The idea was firstly exposed in [143] for a three-phase IM drive, but it has been further developed and extended to the fivephase case in recent works [143-145], where the lead-pursuit concept is incorporated reducing the complexity of the controller with respect to the original approach. The proposed control structure, named Variable Sampling Time Lead Pursuit Control (VSTLPC), is divided in two steps (see Fig. 16). Firstly, the lead-pursuit concept is applied to select the optimal VSI state ( ) based on predefined stator current references. Secondly, its time of application ( ) is calculated using the space-state model of the system and predicting the future behavior of the controlled currents. An observer is also incorporated to estimate the rotor currents thus improving the predictions. The results of these publications validate the effectiveness of the proposal, particularly to reduce the current harmonic content and to improve the current tracking performance when compared to the conventional FCS-MPC approach, as it can be seen in Fig. 17. This is, in essence, a completely new technique that has been only tested using a five-phase IM with symmetrical and distributed windings as a case example. Then, it is expected much more work in the field in the recent future. Finally, among the different possibilities to exploit the additional degrees of freedom in multiphase drives, the fault tolerance has been an interesting research subject in recent times. This inherent capability is highly appreciated, but it typically requires fault detection and localization of the fault in a first stage [146-148], and the reconfiguration of the control scheme in a second one. The standard techniques in normal operation have been modified to become fault-tolerant: IRFOC [28,45-52], DTC [66] and MPC [149,150]. Moreover, the performances of these three controllers are compared in [67] when an open-phase fault appears in a five-phase IM drive, concluding that there is no ideal controller to manage the fault situation (see Table 6). In such controllers, the reconfiguration stage involves the use of different Clarke transformations, cost functions and current references for each of the multiple open-phase 5φ IM VSI isa isc isb isd ise ωm PI ωm ** is (k+2) Current Controller FCS-MPC Sopt * Tem isq1 isd1,isq3 isd3, ωm * isd1 * isq1 * isd3 * isq3 Vdc Isd,rated IVSI Optimal Current References Generator CCS-MPC ωm abcde d1q1d3q3 Fig. 15. Predictive controller scheme considering electrical constraints in the control strategy 5φ IM VSI i sa isc isb isd ise abcde αβxy ωm θ αβ dq PI * isq * isx (to+tL) * isy (to+tL) ωm * * isd * isβ (to+tL) * isα (to+tL)* is (to+tL) Position Estimator * isq * isd Ta computation Selection of Sa VSTLPC Sa Possible Switching Vectors is(to) Si Sa Observer ir (to) Fig. 16. VSTLPC technique for the distributed-windings five-phase IM drive Table 6. Qualitative comparison between IRFOC, DTC and MPC methods in open-phase fault operation. Closed-loop system performance IRFOC DTC MPC Speed tracking error when the fault appears Negligible Slight High Torque tracking loss during a detection delay Yes No Yes Robustness against fault detection delay Change in the Clarke transformation No Yes Yes Computational cost Stator current THD Maximum available torque 56% of 50% of 56% of Fig. 17. Experimental RMS error (RMSp) and total harmonic distortion (THD) of the phase stator currents for different speeds ( ) and load torques ( ) presented in [143], when applying the VSTLPC and conventional FCSMPC techniques to the distributed-windings five-phase IM drive fault scenarios. However, a recent study presented in [151] proposes the implementation of the VV-MPC strategy of [126] for the fault operation, allowing to conduct the control of the x-y currents in open-loop mode. This fact provides FCS-MPC with a natural fault tolerance (a ripple-free post-fault performance without mandatory control reconfiguration), since the conflict between α-β and x-y current controllers is avoided. This, in practice, provides a smoother transient from healthy to faulty operation and makes the control immune to fault detection errors or delays, opening up a new avenue of study in the topic [151,152]. 6. Conclusion Some recent review papers have been published both in the field of multiphase drives and in the area of predictive controllers applied to power electronics. Nevertheless, the covered research content in these works was so vast that the simultaneous analysis of multiphase drives and predictive controllers as a common research field was not possible. Even though this joint field could be initially considered as a subtopic in the study of multiphase drives, the ever-increasing interest in the last decade suggests considering it as a new research area. The number of papers dealing with predictive controllers in multiphase systems has reached a critical mass, and for that reason this work presents a detailed and updated state-of-the-art review of this area. Furthermore, the aim is not only to review the existing works, but to provide a framework of analysis and guidelines for the implementation of predictive controllers to regulate multiphase drives. For this purpose, this paper takes the five-phase case to clearly illustrate the different issues that should be mandatorily considered by researchers and practitioners that are willing to achieve a successful predictive control of multiphase machines. Lastly, this work also points out three fields that are identified as future research trends with a significant potential for contribution: the inclusion of electrical limits in the control of multiphase drives, the use of predictive controllers with variable sampling time and the design of robust multiphase drives with a natural fault-tolerant capability. The whole work is conceived not only to present the recent research to the scientific community, but also to introduce the field to new researchers and practitioners in order to promote future research and engineering applications. 7. Acknowledgments The authors would like to thank Prof. Emil Levi, from the Liverpool John Moores University (UK) for his support in the multiphase drives research field. This work would not have been possible without his selfless help, knowledge, tips and supervision during the last 15 years. 8. References [1] Amsterdam Roundtables Foundation and McKinsey & Company: ‘Electric vehicles in Europe: Gearing up for a new phase?’, available online: https://www.mckinsey.com/featured-insights/europe/electric-vehicles-in-europe -gearing-up-for-a-new-phase, 2014. 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