AMONG POWER SYSTEM CONTROLS IMPACT OF INTERACTIONS EPRI/NSF WORKSHOP PLAYACAR, APRIL 2002 GLOBAL DYNAMIC OPTIMISATION OF THE ELECTRIC POWER GRID

Transcription

1 EPRI/NSF WORKSHOP PLAYACAR, APRIL 00 GLOBAL DYNAMIC OPTIMISATION OF THE ELECTRIC POWER GRID IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS NELSON MARTINS JULIO C.R. FERRAZ, SERGIO GOMES JR. CEPEL COPPE/UFRJ R.,

2 PRESENTATION CONTENTS Adverse effects on intra-plant modes caused by improperly designed power system stabilizers Using zeros to understand the adverse terminal voltage transients induced by the presence of PSSs Hopf bifurcations in the control parameters space Simultaneous partial pole placement for power system oscillation damping control Secondary voltage regulation: preliminary study in the Rio Area

3 IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS ADERSE EFFECTSFFECTS ON INTRA-PLANT MODESODES CAUSEDAUSED BY IMPROPERLY DESIGNED POWEROWER SYSTEMYSTEM STABILIZERS

4 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS Large systems most multi-unit power plants are usually modeled as single equivalent machines Reduces the number of system states, but Does not capture the intra-plant dynamics When improperly designed, PSSs may cause adverse interactions and intra-plant mode instability 4

5 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS Two-unit power plant connected through a high impedance to the infinite bus -Machine system Equivalent SMIB representation pu AR 3 4 AR 50 MA 0. pu 0.6 pu AR 300 MA 0. pu 0.6 pu 5 50 MA

6 6 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS SMIB, pole-zero map of [ω / REF ] 5 0% 5% 0% 5% Exciter Mode Local Mode Real

7 7 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS SMIB system PSS (center frequency =.0 Hz) 5 0% 5% 0% 5% 0 5 Exciter Mode 0 5 Local Mode Real

8 8 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS -machine system, pole-zero map of [ω / REF ] 5 0% 5% 0% 5% Intra-Plant Mode Plant Exciter Mode Local Mode Real

9 9 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS -machine system, pole-zero map of [(ω + ω )/ REF ] 5 5% 0% 5% Intra-Plant Mode Plant Exciter Mode Local Mode Real

10 0 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS Map of zeros for different number of modeled machines (from to 7) 0 5% 0% 5% X Title

11 ADERSE EFFECTS FFECTS ON I 7 Machines, PSS ON INTRA-PLANT MODES CAUSED BY BY PSS 0. 0% 5% 0% 5% 6. Intra-Plant Mode. 7.9 Plant Exciter Mode 3.9 Local Mode Real

12 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS -Machine system PSS (center frequency =.0 Hz) 0 5% 0% 5% 5 0 Plant Exciter Mode Intra-Plant Mode 5 Local Mode Real

13 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS -Machine system PSSs (center frequency =.0 Hz) 5 5% 0% 5% Intra-Plant Mode Plant Exciter Mode 5 Local Mode Real

14 4 ADERSE EFFECTS FFECTS ON I ON INTRA-PLANT MODES CAUSED BY BY PSS -Machine system PSSs (center frequency 5.0 Hz) 5 5% 0% 5% 0 Intra-Plant Mode Plant Exciter Mode Local Mode Real

15 IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS USINGSING ZEROSEROS TO UNDERSTAND THE ADERSE TERMINAL OLTAGE TRANSIENTS INDUCED BY THE PRESENCE OF PSSS

16 ADERSE IMPACTS ON TERMINAL OLTAGE DUE TO PSSS Studying zeros to understand the adverse voltage transients induced by the presence of PSSs Comparing the performances of PSSs derived from either rotor speed or terminal power signals 6

17 7 ACTIE POWER CHANGES FOLLOWING PMEC IN SMIB 0,00 0,05 0,00 0,005 PSSω PSSPT 0,000 0,0 5,0 0,0 5,0 0,0 5,0 Tempo Time (s) (s)

18 REACTIE POWER CHANGES FOLLOWING PMEC IN SMIB 0,004 0,00 0,000-0,00-0, ,006-0,008 0,0 5,0 0,0 5,0 0,0 5,0 Tempo Time (s) (s) PSSω PSSPT

19 9 PT) POLE-ZERO ERO MAP FOR QT/ PMEC (PSSPT Zero near the origin causes bigger overshoot in the step response Badly Located Zero

20 0 POLE-ZERO ERO MAP FOR QT/ PMEC (PSSω)

21 IMPACT MPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS HOPFOPF BIFURCATIONS IN THE CONTROL PARAMETERS SPACEPACE

22 HOPF BIFURCATION ALGORITHMS Compute parameter values that cause crossings of the small-signal stability boundary by critical eigenvalues Hopf bifurcations are computed for: Single-parameter changes Multiple-parameter changes the parameter space) (minimum distance in

23 HOPF BIFURCATIONS TEST SYSTEM UTILIZED Brazilian North-South Interconnection:,400 buses, 3,400 lines, 0 generators and associated ARs, 46 stabilizers, 00 speed-governors, 4 SCs, TCSCs, HDC link Matrix dimension is 3,06 with 48,5 nonzeros and,676 states 5 Eigenvalue Spectrum Real Part (/s)

24 4 HOPF BIFURCATIONS TEST SYSTEM PROBLEM Two TCSCs located at each end of the North-South intertie, equiped with PODs to damp the 0.7 Hz mode The Hopf bifurcation algorithms were applied to compute eigenvalue crossings of the security boundary (5% damping ratio) for gain changes in the two PODs

25 5 ROOT CONTOUR WHEN REDUCING THE GAINS OF THE TCSCs.0 5%.6. North-South mode K= K= Adverse control Interaction mode K=0 K=

26 6 ROOT CONTOUR WHEN HEN INCREASING THE HE GAINS AINS OF THE HE TCSCs.0 5%.6 K=3.6. North-South mode K= Adverse control Interaction mode K= K=

27 7 DETERMINING SECURITY BOUNDARIES THROUGH HOPF (5%).0 5%.6. North-South mode K= K= Adverse control Interaction mode K=

28 8 DETERMINING SECURITY BOUNDARIES THROUGH HOPF (5%).0 5%.6. North-South mode K= Adverse control Interaction mode K= K=

29 HOPF BIFURCATIONS - CONCLUSIONS Two crossings of the security boundary were found, both being related to POD gains far away from the nominal values( pu): 3.59 > K > 0.08 Computational cost of Hopf bifurcation algorithm Single-parameter changes : 0.6 s (per iteration) Multiple-parameter changes : 0.35 s (per iteration) 9

30 IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS SIMULTANEOUS PARTIALARTIAL POLEOLE PLACEMENT FOR POWEROWER SYSTEMYSTEM OSCILLATION DAMPING CONTROL

31 INTRODUCTION Purpose choose adequate gains for the Power System Stabilizers (PSSs) installed on generators of a test system PSSs used to improve the damping factor of electromechanical modes of oscillation Stabilization procedure: Determine the system critical modes Determine the machines where the installation of PSSs would be more effective Assess each PSS contribution to the control effort 3 Tune the gains of the PSSs using transfer function residues associated with other information

32 TEST SYSTEM Simplified representation of the Brazilian Southern system Characteristics: Southeastern region represented by an infinite bus Static exciters with high gain (Ka = 00, Ta = 0.05 s) Itaipu ~ Southeast Foz do Areia Salto Santiago ~ Salto Segredo ~ South ~ 3

33 CRITICAL OSCILLATORY MODES Critical electromechanical modes of oscillation Real Imag. Freq. (Hz) Damping ± % ± % Parameters related to the phase tuning of the PSSs Number of lead blocks Tw (s) Tn (s) Td (s)

34 CRITICAL OSCILLATORY MODES : Itaipu x (South + Southeast) Itaipu ~ = ± j 5.9 Southeast Foz do Areia Salto Santiago ~ Salto Segredo ~ South 34 ~

35 35 CRITICAL OSCILLATORY MODES : Southeast x (Itaipu + South) Itaipu ~ = ± j 4.64 Southeast Foz do Areia Salto Santiago ~ Salto Segredo ~ South ~

36 Impact Impact of of Interactions Interactions Among Among Power Power System System Controls Controls 36 CONTRIBUTION OF ONTRIBUTION OF EACH ACH PSS PSS TO THE TO THE SHIFT HIFT A change in the gain vector Κ will produce shifts in both the real and imaginary parts of the eigenvalues The contribution of each PSS to these shifts can be estimated using the matrix of transfer function residues For and three PSSs: [ ] [ ] = ,,, Im,,, Re Im Re K K K R R R R R R REF PSS REF PSS REF PSS REF PSS REF PSS REF PSS

37 CONTRIBUTION OF EACH PSS TO THE SHIFT Normalized contribution of each PSS in the shifts of the real and imaginary parts of the two critical eigenvalues 37 Re[Res(pss/ref)] 0.5 I II III.5 I II III Im[Res(pss/ref)] 0.5 I II III.5 I II III Oscillatory Modes Itaipu mode Southern mode PSS Location I Itaipu II S. Segredo III Foz do Areia

38 POLE-ZERO ERO MAP OF [ω/ REF ] Map of poles and zeros for the matrix transfer function [ω/ REF ] with PSS in Itaipu % 0.0% 5.0% Real

39 39 Root-Locus for Gain Changes at Itaipu PSS Real

40 Impact Impact of of Interactions Interactions Among Among Power Power System System Controls Controls 40 POLE OLE PLACEMENT LACEMENT M MODES AND ODES AND PSS PSSS Improve the damping factors of two critical oscillatory modes by the use of two PSSs installed in: Itaipu and Salto Segredo The gains of the PSSs are computed for a desired shift in the real part of the eigenvalues Gain vector Κ will be calculated at each Newton iteration using the following relation: = Re,, Re,, Re REF PSS REF PSS REF PSS REF PSS R R R R K K

41 POLE-ZERO ERO MAP OF [ω/ REF ] x Map of poles and zeros for the matrix transfer function [ω/ REF ] x with PSSs in Itaipu and S. Segredo % 0.0% 5.0% Real

42 LACEMENT MODES M AND PSSS POLE PLACEMENT % 0.0% 5.0% K Itaipu = 5 K S.Segredo = 9 ζ = 0.4 % ζ = 0.9 % Real % 0.0% 5.0% Real K Itaipu = 4 K S.Segredo = 9 ζ =.0 % ζ = 3.5 %

43 43 LACEMENT MODES M AND PSSS POLE PLACEMENT The pole location must be carefully chosen `Some specified pole locations may require high PSS gains and cause exciter mode instability Comments on the installation of a third PSS Facilitates the pole placement more convenient pole-zero map Number of PSSs differs from the number of poles to be placed pseudo-inverse of a non-square matrix must be computed Algorithm must be modified

44 PSEUDO-INERSE ALGORITHM Problems without unique solution pseudo-inverse algorithm Re [ R] = [ ] mx mxn K nx Re m = number of modes n = number of PSSs If m < n the algorithm will produce gain values that ensure a minimum norm for the gain vector min K If m > n the algorithm will produce gain values that ensure a minimum norm for the error vector (solution of the least square problem) min Re [ R] K Re[ ] 44

45 Impact Impact of of Interactions Interactions Among Among Power Power System System Controls Controls 45 POLE OLE PLACEMENT LACEMENT M MODES AND ODES AND 3 PSS 3 PSSS Three PSSs installed in: Itaipu, Salto Segredo and Foz do Areia Pseudo-inverse algorithm will provide the solution with minimum norm for the gain vector Κ The gains of the PSSs are computed for a desired shift in the real part of the eigenvalues At every iteration, the pseudo-inverse algorithm updates and solves the following matrix equation: = Re,,, Re,,, Re REF PSS REF PSS REF PSS REF PSS REF PSS REF PSS R R R R R R K K K

46 POLE-ZERO ERO MAP OF [ω/ REF ] 3x3 Map of poles and zeros for the matrix transfer function [ω/ REF ] 3x3 with PSSs in Itaipu, S. Segredo and Foz do Areia % 0.0% 5.0% Real

47 LACEMENT MODES M AND 3 PSSS POLE PLACEMENT % 5.0% 0.0% 5.0% K Itaipu = K S.Segredo = K Foz do Areia = ζ = 5.9 % Real 0.0% 5.0% 0.0% 5.0% Real ζ = 5.9 % K Itaipu = 0.4 K S.Segredo = 6.3 K Foz do Areia = 6.3 ζ =.0 % ζ =.4 %

48 48 CONCLUSIONS Proposed pole placement algorithm: Based on transfer function residues and Newton method Uses generalized inverse matrices to address cases without unique solution Inspection of the pole-zero map is very useful Pole placement method Selected pole location can impose constraints that may be unnecessarily severe Results may be not feasible pole placement may yield undesirably high values for the PSS gains

49 49 FINAL REMARKS Important developments and increased use of modal analysis Large-scale, control-oriented eigenanalysis Much room for further improvements