倪以信动态电力系统PowerSystemDynamicsppt课件

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. stabili

2、ty0.5 Computer-aid P. S. stability analysis0.6 Contents of our courseIntroduction (1)0.1 Requirements of modern power systems (P. S. )Satisfying load demands (as a power source)Good quality: voltage magnitude, symmetric three phase voltages, low harmonics, standard frequency etc. (as a 3-phase ac vo

3、ltage source)Economic operationSecure and reliable operation with flexible controllability Loss of any one element will not cause any operation limit violations (voltage, current, power, frequency, etc. ) and all demands are still satisfied.For a set of specific large disturbances, the system will k

4、eep stable after disturbances.Good energy management systems (EMS)Introduction (2)0.2 Recent trends of P. S.Systems 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. ). Sy

5、stems are often heavily loaded and very stressed. System stability under disturbances is of great concern. New technology applications in power systems. (e.g. computer/ modern control theory/ optimization theory/ IT/ AI tech. etc. ) Power electronics applications: provides flexible controller in pow

6、er systems. ( e. g. HVDC transmission systems, STATCOM, UPFC, TCSC, etc.) Introduction (3)0.3 Complexity of modern P. S.Large scale, Hierarchical and distributed structure, Non-storable electric energy, Fluctuate and random loads, Highly nonlinear dynamic behavior, Unforeseen emergencies, Fast trans

7、ients which may lead to system collapse in seconds or minutes, Complicated 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. b

8、ook ):- The complexity of power systems is continually increasing because 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 pow

9、er systems, power system stability is the most intricate to understand and 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

10、 of P. S. stabilityP. S. stability: the property of a P. S. that enable it to remain in a state of operating equilibrium under normal operating conditions and to return to an acceptable state of equilibrium after being disturbed. Classification of stabilityBased on size of disturbance: large disturb

11、ance stability ( transient stability, IEEE): nonlinear system models small disturbance/signal stability ( steady-state stability, IEEE): linearized system models The time span considered:transient stability: 0 to 10 secondsmid-term stability: 10 seconds to a few minuteslong-term stability(dynamics):

12、 a few minutes to 1 hour Introduction (6)0.4 Definitions of different types of P. S. stability (cont.)Classification of stability (cont.)Based on physical nature of stability:Synchronous operation (or angle) stability: insufficient synchronizing torque - non-oscillatory instabilityinsufficient dampi

13、ng torque - oscillatory instabilityVoltage stability:insufficient reactive power and voltage controllabilitySubsynchronous oscillation (SSO) stabilityinsufficient damping torque in SSOIntroduction (7)0.5 Computer-aid P. S. stability analysisIntroduction (8) 0.6 Contents of the courseIntroductionPart

14、 I: Power system element models 1. Synchronous machine models 2. Excitation system models 3. Prime mover 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

15、 stability and eigenvalue analysis 8. Low-frequency oscillation and control 9. *Voltage stability 10. *Subsynchronous 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

16、S. M. and its model in abc coordinates1.1.1 Ideal S. M. definitionNote: * S. M. is a rotating magnetic element with complex 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

17、study S. M., mathematic models are developed for S. M. * Special assumptions are made to simplify the modeling.Chapter 1 Synchronous machine (S. M.) models1.1.1 Ideal S. M. definition (cont.):Assumptions for ideal S. M.Machine magnetic permeability (m) is a constant with magnetic saturation neglecte

18、d. Eddy current, hysteresis, and skin effects are neglected, so the machine is linear.Symmetric rotor structure in direct (d) and quadratic (q) axes. Symmetric stator winding structure: the three stator windings are 120 (electric) degrees apart in space with same structure. The stator and rotor have

19、 smooth surface with tooth and slot effects neglected. All windings generate sinusoidal distributed magnetic field.Chapter 1 Synchronous machine (S. M.) models1.1.2 Voltage equations in abc coordinatesPositive direction setting:dq and abc axes, speed directionAngle definition: Y directions for abcfD

20、Q windings i directions for abcfDQ u directions for abcfDQ (uD=uQ=0):(leading ahead )120 ,240240 ,120abaacaadaChapter 1 Synchronous machine (S. M.) models1.1.2 Voltage equations in abc coordinates (cont.)Voltage equations for abc windings:where p= d / dt, t in sec. rabc: stator winding resistance, i

21、n W. iabc : stator winding current, in A. uabc: stator winding phase voltage, in V. yabc: stator winding flux linkage, in Wb.Note: * pyabc: generate emf in abc windings * uabciabc: in generator conventional direction. * iabc yabc: positive iabc generates negative yabc respectivelyaaa abbb bccc cupr

22、iupr iupriChapter 1 Synchronous machine (S. M.) models1.1.2 Voltage equations in abc coordinates (cont.)Voltage equations for fDQ windings:rfDQ: rotor winding resistance, in W. f: field winding, D: damping winding in d-axis, Q: damping winding in q-axis.ifDG, ufDG, yfDG: rotor winding currents, volt

23、ages and flux linkages in A, V, Wb.Note: * uD=uQ=0 * ufDQifDQ: in load convention * ifDG yfDG: positive ifDG generates positive yfDG respectively * q-axis leads d-axis by 90 (electr.) deg. 00ffffDDD DQQQ Qupr iupr iupr iChapter 1 Synchronous machine (S. M.) models1.1.2 Voltage equations in abc coord

24、inates (cont.)Voltage 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 iuriurChapter 1 Synchronous machine (S. M.) models1.1.3 Flux linkage equations in abc coordinatesaaaabacaf

25、aDaQabbabbbcbfbDbQbccacbcccfcDcQcffafbfcfffDfQfDDaDbDcDfDDDQDQQaQbQcQfQDQQQLLLLLLiLLLLLLiLLLLLLiLLLLLLiLLLLLLiLLLLLLi 11 3 312 3 3(6 1)(6 6) (6 1)21 3 322 3 3 or =;abcabcfDQfDQLLiLiiLLChapter 1 Synchronous machine (S. M.) models1.1.3 Flux linkage equations in abc coordinates (cont.)In Flux linkage e

26、qn.: 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 windings , y, i : same definition as voltage eqn.Note: * Positive iabc generates

27、negative 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.)Stator winding self/mutual inductance (L11)Stator winding self inductance (Laa, Lbb, Lcc) Laa: reach max d-a aligning (when

28、 qa=0, 180) reach min d-a perpendicular (when qa=90, 270) Laa qa: 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 )aaStaStbbStbStccStcStLLLLLLLLLLLLLLLChapter 1 Synchronous mach

29、ine (S. M.) models1.1.3 Flux linkage equations in abc coordinates (cont.)Stator winding self/mutual inductance (L11)Stator winding mutual inductance Lab: reach max |.| when qa= -30, 150 reach min |.| when qa= 60, 240 Laa qa: sin-curve, with period of 180 (MsLt0, for round rotor: Lt=0)(See appendix 1

30、 of the text book for derivation), , ,0 (0);0 (0)ababa cfD Qbaabb cfD QbaLiLLiii= 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.)Rotor winding self/mutual inductance (L

31、22)Rotor winding self inductance (constant: why?)Lff = Lf = const. 0LDD = LD = const. 0LQQ = LQ = const. 0Rotor 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.)Stator an

32、d rotor winding mutual inductance (L12; L21 )abcf: (Mf=const.0, period: 360, max. when d-abc align)abcD: similar to abcf, MfMD0abcQ:(MQ=const.0, period: 360, max. when q-abc align)coscoscos(120 )cos(120 )affafafbffbfcffcfLLMMLLMLLMcos(90 )sinsin(120 )sin(120 )aQQaQaQbQQbQcQQcQLLMMLLMLLM Chapter 1 Sy

33、nchronous machine (S. M.) models1.1.3 Flux linkage equations in abc coordinates (summary)Time varying L-matrix : related to rotor position L11 (abcabc): 180 period; L12, L21(abcfDG): 360 period.Non-sparse L-matrix: most mutual inductances 0L-matrix: non-user friendly, lead to abc dq0 coordinates!000

34、0aaaabacafaDaQabbabbbcbfbDbQbccacbcccfcDcQcffafbfcfRfDDaDbDcRDDQQaQbQcQQLLLLLLiLLLLLLiLLLLLLiLLLLMiLLLMLiLLLLi Chapter 1 Synchronous machine (S. M.) models1.1.4 Generator power, torque and motion eqns.Instantaneous output power eqn. (Pe in W)Electromagnetic torque eqn. (Te in N-m, q in rad.)ccbbaaei

35、uiuiuPT T11()()()230111 1013110PePabcbcacabPabcabcdLTpiipiiiiiidpi (6 1): number of pole pairs, : (-, )PTTTabcfDQpiiiChapter 1 Synchronous machine (S. M.) models1.1.4 Generator power, torque and motion eqns. (cont.)Rotor motion eqns.According to Newtons law, we have: where Tm: input mechanical torqu

36、e of generator (in N-m) Te: output electromagnetic torque (in N-m) wm/qm: rotor mechanical speed/angle (in rad/s, rad.) we/qe: 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). dmmemmJTTdtddt/;/mePPmePPpppp2iiimrChapter 1 Synchronous