Multi-Level Library of Electrical Machines for Aerospace Applications

Transcription

1 Multi-Level Library of Electrical Machines for Aerospace Applications P. Giangrane C.I. Hill C. Geraa S.V. Bozhko University of Nottingham PEMC Group, Nottingham, NG7 RD, UK. Abstract An electrical machine library, evelope within the framework of the European project Actuation 15, is presente in this paper. The library has been evelope aopting a multi-level approach, in orer to minimize the moels complexity an reuce the computational time. Multi-level approach consists in creating several moels of the same electrical machine topology, with ifrent levels of complexity. Inee, moel complexity increases at higher moel levels an each moel takes into account specific physical efcts. In aition to the funamental behavior, the presente moels aress physical efcts such as losses, magnetic saturation, torque ripple an fault conitions. The interchangeability among moel levels is ensure by using common interfaces. An overview of the library structure is given; however, particular attention is pai on the permanent magnet synchronous machine (PMSM) moels, since they are becoming increasingly wiesprea in aerospace applications. The PMSM moels escription an simulation results are provie, in orer to highlight the implemente physical efcts an confirm the moels efctiveness. Keywors: Permanent Magnet Synchronous Machine, Multi-Level, Losses, Magnetic Saturation, Torque Ripple, Fault conitions. 1 Introuction Accoring to the concept of the More Electric Aircraft (MEA), an increasing number of hyraulic actuators for primary an seconary flight control surfaces are being replace by Electromechanical Actuators (EMAs), in orer to improve efficiency, weight an maintenance of the aircraft [1]. For this reason, EMAs are becoming an attractive research area an part of the research work is focuse on eveloping virtual testing environments an analysis tools. Inee, EMAs manufacturers require simulation tools capable of analyzing EMAs performance an exploring ifrent esign configurations. In response to these requirements, a suitable simulation an analysis tool for EMAs, name Actuator library, has been evelope within the framework of the European project Actuation 15. The multiisciplinary architecture of EMAs coul lea to a large simulation time or even numerical non-convergence ue to the moel complexity []. In orer to avoi these issues, the iea of implementing several moels of the same component (i.e.: inverter, electrical machine, gear box etc ), with ifrent levels of complexity has been exploite. Hence, a multi-level approach has been aopte, with the aim of keeping the moels as simple as possible, since a goo moel is a wise trae-off between realism an simplicity. The moel levels are categorize by the complexity of the physical efcts implemente within the moel. In particular, higher moel levels take into account more complex physical efcts. Consiering that several moels of the same component are available within the library, the interchangeability among the moel levels is crucial, in orer to investigate ifrent physical efcts by simply replacing the moel level. For this reason, the interchangeability has been ensure by using common interfaces among the moel levels. In this paper, the Electrical Machines library, which is part of the Actuator library, is presente. The Electrical Machines library has been implemente using Moelica [3], as moelling language, an Dymola, as simulation environment. This library is organize as three packages an each of them consiers a specific machine topology, such as PMSM, synchronous reluctance machine (SRM) an irect current (DC) machine. Each one of these packages contains the sub-package Examples, which provies several case stuies, helpful for highlighting the atures of each moelling level. Due to space constraints, not all the machine topologies inclue in the Electrical Machines library will be consiere in this paper. Inee, the presente work is mainly focuse on escribing the /ECP Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween 737

2 Multi-Level Library of Electrical Machines for Aerospace Applications PMSM moels as these machines are characterize by an excellent efficiency, together with a high power ensity [4]. These atures make PMSMs very attractive for aerospace applications [5]. Whilst initially resistance to the aoption of these machines was shown by airframes to the possibility of unsuppresse short-circuit currents, it is now more accepte that through fault tolerant esign an heath monitoring schemes these machines ofr an optimum solution. In the next sections, an overview of the Electrical Machines library is presente along with a escription of the moel interfaces. Moreover, etails of the PMSM moelling levels an the physical efcts (i.e.: losses, magnetic saturation, torque ripple an fault conitions), taken into account, are given. Simulation results obtaine using Dymola are also inclue. Library Structure An overview of the Electrical Machines library is provie in this section an figure 1 shows the library structure. Figure 1: Structure of the Electrical Machines library as part of theactuator library. The machines consiere in this library are PMSM, SRM an DC machine. The PMSM type covers a number of topologies from non-salient surface mount to high reluctance interior permanent magnet (IPM) machines. The library is organize in three packages, one for each machine topology earlier mentione, plus the package Basic, which consiers a generic alternating current (AC) electrical machine. Accoring to the multi-level approach previously introuce, several moels with ifrent level of complexity are inclue within each of the four packages. The level of complexity is relate with the physical efcts that the moel takes into account. In other wors, a higher level of complexity implies the moelling of more complex physical efcts, such as nonlinear efcts. The package Basic contains only one moel level (moel Basic), which is the simplest moel for an AC electrical machine. Inee, moel Basic is efine by means of the torque constant an its behavior is ieal (losses an non-linear efcts are neglecte). Package PermanentMagnet inclues the three-phase PMSM moels an three moel levels, such as Stanar, Saturation an Fault moels, are provie. Three-phase SRM moels are organize in the package Reluctance an two moel levels (Stanar an Saturation) are implemente. Finally, the package DirectCurrent consiers the DC machine moels with inepenent excitation. This package consists of two moelling levels (Stanar an Saturation). As previously unerline, the sub-package Examples is provie for each of the mentione packages, in orer to support the user in both familiarizing with the moels an exploring their atures. It is worthy to remark that the contribution of this work is mainly focuse on the package PermanentMagnet an all the consierations presente in the coming sections are mae consiering PMSM. 3 Moels Interfaces As mentione earlier, every moel belonging to a level is replaceable with one belonging to another level. This ature has been achieve by aopting common interfaces, which are efine in Actuator.Electrical.Interfaces. The aopte moel interfaces can be classifie accoring their function in: electrical interface; mechanical interface; thermal interface. All quantities accessible at the mentione interfaces are shown in physical units. Consiering AC electrical machines (packages Basic, PermanentMagnet an Reluctance), the electrical interfaces aopte are the Positive- Plug an NegativePlug, since the stator wining is assume as three-phase wining. In particular, 738 Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween /ECP

3 Session 5A: Aerospace Applications the AC machine moels have been built up consiering a wye-connecte stator wining, with floating neutral point. The aopte electrical interfaces allow connecting the AC machine to a power converter or to a riven voltage source (SignalVoltage). In the case of the DC machine moels, PositivePin an NegativePin have been use as electrical interfaces, for both armature an fiel winings (the DC machine excitation is inepenent). All the machine moels aopt Flange an Support as mechanical interfaces an they are inclue in the moels by extening the PartialOne- FlangeAnSupport. The evelope electromagnetic torque an the loa torque are applie on the machine Flange, while the reaction torque is available on the Support, in case the machine housing is not groune. The PartialConitionalHeatPort is use as thermal interface for all the machine moels an housing temperature an heat flow are available at the heat port. 4 Moel Basic The moel Basic is inclue in the package Basic an it is the simplest moel for a generic three-phase AC machine. The machine behavior is escribe through the torque constant, which establishes the relationship between current an electromagnetic torque. Copper, iron an mechanical losses are not consiere at this level, as well as, efcts such as magnetic saturation, torque ripple an fault conitions are neglecte. Data recors have been use to organize the moel parameters an for the moel Basic the require parameters are: Phase resistance ( R ); Magnetizing inuctance ( L ); Pole pairs number ( pp ); Torque constant ( k t ); Rotor s moment of inertia ( J r ); Stator s moment of inertia ( J s ). The stator s moment of inertia will be use by the moel only when the machine housing is not groune. Since plugs are use as electrical interfaces, the moel Basic is using phase quantities ( abc ) an Park s transformation (invariant amplitue transformation) [6] is aopte for implementing the moel in the rotating rerence frame ( q ), accoring to the following equations: v R i L i e L iq t kt vq R iq L iq e L i e t 3 pp where e (1) is the electrical spee in ra s. The electromagnetic torque ( e ) evelope by the moel Basic is given by: k i () e t q The electrical equations are implemente in the Moelica Text Layer, while the mechanical moel is realize in the Moelica Diagram Layer, using an object-oriente approach. In figure, the Moelica Diagram Layer of the moel Basic is shown. Moel Basic, as well as all the other machine moels presente in the Electrical Machines library, is reversible. This means that the moel Basic can work reversibly as motor or generator. Figure : Moelica Diagram Layer of the moel Basic inclue in theelectrical Machines library. In orer to verify the moel Basic functionality, the simple EMA architecture, reporte in figure 3, has been implemente an simulate in Dymola. The chosen EMA architecture consists of an inverter, which supplies a PMSM mechanically couple to a 5 ra m transmission ratio roller screw, through a gearbox with transmission ratio equal to 5. The inverter is using a 7 V DC link an the PMSM parameters are: 14 pole pairs, 56. g m rotor inertia,.5 phase resistance, mh magnetizing inuctances an.1 Nm A torque constant. Control unit (controller) implements the conventional position control, hence the position is controlle by a cascae structure, where the inner loop controls the q axis current, the outer loop controls the spee an finally the outermost loop controls the position. During the simulation, the controlle sur /ECP Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween 739

4 Multi-Level Library of Electrical Machines for Aerospace Applications face is moving. m forwar an backwar, while an external loa force of -8 N (equivalent to -3 Nm loa torque on the PMSM shaft) is acting on the flight surface. The simulation results are shown in figure 4. In particular the mechanical quantities (position, spee an torque) of the PMSM are reporte an a goo agreement between actual an rerence position is highlighte. The moel is evelope in the rotating rerence frame synchronous with the rotor ( q ) an Park s transformation (invariant amplitue transformation) is use to pass from the abc to the q rerence frame. Figure 5 reports the equivalent circuits in the rotating rerence frame. Figure 3: EMA architecture simulate in Dymola, using the moelbasic. Spee [rpm] Position [ra] 4 Rerence Actual Torque [Nm] Figure 4: Simulation results obtaine using the moel Basic uner position control: mechanical rotor position (top), mechanical rotor spee (mile) an evelope torque (bottom). 5 Moel Stanar The moel Stanar, inclue in the package PermanentMagnet, is base on a lumpe parameters approach an it escribes the behavior of PMSMs taking into account torque generation, losses an thermal moel. Non-linear efcts, such as magnetic saturation, torque ripple an fault conitions are neglecting at this level. Figure 5: an q axis equivalent circuits implemente within the moelstanar. These equivalent circuits take into account the iron losses using an equivalent iron losses resistance ( R ), place in parallel with the series between the magnetizing branch an the electromotive force term [7]. Applying the Kirchhoff s voltage law (KVL) at the main loop of the circuits in figure 5, the following equations can be written: v Rt i L im e Lq iqm t v R i L i L i t q t q q qm e m e PM where (3) Rt is the phase resistance (which is function is the permanent of the wining temperature), PM magnet flux, L an Lq are the an q axis magnetizing inuctances respectively. These parameters ( R, L, Lq an PM ) are provie by the moel user, through the moel's mask. On the other han, applying the Kirchhoff s current law (KCL) at the circuit noes results: i i i m i i i q q qm Accoring (4), the total currents ( i into iron losses currents ( i an magnetizing currents ( i m (4) an i q ) are split an i q ), given by (5), an i qm ). The formers flow through the equivalent iron losses resistance, while the latters are responsible of the torque generation. 74 Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween /ECP

5 Session 5A: Aerospace Applications i L im e Lq iqm R t (5) iq Lq iqm e L im e PM R t In orer to complete the PMSM moel, the electromagnetic torque equation has to be explicit. In general, the torque evelope by the PMSM is the sum of two terms: the fiel torque ue to the permanent magnets an the reluctance torque ue to the machine saliency. PMSM moel Stanar inclues both these torque terms, hence the behavior of surface mounte (SMPM) an interior permanent magnet (IPM) machines can be simulate. The electromagnetic torque is given by (6): 3 pp i L L i i e PM qm q m qm (6) where pp is the pole pairs number, which is provie by the moel user. Moel Stanar is a power balance moel an the losses taken into account are copper, iron an mechanical losses. Copper losses ( P cu ) are a function of the current an the wining resistance, accoring to the following equation: 3 Pcu Rt i iq (7) The coefficient 3 arises from the aoption of the amplitue invariant Park s transformation. As previously sai, the phase resistance R is function of wining temperature ( w ), through the equation: R R 1 t w ref t (8) where R is the phase resistance at the rerence temperature ( ref ) an is linear temperature coefficient, which epens on the wining material (i.e. copper or aluminum). Iron losses ( P ), both hysteretic an ey current, are a function of voltage an frequency as well as the material composition. These losses are calculate as equivalent copper losses: 3 P R i iq (9) Equivalent iron losses resistance is obtaine consiering the specific iron losses ( C ) an the stator mass ( m ): R S 5 PM C m p S p (1) Both these parameters ( C p an m S ) are provie by the moel user, using the moel s mask. Specific iron losses gives the iron losses in 1 Kg mass of a given magnetic material, when it is subject to a flux ensity of 1 Wb m at 5 Hz. Finally, mechanical losses ( P mec ), ue to friction an winage, are functions of rotor spee an they are inclue in the moel using the equivalent viscous friction torque ( f ): B pp e f (11) e P mec f (1) pp where B is the friction coefficient. The stray losses are neglecte in the moel Stanar, ue to their small amount compare to the other losses. Figure 6: Moelica Diagram Layer of the moel Stanar inclue in theelectrical Machines library. Total losses are applie in input to the thermal moel aopting the component PrescribeHeatFlow. The implemente thermal moel consiers the PMSM as a whole block an it is compose by a heat capacitor an a thermal conuctor. The heat capacity ( C ) is efine as: C c m (13) p T where mt is the total motor mass an cp is the equivalent specific heat capacity, which epens by the motor materials (mainly copper an iron). However, the convective thermal conuctance ( G ) between winings an housing is given by: G h A (14) /ECP Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween 741

6 Multi-Level Library of Electrical Machines for Aerospace Applications where A is the convection area an h is the heat transr coefficient, which epens upon the cooling system aopte. Both these parameters, together with mt an cp are provie by the moel user. The wining an housing temperatures are respectively available on port_a an port_b of the thermal conuctor. Finally, the heat flow is available at the heat port of the thermal moel (heatport). Equations (3)-(14) are implemente in the Moelica Text Layer, while the mechanical an thermal moels are inclue in the Moelica Diagram Layer, as shown in figure 6. rerence signal is kept equal to A. Once the spee reaches the steay state value (15 rpm ), a loa torque step of -5 Nm is applie at 1.5 s. Figure 8 shows the PMSM losses (copper, iron an mechanical losses) together with the electrical an mechanical powers. In steay state, the machine efficiency is equal to 93.45%. Spee [rpm] Losses [W] Rerence Actual Copper Iron Friction Power [W] 6 4 Electrical Mechanical Losses Figure 7: Spee control scheme simulate in Dymola, using the moelstanar. Moel Stanar has been simulate uner spee control using the block iagram reporte in figure 7, with the purpose of highlighting the PMSM losses an the thermal behavior. The PMSM parameters are: pole pairs number 14; rotor s moment of inertia 56. g m ; phase resistance.5 ; an q axis inuctance mh ; permanent magnet flux.1 Wb ; specific iron losses 1.1 W kg (M3); stator mass 3 kg ; friction coefficient. Nm s ; motor mass 5 kg ; specific heat capacity 44 J kg K convection area.75 m ; ; heat transr coefficient 1 W K m. During the simulation, the mechanical spee rerence signal is a ramp from rpm (at.1 s ) to 15 rpm (at 1.1 s ), while the axis current Figure 8: Simulation results obtaine using the moel Stanar uner spee control: mechanical rotor spee (top), PMSM losses (mile) an PMSM power (bottom). The trens of the winings an housing temperatures, over a working perio of 1 hr, are reporte in figure 9. Temperature [ o C] Winings Housing Figure 9: Simulation results obtaine using the moel Stanar: wining an housing temperatures. 6 Moel Saturation The moel Saturation, inclue in the package PermanentMagnet, has been obtaine as an extension of the moel Stanar. Therefore it takes into account all the physical efcts alreay presente in the moel Stanar section, plus the magnetic saturation an the torque ripple. As with the moel Stanar, the moel Saturation is also evelope in the rotating rerence frame ( q ) an Park s transformation (amplitue invariant trans- 74 Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween /ECP

7 Session 5A: Aerospace Applications formation) is use to pass from the abc to the q rerence frame. Electromagnetic Torque [Nm] Analitical Calculation Finite Element Data q-axis Current [A] Figure 1: Fiel torque component against q axis current: analytical curve (blue line) an finite element results (green ots). In rromagnetic materials, the relationship between the fiel strength an flux ensity is not a straight line (i.e. constant permeability), but it is efine through the magnetization curve. Since rromagnetic materials reveal a variable permeability accoring to the fiel strength, the magnetization curve has a knee point. Past this knee point, further increases in the fiel strength o not result in proportional increases in flux ensity. The PMSM performance is afcte by the magnetic saturation; in particular, it influences both the permanent magnet flux an the inuctances. Since the permanent magnet flux an the inuctances are a function of the operating point, the evelope torque (both fiel an reluctance terms) is not proportional to the current anymore. In the moel Saturation for PMSM, the magnetic saturation is taken into account consiering only its influence on fiel torque term (i.e. permanent magnet flux), while the reluctance torque term (i.e. magnetic saliency) is not afcte by the magnetic saturation. In the presence of magnetic saturation, the curve of the fiel torque term against the q axis current (torque-current curve) has a tren, like shown in figure 1. The torque-current curve can be inclue in the moel Saturation using two approaches: the look-up table; three given points, which ientify the torquecurrent curve. In the former case, the ata store insie the look-up table may be obtaine by finite element simulations. In the latter case, the moel user provies the following ata: q axis current at the knee of the torque-current curve ( I qmknee ); fiel torque at the knee of the torque-current curve ( knee ); fiel torque at the saturate region of the torquecurrent curve ( sat ); an the evelope torque is analytically calculate using (15). e c i i 1 c where i qm 4 qm qm i qm (15) is the actual magnetizing current along the q axis, while c1 an c are the torque function coefficients. These coefficients are expresse as shown below. c1 sat (16) c I I I 4 qmknee sat qmknee qmknee knee knee (17) Figure 11: Moelica Diagram Layer of the moel Saturation inclue in the Electrical Machines library. In aition to the magnetic saturation, the moel Saturation, also implements the torque ripple, which is function of the electrical rotor position ( e ). In particular, the moel Saturation allows to superimpose a sinusoial torque ripple ( ripple ) on the evelope electromagnetic torque ( e ). The torque ripple waveform is efine accoring (18). fripple ripple Aripple sin e (18) fn where Aripple is the ripple amplitue, fripple is the ripple frequency an f n is the PMSM rate frequency. These parameters are provie by the moel user by /ECP Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween 743

8 Multi-Level Library of Electrical Machines for Aerospace Applications means of a eicate mask. Aripple an fripple are function of [8]: stator wining (concentrate or istribute, single or ouble layer); motor geometry (slot opening, tooth shape, etc ); air-gap flux ensity quality (harmonic content); loa conitions. Equations (15)-(18) are implemente in the Moelica Text Layer, while the look-up table is place in the Moelica Diagram Layer, as shown in figure 11. Spee [rpm] Torque [Nm] q-axis Current [A] 1 Rerence Actual No Saturation With Saturation No Saturation With Saturation Figure 1: Simulation results obtaine using the moel Saturation uner spee control: mechanical rotor spee (top), evelope torque (mile) an q axis current (bottom). In orer to verify the magnetic saturation influence on the PMSM performance, moel Saturation has been simulate uner spee control within Dymola. PMSM parameters are the same aopte for the simulation test shown in the previous section, while the magnetic saturation parameters are: q axis current at the knee equal to 5 A ; fiel torque at the knee equal to 1.5 Nm ; fiel torque in the saturate region equal to 3 Nm. These parameters efine the torque-current curve reporte in figure 1 (blue line). During the simulation, the mechanical spee rerence signal is a ramp from rpm (at.1 s ) to rpm (at. s ), while the axis current rerence signal is kept equal to A. Once the spee reaches the emane steay state value ( rpm ), a loa torque ramp from Nm (at.3 s ) to -5 Nm (at.5 s ) is applie, in orer to emphasize the magnetic saturation efct. Figure 1 shows the simulation results. In particular, the comparison between the q axis currents flowing into the PMSM, with (green line) an without magnetic saturation (blue line), is highlighte. When the magnetic saturation is consiere, in orer to evelop the same electromagnetic torque (as in the absence of magnetic saturation), a higher q axis current is require. Even uring the acceleration phase, the q axis current raw is higher when the magnetic saturation is taken into account. This is ue to the analytical implementation of the torquecurrent curve (15). Inee, torque-current curve is not a straight line in the linear region (see figure 1). Spee [rpm] Position [ra] Torque [Nm] Rerence Actual Figure 13: Simulation results obtaine using the moel Saturation uner position control: mechanical rotor position (top), mechanical rotor spee (mile) an evelope torque (bottom). Figure 13 reports the simulation results obtaine when the PMSM is position controlle an the torque ripple is consiere. Torque ripple parameters have been set equal to.5 Nm amplitue (% ripple) an 11 Hz frequency. During the simulation, a -5 Nm loa torque is applie. The enlargement in figure 13 (bottom plot) highlights the superimposition of the torque ripple on the evelope torque. Torque oscillations, ue to the ripple, have repercussions on both mechanical spee (mile plot) an q axis current. 7 Moels Fault Moels incluing fault conitions have been implemente only for PMSM (package Permanent- Magnet), since the presence of permanent magnets is the source of concern in the event of fault conitions. Inee, fault conition is supplie by the back electromotive force ue to the permanent magnets [9]. PMSM moels incluing fault conitions have been implemente in the phase rerence frame ( abc ), since asymmetric faults are consiere as well. Wining short-circuits, wining open-circuits an permanent magnet emagnetization are the three 744 Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween /ECP

9 Session 5A: Aerospace Applications fault conitions consiere uring the failure moelling. For each of the mentione fault conitions a specific moel has been evelope, in orer to keep low the moel complexity. The realize moels are liste below: moel ShortCircuit, which implements single- an three-phase short-circuits; moel OpenCircuit, which consiers single- an three-phase open-circuits; moel Demagnetization, which takes into account the permanent magnet emagnetization. As suggeste in [1], the wining faults have been implemente by means of ieal electrical switches. Such switches are riven by Boolean variables in orer to open or close the phase winings an inject the fault conitions. Figures 14 an 15 show the Moelica Diagram Layer of moel ShortCircuit an moelopencircuit respectively. (i.e. permanent magnet flux reuction) neglecting the causes that le to the fault. Figure 16 shows the Dymola block iagram use for testing the moels incluing fault conitions. In particular, PMSM is current controlle (with i q 1 A an i A ) an its rotor is spee riven at a constant 5 rpm. For the sake of brevity, only the simulation results regaring moel ShortCircuit an moel OpenCircuit are reporte here. Moreover, the PMSM parameters are the same as those aopte in the moelstanar, within section 5. Using moel ShortCircuit, a three-phase shortcircuit (symmetric fault) has been injecte at.3 s. By this time, the mechanical spee an currents have reache the steay state values. The corresponing simulation results are reporte in figure 17. From the top plot, it is evient that the rotor spee is kept constant even after the fault injection. The mile plot shows the braking torque ( T br ) an its the steay state value is equal to Nm. The same value can be obtaine applying the formula reporte in [11] an written below: T 3 R e Lq pp R R L L br PM e e q (19) Figure 14: Moelica Diagram Layer of the moel ShortCircuit inclue in the Electrical Machines library. Figure 15: Moelica Diagram Layer of the moel OpenCircuit inclue in the Electrical Machines library. Demagnetization is cause by increasing of temperature insie the permanent magnet an/or high current values. In the moel Demagnetization, the fault conition is consiere as consequence of the fault Figure 16: Block iagram implemente in Dymola, for testing both moel ShortCircuit an OpenCircuit. Since the three-phase short-circuit is a symmetric fault, the current components in the q rerence frame can be efine (see bottom plot). The steay state values of the q current components are iqsh -1.7 A an i sh A. These values are in line with those obtaine applying the analytical formulas reporte in [11] /ECP Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween 745

10 Multi-Level Library of Electrical Machines for Aerospace Applications I I Spee [rpm] Torque [Nm] Current [A] sh qsh L R L L e PM q e q R R L L 4 e PM e q () (1) axis q-axis Figure 17: Simulation results obtaine using the moel ShortCircuit, in case of three-phase short-circuit: mechanical rotor spee (top), evelope torque (mile) an q currents (bottom). Spee [rpm] Torque [Nm] Current [A] C B A Figure 18: Simulation results obtaine using the moel OpenCircuit in case of single-phase open-circuit: mechanical rotor spee (top), evelope torque (mile) an abc currents (bottom). In figure 18, the simulation results obtaine using moel OpenCircuit are reporte. In this case, a single-phase open-circuit (asymmetric fault) is injecte into phase a at.3 s. After the fault injection, the evelope torque (mile plot) becomes oscillating, since the PMSM currents are unbalance. The pulsating torque component is shown alongsie the emane torque uner healthy conitions (1 Nm ). Its frequency is twice the operating frequency of the PMSM. Since the stator wining is assume wye-connecte, with a floating neutral point, an the current in phase a is null, ue to the phase opening, the phase currents in phases b an c must be shifte by 18 egrees. The escribe situation can be observe in the bottom plot of figure Conclusions An electrical machines library evelope using Moelica has been presente in this paper. Particular attention has been pai to the PMSM moels, since PMSMs are becoming wiesprea in aerospace applications, ue to their inherent atures. A multilevel approach has been aopte, in orer to keep the moel complexity low an reuce the computation time. The interchangeability among moelling levels has been ensure by using common interfaces. All the moels are power balance an can work as either a motor or generator. The main physical efcts taken into account are losses, thermal behavior, magnetic saturation, torque ripple an fault conitions. Physical efcts inclue in the moels have been iscusse an their implementation has been etaile. The efctiveness of the various moelling levels has been proven through simulation results obtaine in several operating conitions. Rerences [1] A. Boglietti; A. Cavagnino, A. Tenconi an S. Vaschetto, The saty critical electric machines an rives in the MEA: A survey, in IEEE In. Elec., Nov. 9. [] S.V. Bozhko, T. Wu, Y. Tao an G.M. Asher MEA electrical power system accelerate functional moelling, in Power Electr. an Motion Control, Sep. 1. [3] P. Fritzson, Principles of Object-Oriente Moeling an Simulation with Moelica.1, IEEE Press, 4. [4] J.F. Gieras PM Motors Technology: Design an Applications, 3 r eition, Taylor an Francis, 1. [5] C. Geraa an K.J. Braley, Integrate PM Machine Design for an Aircraft EMA, IEEE Trans. on In. Elect., vol. 55, no. 9, pp , Sept. 8. [6] R.H. Park, Two-reaction theory of synchronous machines generalize metho of analysis-part I, Trans. of the American Institute of Electrical Engineers, vol. 48, no. 3, pp , July 199. [7] N. Urasaki, T. Senjyu an K. Uezato A Novel Calculation Metho for Iron Loss Resistance Suitable in Moeling PMSMs IEEE Trans. on Energy Conversion, vol. 18, no. 1, pp , March 3. [8] G. Ferretti, G. Magnani an P. Rocco, Simulating permanent magnet brushless motors in Dymola, n Moelica Conrence, pp , March. [9] S. Khwan-on, L. e Lillo, L. Empringham, P. Wheeler, C. Geraa, N.M. Othman, O. Jasim, an J. Clare, "FT power converter topologies for PMSM rives in aerospace applications", 13 th EPE, pp. 1-9, 8-1 Sept. 9. [1] D. Winkler an C. Gühmann, Moelling of Electrical Faults in IMs Using Moelica, 48 th Scaninavian Conrence on Simulation an Moeling, 7. [11] N. Bianchi, M.D. Pré an S. Bolognani, Design of a fault tolerant IPM motor for electric power steering, IEEE Trans. on Vehicular Technology, vol. 55, no. 4, pp , July Proceeings of the 1 th International MoelicaConrence March 1-1, 14, Lun, Sween /ECP