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2726Vol.27No.26Sep.200720079ProceedingsoftheCSEE©2007Chin.Soc.forElec.Eng.0258-8013(2007)26-0108-07TK472A470⋅20112(11100042150080)NonlinearModelingandStabilityAnalysisofGasTurbineUsedforElectricityGeneratingZHANGHua-guang1,DENGWei1,GENGJia-min2(1.SchoolofInformationScienceandEngineering,NortheasternUniversity,Shenyang110004,LiaoningProvince,China;2.GasTurbineCorp.,HarbinAviationIndustryGroup,Harbin150080,HeilongjiangProvince,China)ABSTRACT:Nonlinearstatespaceequationsofasingle-spoolgasturbinewereestablishedsystematicallyfromthermodyna-micalprinciples.Themixedthermodynamicmechanicalsystemswerecomplexandverystrongnonlinearusedforelectricitygenerating.MathematicalmethodofstabilityanalysiswasproposedbymeansofthetransformedLotka-Volterramodelofthegasturbine.Theestablishedmodeliseasilytobeusedforstudyingdynamicproperties,algorithmandschemeofcontrolofthegasturbine.Experimentofsimulationhasprovedthattheestablishedmodelofthegasturbineiscorrectandeffective.Theproposedmodelingmethodscanbeextendedtostudyothergasturbineswithdifferenttypes.Forexample,atwin-spoolorwithafterburninggasturbinesystem.KEYWORDS:gasturbine;mathematicalmodeling;stabilityanalysis;Lotka-VolterramodelLotka-VolterraLotka-Volterra863(2002AA503020)(6032531160274017)TheNationalHighTechnologyResearchandDevelopmentofChina(863Programme)(2002AA503020);ProjectSupportedbyNationalNaturalScienceFoundationofChina(60325311;60274017).0[1-2][3][4]DeutzT216[5-6][7-8](quasi-polynomialordinarydifferentialequations)Lotka-Volterra[9-15]LV2610911.1[16]12()cpcv(Rg)(κg)κg=κaκa3U*24561.21*11apap=(1)*PaPaa12(6)*4a3ppa=(2)a33**3cham3mcham/TVpRM=(3)Vchamm3RmJ/kg⋅KMchamkg4πcπT,[16]a**2cc1{[()1]/1}TTγπη=−+(4)g**4TT3{1[1()]}TTγπη=−−⋅(5)aaaggg(1)/;(1)/γκκγκκ=−=−5**ca1111**Tg3333//qApqTqApqTββ⎧=⎪⎨=⎪⎩(6)gaga111g1aagaagg22()()11RRκκκκκκββκκ++−−==++1q3q61qcπcn11cc(,)qqnπ=[7]cπcn111cc12c13c14qnnαπαπαα=+++(7)α7cη1qcn()cc1c,qnηη=[17]83qTπuλ(6)331Tu32T33u34qαπλαπαλα=+++(8)9(isentropicefficiency)TηTπuλTTTu(,)ηηπλ=(9)(7)11Tab.1Parametersofmechanicsandthermodynamicsκa1.4κg1.33cpa1004.5J/(kg⋅K)cpg1160.7J/(kg⋅K)cva717.5J/(kg⋅K)cvg872.7J/(kg⋅K)Qu4.28107J/kga10.9888a20.9374a30.9669ηT85.68%ηc67.59%ηB96.65%J3×10-4kg⋅m2α113.532×10−4α12−4.611×10−1α131.110×10−3α141.664×10−1α31−3.248×10α324.784×10−2α331.822×10−3α341.603×10−11.31inoutddMqqt=−(10)inqoutq(10)11027*cham1CfTa11f*1***312g33a111****1311a0**32121314fg3***11a03dd(/)/MpqqqAqqtTpppnAqApTTTTppnqApTTTβββααααβ=+−=+−=++++−⋅31Tu32T33u34()απλαπαλα+++(11)(11)1.2n*3pchamM**cham313cham32333chamddMknpMknpknMt=+++*3/21/2*1/21/2343cham353cham()()()()kpMkpM++*36373383fknkpkbq+++(12)(12)k1k22kTab.2Resultsofthecoefficientkcalculationk117.1765×10-8k10−1.9509×10-6k132.5192×10-2k12−6.848310-1k159.4319×100k14−2.484910102k17−3.195709×102k168.419365106k19−4.9851×10−9k181.3552×10−7k1,11−7.2246×10−3k1,121.9037×100k1,13−7.9657×10−4k1,14−2.1318×103k1,155.45729×104k214.5941×10−9k225.7043×10−3k23−4.8742×10−2k241.6832×103k25−6.6136×10−-8k26−2.3216×10−2k27−1.43747×104k28−7.44712×100k296.3598×101k2,102.52323×105k2,11−2.1548406×106b22.757775×109k313.2815×10-9k325.2664×10−9k33−1.9289×10−5k34−4.7240×10−8k35−1.6583×10−2k361.5540×10−3k37−6.8754×10−6k382.3295×10−1b31.0×100k1,15Tload=50N⋅m2***ininoutoutddUqiqiQt=−+(13)*iJ/kgQJ****vvvdddd()ddddUMTcTMcTcMtttt==+(14)(10)(13)()****ininoutoutvinoutvddqiqiQcTqqTtcM−+−−=(15)**RpMTV=***ddddddpRMRTTMtVtVt=+(16)(10)(15)(16)()**inoutddpRRTqqMtVV=−+⋅***ininoutoutvinoutv()[]qiqiQcTqqcM−+−−(17)(17)()***3mm3cfTcpa2chamvmchamd[dpRRTqqqqcTtVcV=+−+⋅−**Tpg3uBfvm3cfT()]qcTQqcTqqqη+−+−(18)QuJ/kgcvmJ/(kg⋅K)n*3pchamMa*1*2**3213223233d()()dpknpknpknptγ+=+++a**5/21/2243253cham()()()knpkpMγ−++a1*3/21/2*263cham27283()()()kpMknkpγ+−+++a**2932,1032,112f()kpkpkbqγ+++(19)k23dω/dtJ()TCloadd1dJPPPtωω=−−(20)g*TTpg3TT(11/)PqcTγπη=−(21)a*Ccpa1cc(1)/PqcTγπη=−(22)loadloadload335025PTTnω==π(23)n1/sloadTN⋅m(21)~(23)1.2(20)g***Tpg334T2d1{[1(/)]d4nqcTpptJnγη−=−−πa***cpa121loadc13[(/)1]}25qcTppTnγη−−π(24)Jkg⋅m2g5/21*5/21/21*113cham123d()()()dnknpMknptγ−−−−=+×1/21*3/21/21cham133cham14()()()MknpMkn−−−−++×ga3/21*1/21*1*3cham153163()()()pMknpknpγγ−+−−−+++ga21*1*2*173181931,103()()()knpknkpkpγγ−−−++++26111gaa11****1,1131,1231,1331,1431,15()()()kpkpkpkpkγγγ−+++++(25)k2T123[,,]xxx=*T3cham[,,]npMfuq=12.50.512.21430.511.50.5111123121231312311.21430.511.28571141231512161210.2857121.714317121811921,1021.28571,1121,122xkxxxkxxxkxxxkxxxkxxkxxkxxkxkxkxkxkx−−−−−−−−−−−−=++++++++++++0.71430.28571,1321,1421,1521.28570.2857221122212231224122.50.51.50.51.2857252326232712820.28572922,1022,1123311233212331kxkxkxkxxkxxkxxkxxkxxkxxkxkxkxkxkbuxkxxxkxxkx−−++=+++++++++++=++1.50.5334230.50.53523361372383xkxxkxxkxkxkbu⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪++⎪⎪++++⎩(26)SISO()()()uyh=+⎧⎨=⎩xfxgxx(27)T123[,,]xxx=xT123()[(),(),()]fff=fxxxx,T123()[,,]bbb=gx1()hx=xx1123,,bbb10b=22.100(,)xu(26)22.50.522.21430.521.50.51111123121231312321.21430.521.28572141231512161220.285721211.7143171218119121,101211,111(xxAxxxAxxxAxxxAxxxAxxAxxAxxAxAxxAxxAx−−−−−−−−−−−−−−−=++++++++++1.2857110.714321,12121,131210.285711,14121,1510.28570.71432221122