Control Strategies for Induction Motors in Railway Traction Applications

energies

Review Review ControlControl Strategies Strategies for for Induction Induction Motors in Railway TractionTraction ApplicationsApplications

AhmedAhmed Fathy Fathy Abouzeid 11, Juan, Juan Manuel Manuel Guerrero Guerrero 1, Aitor1 , Aitor Endemaño Endemaño 2, Iker2, Muniategui Iker Muniategui 2, David2, OrtegaDavid Ortega2, Igor Larrazabal2, Igor Larrazabal 2 and Fernando2 and Fernando Briz 1,* Briz 1,* 11 Electrical,Electrical, Electronic, Electronic, Computers Computers and and Systems Systems Engineerin, Engineering, University University of Oviedo, of Oviedo, 3204 3204 Oviedo, Oviedo, Spain; Spain; [email protected]@uniovi.es (A.F.A.); (A.F.A.); [email protected] [email protected] (J.M.G.) (J.M.G.) 22 IngeteamIngeteam Power Power Technology Technology S.A. S.A.—Traction, – Traction, 48170 48170 Zamu Zamudio,dio, Spain; Spain; aitor.endema [email protected]@ingeteam.com (A.E.); (A.E.); [email protected]@ingeteam.comom (I.M.); (I.M.); [email protected] [email protected] (D.O.); (D.O.); [email protected] (I.L.)[email protected] (I.L.) ** Correspondence:Correspondence: [email protected] [email protected] Received: 30 December 2019; Accepted: 3 February 2020; Published: 6 February 2020 Received: 30 December 2019; Accepted: 3 February 2020; Published: 6 February 2020

Abstract:Abstract: ThisThis paper paper analyzes analyzes control control strategies for induction motors in railway applications. The The paperpaper will focus onon drivesdrives operatingoperating with with a a low low switching switching to to fundamental fundamental frequency frequency ratio ratio and and in thein theovermodulation overmodulation region region or six-step or six-step operation, operation, as these as are these the most are challengingthe most challenging cases. Modulation cases. Modulationmethods, eﬃ methods,cient modes efficient of operation modes of operation the drive andof the the drive implications and the implications for its dynamic for performance, its dynamic performance,and machine and design machine will also design be discussed. will also be Extensive discussed. simulation Extensive results, simulation as well results, as experimental as well as experimentalresults, obtained results, from obtained a railway from traction a railway drive, traction are provided. drive, are provided.

Keywords:Keywords: railwayrailway traction drives;drives; inductioninduction motor motor drives; drives; high-speed high-speed drives; drives; maximum maximum torque torque per perampere; ampere; overmodulation overmodulation and and six-step six-step operation operation

1.1. Introduction Introduction DespiteDespite being being one one of of the the most most energy-efficient energy-eﬃcient mean meanss for for mass mass transportation transportation (see (see Figure Figure 1)1)[ [1],1], therethere is is pressure pressure to to develop develop a a more more efficient, eﬃcient, reli reliable,able, cheap, cheap, and and compact compact railway railway traction traction system, system, whichwhich should should be be achieved without compromising customer satisfaction.

FigureFigure 1.1. EmissionsEmissions per per passenger passenger per per km fromkm difromfferent different modes ofmodes transport. of transport. From the UKFrom Department the UK Departmentfor Business, Energyfor Business, and Industrial Energy Strategy and Indust 2019rial Government Strategy Greenhouse2019 Government Gas Conversion Greenhouse Factors Gas [1]. Conversion Factors [1]. Three-phase induction motors (IMs) were adopted in the 1990s for traction systems in railways replacingThree-phase DC machines induction [2] motors due to (IMs) their were increased adopted robustness in the 1990s and for reduced traction cost systems and maintenance in railways replacingrequirements. DC machines In addition, [2] precisedue to controltheir increase of the IMd robustness torque/speed and is reduced perfectly cost possible and maintenance thanks to the requirements.development ofIn newaddition, power precise devices control and digitalof the IM signal torque/speed processors, is combinedperfectly possible with the thanks advances to the in developmentAC-driven control of new methods. power devices Furthermore, and digital the inherent signal processors, slip of IM allowscombined multiple with motorsthe advances to be fedin AC-drivenfrom a single control inverter, methods. even if Furthermore, they rotate at dithefferent inherent speeds slip due of toIM di allowsfferences multiple in wheel motors diameters. to be Asfed a

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies Energies 2020, 13, 700; doi:10.3390/en13030700 www.mdpi.com/journal/energies Energies 2020, 13, x FOR PEER REVIEW 2 of 22 from a single inverter, even if they rotate at different speeds due to differences in wheel diameters. Energies 2020, 13, 700 2 of 22 As a result, the voltage-source inverter-fed IM drive (VSI-IM) is currently the preferred option in traction systems for railways [3]. While Permanent Magnet Synchronous Machines (PMSM) have also beenresult, considered the voltage-source and can be inverter-fed found in several IM drive traction (VSI-IM) systems, is currently cost and the reliability preferred concerns option in intrinsic traction tosystems this type for of railways machine, [3 ].mainly While due Permanent to magnets, Magnet have Synchronous so far prevented Machines their widespread (PMSM) have use also [4]. been consideredRolling and stock can can be be found classified in several according traction to systems,the power cost level and of reliability the traction concerns system, intrinsic ranging to from this severaltype of machine,tens of kW mainly for Light due toRail magnets, systems, have to several so far prevented MW for High-Speed their widespread Trains use (HST) [4]. and Heavy Rail LocomotivesRolling stock [5]. can Traction be classified systems according can be toconc theentrated power level or distributed. of the traction In concentrated system, ranging systems, from oneseveral or more tens oflocomotives kW for Light pull Rail unmotorized systems, to coaches. several MWOn the for contrary, High-Speed distributed Trains (HST) traction and systems Heavy Railuse ElectricLocomotives Multiple [5]. TractionUnits (EMU), systems i.e., can self-propelle be concentratedd carriages. or distributed. Both options In concentrated have advantages systems, one and or disadvantages.more locomotives EMUs pull unmotorizedcan provide coaches. a superior On the pe contrary,rformance distributed in terms traction of the systems acceleration use Electric and decelerationMultiple Units times, (EMU), adhesion i.e., self-propelled effort, and carriages. transport Both optionscapacity. have However, advantages passenger and disadvantages. comfort, maintenance,EMUs can provide and pantograph a superior performance operation can in terms be compromised of the acceleration in this and case deceleration [6,7]. For the times, case adhesion of HST, Europeaneffort, and manufacturers transport capacity. have However, predominantly passenger adop comfort,ted the maintenance,concentrated andtraction pantograph option, while operation the distributedcan be compromised option has in been this case preferr [6,7].ed For by theJapanese case of manufacturers HST, European [8]. manufacturers have predominantly adoptedThe thetwo concentrated main elements traction in option,a traction while system the distributed are the electric option hasmotor been and preferred the inverter. by Japanese The developmentmanufacturers of [ 8a]. cost-effective traction system for a given application involves a complex, iterative processThe to two decide main the elements number in aof traction traction system motors, are themotor electric size, motor inverter and rated the inverter. power, The cooling development system, etc.of a Once cost-e theffective physical traction elements system of the for traction a given sy applicationstem have been involves defined, a complex, the control iterative and modulation process to strategiesdecide the need number to be of defined. traction Additionally, motors, motor in size, this inverter case, a complex rated power, iterative cooling process system, can etc. be Oncerequired the asphysical the traction elements system of the must traction comply system with have a number been defined, of requirements. the control These and modulationinclude those strategies imposed need by theto be desired defined. train Additionally, performance in this (e.g., case, torque-spe a complexed iterative characteristic, process maximum can be required torque as and the tractionspeed, acceleration/decelerationsystem must comply with atimes, number etc.), of requirements. electric drive These performance include those (e.g., imposed machine by the and desired inverter train efficiency,performance temperature (e.g., torque-speed limits, maxi characteristic,mum torque maximum ripple, etc.), torque existing and standards speed, acceleration (e.g., electromagnetic/deceleration interference,times, etc.), electricacoustic drive noise, performance etc.), and so (e.g., on. However, machine andthese inverter targets ewillfficiency, often temperaturebe in conflict. limits, The reductionmaximum of torque inverter ripple, losses etc.), requires existing low standards switching (e.g., frequencies, electromagnetic which ininterference, turn result in acoustic higher losses noise, andetc.), large and torque so on. pulsations However, in these the motor, targets and will can often also be compromise in conflict. the The dynamic reduction response of inverter or even losses the stabilityrequires of low the switching drive. Especially frequencies, challenging which in is turn the result operation in higher of the losses traction and drive large torqueat high pulsationsspeeds. The in largethe motor, back-electromotive and can also compromise force, in this the dynamiccase, forc responsees the inverter or even to the operate stability in of the the overmodulation drive. Especially region,challenging including is the square-wave operation of themodes. traction The drivecontrol at oper highates speeds. in this The case large with back-electromotive a reduced (or even force, no) voltagein this case, margin forces and the inverterlarge distortions to operate in in thethe overmodulationcurrents, which region, can further including deteriorate square-wave the modes.drive performance.The control operates in this case with a reduced (or even no) voltage margin and large distortions in the currents,Figure 2 whichshows can a schematic further deteriorate representation the drive of the performance. main blocks involved in the operation of a tractionFigure drive.2 shows The drive a schematic will normally representation receive a oftorque the main command blocks coming involved from in outer the operation control loops of a (e.g.,traction the drive.train driver The drive or speed will control normally loop). receive From a the torque torque command command coming and in from the operating outer control condition loops of(e.g., the the machine, train driver a flux or command speed control is derived; loop). From differen the torquet criteria command can be andfollowed in the for operating this purpose, condition as shownof the machine, in Figure a 2. flux Torque command and flux is derived; are controlled different by criteria the inner can be control followed loops; for thisa number purpose, of solutions as shown arein Figureavailable2. Torquefor this andpurpose. flux areInner controlled control loops by the will inner provide control the loops; voltage a numbercommand of to solutions the Voltage are Sourceavailable Inverter for this (VSI) purpose. feeding Inner the machine, control loops with willselection provide of the modulation voltage command method to being the Voltage of the highestSource Inverterimportance. (VSI) feeding the machine, with selection of the modulation method being of the highest importance.

Figure 2. MainMain blocks blocks of of a a traction traction drive. drive. This paper presents a review of the diﬀerent aspects involved in the control of IM motor drives for railway applications. Section2 reviews the IM motor model, including a discussion on the machine characteristics. Section3 discusses control strategies, with a special focus on their suitability for use Energies 2020, 13, 700 3 of 22 at high speed and low switching frequencies, as this is the most frequent and challenging mode of operation for traction drives. Modulation is discussed in Section4. Section5 discusses e ﬃcient modes of operation and remagnetization strategies. Sections6 and7 provide simulation and experimental results, respectively. Section8 summarizes the conclusions.

2. Induction Motor Model and Machine Characteristics

2.1. Induction Motor Model Complex vectors allow a compact, insightful dynamic representation of the physical effects occurring in AC machines, i.e., the relationships among electromagnetic variables (voltages, currents, and fluxes) and shaft variables (torque and speed) [9]. Equations (1)–(4) show the electromagnetic complex vector equations describing the squirrel cage induction machine in a synchronous reference frame rotating at the flux angular frequency ωe, where vdqs denotes the stator voltage; idqs and idqr are the stator and rotor currents, respectively; λdqs and λdqr represent the stator and rotor fluxes, respectively; Rs and Rr are the stator and rotor resistances, respectively; Ls, Lr, and Lm are the stator, rotor, and mutual inductances, respectively; ωr is the rotor angular speed in electrical units; and p is the derivative operator. vdqs = Rsidqs + pλdqs + jωeλdqs (1)

0 = Rri + pλ + j(ωe ωr)λ (2) dqr dqr − dqr λdqs = Lsidqs + Lmidqr (3)

λdqr = Lmidqs + Lridqr (4)

The electromagnetic torque Te can be expressed as the cross product of stator and rotor currents (5). P is the number of pole-pairs, and “Im” and “ ” denote the imaginary part and ‡ complex conjugate, respectively. 3 T = PL Im i i‡ (5) e 2 m dqs dqr Equations (1)–(4) can be particularized for the case when the d-axis is aligned with the rotor flux, i.e., λdqr = λdr = λr, which is the base of rotor field-oriented control (RFOC). The stator voltage equation in scalar form is, in this case (6), the rotor flux dynamics being given by (7), where τr is the rotor time constant and σ is the leakage factor.  Lm v = Rsi + σLspi ω σLsi + pλr  ds ds ds − e qs Lr  (6) v = R i + σL pi + ω σL i + ω Lm λ  qs s qs s qs e s ds e Lr r 

2 dλr Lr Lm τr + λr = Lmids ; τr = ; σ = 1 (7) dt Rr − LsLr The torque Equation (5) can be rewritten as (8) in this case. Other forms of the torque equation can be obtained by combining (2)–(4) and (5) and will be the basis of diﬀerent control strategies, as will be discussed in further sections. 3 Lm Te = P λriqs (8) 2 Lr Energies 2020, 13, 700 4 of 22

2.2. Machine Characteristics Traction drives commonly receive a torque command from an outer control loop, which is responsible for speed control. The maximum torque that can be produced at a given speed will essentially depend on the current limits of the machine and power converter (due to losses) and on the maximum flux, which is limited by saturation and the available DC link voltage. For most IM designs, the maximum voltage and field weakening occur at the same speed, i.e., field weakening is a direct consequence of reaching the voltage limit. This is shown schematically in Figure3 (continuous line case). For rotor speeds ωr < ω1, the machine operates with a rated flux and current, with the voltage increasing proportionally to the rotor speed, mainly due to the back-emf. If ωr > ω1, the flux, and consequently torque, must be decreased. The current (Figure3b) can still be maintained at its rated value until the machine enters field-weakening region II (not shown in the figure) [10]. Therefore, forEnergies the 2020 machine, 13, x FOR denoted PEER REVIEW as conventional in Figure3, region O1 corresponds to a constant torque5 of 22 operation, while regions O2 +O3 have constant power.

Figure 3. Conventional ( ) and extended full flux range (- -) induction motor (IM) design behavior: (a) Figure 3. Conventional (−−) and extended full flux range (--) induction motor (IM) design behavior: (a) Stator voltage magnitude; (b) Stator current magnitude; (c) Flux density; (d) Electromagnetic torque Stator voltage magnitude; (b) Stator current magnitude; (c) Flux density; (d) Electromagnetic torque (rated&pull-out). Both machines are designed to provide the same torque vs. speed characteristic and (rated&pull-out). Both machines are designed to provide the same torque vs. speed characteristic and have the same voltage limit. have the same voltage limit. IM designs for railway traction are often aimed at reducing the size of the machine, which can be However, the design with an extended full flux range offers other possibilities. The torque of an desirable or even imperative due to room constraints. For this purpose, the voltage characteristic of the IM can be written as (9), where 𝑉 is the active volume of the rotor, 𝐽 is the stator surface current conventional design in Figure3 can be modified by rewinding the stator, varying the number of turns, density, 𝐵 is the air gap flux density, ∅ is the angle between 𝐽 and 𝐵 vectors, and 𝑘 is a and gauging the wire [10,11]. If the modification is made such that N2 < N1, with N1 and N2 being the constant which depends on the machine winding design [11]. number of turns for the conventional and modified designs, respectively, and the active conductor area in each stator slot remaining unchanged,𝑇 =𝑘 ∙𝑉 i.e., N ∙𝐽∙𝐵∙𝑐𝑜𝑠∅S = N S , and S and S being the area of the(9) 1· 1 2· 2 1 2 conductor for the conventional and modified designs, respectively, both machines should be able to As the extended full flux range design provides higher flux densities at high speeds and the produce the same amount of torque, as the total current circulating within the stator slots and the rest current density 𝐽 remains constant, it is possible to reduce the volume of the rotor, and consequently of the machine dimensions are the same in both cases [11]. Since the number of turns has been reduced, the size of the machine, without affecting the torque production capability, i.e., the extended full flux the voltage vs. speed characteristic is also modified. As seen in Figure3a (dashed line), for ω = ω , design in Figure 3 will be smaller. r 1 It must be noted, however, that redesigning the machine brings drawbacks that must also be considered. First, the size of the inverter is increased, as the current that the semiconductors must

handle is increased by a factor of 𝑁/𝑁, while the voltage and power remain unaffected. However, this penalty is not so relevant nowadays thanks to the latest developments in power devices [10]. Second, the pull-out torque in the low-speed region is significantly decreased, as shown in Figure 3d [11], which must be considered to guarantee that the machine meets the application requirements.

Energies 2020, 13, 700 5 of 22

the machine is far from its voltage limit. It can also be observed that for ωr < ω1, the current of the modified machine design is N1/N2 larger than for the conventional design. This does not imply an increase of joule losses, as the wire in the modified design is thicker, and the current density is the same in both cases. Since, at ωr = ω1, the modified machine operates well below its voltage limit, there is no need to decrease the flux at this point; instead, the nominal air gap flux density can be maintained until ωr = ω2 (region O2 in Figure3), i.e., the full flux range is extended. The fact that the flux weakening region is reduced while the torque characteristic remains unchanged enables a reduction of the stator current for ωr > ω1, as can be readily deduced from (8). Consequently, assuming that the dimensions of the machine do not change, the extended full flux range design in Figure3 would allow a significant decrease of the current density in regions O2 and O3 (i.e., at high train speeds) and consequently of Joule losses, i.e., would be more efficient compared to the conventional design. However, the design with an extended full flux range offers other possibilities. The torque of an IM can be written as (9), where Vrotor is the active volume of the rotor, J is the stator surface current density, B is the air gap flux density, ∅ is the angle between J and B vectors, and k1 is a constant which depends on the machine winding design [11].

Te = k1 Vrotor J B cos(∅) (9) · · · · As the extended full flux range design provides higher flux densities at high speeds and the current density J remains constant, it is possible to reduce the volume of the rotor, and consequently the size of the machine, without affecting the torque production capability, i.e., the extended full flux design in Figure3 will be smaller. It must be noted, however, that redesigning the machine brings drawbacks that must also be considered. First, the size of the inverter is increased, as the current that the semiconductors must handle is increased by a factor of N1/N2, while the voltage and power remain unaffected. However, this penalty is not so relevant nowadays thanks to the latest developments in power devices [10]. Second, the pull-out torque in the low-speed region is significantly decreased, as shown in Figure3d [ 11], which must be considered to guarantee that the machine meets the application requirements.

3. Overview of Control Methods for Three-Phase Induction Machines This section discusses control strategies for IMs in railway applications. The drives must be able to perform properly from zero to relatively high rotational frequencies. On the other hand, the switching frequencies are often limited to several hundred Hz due to the switching losses of high-power semiconductor devices. At low rotational frequencies, the switching to fundamental frequency ratio is still relatively large and the inverter will operate far from its voltage limit. On the contrary, operation at high speeds is characterized by a reduced switching to fundamental frequency ratio and a reduced (or even inexistent) voltage margin in the inverter. Due to this, both control and modulation strategies are often dynamically modified, depending on the IM speed. The following discussion will primarily focus on the most challenging high-speed case. Control methods for IMs can be classified into scalar and vector types, as shown in Figure4. Scalar methods are derived from the machine equivalent circuit in a steady-state. Consequently, they can operate properly in applications in which fast changes in the operating conditions of the machine (torque, speed, flux, ... ) are not required. On the contrary, vector control methods are based on the dynamic equations of the machine, which, combined with proper control loops, allow the machine’s torque capabilities to be fully exploited, without surpassing machine or power converter limits. Both types of methods are briefly discussed in the following. It must be noted, however, that the borderline between scalar- and vector-based methods is sometimes blurred, as there have been several proposals to enhance the dynamic response of scalar methods by adding control loops based on dynamic models. Energies 2020, 13, x FOR PEER REVIEW 6 of 22

modulation strategies are often dynamically modified, depending on the IM speed. The following discussion will primarily focus on the most challenging high-speed case. Control methods for IMs can be classified into scalar and vector types, as shown in Figure 4. Scalar methods are derived from the machine equivalent circuit in a steady-state. Consequently, they can operate properly in applications in which fast changes in the operating conditions of the machine (torque, speed, flux, …) are not required. On the contrary, vector control methods are based on the dynamic equations of the machine, which, combined with proper control loops, allow the machine’s torque capabilities to be fully exploited, without surpassing machine or power converter limits. Both types of methods are briefly discussed in the following. It must be noted, however, that the borderline between scalar- and vector-based methods is sometimes blurred, as there have been several proposals to enhance the dynamic response of scalar methods by adding control loops based on dynamic models.Energies 2020 , 13, 700 6 of 22

Figure 4. Control methods for IMs. Figure 4. Control methods for IMs. 3.1. Scalar-Based Control 3.1. Scalar-Based Control 3.1.1. Open-loop V/F 3.1.1. Open-loop V/F Open-loop V/F varies the stator voltage magnitude proportional to the frequency. This results in an (almost)Open-loop constant V/F varies ﬂux. Whilethe stator simple, voltage V/F magnitu control hasde proportional some relevant to limitations. the frequency. The This rotor results speed inis an not (almost) precisely constant controlled flux. due Wh toile slip.simple, Additionally, V/F control an has incorrect some re voltagelevant limitations. to frequency The ratio, rotor voltage speed isdrop not inprecisely the stator controlled resistance, due variations to slip. Additionally of the DC link, an voltage incorrect feeding voltage the to inverter, frequency etc., ratio, will resultvoltage in dropincorrect in the ﬂux stator levels, resistance, eventually variations modifying of the the DC operating link voltage point feeding of the machine the inverter, from etc., the desiredwill result value. in incorrect flux levels, eventually modifying the operating point of the machine from the desired value. 3.1.2. V/F with Feedback Control 3.1.2. Closed-loopV/F with Feedback speed controlControl with slip regulation (Figure5) has been widely used in IM traction

drivesClosed-loop [12]. Speed speed error control generates with slip the slipregulation command (Figureωsl∗ 5)through has been a Proportional-Integratorwidely used in IM traction (PI) Energies 2020, 13, x FOR PEER REVIEW ∗ 7 of 22 drivescontroller, [12]. which, Speed whenerror addedgenerates to the the measured slip command speed, provides𝜔 through the angulara Proportional-Integrator frequency of the stator (PI) controller,voltage ωe∗ .which, when added to the measured speed, provides the angular frequency of the stator ∗ voltage 𝜔.

Figure 5. V/F with speed control scheme.

Flux and torque control loopsFigure can 5. V/F be with used speed instead control of the scheme. V/F ratio to obtain the desired stator voltage magnitude and angle (Figure6). Torque and flux can be estimated from the (commanded) statorFlux voltages and torque and the control (measured) loops statorcan be currents used instea usingd theof the voltage V/F ratio model to (10); obtain “ˆ” indicatesthe desired estimated stator voltage magnitude and angle (Figure 6). Torque and flux can be estimated from the (commanded) variables/parameters. The pure integrator in (10) is replaced in practice by a first-order system to stator voltages and the (measured) stator currents using the voltage model (10); “^” indicates avoid the drift problems derived from the integrator infinite gain at DC [13]. The torque is obtained estimated variables/parameters. The pure integrator in (10) is replaced in practice by a first-order using (11). system to avoid the drift problems derived fromZ the integrator infinite gain at DC [13]. The torque is λˆ s = V∗ Rˆ si s dt (10) obtained using (11). αβ αβs − αβ ∗ 𝜆 =𝑉3 −𝑅𝑖𝑑𝑡 (10) Tˆ e = P λˆ αsi s λˆ siαs (11) 2 β − β 3 𝑇 = 𝛲𝜆 𝑖 −𝜆 𝑖 (11) 2

Figure 6. Torque-flux scalar control scheme.

The methods in Figures 5 and 6 are relatively simple to implement, with the second enabling precise control of the machine’s operating point in a steady-state. A further advantage of scalar methods is that operation near or at the inverter voltage limit is relatively easy to achieve. However, the fact that coupling between flux and torque is not considered for the control design requires a very slow dynamic response to avoid over currents and torque pulsations.

3.1.3. Torque/Flux Scalar Control with Feedforward The dynamic response of the closed-loop V/F control scheme in Figure 6 can be enhanced by adding two feedforward terms, as can be seen in Figure 7. The first uses the desired V/F characteristic ∗ to provide the base value of the stator voltage magnitude 𝑉_ , with the rotor flux regulator providing the incremental voltage required to track the desired rotor flux with no error. The second ∗ provides the base value for the slip 𝜔_ , which is obtained from the desired torque and the estimated rotor flux using (12). The torque regulator corrects the slip so that the desired torque is followed with no error.

Energies 2020, 13, x FOR PEER REVIEW 7 of 22

Figure 5. V/F with speed control scheme.

Flux and torque control loops can be used instead of the V/F ratio to obtain the desired stator voltage magnitude and angle (Figure 6). Torque and flux can be estimated from the (commanded) stator voltages and the (measured) stator currents using the voltage model (10); “^” indicates estimated variables/parameters. The pure integrator in (10) is replaced in practice by a first-order system to avoid the drift problems derived from the integrator infinite gain at DC [13]. The torque is obtained using (11). ∗ 𝜆 =𝑉 −𝑅𝑖𝑑𝑡 (10)

3 𝑇 = 𝛲𝜆 𝑖 −𝜆 𝑖 (11) Energies 2020, 13, 700 2 7 of 22

FigureFigure 6. 6. Torque-fluxTorque-flux scalar control scheme. Energies 2020, 13, x FOR PEER REVIEW 8 of 22 TheThe methods in in Figures 55 andand6 6are are relatively relatively simple simple to to implement, implement, with with the the second second enabling enabling precise control of the machine’s operating point in aa steady-state.steady-state. A A further further advantage advantage of of scalar ∗ 2 1 𝑅 ∗ methodsmethods is is that that operation operation near near or or at at 𝜔the the_ inverter inverter= vo voltageltage𝑇 limit limit is is relatively relatively easy easy to to achieve. achieve. However, However,(12) 3 P thethe fact fact that that coupling coupling between between flux flux and and torque torque is is 𝜆not not considered considered for for the the control control design design requires requires a a very very slowslow Duedynamic dynamic to the response fact that to avoid the voltage ov overer currents command and magnitude torque pulsations. and phase angle are independently controlled, flux and torque controllers must be tuned for relatively low bandwidths. A dynamic 3.1.3. Torque/Flux Scalar Control with Feedforward response3.1.3. Torque/Flux eventually Scalar relies Control on the withaccuracy Feedforward of the feedforward terms. As for the scheme in Figure 6, the schemeTheThe dynamic in Figure response response 7 can easily of of the the operate closed-loop closed-loop in the V/Ffield-weakening V/F co controlntrol scheme scheme region, in in Figure Figure including 66 cancan that bebe enhancedofenhanced six-step. by by addingaddingAn two alternative feedforward approach terms, for as the can implementation be seen in Figu Figure reof 7 7.the. The feedforward firstfirst uses the action desired is to VV/F use/F characteristic characteristicthe machine to provide the base value of the stator voltage magnitude V , with∗ the rotor flux regulator providing d-qto providemodel in the the baserotor valueflux reference of the statorframe. voltage The desir magnitudeed d- ands∗_v f q-axis𝑉_ , currentswith the are rotor first fluxobtained regulator from theprovidingthe commanded incremental the incremental voltagetorque and required voltage rotor toflux required track using the (7)to desired andtrack (8) the rotor (see desired fluxFigure with rotor 8). no The flux error. d- with and The q-axisno second error. stator providesThe voltages second the base value for the slip ω , which is obtained∗ from the desired torque and the estimated rotor flux requiredprovides tothe achieve base valuethe desiredsl∗ _forf f the currents slip 𝜔 are_ the, which midd leis termsobtained in (13), from which the aredesired obtained torque from and (6). the using (12). The torque regulator corrects the slip so that the desired torque is followed with no error. estimated rotor flux using (12). The torque regulator𝐿 corrects the slip so that the desired torque is 𝑣∗ =𝑅 𝑖∗ +𝜎𝐿 𝑝𝑖∗ −𝜔∗𝜎𝐿 𝑖∗ + 𝑝𝜆∗ ≅−𝜔∗𝜎𝐿 𝑖∗ ⎫ followed with no_ error. ⎪ 2 1 𝐿Rˆ ω = r T (12)(13) sl∗ _ f f 2 e∗ ∗ ∗ ∗ ∗ ∗ 3 P ∗ 𝐿 ∗ ∗ ∗ ∗ 𝐿 ∗ ⎬ 𝑣 =𝑅 𝑖 +𝜎𝐿 𝑝𝑖 +𝜔 𝜎𝐿 𝑖 +𝜔 λˆ r 𝜆 ≅𝜔𝜎𝐿 𝑖 +𝜔 𝜆 _ ⎪ 𝐿 𝐿 ⎭

FigureFigure 7. 7. Closed-loopClosed-loop V/F V/F with with torque/flux torque/ﬂux control control (CLVFC) (CLVFC) scheme.

Ideally,Due to the (13) fact will that produce the voltage the voltage command needed magnitude to obtain and the phase desired angle torque are independently and rotor flux controlled, with no error.ﬂux and However, torque controllers there are must a number be tuned of for issues relatively to consider. low bandwidths. Mismatch A dynamicbetween responsemodel and eventually actual parameters must be expected and will produce errors in the feedforward voltages. In addition, (13) includes derivatives which are problematic in practice. It is noted, however, that the signals affected by the derivative (13) are (clean) commanded variables, i.e., do not involve (noisy) measured variables. Furthermore, the torque derivative will be limited by the application, meaning that the derivative of q-axis current and flux commands will be limited too. Finally, the terms depending on the stator resistance will have a reduced weight considering that the control is only intended to operate at a high speed. Based on the previous considerations, the feedforward voltage can be safely simplified to form the right hand of (13). The resulting block diagram is shown in Figure 8, with the feedforward term being either the complete or simplified voltage equation in (13).

Energies 2020, 13, 700 8 of 22 relies on the accuracy of the feedforward terms. As for the scheme in Figure6, the scheme in Figure7 can easily operate in the field-weakening region, including that of six-step. An alternative approach for the implementation of the feedforward action is to use the machine d-q model in the rotor flux reference frame. The desired d- and q-axis currents are first obtained from the commanded torque and rotor flux using (7) and (8) (see Figure8). The d- and q-axis stator voltages required to achieve the desired currents are the middle terms in (13), which are obtained from (6).

ˆ  ˆ ˆ ˆ Lm ˆ  v∗ = Rsi∗ + σˆLspi∗ ωe∗σˆLsiqs∗ + pλ∗ ωe∗σˆLsiqs∗  ds_ f f ds ds Lˆ r dr  − ˆ − ˆ (13) ˆ ˆ ˆ Lm ˆ Lm  v∗ = Rsiqs∗ + σˆLspiqs∗ + ωe∗σˆLsi∗ + ωe∗ λ∗ ωe∗σˆLsi∗ + ωe∗ λ∗  Energies 2020, 13, x FORqs _PEERf f REVIEW ds Lˆ r dr ds Lˆ r dr  9 of 22

Figure 8. Figure 8. ClosedClosed loop loop V/F V/F with with torque/flux torque/flux cont controlrol and feedforward (CLVFC&FF) scheme. Ideally, (13) will produce the voltage needed to obtain the desired torque and rotor flux with 3.2. Vector-Based Control no error. However, there are a number of issues to consider. Mismatch between model and actual parametersVector mustcontrol be methods expected are and aimed will produce at directly errors manipulating in the feedforward the IM voltages.fields and In torque. addition, These (13) methodsincludes derivativesare based on which well-known are problematic d-q models. in practice. Field-Oriented It is noted, Control however, (FOC) that the represents signals a fffluxected and by torquethe derivative as a function (13) are of stator (clean) currents commanded in a synchronous variables, i.e., reference do not frame, involve with (noisy) high-bandwidth measured variables. current regulatorsFurthermore, being the used torque to provide derivative the will voltage be limited comman byd the to the application, inverter. Alternatively, meaning that theDirect derivative Torque Controlof q-axis (DTC) current methods and flux implement commands torque will beand limited flux controllers too. Finally, which the termsdirectly depending provide the on IGBT the stator gate signalsresistance for willthe haveinverter, a reduced i.e., without weight th consideringe explicit control that the of controlstator currents. is only intended to operate at a high speed. Based on the previous considerations, the feedforward voltage can be safely simplified to form 3.2.1.the right Rotor hand Field-Oriented of (13). The Control resulting (RFOC) block diagram is shown in Figure8, with the feedforward term beingRFOC either (see the Figure complete 9) is or one simplified of the most voltage popular equation options in (13). for the high-performance control of IM drives [14,15], although its discussion is beyond the scope of this paper. RFOC is often used in HST 3.2. Vector-Based Control at relatively low speeds, the inverter operates in the linear region and with an adequate switching to fundamentalVector control frequency methods ratio. areHowever, aimed its at use directly at high manipulating speeds presents the IMmultiple fields problems, and torque. including These themethods lack of are a voltage based onmargin well-known in the inverterd-q models. for proper Field-Oriented operation of Control the current (FOC) regulator, represents distortions flux and intorque the currents as a function due to of overmodulation, stator currents in and a synchronous delays intrinsic reference to the frame, reduced with switching high-bandwidth frequency. current The modificationregulators being of RFOC used to enable provide operation the voltage at the command voltage tolimit the was inverter. discussed Alternatively, in [16]. Direct Torque Control (DTC) methods implement torque and flux controllers which directly provide the IGBT gate signals for the inverter, i.e., without the explicit control of stator currents.

Figure 9. Rotor field-oriented control (RFOC) scheme.

Energies 2020, 13, x FOR PEER REVIEW 9 of 22

Figure 8. Closed loop V/F with torque/flux control and feedforward (CLVFC&FF) scheme.

3.2. Vector-Based Control Vector control methods are aimed at directly manipulating the IM fields and torque. These methods are based on well-known d-q models. Field-Oriented Control (FOC) represents flux and torque as a function of stator currents in a synchronous reference frame, with high-bandwidth current regulators being used to provide the voltage command to the inverter. Alternatively, Direct Torque Control (DTC) methods implement torque and flux controllers which directly provide the IGBT gate signalsEnergies for2020 the, 13 ,inverter, 700 i.e., without the explicit control of stator currents. 9 of 22

3.2.1. Rotor Field-Oriented Control (RFOC) 3.2.1. Rotor Field-Oriented Control (RFOC) RFOC (see Figure 9) is one of the most popular options for the high-performance control of IM drivesRFOC [14,15], (see although Figure 9its) isdiscussion one of the is most beyond popular the scope options of this for thepaper. high-performance RFOC is often used control in ofHST IM atdrives relatively [14,15 low], although speeds, the its discussioninverter operates is beyond in th thee linear scope region of this and paper. with RFOC an adequate is often used switching in HST to at fundamentalrelatively low frequency speeds, ratio. the inverter However, operates its use in at the high linear speeds region presents and withmultiple an adequate problems, switching including to thefundamental lack of a voltage frequency margin ratio. in the However, inverter its for use proper at high operation speeds presents of the current multiple regulator, problems, distortions including inthe the lack currents of a voltage due to overmodulation, margin in the inverter and delays for proper intrinsic operation to the reduced of the current switching regulator, frequency. distortions The modificationin the currents of RFOC due to to overmodulation, enable operation and at the delays voltage intrinsic limit towas the discussed reduced switchingin [16]. frequency. The modiﬁcation of RFOC to enable operation at the voltage limit was discussed in [16].

Figure 9. Rotor ﬁeld-oriented control (RFOC) scheme. Figure 9. Rotor field-oriented control (RFOC) scheme. 3.2.2. Direct Flux Vector Control (DFVC)

DFVC [17] is a stator-flux-oriented control approach. By writing the voltage Equation (1) in stator flux, reference frame (14) can be obtained. It can be observed from (14) that the stator flux variation can be regulated through the d-axis voltage, and the torque is then controlled through the q-axis current (15), with a current regulator being used for this purpose. The DFVC scheme is shown in Figure 10. ) v = Rˆ si + pλˆ ds ds ds (14) = ˆ + ˆ vqs Rsiqs ωˆ s f λds

3 T = Pλˆ i (15) e 2 ds qs Stator flux αβ-components are estimated from the voltage-model-based flux estimator. The synchronous frequency can be obtained from the estimated stator flux and back-emf (16) [18], avoiding the use of stator flux angle derivative and time-consuming trigonometric functions.    λˆ λˆ eˆ λˆ eˆ ˆ d  1 βs  αs βs βs αs ωˆ s f = pθs f = tan−   = · − · (16) dt  ˆ  2 λαs λˆ s

At low speeds, DFVC can operate either with rated stator flux or a maximum torque per ampere (MTPA) strategy to improve the efficiency. Above the base speed, flux is reduced according to (17), where Vmax is the maximum output voltage of the inverter, which depends on the available DC-link voltage and the modulation method. Operation in overmodulation is feasible, but a voltage margin must be preserved for proper operation of the q-axis current regulator, meaning that operation with a maximum output voltage (i.e., six-step) is not possible. Furthermore, operation in overmodulation Energies 2020, 13, x FOR PEER REVIEW 10 of 22

3.2.2. Direct Flux Vector Control (DFVC) DFVC [17] is a stator-flux-oriented control approach. By writing the voltage Equation (1) in stator flux, reference frame (14) can be obtained. It can be observed from (14) that the stator flux variation can be regulated through the d-axis voltage, and the torque is then controlled through the q-axis current (15), with a current regulator being used for this purpose. The DFVC scheme is shown in Figure 10. 𝑣 =𝑅𝑖 +𝑝𝜆 (14) 𝑣 =𝑅𝑖 +𝜔𝜆

3 𝑇 = 𝛲𝜆 𝑖 (15) 2 Stator flux αβ-components are estimated from the voltage-model-based flux estimator. The synchronous frequency can be obtained from the estimated stator flux and back-emf (16) [18], avoiding the use of stator flux angle derivative and time-consuming trigonometric functions. 𝑑 𝜆 𝜆 ⋅𝑒̂ −𝜆 ⋅𝑒̂ 𝜔 =𝑝𝜃 = 𝑡𝑎𝑛 = (16) 𝑑𝑡 𝜆 𝜆 At low speeds, DFVC can operate either with rated stator flux or a maximum torque per ampere (MTPA) strategy to improve the efficiency. Above the base speed, flux is reduced according to (17), where 𝑉 is the maximum output voltage of the inverter, which depends on the available DC-link voltage and the modulation method. Operation in overmodulation is feasible, but a voltage margin must be preserved for proper operation of the q-axis current regulator, meaning that operation with Energies 2020, 13, 700 10 of 22 a maximum output voltage (i.e., six-step) is not possible. Furthermore, operation in overmodulation forces a reduction of the current regulator bandwidth to mitigate the effects of the resulting current harmonicsforces a reduction in this case. of the Therefore, current regulator current bandwidthregulator gains to mitigate may need the etoff ectsbe adapted of the resulting with machine current speeds.harmonics in this case. Therefore, current regulator gains may need to be adapted with machine speeds. 𝑉 − 𝑅 𝑖 ∗ ˆ 𝜆 Vmax Rsiqs (17) λ 𝜔− (17) s∗ ≤ ωˆ s f It is finally noted that Figure 10 includes a mechanism to limit the torque angle  between the statorIt and is finally rotor notedfluxes thatso that Figure it is 10 smaller includes than a mechanism the pull-out to torque limit the angle torque of angle =45δ electricalbetween thedegrees stator [17].and rotor fluxes so that it is smaller than the pull-out torque angle of δ = 45 electrical degrees [17].

FigureFigure 10. 10. DirectDirect Flux Flux Vector Vector Control Control (DFVC) (DFVC) scheme. scheme. 3.2.3. Direct Torque Control (DTC)

IM torque can be expressed as (18), with δ being the torque angle. DTC methods control torque by controlling the stator flux magnitude and angle with respect to rotor flux. Stator flux is controlled through the stator voltage (19) (stator resistance neglected), with Vs being the inverter output voltage vector.

Lm Te = λsλrsin(δ) (18) σLsLr Z λs = Vsdt (19)

Switching-Table-Based (ST-DTC) was introduced by Takahashi and Noguchi [19] in the mid-1980s. Two hysteresis controllers are used to control the stator flux and torque directly. The hysteresis control signals are sent to a look-up table to select the voltage vectors required to achieve high dynamics (see Figure 11). The fact that the switching frequency is not defined and operation in overmodulation and six-step is not straightforward makes this method inadequate for high-power railway drives [20]. Direct-Self Control (DSC) was proposed by Depenbrock [21] for high-power drives. Three hysteresis controllers determine the voltage applied to the machine by comparing a flux magnitude command with the estimated flux for each phase, and a two-level hysteresis torque controller determines the amount of zero voltage (see Figure 12). DSC produces a hexagonal stator flux trajectory, which enables a smooth transition into overmodulation and eventually six-step. However, hexagonal flux trajectories make DSC problematic below 30% of the base speed, and remedial actions can be found ≈ in [22,23]. Energies 2020, 13, 700 11 of 22

Figure 11. Switching-Table-Based Direct Torque Control (ST-DTC) scheme.

Figure 12. Direct-Self Control (DSC) scheme.

Several modifications have been proposed to overcome the limitations of DTC methods [24]. DTC with a constant switching frequency calculates the required stator voltage vector over a sampling period to achieve the desired torque and stator flux. The voltage vector is synthesized using Space-Vector Modulation (SVM), and these methods are often referred to as DTC-SVM. In the implementation in Figure 13, a PI controls the torque through the torque angle [25]. The stator flux angle is obtained from the estimated rotor flux angle and the commanded torque angle. The stator voltage vector command

Vαβ∗ s employed to cancel the stator ﬂux error ∆λαβ∗ s at the end of the next sampling period ∆t is obtained as: ∆λαβ∗ s V∗ = + Rˆ si . (20) αβs ∆t αβs

1 1

Energies 2020, 13, x FOR PEER REVIEW 12 of 22

Figure 12. Direct-Self Control (DSC) scheme.

Several modifications have been proposed to overcome the limitations of DTC methods [24]. DTC with a constant switching frequency calculates the required stator voltage vector over a sampling period to achieve the desired torque and stator flux. The voltage vector is synthesized using Space-Vector Modulation (SVM), and these methods are often referred to as DTC-SVM. In the implementation in Figure 13, a PI controls the torque through the torque angle [25]. The stator flux angle is obtained from the estimated rotor flux angle and the commanded torque angle. The stator voltage vector command 𝑉∗ employed to cancel the stator flux error 𝛥𝜆∗ at the end of the next sampling period 𝛥𝑡 is obtained as: 𝛥𝜆∗ ∗ 𝑉 = +𝑅𝑖. (20) 𝛥𝑡 The scheme in Figure 13 is easy to implement and retains the fast dynamics of DTC if the inverter operates in the linear region. However, voltage distortions intrinsic to overmodulation can result in magnitude and phase deviations of the actual stator flux vector, leading to instability problems. Furthermore, (20) effectively cancels the flux error for relatively small values of 𝛥𝑡, but can result in large steady-state errors in the case of low switching frequencies. DTC-SVM suffers from the same limitation as ST-DTC when operating in overmodulation and six-step, which raises concerns on their use for high-power, high-speed railway traction drives. A predictive term for mitigating the stator flux delay and extending the operation to six-step was proposed in [26]. However, this was at the

priceEnergies of2020 a significant, 13, 700 complexity increase. 12 of 22

Figure 13. Figure 13. Direct-TorqueDirect-Torque Control Control Spac Space-Vectore-Vector Modulation (DTC-SVM) block diagram. The scheme in Figure 13 is easy to implement and retains the fast dynamics of DTC if the inverter 3.3. Control Strategies Summary operates in the linear region. However, voltage distortions intrinsic to overmodulation can result in magnitudeTable 1 summarizes and phase deviationsthe main conclusions of the actual for stator the control flux vector, methods leading discussed to instability in this problems. section, includingFurthermore, controlled (20) eff ectivelyvariables cancels and the the easiness flux error of foroperation relatively at low small speeds, values overmodulation of ∆t, but can result (high in speed),large steady-state and the transition errors in to the six-step. case of Regarding low switching the dynamic frequencies. response, DTC-SVM it is important suffers from to note the samethat thelimitation torque asramp ST-DTC is normally when operating limited inin overmodulation railway traction. and Consequently, six-step, which not raises only concerns the maximum on their dynamicuse for high-power, response (e.g., high-speed the minimu railwaym time traction required drives. to A respond predictive to terma step-like for mitigating torque command) the stator flux is relevant,delay and but extending also the the capability operation of to the six-step drive wasto meet proposed the maximum in [26]. However, torque ramp this was requested at the price by ofthe a application,significant complexity especially increase.when the machine operates at a high speed in the field-weakening region. CLVFC, CLVFVC&FF, DFVC, and DTC-SVM have been selected as a representative subset of the methods3.3. Control in Table Strategies 1, and Summary their behavior will be analyzed by means of simulation in Section 6. Table1 summarizes the main conclusions for the control methods discussed in this section, Table 1. Summary of the presented control schemes for traction applications. including controlled variables and the easiness of operation at low speeds, overmodulation (high speed), and the transitionV/Hz to with six-step. Feedback Regarding the dynamic FOC response, it is important DTC to note that Properties/ V/Hz CLVFVC CLVFVC&FF RFOC DFVC DTC DSC DTC-SVM thePerformance torque ramp is normally limited in railway traction. Consequently, not only the maximum (Figure 5) (Figure 7) (Figure 8) (Figure 9) (Figure 10) (Figure 11) (Figure 12) (Figure 13) dynamic response (e.g., the minimum time required to respond to a step-like torque command) is Reference frame 𝜆 𝜆 𝜆 𝜆 𝜆 SRF. SRF 𝜆 relevant, but also the capability of the drive to meet𝜆 &𝑖 the;𝑖 maximum𝜆 ;𝑖 torque ramp requested by the Controlled variables 𝜔† 𝜆; 𝑇 𝜆; 𝑇 𝜆; 𝑇 𝜆; 𝑇 𝜆; 𝑇 application,Defined especially when the machine operates at a high speed in the field-weakening region. Yes Yes Yes Yes Yes No No Yes switchingCLVFC, frequency CLVFVC&FF, DFVC, and DTC-SVM have been selected as a representative subset of the methods in Table1, and their behavior will be analyzed by means of simulation in Section6.

Table 1. Summary of the presented control schemes for traction applications.

V/Hz with Feedback FOC DTC Properties/ Performance V/Hz CLVFVC CLVFVC&FFRFOC DFVC DTC DSC DTC-SVM (Figure5) (Figure7) (Figure8) (Figure9) (Figure 10) (Figure 11) (Figure 12) (Figure 13)

Reference frame λr λr λr λr λs SRF. SRF λr

Controlled variables ωr † λr; Te λr; Te λr&ids; iqs λs; iqs λs; Te λs; Te λs; Te Deﬁned Yes Yes Yes Yes Yes No No Yes switching frequency

Low speed (linear mod.) High speed —— (overmodulation) Six-step operation

Dynamic response †† / /——/ /— /— / / /

: favorable; —: neutral; : unfavorable; “SRF” stands for stationary reference frame. †: Implementation of an outer speed control loop for the rest of the methods is straightforward. ††: (1) maximum torque dynamic response/ (2) capability to provide 3 kNm/s in the overmodulation region. Energies 2020, 13, x FOR PEER REVIEW 13 of 22

Low speed         (linear mod.) High speed    — —    (overmodulation) Six-step operation         Dynamic response†† / /— —/ /— /— / / / : favorable; —: neutral; : unfavorable; “SRF” stands for stationary reference frame. †: Implementation of an outer speed control loop for the rest of the methods is straightforward. ††: (1) Energiesmaximum2020, 13, 700 torque dynamic response/ (2) capability to provide 3 kNm/s in the overmodulation region.13 of 22

4. Modulation Techniques 4. Modulation Techniques High-power traction drives usually operate with low switching frequencies (<1 kHz) to reduce switchingHigh-power losses. tractionThis results drives in usuallysignificant operate current with and low consequently switching frequencies torque ripples, (<1 kHz)which to can reduce have switchingimplications losses. for mechanical This results transmission in significant stress, current train and comfort, consequently standards torque compliance, ripples, etc. which Trading- can haveoff switching implications losses for and mechanical torque pulsations transmission is a challenge stress, train for comfort,the selection standards of modulation compliance, methods. etc. Trading-oFurthermore,ff switching modulation losses and and contro torquel strategies pulsations often is achange challenge with for the the output selection frequency. of modulation Figure 14 methods.shows an Furthermore,example of this modulation [27]. Asynchronous and control Pulse-Width strategies Modulation often change (PWM) with the is used output at low frequency. speeds, Figurechanging 14 shows to synchronous an example modulati of this [27on]. with Asynchronous Selective Harmonic Pulse-Width Elimination Modulation (SHE) (PWM) and is finally used at single low speeds,pulse modes changing as the to synchronousspeed increases. modulation The three with opti Selectiveons are briefly Harmonic described Elimination in the following, (SHE) and and finally are singleparticularized pulse modes for asa thethree-level speed increases. Neutral-Point-Cl The threeamped options (3L-NPC) are briefly scheme described [28], in theas this following, is the andconfiguration are particularized used in forthis aproject. three-level Neutral-Point-Clamped (3L-NPC) scheme [28], as this is the configuration used in this project.

Figure 14. Modulation technique vs. train speed for a High-Speed Train (HST). Figure 14. Modulation technique vs. train speed for a High-Speed Train (HST). 4.1. Asynchronous Modulation 4.1. Asynchronous Modulation Carrier-Based Pulse-Width Modulation (PWM) or Space-Vector Modulation (SVM) can be used at low speeds.Carrier-Based The first Pulse-Width compares the Modulation reference voltages(PWM) orVabc ∗Space-Vectorwith two carriers, Modulation as shown (SVM) in can Figure be used15a. ∗ Aat level-shifted low speeds. carrierThe first is compares normally preferredthe reference as itvoltages results in𝑉 a lowerwith two voltage carriers, harmonic as shown content in Figure [28]. A15a. common-mode A level-shifted (homopolar) carrier is normally voltage preferred should be as added it results to fullyin a lower use the voltage available harmonic DC link content voltage. [28]. Space-VectorA common-mode Modulation (homopolar) (SVM) voltage for three-level should invertersbe added shares to fully the use same thebasic available principles DC link as thatvoltage. for two-levelSpace-Vector inverters, Modulation but 24 active(SVM) voltage for three-level and three inverters zero vectors shares are the available. same basic The principles implementation as that offor SVMtwo-level is shown inverters, in Figure but 2415 b.active It typically voltage and consists three of zero three vectors steps: are (1) available. sector identification, The implementation (2) region of identification,SVM is shown and in (3) Figure the selection 15b. It oftypically an appropriate consists switchingof three steps: sequence. 1) sector Redundant identification, states are 2) used region to balanceidentification, DC link and capacitor 3) the selection voltages. of SVM an appropri offers theate same switching DC voltage sequence. utilization Redundant as the states PWM are with used a homopolarto balance voltage,DC link andcapacitor it has voltages. a larger computational SVM offers the burden, same DC but voltage makes utilization better use ofas thethe redundantPWM with statesEnergiesa homopolar [29 2020,30, 13]. ,voltage, x FOR PEER and REVIEW it has a larger computational burden, but makes better use of the redundant14 of 22 states [29,30].

(a) (b)

FigureFigure 15.15. AsynchronousAsynchronous modulationmodulation techniques:techniques: (aa)) Pulse-WidthPulse-Width ModulationModulation (PWM)(PWM) withwith tripletriple harmonicharmonic injection;injection; ((bb)) Space-Vector Space-Vector Modulation Modulation (SVM). (SVM).

4.2. Synchronous Modulation—Selective Harmonic Elimination (SHE) SHE performs a predefined number of commutations per quarter of the fundamental cycle. Commutations are synchronized with the fundamental wave. Commutation angles are pre- calculated via Fourier analysis [31], with the aim of eliminating specific harmonics of the output voltage. An example of SHE with three switching angles is shown in Figure 16a. With three angles, it is possible to cancel two harmonics of the output voltage (typically the 5th and 7th), in addition to controlling the magnitude of the fundamental voltage. As the speed increases, SHE changes to one pulse mode (Figure 16b) to reduce switching losses. SHE implementation is schematically shown in Figure 16c.

(a)

(c)

(b)

Figure 16. Selective Harmonic Elimination (SHE) for three-level Neutral-Point-Clamped (3L-NPC): (a) Phase voltage for the case of three switching angles; (b) phase voltage for the case of one switching angle; (c) Selective Harmonic Elimination (SHE) block diagram.

5. Operation with Reduced Flux and Remagnetization Strategies Electric drives in high-speed traction applications can work for certain periods of time with light loads. It is possible in this case to decrease the flux level to reduce the stator current and consequently Joule losses, which is commonly termed MTPA [32]. However, operating with reduced flux levels will penalize the dynamic response of the drive. If a torque increase is demanded, the machine must

Energies 2020, 13, x FOR PEER REVIEW 14 of 22

(a) (b)

Figure 15. Asynchronous modulation techniques: (a) Pulse-Width Modulation (PWM) with triple harmonic injection; (b) Space-Vector Modulation (SVM). Energies 2020, 13, 700 14 of 22 4.2. Synchronous Modulation—Selective Harmonic Elimination (SHE)

4.2. SynchronousSHE performs Modulation—Selective a predefined number Harmonic of commutations Elimination (SHE) per quarter of the fundamental cycle. Commutations are synchronized with the fundamental wave. Commutation angles are pre- calculatedSHE performsvia Fourier a predeﬁnedanalysis [31], number with the of commutationsaim of eliminating per quarterspecific ofharmonics the fundamental of the output cycle. voltage.Commutations An example are synchronized of SHE with withthree the switching fundamental angles wave. is shown Commutation in Figure 16a. angles With are three pre-calculated angles, it isvia possible Fourier to analysis cancel two [31 ],harmonics with the of aim the of output eliminating voltage speciﬁc (typically harmonics the 5th and of the7th), output in addition voltage. to controllingAn example the of SHEmagnitude with three of the switching fundamental angles voltag is showne. As in Figurethe speed 16a. increases, With three SHE angles, changes it is possible to one pulseto cancel mode two (Figure harmonics 16b) to of reduce the output switching voltage losses (typically. SHE implementation the 5th and 7th), is in schematically addition to controlling shown in Figurethe magnitude 16c. of the fundamental voltage. As the speed increases, SHE changes to one pulse mode (Figure 16b) to reduce switching losses. SHE implementation is schematically shown in Figure 16c.

(a)

(c)

(b)

Figure 16. Selective Harmonic Elimination (SHE) for three-level Neutral-Point-Clamped (3L-NPC): (a) Figure 16. Selective Harmonic Elimination (SHE) for three-level Neutral-Point-Clamped (3L-NPC): Phase voltage for the case of three switching angles; (b) phase voltage for the case of one switching (a) Phase voltage for the case of three switching angles; (b) phase voltage for the case of one switching angle; (c) Selective Harmonic Elimination (SHE) block diagram. angle; (c) Selective Harmonic Elimination (SHE) block diagram. 5. Operation with Reduced Flux and Remagnetization Strategies 5. Operation with Reduced Flux and Remagnetization Strategies Electric drives in high-speed traction applications can work for certain periods of time with light loads.Electric It is possible drives in in high-speed this case to traction decrease applications the flux level can to work reduce for the certain stator periods current of and time consequently with light loads.Joule losses,It is possible which in is this commonly case to termeddecrease MTPA the flux [32 level]. However, to reduce operating the stator with current reduced and flux consequently levels will Joulepenalize losses, the which dynamic is commonly response of termed the drive. MTPA If a torque[32]. However, increase operating is demanded, with the reduced machine flux must levels be willremagnetized penalize the first. dynamic The remagnetization response of the time drive. is determined If a torque increase by the rotor is demanded, time constant the (7)machine and applied must magnetizing current. Due to the relatively large values of the rotor time constant, fast torque changes of torque are not feasible. It must be noted, however, that fast torque changes are not desirable for traction applications, as they might exert stress on the mechanical transmission, produce wheel slip, and raise comfort concerns. The maximum torque-allowed gradient will depend on the application. For the machine considered in this paper, it has a value of 3 kNm/s. Figure 17 shows two possible remagnetization strategies. RFOC principles are used for the discussion. It is noted, however, that equivalent strategies can be used with other control methods by simply transforming d-q axis current commands into other commands, e.g., stator flux and slip. Energies 2020, 13, x FOR PEER REVIEW 15 of 22 be remagnetized first. The remagnetization time is determined by the rotor time constant (7) and applied magnetizing current. Due to the relatively large values of the rotor time constant, fast torque changes of torque are not feasible. It must be noted, however, that fast torque changes are not desirable for traction applications, as they might exert stress on the mechanical transmission, produce wheel slip, and raise comfort concerns. The maximum torque-allowed gradient will depend on the application. For the machine considered in this paper, it has a value of 3 kNm/s. Figure 17 shows two possible remagnetization strategies. RFOC principles are used for the discussion.Energies 2020, It13 is, 700 noted, however, that equivalent strategies can be used with other control methods15of by 22 simply transforming d-q axis current commands into other commands, e.g., stator flux and slip.

(a) Profile 1: step-like d-axis, ramp-like q axis (b) Profile 2: 3kNm/s torque ramp, minimum current

FigureFigure 17. 17. RemagnetizationRemagnetization (a (a) )using using the the rated rated d-axis d-axis current current and and ( (bb)) target target torque torque gradient. gradient. Left: Left: CurrentCurrent trajectories trajectories in in the the dd--qq plane;plane; right: right: torque, torque, rotor rotor flux, ﬂux, and and current current trajectories trajectories vs. vs. time. time.

TheThe strategy strategy in in Figure Figure 14a14a uses a step-like d-axis current command.command. WhileWhile simple,simple,this this results results in in a aslow slow remagnetization, remagnetization, with with the the 3 kNm 3 kNm/s/s target target not beingnot being achieved. achieved. The option The option in Figure in Figure14b is derived14b is derivedfrom the from method the method described described in [33] and in [33] is aimed and is at aimed providing at providing a target a torque target ramp torque with ramp the with smallest the smallestpossible possible current duringcurrent the during remagnetization the remagnetizatio process.n This process. reduces This the reduces stress inthe the stress power in devicesthe power and devicesthe risk and of surpassing the risk of theirsurpassing current their limit. current This strategy limit. This will strategy be used will for thebe simulationused for the results simulation in the resultsnext section. in the next section.

6.6. Simulation Simulation Results Results SelectedSelected control control methods methods from from Section Section 3 have been evaluated by means of simulationsimulation using MATLAB/Simulink.MATLAB/Simulink. IM IM parameters parameters for for the the base base sp speedeed are are given given in in Table Table 22.. The simulation model implementsimplements asynchronous asynchronous SVM SVM with with a a switching switching freq frequencyuency of of 1 1 kHz kHz at at low low speeds speeds and and SHE SHE at at high high speeds,speeds, as as shown shown in in Figure Figure 14.14.

Table 2. Speciﬁcations of the induction motor at base speed ω (extended full ﬂux range design). Table 2. Specifications of the induction motor at base speed 𝜔base (extended full flux range design). Variable Value Unit DC-link voltageVariable 3600Value Unit V Rated PowerDC-link voltage 1084 3600 kW V Rated Voltage (L-L,Rated rms)Power 2727 1084 kWV Pole-pairsRated Voltage (P) (L-L, rms) 2 2727 Pole V Pole-pairs (P) 2 Pole Stator resistance (Rs) 55.38 mΩ Stator resistance (Rs) 55.38 mΩ Stator inductance (Ls) 26.45 mH TorqueStator inductance (Ls) 324126.45 NmmH Torque 3241 Nm Speed 3194 rpm Speed 3194 rpm

Since the main focus of this paper is high-speed operation, only results at high speed using SHE Since the main focus of this paper is high-speed operation, only results at high speed using SHE are provided in this section. Infinite inertia is assumed. Consequently, the rotor speed remained are provided in this section. Infinite inertia is assumed. Consequently, the rotor speed remained constant throughout the simulation. This assumption is realistic and has no effect on the conclusions. constant throughout the simulation. This assumption is realistic and has no effect on the conclusions. Profile 2 in Figure 17b was used during remagnetization. The maximum torque ramp was limited to Profile 2 in Figure 17b was used during remagnetization. The maximum torque ramp was limited to 3 kNm/s, which was imposed by the application. Simulation results are shown in Figure 18. 3 kNm/s, which was imposed by the application. Simulation results are shown in Figure 18. The most remarkable difference is the slowest transient response of CLVFC due to dynamic limitations intrinsic to scalar control. The dynamic response is seen to improve and be comparable to the other methods when the feedforward defined by (13) is used (CLVFC&FF in Figure 18b). DFVC and DTC-SVM are seen to provide similar dynamic responses to CLVFC&FF. Regarding DFVC, it must be noted that to achieve proper operation in the overmodulation region, the q-axis current regulator bandwidth was reduced in the range of ten times to avoid a current regulator reaction to low-order current harmonics due to the non-linear operation of the inverter. The need to dynamically adapt the gains of the current regulator in the high-speed region is an obvious concern. Energies 2020, 13, x FOR PEER REVIEW 16 of 22 Energies 2020, 13, 700 16 of 22 The most remarkable difference is the slowest transient response of CLVFC due to dynamic limitations intrinsic to scalar control. The dynamic response is seen to improve and be comparable to Itthe can other be observed methods when that DTC-SVMthe feedforward suff ersdefined from by a (13) steady-state is used (CLVFC&FF error in the in controlledFigure 18b). flux due to the low samplingDFVC and frequency DTC-SVM (∆ aret) whenseen to SHE provide is used similar in thedynamic inverter. responses This resultsto CLVFC&FF. in an increase Regarding in the load angle.DFVC, This it must could be leadnoted to that overcurrent to achieve orproper instability operation if the in loadthe overmodula angle is nottion monitored. region, the q-axis Figurecurrent 19 regulator summarizes bandwidth the performance was reduced in ain steady the range state of for ten the times four to control avoid methods,a current regulator i.e., once the machinereaction is providing to low-order its maximum current harmonics torque. due The to steady-state the non-linear error operation in the of flux the for inverter. DTC-SVM The need is seen to to affect thedynamically modulation adapt index the gains and of slip. the Thiscurrent will regulator eventually in the a ffhigh-speedect the machine region is loss an obvious distribution, concern. which is a concernIt can as tractionbe observed motors that DTC-SVM can be required suffers from to operate a steady-state close to error their in thermalthe controlled limit. flux CLVFC due to and the low sampling frequency (𝛥𝑡) when SHE is used in the inverter. This results in an increase in the CLVFC&FF are seen to have a higher torque error compared to DFVC, but with little impact on the load angle. This could lead to overcurrent or instability if the load angle is not monitored. modulation index and slip. It is noted that a torque error in the range of 1% is perfectly assumable.

(a) (b)

FigureFigure 18. Simulation 18. Simulation results results of using of using (a) CLVFC, (a) CLVFC, (b) CLVFC&FF, (b) CLVFC&FF, (c) DFVC, (c) DFVC, and (andd) DTC-SVM(d) DTC-SVM control control methods with SHE. Rotor speed 𝜔 = 1.328𝜔; torque was increased from 10% (i.e., with methods with SHE. Rotor speed ωr = 1.328ωbase; torque was increased from 10% (i.e., with the machine the machine operating with reduced flux in MTPA) to 100%. From top to bottom: commanded and operating with reduced flux in MTPA) to 100%. From top to bottom: commanded and actual torque; actual torque; d- and q-axis currents; commanded and estimated flux (can be stator or rotor flux, d- and q-axis currents; commanded and estimated flux (can be stator or rotor flux, depending on the depending on the method); and output voltage magnitude. All the variables are shown in p.u. method); and output voltage magnitude. All the variables are shown in p.u. Figure 19 summarizes the performance in a steady state for the four control methods, i.e., once the machine is providing its maximum torque. The steady-state error in the flux for DTC-SVM is seen

Energies 2020, 13, x FOR PEER REVIEW 17 of 22

to affect the modulation index and slip. This will eventually affect the machine loss distribution, which is a concern as traction motors can be required to operate close to their thermal limit. CLVFC and CLVFC&FF are seen to have a higher torque error compared to DFVC, but with little impact on the modulation index and slip. It is noted that a torque error in the range of 1% is perfectly assumable. It can be concluded that CLVFC&FF is more adequate compared to the simulated schemes at high speeds due to its high dynamics, and the controllers are not affected by low-order harmonics resulting from a square-wave operation, i.e., six-step, as in the case of DFVC, and are simple to Energiesimplement.2020, 13 , 700 17 of 22

Figure 19. From left to right: modulation index, slip, torque error, and error in the ﬂux being controlled Figure 19. From left to right: modulation index, slip, torque error, and error in the flux being for the four control methods being considered, once the machine has reached a steady state, i.e., is its controlled for the four control methods being considered, once the machine has reached a steady state, maximum torque. Torque and slip have been low-pass ﬁltered to eliminate the harmonic content i.e., is its maximum torque. Torque and slip have been low-pass filtered to eliminate the harmonic producedcontent produced by SHE by modulation. SHE modulation.

7. ExperimentalIt can be concluded Results that CLVFC&FF is more adequate compared to the simulated schemes at high speeds due to its high dynamics, and the controllers are not affected by low-order harmonics resulting A schematic diagram of the high-power traction system test bench is shown in Figure 20a. It from a square-wave operation, i.e., six-step, as in the case of DFVC, and are simple to implement. consists of two identical IMs and converters connected back-to-back, which are supplied from a High- 7.Voltage Experimental (HV) DC Results power supply. The power converter module (see Figure 20b) consists of a three- phase, three-level Neutral-Point Clamped (NPC) inverter feeding the IMs. Single-phase inverters feedA auxiliary schematic loads, diagram such as ofcooling the high-powersystems, control traction power systemsupply units, test benchetc. A DC-DC is shown chopper in Figure is 20a. Itimplemented consists of two for identicaldissipative IMs braking and convertersand DC bus connected overvoltage back-to-back, protection. A which specially are supplieddesigned from a High-Voltagetraction transformer (HV) DC is used power to filter supply. off catenary The power harmonics converter and moduleallow the (see interconnection Figure 20b) of consists the of a three-phase,different converters. three-level A 100 Neutral-Point Hz (2f) filter Clamped is included (NPC) in the inverter DC bus. feeding The overall the IMs.experimental Single-phase test rig inverters is shown in Figure 20c. feed auxiliary loads, such as cooling systems, control power supply units, etc. A DC-DC chopper is implemented for dissipative braking and DC bus overvoltage protection. A specially designed traction transformer is used to filter off catenary harmonics and allow the interconnection of the different converters. A 100 Hz (2f) filter is included in the DC bus. The overall experimental test rig is shown in Figure 20c.

Energies 2020, 13, 700 18 of 22 Energies 2020, 13, x FOR PEER REVIEW 18 of 22

(a)

(b) (c)

FigureFigure 20. 20. High-powerHigh-power traction traction test test bench: bench: (a (a) )Schematic Schematic diagram; diagram; (b (b) )power power converter converter module module (INGETRAC);(INGETRAC); and and ( (cc)) overall overall view view of of the the laboratory laboratory setup. setup.

PreliminaryPreliminary experimental experimental results results for for a a full-scale full-scale HS HS traction traction drive drive are are presented presented in in the the following. following. TheThe control control uses RFOC atat lowlow speedsspeeds and and CLVFC CLVFC at at high high speeds. speeds. The The main main system system parameters parameters are are the thesame same as thoseas those used used in the in the simulation simulation shown shown in Table in Ta2ble. The 2. The torque-flux torque-flux characteristic characteristic of the of motor the motor is of isthe of typethe type named named as the as extendedthe extended full fluxfull flux range range in Figure in Figure3. 3. FigureFigure 2121aa showsshows the the rotor rotor speed, speed, modulation modulati index,on index, commanded commanded and estimated and estimated torques, estimatedtorques, estimatedrotor flux, rotor and magnitudeflux, and magnitude of the stator of currentthe stator vector current during vector an acceleration during an acceleration (left) and deceleration (left) and deceleration(right) process. (right) Figure process. 21b Figure shows 21b the shows spectrogram the spectrogram of the stator of the current stator vector. current For vector.ωr < For0.12 𝜔p.u., < 0.12RFOC-SVM p.u., RFOC-SVM with a switching with a frequency switching of 850frequency Hz is used; of 850 the Hz switching is used; frequency the switching increases frequency to 1 kHz increasesfor 0.12 < to ω r1kHz< 0.94 forp.u. 0.12 For <ω 𝜔r><0.940.94 p.u., p.u. CLVFC For 𝜔 combined>0.94 p.u., with CLVFC SHE with combined one switching with SHE angle with is oneused. switching Changes angle in the is modulation used. Changes method in arethe readilymodulation observable method in theare spectrogramreadily observable of Figure in 21theb, spectrogramand are aim toof trade-oFigure ff21b,switching and are lossesaim to and trade-off torque switching ripple. The losses control and is torque seen to ripple. precisely The followcontrol the is seencommanded to precisely torque follow and rotorthe commanded flux in the whole torque speed and range.rotor flux It is notedin the thatwhole the speed changes range. in the It estimated is noted thatrotor the flux changes observed in the in estimated the flux-weakening rotor flux observed region respond in the flux-weakening to changes in the region corresponding respond to command changes in(not the shown corresponding in the figure). command Transitions (not shown between in the the figure). different Transitions control and between modulation the different strategies control can andbe a modulation challenge due strategies to the highcan be power a challenge and low due switching to the high frequencies. power and However, low switching as can frequencies. be observed However,from Figure as can21, suchbe observed transitions from are Figure satisfactory, 21, such i.e., transitions the spikes are observed satisfactory, in the i.e., currents the spikes are observed perfectly inacceptable the currents and doare not perfectly represent acceptable a risk for theand powerdo not devices. represent Implementation a risk for the of thepower other devices. control Implementationmethods and remagnetization of the other control strategies methods discussed and re inmagnetization Sections3 and strategies6 is ongoing. discussed in Sections 3 and 6 is ongoing.

EnergiesEnergies2020 2020, 13,, 70013, x FOR PEER REVIEW 19 of 22 19 of 22

(a)

(b)

Figure 21. Experimental results. Acceleration (left)-deceleration (right) tests between 𝜔 =0.1 and 𝜔 = Figure 21. Experimental results. Acceleration (left)-deceleration (right) tests between ωr = 0.1 1.328 p.u. (a) From top to bottom: rotor speed, modulation index, commanded and estimated torques, and ωr = 1.328 p.u. (a) From top to bottom: rotor speed, modulation index, commanded and estimated rotor flux, and magnitude of the stator current vector; (b) stator current vector spectrogram. estimated torques, estimated rotor flux, and magnitude of the stator current vector; (b) stator current vector spectrogram. 8. Conclusions 8. ConclusionsIn this paper, a comparative analysis of scalar and vector control strategies for railway traction applications has been presented, with a special focus on their operation at high speeds. In this paper, a comparative analysis of scalar and vector control strategies for railway traction HSTs normally use medium-voltage, high-power IMs. Rotor flux Oriented Control (RFOC) has applicationsbeen widely has adopted been presented, at low and with medium a special speeds. focus However, on their high operation fundamental at high frequencies speeds. intrinsic toHSTs high-speed normally operations, use medium-voltage, combined with high-powerthe need to reduce IMs. Rotor inverter flux losses, Oriented force Controlthe inverter (RFOC) to has beenoperate widely with adopted reduced at switching low and mediumfrequencies speeds. and a high However, modulation high index fundamental or even at frequencies the six-step limit. intrinsic to high-speedThese limitations operations, seriously combined compromise with the the need performa to reducence of RFOC inverter at high losses, speeds. force A thecommon inverter practice to operate withis reduced to use RFOC switching at low speeds, frequencies rather and than a switch high modulation to strategies able index to orperform even atproperly the six-step under limit.severe These limitationsvoltage constraints seriously compromiseat high speeds. the performance of RFOC at high speeds. A common practice is to use RFOCMethods at lowconsidered speeds, for rather the analysis than switchincluded to di strategiesfferent types able of Closed-loop to perform Voltage/Frequency properly under severe voltage(V/F), constraints Field-Oriented at high Control speeds. (FOC), and Direct-Torque Control (DTC) strategies. Four different control strategies have been selected and tested by means of simulation, namely, Closed Loop V/F Methods considered for the analysis included different types of Closed-loop Voltage/Frequency with flux/torque Control (CLVFC), CLVFC with feedforward (CLVFC&FF), Direct Flux Vector (V/F),Control Field-Oriented (DFVC), and Control Direct-Torque (FOC), Control and Direct-Torque Space-Vector Modulation Control (DTC) (DTC-SVM). strategies. The modulation Four diff erent control strategies have been selected and tested by means of simulation, namely, Closed Loop V/F with flux/torque Control (CLVFC), CLVFC with feedforward (CLVFC&FF), Direct Flux Vector Control (DFVC), and Direct-Torque Control Space-Vector Modulation (DTC-SVM). The modulation methods that have been considered are PWM/SVM, SHE, and six-step. Their advantages include the easiness Energies 2020, 13, 700 20 of 22 of operation with a high modulation index, including six-step; switching frequency; and dynamic response to both torque change demands and rotor flux change demands during remagntization. The CLVFC&FF method described in Section 3.1.3 and the remagnetization strategy discussed in Section5 are the original contributions of this paper. It was concluded from the simulation results that CLVFC, CLVFC&FF, and DFVC provide similar performances. However, DFVC requires a modification of the q-axis current controller gains when the drive enters the overmodulation region. Specifically, CLVFC&FF proposed in this paper operates properly with a high modulation index, including six-step, and provides a good dynamic response during remagnetization. Preliminary experimental results using CLVFC in a full-scale traction drive have been provided, which are in good agreement with the simulation results, and confirm the viability of this strategy. Implementation of the other strategies, including remagnetization, is ongoing.

Author Contributions: Conceptualization, F.B. and D.O.; methodology, F.B., J.M.G. and D.O.; formal analysis, A.F.A., J.M.G. and F.B.; simulation and programing, A.F.A., A.E. and I.M.; validation, A.F.A., A.E. and I.M.; writing—original draft preparation, A.F.A.; writing—review and editing F.B. and J.M.G.; supervision, F.B., D.O. and I.L.; All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the European Commission H2020 under grant UE-18-POWER2POWER-826417; The Spanish Ministry of Science, Innovation and Universities under grant MCIU-19-PCI2019-103490; and by the Government of Asturias under grant IDI/2018/000188 and FEDER funds. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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