Matthieu Sautreuil, Olivier Sename, Delphine Riu, Nicolas Retière. HAL Id: hal

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1 Prformanc spcifications and analysis of a variabl spd synchronous gnrator witha diod rctifir for th all lctric aircraft using th Hinf control approach Matthiu Sautruil, Olivir Snam, Dlphin Riu, Nicolas Rtièr To cit this vrsion: Matthiu Sautruil, Olivir Snam, Dlphin Riu, Nicolas Rtièr. Prformanc spcifications and analysis of a variabl spd synchronous gnrator witha diod rctifir for th all lctric aircraft using th Hinf control approach. Europan Control Confrnc, ECC 9, Aug 29, Budapst, Hungary. Procdings of th Europan Control Confrnc, ECC 9, 29. <hal396273> HAL Id: hal Submittd on 17 Jun 29 HAL is a multidisciplinary opn accss archiv for th dposit and dissmination of scintific rsarch documnts, whthr thy ar publishd or not. Th documnts may com from taching and rsarch institutions in Franc or abroad, or from public or privat rsarch cntrs. L archiv ouvrt pluridisciplinair HAL, st dstiné au dépôt t à la diffusion d documnts scintifiqus d nivau rchrch, publiés ou non, émanant ds établissmnts d nsignmnt t d rchrch français ou étrangrs, ds laboratoirs publics ou privés.

2 Prformanc Spcifications and Analysis of a Variabl Spd Synchronous Gnrator with a Diod Rctifir for th All Elctric Aircraft Using th H Control Approach M. Sautruil, O. Snam, D. Riu, N. Rtièr Abstract This papr dals with th modling and control of an lctrical sourc for th futur All Elctric aircraft. It is constitutd by a rotor woundd synchronous gnrator and a diod rctifir fding th DC powr systm. Using H control thory, this papr shows that usual disturbanc rjction standards can not b mt with such an lctrical powr sourc and nw standards should b dfind. Simulations on an xact nonlinar modl of th powr sourc ar usd for control validation. W I. INTRODUCTION ITH th dvlopmnt of rliabl and fficint powr lctronics convrtrs, aircraft powr ntworks hav bn considrably changd. First volutions concrnd th rplacmnt of hydraulic and pnumatic dvics by lctrohydraulic and lctropnumatic loads in th Mor Elctric aircraft. In ths aircrafts, th lctrical powr is distributd mainly through AC buss and includs many AC/DC/AC convrsion stags to fd th motor loads. With th All Elctric aircraft, AC/DC convrsion stags ar supprssd and th lctrical powr is distributd through a DC bus. This volution was initiatd with th Europan Powr Optimizd Aircraft projct, followd by th currnt Mor Opn Elctrical Tchnologis projct in which this work lis [2]. In [1], a first All Elctric structur is studid from a DC voltag prformanc point of viw. Th lctrical powr sourc is dirctly drivd from th Mor Elctric structur and is shown in Fig. 1. Exc. ufd AC voltag control 18pulss ATRU Fig. 1: Powr sourc with Auto Transformr Rctifir Unit [1] Manuscript rcivd Octobr 15, 28. M. Sautruil, D. Riu and N. Rtièr ar with th Grnobl Elctrical Enginring Laboratory (G2ELab), Grnobl, Franc. (mail: matthiu.sautruil@g2lab.inpg.fr,dlphin.riu@g2lab.inpg.fr,nicolas.rti r@g2lab.inpg.fr). O. Snam is with th Gipsa Laboratory, dpartmnt of automatic control, Grnobl, Franc.(mail: Olivir.snam@gipsalab.inpg.fr). DC load subsystm DC voltag sourc Th AC sid voltag is controlld with a simpl PI controllr and th analysis in [1] shows that this simpl control allows th rspct of th disturbanc rjction prformancs imposd by th standards on th DC sid. Howvr, th 18 pulss ATRU is a havy dvic and othr sourc structurs ar studid for th futur All Elctric aircraft. In this papr, th authors study th control dsign of a lightr powr sourc for th All Elctric aircraft. It is constitutd by a 29kVA synchronous gnrator with a diod rctifir fding th DC load. Th DC voltag is controlld through th xcitation voltag of th synchronous gnrator (Fig. 2). Th stator lctrical frquncy (f) dpnds on th rotor spd, and varis from 36Hz to 8Hz. Howvr, bcaus th shaft spd varis slowly rgarding lctrical tim constants, th systm is assumd to b Tim Invariant in this papr. Our aim is to valuat if th usual disturbanc rjction spcifications can b mt with this powr sourc structur. If not, nw standards should b proposd. Th H control thory is applid to obtain an optimal controllr towards disturbanc rjction control objctivs. Ths objctivs will hav to b mt for svral oprating conditions corrsponding to th variabl frquncy opration of th gnrator. Th papr is organizd as follows. In Sction II, th linar modl of th systm is first drivd. Th control spcifications ar thn dfind. On of ths spcifications is th rspct of th usual disturbanc rjction standard. Sction III proposs th dsign of a H controllr at a givn oprating point (f=4hz) and a prformanc analysis ovr all th oprating conditions is prformd. Sction IV will conclud on th fasibility of a control for th prformanc spcifications givn in sction II. It is shown that th standards, which impos th prformancs from a disturbanc rjction point of viw, should b modifid if this sourc is finally usd in th All Elctric aircraft. f = 36Hz 8Hz ufd Variabl shaft spd K C Vdc rf = 54V Voltag mas. Fig. 2: Studid Powr sourc DC load subsystm DC voltag sourc

3 II. MODELING AND CONTROL SPECIFICATIONS A. Modling 1) Th synchronous gnrator modl Th gnrator quations ar writtn in th (d,q,) rotating fram using th Park transform dscribd in th appndix. W mak th assumption of a balancd thr phas systm, and axis componnts ar st to zro. Th stat spac quations of th synchronous gnrator ar givn by: d uds = Rsids. w. ( Llsiqs. Lmq. ( iqs ikq) ) ( Llsids.. ( ids ifd ikd) ) d uqs = Rsiqs. w. ( Llsids.. ( ids ifd ikd) ) ( Llsiqs. Lmq. ( iqs ikq) ) dikd d = Rkd. ikd Llkd...( ids ifd ikd) dikq d = Rkq. ikq Llkq Lmq. ( ikq iqs) d ufd = Rfdifd. ( Llfdifd.. ( ids ifd ikd) ) (1) (uds, uqs) ar th stator voltags, (ids, iqs) th stator currnts, (ikd, ikq) th damping windings currnts, ifd is th xcitation currnt and ufd th xcitation voltag of th gnrator. w is th lctrical pulsation. Th paramtrs ar dfind in th appndix. 2) Th diod rctifir modl Th approach prsntd in this papr is a smianalytical modling mthod, which was originally proposd and validatd in [3]. It consists in considring th diod rctifir as a voltag gain to calculat DC sid voltag from AC sid voltag, and a currnt gain to obtain AC sid currnt from DC sid currnt. w ufd Rctifir modl DC load Fig. 3: Powr sourc modl [3] Th basic ida is to link th avrag valus of th (d,q) variabls of th AC sid to th avrag valus of th DC sid voltag and currnt (2,3): Vdc = kv. uds uqs (2) Idc Gnrator modl in (d,q) axis = ki. ids iqs (3) In ths quations, kv and ki ar voltag and currnt gains, which ar nonlinar and dpnd on th oprating point of th systm [3]. Th rsulting spac vctor diagram is shown in Fig. 4: q axis Vdc/kv δ uds uqs φ ids iqs Idc/ki Idc Vdc d axis C I load From this diagram, th following quations ar obtaind: Vdc = kv. uds uqs (4) Idc ids = ( kcos. uds ksinuqs). Vdc (5) Idc iqs = ( kcos. uqs ksinuds). Vdc (6) with: kv.cosϕ kcos = and kv k ki.sin ϕ sin ki (7,8) In (7) and (8), φ is th phas displacmnt btwn AC voltag and currnts. To obtain th linar modl of th rctifir, th abov quations ar linarizd around th chosn oprating point. Th linar quations ar givn by: Vdc = kv. uds. uds kv. uqs. uqs (9) uds uqs 2 2 uds uqs kcos_ idc ksin_ idc kcos_ uds ksin_ uqs ids (1) ids = uds uqs idc vdc vdc vdc vdc vdc ksin_ idc kcos_ idc kcos_ uqs ksin_ uds (11) iqs = uds uqs idc vdc vdc vdc Indx dnots th quilibrium valus of th variabls. Th following DC sid quation is addd to ths quations: dvdc (12) idc = C. i load whr i load is th load currnt. 3) Statspac quations of th synchronous gnrator with diod rctifir systm To dvlop th modl of th synchronous gnrator with th diod rctifir, th gnrator quations ar associatd to th rctifir quations. Th load currnt is an input of th systm and will b considrd as th systm disturbanc for control dsign. Th following rprsntation is finally obtaind: = E. X F X V. U. with U th input vctor, and X th stat vctor: U = [ i ] T load ufd [ ids ifd ikd iqs ikq Vdc] T X = Matrix V, E and F ar givn by: L21 L22 L13 1 V = L31 L32L13 L13 Rs L2 L22L E = wld L32L11 L11 11 Rfd Rkd wlq L L.3 L w w Rs L L L (12) wlmq L23 L22L1 L33 L32L1 Rkq L1 (13) Fig. 4: spac vctor diagram for th rctifir modl

4 Ld F = Lf LD Lq Lmq Lmq LQ 1 (14) Cofficints L ij ar quit complx and ar not givn in this papr. Thn, th opnloop statspac rprsntation of th systm is obtaind: X = A. X BU. (15) Y = C. X with : F 1 1 A=. E', B = F. V,and C =[ 1] (16) B. Control spcifications 1) Disturbanc rjction Following a load currnt stp on th DC sid of th rctifir, th standards usually impos that th DC voltag rmains in a transint nvlop dfind by Fig. 5, as prsntd in [1]. DC voltag (V) Load stp at tim t t t.2 t.4 Tim (s) Fig. 5: Assignd transint nvlop aftr a load stp at Point Of Rgulation Ths spcifications should b mt for all oprating conditions, which is a robust prformanc critrion. 2) Limitations on th xcitation voltag To avoid control saturation, th minimum / maximum amplitud of th xcitation should b limitd. Saturation limits ar ufd = V (th xcitation voltag can not b ngativ) and ufd = 48V (uppr limit of saturation). Th bandwih of th control should also b limitd for nois attnuation. In this application, th nois on th DC voltag masurmnt is th harmonic contnt of th DC voltag du to th 6pulss rctification. This harmonic contnt is at frquncy fn = 6*f, with f th frquncy of th AC voltag. Consquntly it varis from 216Hz (f=36hz) to 48Hz (f=8hz). III. H CONTROL OF THE GENERATOR WITH DIODE RECTIFIER SYSTEM AT THE NOMINAL 4HZ OPERATING POINT In this sction, th first part is dvotd to a background on th H control approach. Th scond on concrns th application of H control thory to th systm introducd in sction II at th nominal oprating condition of th systm dfind by f=4hz. Th prformanc of this H controllr will finally b valuatd for various oprating conditions. A. Som background on H control Th H control problm rlis on th gnral control configuration (Fig. 6), whr P(s) is th gnralizd plant modl. v ar th control variabls, y th masurd variabls, w th xognous signals and th controlld output variabls. Givn γ, a prspcifid attnuation lvl, a suboptimal H control problm is to dsign a controllr that intrnally stabilizs th closdloop systm and nsurs: N w (s) γ (17) whr N w is th closdloop transfr matrix from to w. Wights ar considrd to tak th prformanc spcifications in th frquncy domain into account. In Fig. 6, G is th plant modl and W i/o th frquncy domain wights. P w v W i Fig. 6: Gnral control configuration [4] Th H suboptimal control problm (17) is solvd using th Riccati quations or LMI, allowing to gt th minimal valu of gamma. Th ails can b found in [4]. B. H control dsign at th nominal 4Hz frquncy. In this part, th authors apply th H control thory to th proposd powr sourc. Th oprating point is st to f=4hz at th maximum powr point (15kW, i load =27A). Th studid control configuration is prsntd in Fig. 7. P Wp(s) Wu(s) i load w ufd G(s) v Vdc y K(s) G K W o Fig. 7: th control schm with th wights It includs th plant modl G(s), th controllr to b dsignd K(s) and th wighting functions Wp(s) and Wu(s). Wp(s) is th frquncy domain wight rprsnting th rquird disturbanc rjction prformancs. Wu(s) is th wight linkd to th xcitation voltag limitations xplaind uppr. Thy ar chosn as follows. Wp: Th invrs of th function Wp dfins th tmplat of th transfr function Vdc/i load. This tmplat should guarant that aftr a load currnt stp, th DC voltag rmains in th nvlop dfind in Fig. 5. A maximum load currnt stp of 135A is considrd (which corrsponds to a y

5 5% load powr stp). Th wighting function is givn by: s wb Wp( s) = Ms (18) s wb.εs with Ms = 12/135, wb = 75 rad/s and εs. 1 1 Vdc/i load at 8Hz Wu: Th control input ufd is limitd byond 1Hz in ordr to avoid nois snsitivity. For f = 4Hz, nois occurs at 6*4 = 24Hz. Morovr, th amplitud of Wu is limitd bfor 1Hz to avoid xcitation voltag saturation. Th wighting function Wu is givn by: s wbu Wu ( s) = Mu (19) εu. s wbu Th H problm has a solution. This mans that th control objctivs ar mt at th oprating point corrsponding to f=4hz. Th amplituds of th obtaind closdloop transfr functions Vdc/i load and ufd/i load ar rspctivly givn in Fig. 8 and Fig. 9 and compard to th tmplats and Fig. 1: Amplitud of th closdloop transfr function Vdc/i load for oprating frquncis from 36Hz to 8Hz and Vdc/i load at 36Hz ufd/i load at 8Hz ufd/i load at 36Hz Vdc/i load Fig. 11: Amplitud of th closdloop transfr function ufd/i load for oprating frquncis from 36Hz to 8Hz and tmplat Fig. 8: Amplitud of th closdloop transfr function Vdc/i load and tmplat ufd/i load Fig. 9: Amplitud of th closdloop transfr function ufd/i load and tmplat. Th controllr prformancs ar now valuatd at diffrnt oprating conditions, for f varying from 36Hz to 8Hz. Th closdloop transfr function Vdc/i load and ufd/i load ar plottd for f=36hz, 4Hz, 5Hz, 6Hz, 7Hz and 8Hz (Fig. 1 and 11) Th analysis of Fig. 1 and Fig. 11 shows that th rquird prformancs ar not mt for all th oprating conditions of th systm. It can also b concludd that th worst oprating point is at high shaft spd, i.. for f=8hz. As a conclusion, a H controllr synthsizd at 8Hz that would mt th prformancs spcifications would also mt th spcifications for lowr oprating frquncis. In th nxt sction, th authors look for such a controllr. IV. H CONTROL DESIGN AT THE WORST OPERATING CONDITION A. Prformanc spcifications A controllr dsignd at th worst oprating condition (f=8hz) would also mt th prformanc spcifications for lowr frquncis. As xplaind uppr, th voltag masurmnt nois dirctly dpnds on th DC voltag harmonic lvl, which is causd by th 6pulss rctification. It xplains that th nois frquncy varis from 216Hz to 48Hz, according to th oprating AC sid frquncy. To guarant nois rjction at all oprating frquncis, th control should not b snsitiv to th nois which occurs at th frquncy 6*36 = 216Hz. For this, th cut off frquncy in Wu is chosn to rjct 216Hz nois. Th rquird disturbanc rjction prformancs ar th sam and th Wp paramtrs ar not changd (18).

6 B. H control dsign at th worst oprating condition Th rsults ar plottd in Fig. 12 and 13. Th amplituds of th closdloop transfr functions Vdc/i load and ufd/i load ar compard to th tmplats and Vdc/i load at 8Hz Fig. 12: Amplitud of th closdloop transfr function Vdc/i load at th worst oprating frquncy (8Hz) and rjction standards ar not suitabl if th synchronous gnrator diod rctifir sourc is chosn. In th nxt sction, a nw disturbanc rjction standard is proposd. For this, th bst prformancs achivabl by an H controllr for all th oprating conditions ar sought. 2) Bst achivabl prformancs by H control for all th oprating conditions Wu is not changd (tmplat of in Fig. 13) bcaus thy guarant an adquat opration of th controllr on th ral plant (no nois snsitivity and no saturation). Only Wp is changd. W choos to kp almost th sam rquirmnts on ovrvoltag / undrvoltag aftr th load stp. But th rquird tim rspons is xtnsivly modifid until th H problm has a solution. Th obtaind closdloop transfr functions ar givn in Fig. 14 and ufd/i load at 36Hz 2 3 Vdc/i load at 8Hz Fig. 13: Amplitud of th closdloop transfr function ufd/i load at th worst oprating frquncy (8Hz) and tmplat. As shown on Fig. 12 and 13, th prformanc spcifications ar not mt. From Fig. 12, it is concludd that a disturbanc can not b rjctd as fast as rquird. From Fig. 13, w notic that th rsulting controllr is snsitiv to nois and xhibits saturation aftr a load stp. This is a vry important rsult bcaus it shows that th prformanc rquirmnts can not b simultanously mt for th worst oprating condition. In othr words, conflicting objctivs wr dfind in th H control problm (17). On on hand, from th analysis of th closdloop transfr functions in Fig. 12 and 13, w conclud that th bandwih and amplitud limitations on th xcitation voltag ar not compatibl with th rquird disturbanc rjction spd. On th othr hand, th prformanc spcifications on th xcitation voltag can not b rlasd for controllr practical implmntation rasons. C. Towards nw prformanc spcifications 1) Considrations on control achivability for usual disturbanc rjction standards Othr control solutions could b prformd, for xampl a gainschduling control which would adapt th controllr paramtrs to th AC sid frquncy. But it could b shown that at th oprating 8Hz condition, with th maximum admissibl bandwih on (chosn to rjct nois at 6*8 = 48Hz), no solutions can b found. Morovr, in mor classical sourc structurs [1], a simpl PI control of th gnrator xhibits satisfying disturbanc rjction prformancs and th standards ar asily mt. From ths considrations, w conclud that th usual disturbanc Fig. 14: Bst achivabl prformanc in and closdloop transfr function Vdc/i load (Amplituds) ufd/i load at 8Hz Fig. 15: Amplitud of th closdloop transfr function ufd/i load and To find a solution to th H problm, th cutoff frquncy wb of th tmplat has bn dividd by 7,5 and th Ms factor in (18) was incrasd from 12/135 to 14/135. In othr words, in th tim domain th rquird tim rspons is 7,5 tims largr than with th classical rquirmnts, and an ovrshoot of 14V is allowd aftr a 135A load stp. D. Proposition of a nw disturbanc rjction standard Considring th rsults prsntd in this papr, th author propos to us th following disturbanc rjction standard. 68 Nw proposd standard 66 DC Currnt standard voltag 56 (V) Tim (s) t= 2m 4m 1m 3m Fig. 16: Proposition of a nw standard.

7 This nw prformanc spcification is th translation of th frquncy domain tmplat into tim domain prformancs. E. Validation by nonlinar simulation Our approach is validatd using th nonlinar simulation tool SABER. Th topological modl prsntd in Fig. 2 is simulatd, whr th DC load is an idal constant powr load, which is a typical aircraft lctrical load [1]. At t=,5s, a load dcras from 15kW (th nominal gnrator powr) to 75kW is simulatd. DC Voltag (V) Tim (s) Fig. 17: DC voltag transint aftr a load powr stp from 15kW to 75kW Excitation Voltag (V) Saturation constraint Tim (s) Fig. 18: Excitation voltag transint aftr a load powr stp from 15kW to 75kW As a conclusion, th nw standard w propos in Fig. 16 is mt. Morovr, no saturation appars aftr th load stp and th maximal distortion of th xcitation voltag is about 3% of th avrag valu of ufd. This can b considrd as bing a maximum admissibl valu and lowr nois dsnsitization prformancs would hav bn unaccptabl. This supposs that th wighting function Wu was appropriatly chosn from a practical implmntation point of viw. V. CONCLUSION 36 Hz 4 Hz 8 Hz Proposd standard Hz 4 Hz 8 Hz This papr has dalt with th us of optimal H control thory to prov that usual disturbanc rjction standards can not b mt for th studid aircraft powr sourc. Th bst achivabl frquncy domain prformancs hav thn bn found and translatd in th tim domain. This lads to th proposition of a nw standard for aircraft powr systms. This standard should b usd if th synchronous gnrator rctifir sourc is chosn for th futur All Elctric aircraft. This sourc has th advantag to b lightr than th powr sourc studid in [1]. But using a mor rlaxd standard could lad to ovrsiz othr powr lmnts (for xampl th brakrs). Thn th wight gain obtaind by th us of th proposd powr sourc may b compnsatd by an incras in othr powr lmnts wight. That is why othr powr sourcs will b studid in futur publications. In particular, sourcs with lss stringnt bandwih should b studid as a controlld rctifir, for xampl. For ths othr powr sourcs, th bst achivabl prformancs will b sarchd from a H control point of viw and compard togthr. APPENDIX Th Park transform is dfind by: xd cos wt = xq 2 / 3 sin wt x 1/ 2 cos( wt 2π / 3) sin( wt 2π / 3) 1/ 2 cos( wt 2π / 3) xa sin( wt 2π / 3) xb 1/ 2 xc whr (x a, x b, x c ) ar th AC variabls and (x d, x q, x ) th rotating fram variabls. Th paramtrs of th powr sourc ar givn in Tabl I: TABLE I SYSTEM PARAMETERS Symbol Dscription Valu Rs Stator windings rsistor 11mΩ Lls Stator (d,q) axis lakag inductanc 25,1µH Stator d axis magntizing inductanc 737µH Lmq Stator q axis magntizing inductanc 659µH Rkd Rsistanc of d axis dampr windings sn 33mΩ from stator Rkq Rsistanc of q axis dampr windings sn 44mΩ from stator Rfd Rsistanc of xcitr windings 3,6mΩ Llkd D axis dampr lakag inductanc 5,2µH Llkq Q axis dampr lakag inductanc 14,9µH Llfd Fild winding lakag inductanc 159µH C Output capacitor of th diod rctifir 2mF Sn Nominal powr of th gnrator 29 kva ACKNOWLEDGMENT This rsarch is bing conductd in th fram of th MOET projct, a FP6 Europan Intgratd Projct. Th authors would lik to thank MOET partnrs for modl paramtrs and on board structur dfinition. REFERENCES [1] M. Sautruil, N. Rtièr, D. Riu, O. Snam. A gnric mthod for robust prformanc analysis of aircraft DC powr systms, prsntd at th 34 th Annual Confrnc of th IEEE Industrial Elctronics Socity IECON 8, 28. [2] Mor Opn Elctrical Tchnologis (MOET) projct wb sit, [3] I. Jadric, D. Borojvic, M. Jadric, Modling and control of a Synchronous gnrator with an activ DC load, IEEE Trans. on Powr Elctronics, vol. 15, NO. 2, March 2. [4] S. Skogstad, I. Postlthwait, Multivariabl Fdback Control: Analysis and Dsign, John Wily and Sons, 25.