Permanent Magnet Machine based Starter-Generator System with Modulated Model Predictive Control

Transcription

1 Permanent Magnet Machne base Starter-Generator System wth Moulate Moel Prectve Control Seang Shen Yeoh, Tao Yang, Luca Tarscott, Member, IEEE, Chrstopher Ian Hll, Member, IEEE, Serhy Bozhko, Member, IEEE, an Percle Zanchetta, Senor Member, IEEE Abstract The paper escrbes a hybr control scheme for a permanent magnet machne base starter-generator (S/G) system. There has been ncrease usage of electrc rve systems n the transportaton sector for ncrease effcency an reuce emssons. One of the avantages of utlsng sutable electrc rves s the capablty to operate as a starter or generator. The control esgn of such a system shoul be consere ue to the operatng reurements an fast loa changes. Dfferent control approaches shoul therefore be consere n orer to acheve these goals, whch are a current tren n the transportaton sector. Moel Prectve Control (MPC) s consere ue to ts very fast ynamc performance. In partcular, Moulate Moel Prectve Control (M 2 PC) was recently ntrouce an showe sgnfcantly better performance than the stanar MPC. The control scheme use n ths paper utlses M 2 PC for the current nner loop an PI controllers for the outer loop. The use of M 2 PC allows very fast transent current response for the S/G system. The propose overall control benefts from reuce current rpple when compare wth a full cascae PI control scheme. Smulaton analyses an expermental results show the capablty an performance of the esgne controller across both starter an generator moes. Inex Terms permanent magnet machne, starter generator, moel prectve control, moulate moel prectve control. T I. INTRODUCTION HERE s a current tenency to mplement electrcal rves n transportaton systems n orer to acheve greater system effcency an reuce emssons [1, 2]. For the aerospace sector, the More Electrc Arcraft (MEA) concept s n-lne wth ths rve n aton to mprovng relablty, complexty, an costs [3-5]. Wth the approprate power converter, electrcal machne, an control scheme, the rve system can operate as a starter/generator (S/G). An electrcal machne can be use as a starter, or motor, to move the mechancal loa, n ths case the arcraft engne. Alternatvely, t can functon as a generator when the engne rves the electrcal machne. Manuscrpt receve January ; revse May ; accepte July Date of current verson July S.S. Yeoh, T. Yang, L. Tarscott, C.I. Hll, S. Bozhko, an P. Zanchetta are wth the Department of Electrcal an Electronc Engneerng, Unversty of Nottngham, Nottngham, NG7 2RD, U.K. (emal: Seang.Yeoh@nottngham.ac.uk; Tao.Yang@nottngham.ac.uk; Luca.Tarscott@nottngham.ac.uk; C.Hll@nottngham.ac.uk; Serhy.Bozhko@nottngham.ac.uk; Percle.Zanchetta@nottngham.ac.uk). The use of S/G system n applcatons that run n both moes have avantages n terms of hgh nstant power/torue output an better effcency over a we spee range. Permanent magnet machnes (PMMs) have been a popular choce ue to ther power ensty. Ths contrbutes to the hgh performance of the S/G system [6-9]. The S/G system may smplfy the power generaton system by reucng the complexty of the mechancal sub-system, especally n aerospace an automotve applcatons. Ths woul result n ncrease relablty an reuce overall weght [10]. However, the fferent operatng crtera of the S/G, together wth uck loa changes an hgh electrcal power crculatng between the machne an converter, s a challengng control esgn task. Rgorous analyss has to be performe n orer to ensure the performance an stablty of the esgne control system. Exstng solutons such as cascae PI vector control, whch are wely use for rve systems, may be unable to fulfl the crtera of achevng faster ynamc response. Hence, alternatve control solutons shoul be consere. Moel Prectve Control (MPC) has been consere as a soluton for the control of power converters an rve systems ue to ts fast ynamc performance, ease of constrant mplementaton, multvarable control, an absence of sgnal moulaton schemes. It can also be aopte for non-mnmum phase systems an to eal wth non-lnear ynamcs [11, 12]. MPC can compute ts soluton onlne whle reang the current state of the controlle plant nstea of conserng all of the states. Because of ths, MPC s usually mplemente n the screte oman whle conserng the swtchng states of the power converter. There are savantages of usng MPC. Obvously snce MPC s a moel base control strategy, ts performance largely epens on the accuracy of the moel. Furthermore, the lack of a moulaton scheme results n a swtchng state apple across the whole swtchng pero. It may therefore result n larger rpples n controlle varables wth slow swtchng freuences. Large rpples n current an voltage outputs from power converters have hgh harmonc content an hence have lower output power ualty. The use of MPC wthn rve systems have been covere n [7, 11, 13-17]. Prenl mplemente MPC for torue control of a PMM rve system [13]. Smlar work was also one by Bolognan n [15]. The paper hghlghte the use of MPC as a multvarable controller rather than beng part of the conventonal cascae control structure. Overall, MPC was consere as an alternatve control scheme ue to ts fast ynamc response, however the possble power ualty ssue was another conseraton factor. A varant of the MPC metho was ntrouce wth an ntrnsc moulaton scheme calle Moulate Moel Prectve Control (M 2 PC) wth the am of mprovng the performance of tratonal MPC n terms of power ualty. Ths metho was propose by Tarscott an stues have been performe n [18-

2 21]. Ths control metho ntens to mprove the output electrcal power ualty of the system wth an ntrnsc moulator whle preservng the avantages of MPC. The use of a moulator allows better output of the swtchng state that resembles the nput reference. Wth relaton to PI controllers wth moulator, much faster control response an possbly reuce current rpples are expecte from M 2 PC. Space vector moulaton (SVM) was selecte as the ntrnsc moulator ue to s effcent use of selecte voltage vectors for fnte swtchng power systems [19]. Ths resulte n less total harmonc storton (THD) an swtchng losses from the output waveforms. The gans offere by M 2 PC may be crucal n meetng transport power ualty an voltage regulaton stanars such as MIL-STD-704F for arcraft electrcal power systems [22]. In [21], the AC current rpples of a seven-level H-brge were reuce ue to the presence of the moulator. The emonstraton of fferent DC bus voltage control has also been presente n [19]. M 2 PC has also been nvestgate on an IM base rve system wth matrx converter [23]. Better current output waveforms were reporte for both papers when compare to the smlar control scheme wth fferent types of nner current loop controllers. Several varatons of M 2 PC have been erve an nvestgate, one base on ea beat control an the other was base on a cost functon rato [21, 23] to etermne the uty cycles for the SVM. Dea beat control s a varant of prectve control where the output converter voltage reference s calculate base on the moel. Ths allows the controlle varable to reach ts reure reference urng the next samplng pero. Dea beat control also has the avantage of provng a fast ynamc response, but reures a moulator to work an system constrants cannot be nclue rectly [11]. In M 2 PC, ea beat control s use to prect the voltage vectors reure at each swtchng state. The cost functon then selects the optmal voltage vectors for the moulaton scheme an the output s sent to the power converter. Cost functon rato base M 2 PC works by calculatng multple cost functons for each actve voltage vector an then selectng the optmal vector for the moulaton scheme. More research s reure to analyse the use of M 2 PC wthn rve systems. The nherent avantages of fast ynamc response an reuce current rpple coul potentally contrbute to reuce flter szes that beneft the transportaton sector n terms of overall weght an volume reucton. M 2 PC wll be nvestgate as a potental control strategy for PMM base S/G system n ths paper. It s an extenson of the paper [24]. The contrbutons of ths paper are: Improvement of the hybr PI M 2 PC scheme cost presente n [24] by atonal mnmsaton terms n orer to reuce the current rpples. Expermental valaton of the propose control scheme. System parameter varaton wll be conucte to etermne the robustness of the hybr control scheme. The analytcal fnngs wll be confrme wth smulaton an experment results base on a prototype S/G system. The paper wll be structure as follows; Secton II escrbes the S/G system uner nvestgaton an Secton III explans the control approach. Secton IV an V show the smulaton an expermental results respectvely to confrm the control scheme performance. The fnal secton conclues the paper. II. S/G MODEL The S/G system nvestgate n ths paper s shown n Fg. 1, where ω r s the rotor spee, abc s the three phase currents, an C s the DC lnk capactor. c an E c are the DC lnk current an voltage respectvely. A surface mounte PMM s attache to a two level Actve Front-En (AFE) converter. In starter moe, the PMM rves a loa usng electrcal power from the DC bus. On the other han, n generator moe, the loa motor rves the PMM that acts as a generator to prove electrcal power to the man DC lnk bus. It s assume that the loa motor s controlle externally, an behaves as an eal spee source for the PMM. The S/G system was esgne base on toruespee characterstcs for a typcal busness et engne that can be seen n Fg. 2. It shows the torue reurements at fferent operatng temperatures an spees (maxmum spee of 32krpm). The torue eman at -40 C s the hghest for ths gven characterstc an the PMM was esgne to meet ths reurement as llustrate by the sol black lne n the fgure. Whle the engne torue characterstcs can be consere, the maxmum possble torue s suffcent to test the feasblty of the hybr control scheme. 40 r abc Fg. 1. PMM base S/G power system n stuy. Fg. 2. A typcal busness et engne torue-spee characterstcs. For the nvestgate S/G system, euatons (1) an (2) n reference frame are use as the moel of the PMM: v Rs L L e (1) t v Rs L L m (2) e t where R s s the stator resstance, ψ m s the mutual flux of the machne, an ω e s the electrcal spee. v, an, are the AC voltages an currents of the PMM n frame. L, are the PMM nuctances n frame. The ervatve terms wthn these euatons are scretse usng the forwar Euler metho. It s assume that the state varables reman constant urng the samplng pero, T s. c C E c ( t) ( k 1) ( k) (3) t T s

3 The screte moel of the PMM can therefore be erve as: L k 1 k Rs k v k Ts (4) Le k k 1 L k k k Le k k me k Rs v k Ts v, can be relate to the swtchng states of the AFE, S abc, an E c, by the followng euaton f the mpeance of the transmsson lne between the AFE an PMM s neglecte: (5) v, ( k ) E c ( k ) k S abc ( k ) (6) where k s the transformaton matrx where three-phase varables can be transforme to frame: k k k x k k a x k x k b x x 2 2 cos k cos k - cos k sn k - sn k - - sn k c 3 3 For a typcal two level three-phase converter, Table 1 shows the possble swtchng states, S abc, assumng an nverte par of sgnals s prove to the two swtches connecte to each converter leg. A. MPC Table 1. Two level three-phase converter possble swtchng states. Sa Sb Sc III. CONTROL APPROACH The nherent avantage of MPC s ts ablty to prect future states over a fxe set tme horzon base on the measure present states an control nputs. For a power converter, ths nformaton s optmse wthn a cost mnmsaton functon that etermnes the most sutable converter swtchng state for the next samplng pero. Snce a converter wth fnte swtches has a fnte number of swtchng states, the optmsaton stage an the tme t takes can be reuce. The process of precton an cost mnmsaton recurs for every samplng pero [11, (7) (8) 12]. A flow agram summarsng the MPC process s epcte n Fg. 3. Fg. 3. MPC flow agram. The workng prncple of MPC s llustrate n Fg. 4, where k s the current nstant tme, t, n the screte oman an e s the e-th number of samplng steps from k. The states of a system are measure at tme k. These values are then use to prect the future swtchng states up to step k + e by usng the moel of the system. An optmsaton cost functon s use over the precton horzon to etermne the optmum control sgnals [25]: N 2 2 e (9) e J mn w r x w c x e e u e e1 e1 where N s the number of state varables, x e s the e-th state varable, r e s the e-th reference varable, an α e s the e-th error of the precte varables, w xe s the weghtng factor for the error between the state varables to ther reference, an w ue s the weghtng factor for the error of the precte varables. The utlsaton of the cost functon forms a precte traectory (re) f the state values at k are use throughout the precton horzon. However, at tme nstant k + 1, f the precton s performe wth the state values at k + 1 a more approprate traectory s forme (blue). In general, the greater number of steps that are performe wth upate states, the more accurate the precton. Eventually, the measure state wll follow the precte traectory an hence reach the esre state. Fel orente vector control s mplemente for the control of ths S/G system, hence an are regulate n orer to prouce approprate swtchng sgnals. The precton moel of the currents are base on euatons (4) an (5): R T k s s k L k 1 k T L k e s T v k s L L R T k s s k L k T L k e s k 1 L T v k s k T m e s L L N (10) (11)

4 k k 1 k e Fg. 4. Workng prncple of MPC. Snce a computatonal elay s always present n the practcal system, the control output calculate at tme nstant k can only be apple at the tme nstant k+1. Ths one sample elay can be se-steppe by prectng values two steps ahea. Euatons (10) an (11) for two step precton can be formulate as: R T k 1 s s k 1 L k 2 (12) k 1T L k 1 e s T v k 1 s L L RsTs k 1 k 1 L e s k 2 L me k 1Ts L k 1T L k 1 T v k 1 The cost functon for MPC can be formulate as: s L 2 2 MPC (13) g k k (14) where the varables wth superscrpt of enote ther respectve reference values. The swtchng state offerng the least error for the cost functon s selecte an apple for the whole samplng pero. The process then repeats startng from the varable measurement stage. B. M 2 PC Generally, M 2 PC has the same precton an optmsaton pattern as MPC except wth the aton of another stage for SVM. Two actve voltage vectors (v 1, v 2) are precte for M 2 PC operaton nstea of ust one overall voltage vector. The two actve vectors are selecte from all the possble aacent vector pars usng a mofe cost functon that consers the current precton an uty cycles, 0 to 2. These uty cycles etermne the approprate rato for the actve an zero voltage vectors (v 01, v 02) wthn each samplng pero, as shown n Fg. 5. The actve voltage vectors are calculate base on (12) an (13), an these are use to calculate (k+2), (k+2), (k+2) an (k+2). The varables wth superscrpt an use swtchng state vectors n the orer [1,2,3,4,5,6] an [2,3,4,5,6,1] respectvely. The zero vector currents, 0 (k+2) an 0 (k+2) are calculate usng (4) an (5) wth v = v = 0, an ths s use to prect v 01 an v 02. Snce SVM s use, euaton (6) can be re-arrange to gve: v ( k 1) Ec ( k) 1S ( k) 2S ( k) (15) v ( k 1) Ec ( k) 1S ( k) 2S ( k) (16) where 1 an 2 are the uty cycles for v 1 an v 2 respectvely. S, S, S, an S are the swtchng states n frame. If v (k+1) an v (k+1) are consere as voltage references n (15) an (16), then 1 an 2 can be solve smultaneously: 2 1 v k 1 S (k) v k 1 S ( k ) E S ( k) S ( k) S ( k ) S ( k ) c v k 1 S ( k ) v k 1 S ( k ) E S ( k ) S ( k ) S ( k ) S ( k ) c (17) (18) The zero vector currents are compare wth the reference currents assumng that the precte (k+1) an (k+1) s eual to an respectvely: 1 1 k k (19) k k (20) 0 v (k+1) an v (k+1) can then be precte to be eual to the voltage change across the nuctances: k 1 L k 1 (21) Ts v 1 k L k 1 (22) Ts v The zero voltage vector uty cycle can be calculate usng: 1 (23) v a v b v c T 0 s v01 v1 v2 v 02 v2 v 1 v s 2Ts 0T T s 1T s0ts T 2 s Fg. 5. M 2 PC typcal swtchng pattern [18]. E c T s E c T s E c T s The precte an n step k+2 are base on the swtchng states of the converters that woul heavly nfluence the cost functons. Generally, the man mnmsng obectve for the cost functon s to reuce the steay state error of the controlle varables, as shown wth euaton (14). The precte an at step k+2 can vary n orer to satsfy ths crtera n the cost functon. Ths nfluences the change n precte voltage vector for each samplng pero, especally for low nuctance rve systems (see euatons (21) an (22)). Ths woul result n

5 sgnfcant current rpples as the solutons are usually close to the swtchng states of the converter. In orer to reuce the rpples cause by ths use of precte currents, atonal weghng terms were propose. These precte currents are specfcally for each of the actve vectors, an compare wth the measure current vector n orer to normalse the output of the cost functons. Hence, the fference between the precte an measure current values are consere. The two cost functons use for the precton of the two actve vectors are as follows: g g 2 M PC1 2 M PC ( k) k 2 k k ( k) k ( k) k 2 k k ( k) k (24) (25) The cost functon mnmsaton algorthm s neffcent snce the uty cycles can alreay be calculate from the voltage references (17) an (18). However, the use of cost functon proves atonal flexblty n ang constrants to the vector selecton algorthm. For ths paper, t allows for the atonal current rpple mnmsaton terms to be consere wthn the M 2 PC. Together wth 1 an 2, the general cost functon, g M2PC, can then be forme as: g g g (26) M 2 P C 1 M 2 P C 1 2 M 2 P C 2 The general cost functon takes nto conseraton elements precte one step ahea from the uty cycles an has elay compensaton from the actve voltage vector two step prectons. The swtchng combnaton of S, S, S, an S that offers the smallest g M2PC wll therefore be apple n the three-phase frame wth approprate 0, 1, an 2 usng the moulaton scheme. The whole process for M 2 PC can be summarse usng a flow agram as shown n Fg. 6. The relevant control varables are measure such as abc, ω e, an E c. These nformaton can be use to prect (k+1) an θ (k+1). 0 (k+1) an Δ (k+1) can be use to prect the actve voltage vectors, v (k+1). After that, S abc are converte to frame epenng on θ (k+1). For each possble swtchng state, the currents an uty cycles for each actve voltage vector are calculate for step k+2. The overall cost functon, g M2PC, etermnes the swtchng state that offers the smallest error base on the actve vector cost functons an uty cycles. Fnally, SVM s use to output the chosen swtchng state wth relevant uty cycles. C. Control Scheme Fg. 7 shows the propose hybr PI-M 2 PC, where V s the AC magntue voltage. The control scheme can be ve nto two parts; outer an nner loop. The choce of outer loop controller varables are as follows: the spee controller, W s, s use urng starter moe an swtches to the DC lnk voltage controller, W c, when operatng n generator moe. Droop control s employe together wth W c to enable parallel source operaton f reure. The swtch between the two outer controllers (W s an W c) represents the actual swtch plus ntegrator reset logc. When operatng n starter moe, W s s connecte to the nner current loop whle W c ntegrator output s set to zero. When operatng n generator moe, W c s connecte to the nner current loop an the W s ntegrator output s set to zero. The flux weakenng controller, W fw, s connecte an operatonal for both moes to ensure control operaton of the S/G system throughout the spee range by preventng converter overmoulaton. lm s the lmt for the ynamc lmter that functons as part of the flux weakenng control an s calculate from the maxmum stator current, max an. PI base controllers wll be use for the outer loop an ther corresponng values are n Table 2. The proportonal gan of W fw has sgnfcant mpact on the controller stablty base on the stues reporte n [26]. Hence, t s selecte to be zero to reuce possble control nstablty. The nner loops control an usng M 2 PC accorng to the current references ece by the outer loop PI controllers. The currents are precte conserng all possble swtchng states. The optmal voltage vectors (v 1, v 2, v 01, v 02) are selecte for each sample pero an s sent to the moulator to prouce swtchng sgnals for the AFE. Measure ( k), E ( k), ( k), ( k) abc c e c Calculate ( k 1), ( k 1) Calculate ( k 1), ( k 1), v ( k 1) 0 Calculate 1, 2 Calculate ( k 2),,, Calculate {, } g Calculate {, S } ( k 1), g M PC1 M PC 2 g M 2 PC 1, 1 6? Yes Choose base on smallest SVM Apply swtchng seuence No g M 2 PC Fg. 6. Flow agram of M 2 PC.

6 D. Electrcal Angle Compensaton For rve systems that operate at hgh spees, [16] state that the precton of the electrcal angle, θ, nees to be compensate. Ths s because θ s proportonal to the machne rotor poston, θ r, an therefore there woul be an error between the precte an actual rotor poston epenng on the spee. To reuce ths error, θ r has to be compensate 1.5 sample peros ahea n orer to obtan the mean rotor poston after one sample elay. Ths can be represente by: k p r k T s k (27) IV.SIMULATION RESULTS The hybr control scheme was teste usng an euvalent non-lnear Matlab /Smulnk moel of the S/G system. In ths example, the S/G system parameters esgne for the More Electrc Arcraft were use n the smulaton, as shown n Table 3. The full PI control scheme esgne n [27] was use as a benchmark moel. Ths control scheme s epcte n Fg. 8. W an W are the PI base current loops. Not shown n the fgure are the ecouplng terms connecte to the control outputs v (k) an v (k). They are the last terms of euatons (1) an (2). All of the PI base controllers aopt the commonly use back calculaton type ant-wnup scheme. Typcally, PI type controllers work base on the control varables measure at present tme. If the controllers were to be tune to be as fast as M 2 PC for current control (capable of followng reference wthn several sample peros), the AC voltage rate of change woul be very hgh an stablty cannot be guarantee. The current PI controller values use for ths stuy have been selecte to acheve the fastest possble banwth an stablty throughout the operatng spee. For ths S/G system, the banwth was selecte to be 1kHz an ampng rato of [26]. Table 2. Outer Loop Controller Parameters Parameter Value Wfw proportonal gan 0 Wfw ntegral gan 500 Ws proportonal gan 50 Ws ntegral gan 3000 Wc proportonal gan 0.5 Wc ntegral gan 200 Droop gan 8 Table 3. S/G system parameters. Parameter Value Stator resstance, Rs 1.058mΩ frame stator nuctance, L = L 99µH Pole pars, p 3 Magnet flux-lnkage, ψm Vs Rate power, Prate 45kW Combne machne an engne nerta, J 0.103kgms 2 DC bus capactance, C 1.2mF Samplng pero, Ts 62.5µs Rate DC bus voltage, Ecrate 270V Maxmum AC current, max 400A Maxmum torue, Tmax 40Nm V r V r E c c c W ( ) fw z Ws ( z) Wc ( z) 1 lm 2 2 max ( k) ( k) ( k), ( k), ( k) ( k), ( k 2), ( k 2) v ( k 2) 1 v2( k 2) v ( k 2) 01 v ( k 2) 02 ( k 2) 1 2( k 2) ( k 2) 0 S ( 2) abc k z 1 v ( k 2), v ( k 2) V abc Fg. 7. Hybr PI M 2 PC scheme. V r V r E c c W ( ) fw z Ws ( z) W ( ) c z 1 lm 2 2 max ( ) k ( ) k W ( z) v W ( ) z ( k) v ( ) k Sabc ( k) z 1 V ( k) c Fg. 8. Full PI control scheme.

7 A. Control Operaton Fg. 9 shows the responses of the key state varables urng operaton n starter moe. The spee reference s set at 2094ra/s (20krpm). Flux weakenng was operatonal when V reache ts reference value of E crate/ 3 = 155.9V by necton nto the PMM. Both the control schemes performe satsfactorly, an were able to react to the changes n loa torue, T L ue to the ntegral terms present n the outer loop PI controllers. Usng the hybr PI-M 2 PC scheme, sgnfcant current rpple reucton was observe throughout the smulaton pero ue to the use of M 2 PC as part of the control structure. Fg. 9. Tme oman smulaton results for starter moe wth mpact an spatch of T L = 20Nm at t = 0.1s an 0.3s operatng at 20krpm wth the full PI (purple) an hybr PI-M 2 PC scheme (green). n the reverse orer. Both control schemes were able to operate wth the subecte electrcal loas at 20krpm. Sgnfcant reucton n the current rpple was observe here as well when usng the hybr PI-M 2 PC. Durng the pero when the loa s connecte, there was some fference n the steay state for E c an magntue stator current, s between the two control schemes. Ths was resulte from the precton moel n the hybr PI-M 2 PC becomng less accurate as more loa s ae whch can be consere as sturbances. The reuce current eman s compensate by the outer loop PI controllers n terms of ncrease E c level n orer to satsfy the loa power reurement. Alternatvely, observers can be employe wthn the control scheme to ensure a more accurate moel precton however ths s out of the scope of ths paper. B. Parameter Varaton For moel base controllers such as M 2 PC, t s mportant to assess the robustness of the technue towars parameter changes n the power system, especally f there are no parameter observer algorthms to aapt to the changes. Parameters that coul change n actual rve systems ue to operatng temperature or other factors such as R s, L, an C were assesse. Hence, the smulaton moel parameters were vare n orer to check the robustness of the hybr control scheme. Changes n the currents n terms of steay state an rpple value were observe when the parameters were vare nvually. An electrcal loa of 5kW was use n ths stuy to etermne any current fferences between loa/no-loa contons. The varaton of R s s usually base on the copper wre wnngs n actual electrcal machnes [28]. Fg. 11 shows the response when R s was change by 2, 4, an 8 tmes ts nomnal value (1.058mΩ). It can be seen that there was a small fference n steay state values that are ncreasng n the negatve recton as ha to compensate for the hgher R s. Fg. 11. responses wth fferent values of R s. Fg. 10. Tme oman smulaton results for generator moe operatng at 20krpm between the full PI (purple) an hybr PI-M 2 PC scheme (green). The two control schemes were teste for generator moe operaton as well an Fg. 10 shows the key state varable responses. Durng ths smulaton pero the DC lnk bus was subecte to constant power loa emans of 10kW, 20kW, 30kW n ntervals of 0.03s. After that, they were spatche The stator nuctances were vare n ncrements of 10% of ther nomnal value wth the same loa contons. Both currents were foun to be affecte by the change n nuctance when the nuctances were smaller than the nomnal value, as can be seen n Fg. 12. Large rpples can be seen when the nuctances were at 70% of the nomnal value (99µH). The varaton n stator nuctances affect the accuracy of the moel precton an as such causes the fferent steay state values of when the S/G s operatng n flux weakenng moe. The change n capactance value of the DC bus capactors has lttle mpact on the M 2 PC scheme as

8 the moel euatons am for AC current prectons. However, as an atonal stuy, the varaton of C has been performe to gauge the robustness of the hybr control scheme. Fg. 13 shows responses to changes of C when reuce by 20% ncrements. The varaton of C manly affecte the DC voltage controller whch explans the ncrease unerampe transent responses. The steay state rpples ncrease when C was reuce below 40% of ts nomnal value. Ths coul be ue to the smaller sze capactance that affects ts mpact as an energy storage an flter on the DC bus. nstablty to the hybr control scheme. Real measurements of the machne parameters were performe at fferent operatng freuences (400Hz 1600Hz to cover arcraft electrcal system varable freuency range). Fg. 14 shows the maxmum varaton of machne nuctance n frame. It can be seen that the varaton s up to 22% (nomnal value of L = L = 99μH). In comparson wth the worst case precte varaton range (change of L up to 30%), the practcal varaton falls wthn the stable range. Hence, parameter estmaton was not consere for stable control performance. V. EXPERIMENT RESULTS A small prototype of the S/G system was bult to prove the usefulness of the hybr control scheme. Fg. 15 shows the overall test rg bult for ths purpose. A DC machne (TT Electrc, LAK 2100-A) s use as the loa motor. A ecate DC rve (Sprnt Electrc, PLX 10) s connecte to the DC machne whch controls the machne spee/torue output. The DC machne can be use to apply loa torue or rve the PMM epenng on starter or generator operaton. AFE DC Drve Fg. 12. (top) an (bottom) responses wth fferent values of machne nuctance. PMM Fg. 15. Overall expermental setup. DC machne Fg. 13. responses wth fferent values of C. The man machne use s a PMM (Emerson, 115UMC Seres) an s powere by a two-level AFE bult n-house an s controlle by a gtal sgnal processor (DSP) (Texas Instrument, TMS320C6713 DSP Starter Kt). It s a sx pole (three pole par) machne wth rate spee of 3krpm. The nomnal power ratng s 2.54kW an the rate torue s 8.1Nm (from 5A rate current). The relevant machne parameters can be seen n Table 4. Table 4. Test rg parameters Parameter Value Rate phase voltage 230V Machne stator resstance, Rs 1.2Ω Machne -axs nuctance, L 6.17mH Machne -axs nuctance, L 8.379mH Machne mutual flux, ψm 0.23Vs Combne AC an DC machne nerta, J kgm 2 Vscous ampng, B Nms Mechancal frcton, fc Nm Fg. 14. Varaton of L an L at fferent operatng freuences (400Hz 1600Hz). Overall, the nfluence of L varaton that cause the most sgnfcant effect to the hybr PI-M 2 PC control performance. A change of at least 30% L woul be reure that ncreases the current rpples of the S/G system an thus cause potental The current an voltage operatonal lmts of the rve system are etermne base on the PMM reurements. Hence E crate s selecte as 600V for operaton of ths rve system. The maxmum current lmt, max, s selecte as 8A n orer to suffcently supply the rate current of 5A. The loa emans (n terms of ) wll therefore not normally excee the rate current value. The AC voltage lmt, V max, s

9 selecte as 250V. These lmts are chosen wthn the actual maxmum lmts wth the purpose of control esgn verfcaton. A samplng freuency of 12.5kHz (80µs samplng pero) s selecte for the control scheme. A. Inner Current M 2 PC Loop The applcablty of M 2 PC was nvestgate usng the test rg. M 2 PC was mplemente as the current loop control wth the rg parameters. The control was teste wth a step nput of 5A for the currents an the results can be seen n Fg. 16 an Fg. 17. B. Starter Operaton The test rg was frst teste to run as a starter by usng both spee an flux weakenng outer loop controllers n orer to prove references for the nner current loops. Fg. 18 shows the key results from the expermental S/G system n start-up moe. (a) Fg. 16. comparson between PI base (top) an M 2 PC (bottom) nner current loop to = 5A. Fg. 17. comparson between PI base (top) an M 2 PC (bottom) nner current loop to = 5A. It can be seen from the mentone fgures that a fast ynamc response was observe one samplng pero after the step change was mae wth the M 2 PC current controller. As a comparson, the PI controllers ha the esgne 250Hz banwth whle the M 2 PC acheve 3kHz banwth. The slower response (about 1kHz) for was ue to the mechancal nteracton wth the loa motor. However, there s some steay state error between the reference an measure currents. Ths s the result of the penalsaton of the current varaton wth respect to ts prevous value an the fact that M 2 PC oes not use ntegraton. Another reason may be ue to screpances between the moel use for precton an the actual system parameters. Ths s cause by parameter varaton or voltage rop across the power swtches. The steay state error s not sgnfcant an the use of outer loop PI controllers wll compensate for ths error. Fg. 16 an Fg. 17 also showe a comparson between the PI base nner current loops an M 2 PC. These results show the very fast control ynamcs an reuce current rpple that can be acheve by the use of M 2 PC on the S/G system. (b) Fg. 18. Start-up moe from stanstll to 376.8ra/s (3.6krpm) usng (a) full PI an (b) hybr PI-M 2 PC. The non-zero whle at stanstll was ue to T L whch was ntally apple by the DC machne. The spee controller for the PMM therefore prouces an euvalent n orer to compensate for ths sturbance an mantan the spee at zero. As the spee ncreases ue to the change n spee reference, V also ncreases but s lmte at V max = 250V. s emane as a result of flux weakenng n orer to regulate V. It can be seen from Fg. 18 that reuces as ncreases ue to the use of the current ynamc lmt. Some level of steay state error exsts for the currents when the hybr PI-M 2 PC s use but t s progressvely reuce as the spee ncreases. The cause of ths error s ue to the precton moel n the M 2 PC havng less accuracy when operatng wth loa sturbances. When T L s remove as seen n Fg. 19, the steay state error of reuces. The steay state error of when operatng below V max s not consstent ue to W fw only responng when V reaches V max. Durng the acceleraton from stanstll to 3.6krpm, the maxmum lmt of 8A was not emane ue to the observe steay state error. As a result, the torue output of

10 the PMM was slghtly less an ths affecte the tme for the spee to reach steay state compare to the full PI control scheme. Fg. 19 shows the same state varables when TL spatches. Both control schemes respone to the loa change an the controlle varables are agan regulate approprately. Goo ynamc performance of the hybr PI-M2PC control for starter moe was therefore emonstrate an verfe by ths test. Fg. 20. Generator moe runnng at 387.5ra/s (3.7krpm) wth loa mpact (left) an loa spatch (rght) scenaros for the full PI control scheme. (a) Fg. 21. Generator moe runnng at 387.5ra/s (3.7krpm) wth loa mpact (left) an loa spatch (rght) scenaros for the hybr PI-M 2PC. (b) Fg. 19. Starter moe operatng at 376.8ra/s (3.6krpm) usng (a) full PI an (b) hybr PI-M2PC. C. Generator Operaton In orer to perform tests n generator moe, the spee controller ha to be replace wth a DC lnk controller. Fg. 20 shows the expermental results of the S/G system n generator moe wth the flux weakenng an DC lnk controllers as the outer loop control. A resstve loa of 320Ω was connecte to the DC lnk bus an Ec roope to 598V accorng to the roop gan n Table 2. The loa was sconnecte from the DC lnk, an the control scheme respone to the loa change an regulate the controlle varables accorngly, as seen n the rght se of the fgure. In ths case, Ec returne to 600V. The hybr PI-M2PC scheme was also teste n generator moe. The test results can be seen n Fg. 21 that s smlar to generator moe wth full PI control. Ths experment confrms the esgne controllers are capable of mantanng stable operaton of the rve system urng generator moe. The harmonc spectrum for the currents of both control schemes shown n Fg. 20 an Fg. 21 have been prouce. They are epcte n Fg. 22 an Fg. 23 respectvely. The purpose s to confrm the low freuency harmoncs (about 10Hz) that are present wthn the currents. The harmonc components for PI-M2PC was foun to be lower throughout the freuency range compare to the full PI. Smlar low freuency harmoncs were present wthn the currents, especally n. The hybr PI-M2PC scheme s capable of reucng the low freuency harmoncs compare to the full PI. The source of these harmoncs are from the spee control of the loa rve that was use to mantan the spee of the S/G operatng n generator moe. The harmoncs can also be reuce by changng the loa rve spee control banwth. Current rpple reucton n terms of smaller THD has been confrme when usng the propose hybr PI-M2PC scheme n comparson to the full PI control. VI. CONCLUSION A varant of MPC, namely M2PC, was mplemente n orer to assess ts potental for mprovng the control performance of a PMM base S/G system. The M2PC scheme was

11 employe for the current control loop. The outer control loops were controlle usng PI controllers. Atonal weghng terms were ae nto the cost functon n orer to reuce the output current rpples. The resultant hybr PIM2PC scheme was foun to be a sutable control alternatve for PMM base S/G system an showe mprovements of reuce current rpple n comparson to the conventonal full PI control scheme. Parameter varaton stues ncate that the hybr control performance was most vulnerable to the change of L wth a change of at least 30%. Expermental work was performe to verfy the applcaton of M2PC as current control for the PMM base S/G an as a hybr control scheme for S/G operaton. Fast ynamc response was observe wth the M2PC n comparson to the PI controller for the nner current control. Furthermore, the use of hybr PI-M2PC showe reuce current rpples from both smulaton an expermental results. As for future works, the propose control strategy wth a sutable parameter estmaton algorthm wll be consere to elmnate the current steay state error. The mplementaton of full prectve control for the S/G system wll also be analyse. Both of these stues shall be reporte n future publcatons. ACKNOWLEDGEMENTS The stuy has be supporte by Clean Sky 2 (Systems ITD), European H2020 programme. REFERENCES [1] (a) [2] [3] [4] [5] (b) Fg. 22. Harmonc content of (a) an (b) for the full PI control scheme n generator moe. [6] [7] [8] [9] [10] (a) [11] [12] [13] [14] (b) Fg. 23. Harmonc content of (a) an (b) for the PI-M2PC scheme n generator moe. [15] H. Zhang, C. Sauemont, B. Robyns, an M. Pett, "Comparson of techncal features between a More Electrc Arcraft an a Hybr Electrc Vehcle," n Vehcle Power an Propulson Conference VPPC '08. IEEE, 2008, pp A. Battston, E. H. Mlan, S. Perfeerc, an F. MeboyTabar, "Effcency Improvement of a Quas-Z-Source InverterFe Permanent-Magnet Synchronous Machne-Base Electrc Vehcle," IEEE Trans. Transport. Elec., vol. 2, pp , A. Abel-Hafez an A. J. Forsyth, "A Revew of More-Electrc Arcraft," n Aerospace Scence an Avaton Technology ASAT13, 2009, pp J. A. Rosero, J. A. Ortega, E. Alabas, an L. Romeral, "Movng towars a more electrc arcraft," IEEE Aerosp. Electron. Syst. Mag., vol. 22, pp. 3-9, B. Sarloglu an C. T. Morrs, "More Electrc Arcraft: Revew, Challenges, an Opportuntes for Commercal Transport Arcraft," IEEE Trans. Transport. Elec., vol. 1, pp , L. Jae Hyuk, L. Jung Hyo, P. Jn ho, an W. Chung Yuen, "Felweakenng strategy n conton of DC-lnk voltage varaton usng on electrc vehcle of IPMSM," n Internatonal Conference on Electrcal Machnes an Systems (ICEMS), 2011, pp S. C. Carpuc an C. Lazar, "Fast Real-Tme Constrane Prectve Current Control n Permanent Magnet Synchronous Machne-Base Automotve Tracton Drves," IEEE Trans. Transport. Elec., vol. 1, pp , K. D. Hoang an H. K. A. Aorth, "Onlne Control of IPMSM Drves for Tracton Applcatons Conserng Machne Parameter an Inverter Nonlneartes," IEEE Trans. Transport. Elec., vol. 1, pp , F. Gao, X. Zheng, S. Bozhko, C. I. Hll, an G. Asher, "Moal Analyss of a PMSG-Base DC Electrcal Power System n the More Electrc Arcraft Usng Egenvalues Senstvty," IEEE Trans. Transport. Elec., vol. 1, pp , P. Wheeler an S. Bozhko, "The More Electrc Arcraft: Technology an challenges," Electrfcaton Magazne, IEEE, vol. 2, pp. 6-12, P. Cortes, M. P. Kazmerkowsk, R. M. Kennel, D. E. Queveo, an J. Rorguez, "Prectve Control n Power Electroncs an Drves," IEEE Trans. Ins. Elec., vol. 55, pp , J. Rorguez, M. P. Kazmerkowsk, J. R. Espnoza, P. Zanchetta, H. Abu-Rub, H. A. Young, an C. A. Roas, "State of the Art of Fnte Control Set Moel Prectve Control n Power Electroncs," IEEE Trans. Ins. Info., vol. 9, pp , M. Prenl an S. Bolognan, "Moel Prectve Drect Spee Control wth Fnte Control Set of PMSM Drve Systems," IEEE Trans. Power Elec., vol. 28, pp , M. Prenl an S. Bolognan, "Moel Prectve Drect Torue Control Wth Fnte Control Set for PMSM Drve Systems, Part 1: Maxmum Torue Per Ampere Operaton," IEEE Trans. Ins. Info., vol. 9, pp , S. Bolognan, L. Perett, an M. Zglotto, "Desgn an Implementaton of Moel Prectve Control for Electrcal Motor Drves," IEEE Trans. Ins. Elec., vol. 56, pp , 2009.

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