倪以信动态电力系统PowerSystemDynamics

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1、Power System Dynamics-Postgraduate Course of Tsinghua Univ.Graduate School at ShenzhenNI YixinAssociate ProfessorDept.of EEE,HKUIntroduction0.1 Requirements of modern power systems(P.S.)0.2 Recent trends of P.S.0.3 Complexity of modern P.S.0.4 Definitions of different types of P.S.stability0.5 Compu

2、ter-aid P.S.stability analysis0.6 Contents of our courseIntroduction(1)0.1 Requirements of modern power systems(P.S.)nSatisfying load demands(as a power source)nGood quality:voltage magnitude,symmetric three phase voltages,low harmonics,standard frequency etc.(as a 3-phase ac voltage source)nEconomi

3、c operationnSecure and reliable operation with flexible controllability nLoss of any one element will not cause any operation limit violations(voltage,current,power,frequency,etc.)and all demands are still satisfied.nFor a set of specific large disturbances,the system will keep stable after disturba

4、nces.nGood energy management systems(EMS)Introduction(2)0.2 Recent trends of P.S.nSystems interconnection:to obtain more benefits.It may lead to new stability issues(e.g.low-frequency power oscillation on the tie lines;SSR caused by series-compensated lines etc.).nSystems are often heavily loaded an

5、d very stressed.System stability under disturbances is of great concern.nNew technology applications in power systems.(puter/modern control theory/optimization theory/IT/AI tech.etc.)nPower electronics applications:provides flexible controller in power systems.(e.g.HVDC transmission systems,STATCOM,

6、UPFC,TCSC,etc.)Introduction(3)0.3 Complexity of modern P.S.nLarge scale,nHierarchical and distributed structure,nNon-storable electric energy,nFluctuate and random loads,nHighly nonlinear dynamic behavior,nUnforeseen emergencies,nFast transients which may lead to system collapse in seconds or minute

7、s,nComplicated control and their coordination requests.-Modern P.S.is much more complicated than ever and in the meantime it plays a significant role in modern society.Introduction(4)Some viewpoints of Dr.Kundur(author of the ref.book):-The complexity of power systems is continually increasing becau

8、se of the growth in interconnections and use of new technologies.At the same time,financial and regulatory constrains have forced utilities to operate the systems nearly at stability limits.-Of all the complex phenomena on power systems,power system stability is the most intricate to understand and

9、challenging to analyze.Electric power systems of the 21 century will present an even more formidable challenge as they are forced to operate closer to their stability limit.Introduction(5)0.4 Definitions of different types of P.S.stabilitynP.S.stability:the property of a P.S.that enable it to remain

10、 in a state of operating equilibrium under normal operating conditions and to return to an acceptable state of equilibrium after being disturbed.nClassification of stabilitynBased on size of disturbance:nlarge disturbance stability(transient stability,IEEE):nonlinear system models nsmall disturbance

11、/signal stability(steady-state stability,IEEE):linearized system models nThe time span considered:ntransient stability:0 to 10 secondsnmid-term stability:10 seconds to a few minutesnlong-term stability(dynamics):a few minutes to 1 hour Introduction(6)0.4 Definitions of different types of P.S.stabili

12、ty(cont.)nClassification of stability(cont.)nBased on physical nature of stability:nSynchronous operation(or angle)stability:ninsufficient synchronizing torque-non-oscillatory instabilityninsufficient damping torque-oscillatory instabilitynVoltage stability:ninsufficient reactive power and voltage c

13、ontrollabilitynSubsynchronous oscillation(SSO)stabilityninsufficient damping torque in SSOIntroduction(7)0.5 Computer-aid P.S.stability analysisIntroduction(8)0.6 Contents of the courseIntroductionPart I:Power system element models 1.Synchronous machine models 2.Excitation system models 3.Prime move

14、r and speed governor models 4.Load models 5.Transmission line and transformer models Part II:Power system dynamics:theory and analysis 6.Transient stability and time simulation 7.Steady-state stability and eigenvalue analysis 8.Low-frequency oscillation and control 9.*Voltage stability 10.*Subsynchr

15、onous oscillation 11.Improvement of system stability SummaryPart I Power system element modelsChapter 1 Synchronous machine models(a)Chapter 1 Synchronous machine(S.M.)models1.1 Ideal S.M.and its model in abc coordinates1.1.1 Ideal S.M.definitionnNote:*S.M.is a rotating magnetic element with complex

16、 dynamic behavior.It is the heart of P.S.It *It provides active and reactive power to loads and has strong power,frequency and voltage regulation/control capability.*To study S.M.,mathematic models are developed for S.M.*Special assumptions are made to simplify the modeling.Chapter 1 Synchronous mac

17、hine(S.M.)models1.1.1 Ideal S.M.definition(cont.):nAssumptions for ideal S.M.nMachine magnetic permeability(m m)is a constant with magnetic saturation neglected.Eddy current,hysteresis,and skin effects are neglected,so the machine is linear.nSymmetric rotor structure in direct(d)and quadratic(q)axes

18、.nSymmetric stator winding structure:the three stator windings are 120(electric)degrees apart in space with same structure.nThe stator and rotor have smooth surface with tooth and slot effects neglected.All windings generate sinusoidal distributed magnetic field.Chapter 1 Synchronous machine(S.M.)mo

19、dels1.1.2 Voltage equations in abc coordinatesnPositive direction setting:ndq and abc axes,speed directionnAngle definition:nY Y directions for abcfDQ windings ni directions for abcfDQ nu directions for abcfDQ(uD=uQ=0):(leading ahead)120,240240,120abaacaadaChapter 1 Synchronous machine(S.M.)models1.

20、1.2 Voltage equations in abc coordinates(cont.)nVoltage equations for abc windings:where p=d/dt,t in sec.rabc:stator winding resistance,in W W.iabc:stator winding current,in A.uabc:stator winding phase voltage,in V.y yabc:stator winding flux linkage,in Wb.Note:*py yabc:generate emf in abc windings *

21、uabciabc:in generator conventional direction.*iabc y yabc:positive iabc generates negative y yabc respectivelyaaa abbb bccc cupr iupr iupriChapter 1 Synchronous machine(S.M.)models1.1.2 Voltage equations in abc coordinates(cont.)nVoltage equations for fDQ windings:rfDQ:rotor winding resistance,in W

22、W.f:field winding,D:damping winding in d-axis,Q:damping winding in q-axis.ifDG,ufDG,y yfDG:rotor winding currents,voltages and flux linkages in A,V,Wb.Note:*uD=uQ=0 *ufDQifDQ:in load convention *ifDG y yfDG:positive ifDG generates positive y yfDG respectively *q-axis leads d-axis by 90(electr.)deg.0

23、0ffffDDD DQQQ Qupr iupr iupr iChapter 1 Synchronous machine(S.M.)models1.1.2 Voltage equations in abc coordinates(cont.)nVoltage equations in matrix format:where before iabc is caused by generator convention of stator windings.TTTT(,)(,)diag(,)(,)abcfDQabcfDQaaafDQabcfDQpu u u uuu r r r r rriii iii

24、iuriurChapter 1 Synchronous machine(S.M.)models1.1.3 Flux linkage equations in abc coordinatesaaaabacafaDaQabbabbbcbfbDbQbccacbcccfcDcQcffafbfcfffDfQfDDaDbDcDfDDDQDQQaQbQcQfQDQQQLLLLLLiLLLLLLiLLLLLLiLLLLLLiLLLLLLiLLLLLLi 11 3 312 3 3(6 1)(6 6)(6 1)21 3 322 3 3 or=;abcabcfDQfDQLLiLiiLLyyyChapter 1 Sy

25、nchronous machine(S.M.)models1.1.3 Flux linkage equations in abc coordinates(cont.)nIn Flux linkage eqn.:Lij(i,j=a,b,c,f,D,Q):self and mutual inductances,L11 :stator winding self and mutual inductance,L22 :rotor winding self and mutual inductances,L12 ,L21 :mutual inductances among stator and rotor

26、windings,y y,i:same definition as voltage eqn.Note:*Positive iabc generates negative y yabc respectively.*The negative signs of iabc make Laa,Lbb,Lcc 0.Chapter 1 Synchronous machine(S.M.)models1.1.3 Flux linkage equations in abc coordinates(cont.)nStator winding self/mutual inductance(L11)nStator wi

27、nding self inductance(Laa,Lbb,Lcc)Laa:reach max d-a aligning(when a=0,180)reach min d-a perpendicular(when a=90,270)Laa a:sin-curve,with period of 180 (LsLt0,for round rotor:Lt=0)(See appendix 1 of the text book for derivation)0(,0)aaabcfDQaLi i iiiicos2cos2cos2cos2(120)cos2cos2(120)aaStaStbbStbStcc

28、StcStLLLLLLLLLLLLLLLChapter 1 Synchronous machine(S.M.)models1.1.3 Flux linkage equations in abc coordinates(cont.)nStator winding self/mutual inductance(L11)nStator winding mutual inductance Lab:reach max|.|when a=-30,150 reach min|.|when a=60,240 Laa a:sin-curve,with period of 180 (MsLt0,for round

29、 rotor:Lt=0)(See appendix 1 of the text book for derivation),0(0);0(0)ababa cfD Qbaabb cfD QbaLiLLiiiyy=cos2(30)(cos2(30)=(cos2(90)=(cos2(150)abbastastbccbstcaacstLLMLMLLLMLLLML Chapter 1 Synchronous machine(S.M.)models1.1.3 Flux linkage equations in abc coordinates(cont.)nRotor winding self/mutual

30、inductance(L22)nRotor winding self inductance(constant:why?)Lff =Lf =const.0LDD=LD=const.0LQQ=LQ=const.0nRotor winding mutual inductance LfQ=LfQ=0,LDQ=LQD=0 LfD=LDf=MR=const.0Chapter 1 Synchronous machine(S.M.)models1.1.3 Flux linkage equations in abc coordinates(cont.)nStator and rotor winding mutu

31、al inductance(L12;L21)nabcf:(Mf=const.0,period:360,max.when d-abc align)nabcD:similar to abcf,MfMD0nabcQ:(MQ=const.0,period:360,nmax.when q-abc align)coscoscos(120)cos(120)affafafbffbfcffcfLLMMLLMLLMcos(90)sinsin(120)sin(120)aQQaQaQbQQbQcQQcQLLMMLLMLLM Chapter 1 Synchronous machine(S.M.)models1.1.3

32、Flux linkage equations in abc coordinates(summary)nTime varying L-matrix:related to rotor position nL11(abcabc):180 period;L12,L21(abcfDG):360 period.nNon-sparse L-matrix:most mutual inductances 0nL-matrix:non-user friendly,lead to abc dq0 coordinates!0000aaaabacafaDaQabbabbbcbfbDbQbccacbcccfcDcQcff

33、afbfcfRfDDaDbDcRDDQQaQbQcQQLLLLLLiLLLLLLiLLLLLLiLLLLMiLLLMLiLLLLi Chapter 1 Synchronous machine(S.M.)models1.1.4 Generator power,torque and motion eqns.nInstantaneous output power eqn.(Pe in W)nElectromagnetic torque eqn.(Te in N-m,in rad.)ccbbaaeiuiuiuPT T11()()()230111 1013110PePabcbcacabPabcabcdL

34、Tpiipiiiiiidpiyyyy(6 1):number of pole pairs,:(-,)PTTTabcfDQpiiiChapter 1 Synchronous machine(S.M.)models1.1.4 Generator power,torque and motion eqns.(cont.)nRotor motion eqns.nAccording to Newtons law,we have:where Tm:input mechanical torque of generator(in N-m)Te:output electromagnetic torque(in N

35、-m)w wm/m:rotor mechanical speed/angle(in rad/s,rad.)w we/e:rotor electrical speed/angle(in rad/s,rad.),J:rotor moment of inertia(also called rotational inertia)J=Kg-m2 In the manufacturers handbook,J is given by GD2,in ton-m2.GD2(ton-m2)103/4 J(Kg-m2).dmmemmJTTdtddtww/;/mePPmePPppppwww2iiimrChapter

36、 1 Synchronous machine(S.M.)models1.1.4 Generator power,torque and motion eqns.(cont.)nRotor motion eqns.(cont.)1ddmmemePmmJTTJTTpdtdtdddtdtwwww(/;/)mePPmePPppppwww1()()()3ePabcbcacabTpiiiiiiyyyChapter 1 Synchronous machine(S.M.)models1.1.5 Summary of S.M.model in abc coordinates and SI units:n6 vol

37、t.DEs.(abcfDQ):n6 flux linkage AEs.(abcfDQ):n2 rotor motion eqns.(w w,:nTotally 14 eqns.with 8 DEs and 6 AEs.n8th order nonlinear model.n8 state variables are:y y(6 1)and w w,(related to 8 DEs)nTotally 19 variables:u:4(vD=vQ=0),i:6,y y:6,plus(Tm,w w,.nIf 5 variables are known,remaining 14 variables

38、can be solved.nUsually uf and Tm are known(as input signals),3 network interface eqns.(3 vabc-iabc relations from network)are known.1()()()3ePabcbcacabTpiiiiiiyyyupriyLiy1d;mePdJTTpdtdtwwChapter 1 Synchronous machine(S.M.)models1.1.5 Summary of S.M.model in abc coordinates(cont.)nRequest of transformation of S.M.model:nabc to dq0 coordinates:Parks transformation,Parks eqns.nper unit system and S.M.pu modelnReduced-order practical models:-Neglect stator abc winding transients(8th order 5th order).It can interface with network Y-matrix in Aes.-Introduce practical variables(Edq,E”dq,Ef etc.)