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EPRI/NSF WORKSHOP – PLAYACAR, APRIL 2002 GLOBAL DYNAMIC OPTIMISATION OF THE ELECTRIC POWER GRID IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS NELSON MARTINS1 JULIO C.R. FERRAZ1,2 SERGIO GOMES JR.1,2 1CEPEL 2COPPE/UFRJ 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 2 Impact of Interactions Among Power System Controls IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY IMPROPERLY DESIGNED POWER SYSTEM STABILIZERS ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS systems most multi-unit power plants are usually modeled as single equivalent machines Large Reduces Does the number of system states, but… not capture the intra-plant dynamics When improperly designed, PSSs may cause adverse interactions and intra-plant mode instability 4 Impact of Interactions Among Power System Controls ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS Two-unit power plant connected impedance to the infinite bus 2-Machine system Equivalent SMIB representation 1 3 through a high 4 0.2 pu AVR 1 4 0.1 pu 150 MVA 0.6 pu 2 AVR 300 MVA 0.2 pu AVR 150 MVA 5 3 Impact of Interactions Among Power System Controls 0.6 pu ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS SMIB, pole-zero map of [Dw1/DVREF1] 20% 15% 10% 5% 15 12 9 6 Local Mode Exciter Mode 3 0 -10 6 -9 -8 -7 -6 -5 -4 Real Impact of Interactions Among Power System Controls -3 -2 -1 0 1 2 ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS SMIB system – PSS (center frequency = 1.0 Hz) 20% 25 15% 10% 5% 20 15 Exciter Mode 10 Local Mode 5 0 -10 7 -9 -8 -7 -6 -5 -4 Real Impact of Interactions Among Power System Controls -3 -2 -1 0 1 2 ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS 2-machine system, pole-zero map of [Dw1/DVREF1] 20% 15% 10% 5% 15 12 Intra-Plant Mode 9 6 Plant Exciter Mode Local Mode 3 0 -10 8 -9 -8 -7 -6 -5 -4 Real Impact of Interactions Among Power System Controls -3 -2 -1 0 1 2 ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS 2-machine system, pole-zero map of [(Dw1 + Dw2)/DVREF1] 15% 10% 5% 15 12 Intra-Plant Mode 9 6 3 0 -10 9 Local Mode Plant Exciter Mode -9 -8 -7 -6 -5 -4 Real Impact of Interactions Among Power System Controls -3 -2 -1 0 1 2 ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS Map of zeros for different number of modeled machines (from 1 to 7) 20 15% 10% 5% -3 -2 -1 15 10 5 0 -10 10 -9 -8 -7 -6 -5 -4 X Title Impact of Interactions Among Power System Controls 0 1 2 ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS 7 Machines, 1 PSS 20% 20. 15% 10% 5% Intra-Plant Mode 16. 12. 7.9 Plant Exciter Mode Local Mode 3.9 -0.1 -10. 11 -8. -6. -4. Real Impact of Interactions Among Power System Controls -2. 0. 2. ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS 2-Machine system – 1 PSS (center frequency = 1.0 Hz) 15% 20 10% 5% Intra-Plant Mode 15 Plant Exciter Mode 10 5 Local Mode 0 -10 12 -9 -8 -7 -6 -5 -4 Real Impact of Interactions Among Power System Controls -3 -2 -1 0 1 2 ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS 2-Machine system – 2 PSSs (center frequency = 1.0 Hz) 15% 25 10% Intra-Plant Mode 5% 20 15 Plant Exciter Mode 10 5 Local Mode 0 -10 13 -9 -8 -7 -6 -5 -4 Real Impact of Interactions Among Power System Controls -3 -2 -1 0 1 2 ADVERSE EFFECTS ON INTRA-PLANT MODES CAUSED BY PSS 2-Machine system – 2 PSSs (center frequency 5.0 Hz) 15% 25 10% 5% Intra-Plant Mode 20 15 10 5 0 -10 14 Plant Exciter Mode -9 -8 -7 -6 Local Mode -5 -4 Real Impact of Interactions Among Power System Controls -3 -2 -1 0 1 2 BRAZILIAN SOUTH/SOUTHEAST INTERCONNECTED SYSTEM Open-Loop 15 Eigenvalues Impact of Interactions Among Power System Controls BRAZILIAN SOUTH/SOUTHEAST INTERCONNECTED SYSTEM Pole-Zero 16 Map (22 PSSs) Impact of Interactions Among Power System Controls BRAZILIAN SOUTH/SOUTHEAST INTERCONNECTED SYSTEM Pole-Zero 17 Map (33 PSSs) Impact of Interactions Among Power System Controls IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS USING ZEROS TO UNDERSTAND THE ADVERSE TERMINAL VOLTAGE TRANSIENTS INDUCED BY THE PRESENCE OF PSSS ADVERSE IMPACTS ON TERMINAL VOLTAGE 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 19 Impact of Interactions Among Power System Controls Xingó ACTIVE POWER CHANGES FOLLOWING DPMEC IN SMIB ESP com sinal de velocidade do rotor ESP com sinal de potência terminal 0,020 0,015 0,010 0,005 PSSw 0,000 0,0 PSSPT 5,0 10,0 15,0 Tempo Time (s)(s) 20 Impact of Interactions Among Power System Controls 20,0 25,0 Xingó REACTIVE POWER CHANGES FOLLOWING DPMEC IN SMIB ESP com sinal de velocidade do rotor ESP com sinal de potência terminal 0,004 0,002 0,000 -0,002 -0,004 PSSw -0,006 PSSPT -0,008 0,0 5,0 10,0 15,0 Time (s) Tempo (s) 21 Impact of Interactions Among Power System Controls 20,0 25,0 POLE-ZERO MAP FOR DQT/ DPMEC (PSSPT) Zero near the origin causes bigger overshoot in the step response 8.5 5.5 Badly Located Zero 2.5 -0.5 -2.5 22 -2 -1.5 -1 Impact of Interactions Among Power System Controls -0.5 0 0.5 POLE-ZERO MAP FOR DQT/ DPMEC (PSSw) 8.5 5.5 2.5 -0.5 -2.5 23 -2 -1.5 -1 Impact of Interactions Among Power System Controls -0.5 0 0.5 IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS HOPF BIFURCATIONS IN THE CONTROL PARAMETERS SPACE 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) 25 Impact of Interactions Among Power System Controls (minimum distance in HOPF BIFURCATIONS – TEST SYSTEM UTILIZED Brazilian North-South Interconnection: 2,400 buses, 3,400 lines, 120 generators and associated AVRs, 46 stabilizers, 100 speed-governors, 4 SVCs, 2 TCSCs, 1 HVDC link Matrix dimension is 13,062 with 48,521 nonzeros and 1,676 states Eigenvalue Spectrum 15 10 5 0 -5 -10 -15 -10 26 Impact of Interactions Among Power System Controls -8 -6 -4 Real Part (1/s) -2 0 HOPF BIFURCATIONS – TEST SYSTEM PROBLEM Two TCSCs located at each end of the North-South intertie, equiped with PODs to damp the 0.17 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 27 Impact of Interactions Among Power System Controls ROOT CONTOUR WHEN REDUCING THE GAINS OF THE 2 TCSCs 5% 2.0 1.6 1.2 North-South mode K=1 K=0 0.8 0.4 Adverse control Interaction mode 0.0 -0.8 28 K=0 -0.6 K=1 -0.4 Impact of Interactions Among Power System Controls -0.2 0. ROOT CONTOUR WHEN INCREASING THE GAINS OF THE 2 TCSCs 5% 2.0 K=3.6 1.6 1.2 North-South mode K=1 0.8 0.4 Adverse control Interaction mode 0.0 -0.8 29 -0.6 K=3.6 K=1 -0.4 Impact of Interactions Among Power System Controls -0.2 0. DETERMINING SECURITY BOUNDARIES THROUGH HOPF (5%) 5% 2.0 1.6 1.2 North-South mode K=1 K=0.108 0.8 0.4 Adverse control Interaction mode 0.0 -0.8 30 -0.6 K=1 -0.4 Impact of Interactions Among Power System Controls -0.2 0. DETERMINING SECURITY BOUNDARIES THROUGH HOPF (5%) 5% 2.0 1.6 1.2 North-South mode K=1 0.8 0.4 Adverse control Interaction mode 0.0 -0.8 31 -0.6 K=3.529 K=1 -0.4 Impact of Interactions Among Power System Controls -0.2 0. HOPF BIFURCATIONS - CONCLUSIONS Two crossings of the security boundary were found, both being related to POD gains far away from the nominal values(1 pu): 3.529 > K > 0.108 Computational cost of Hopf bifurcation algorithm Single-parameter changes : 0.16 s (per iteration) Multiple-parameter 32 changes : 0.35 s (per iteration) Impact of Interactions Among Power System Controls IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS SIMULTANEOUS PARTIAL POLE PLACEMENT FOR POWER SYSTEM OSCILLATION DAMPING CONTROL INTRODUCTION Purpose choose adequate gains for the Power System Stabilizers (PSSs) installed in 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 Tune the gains of the PSSs using transfer function residues in association with other information 34 Impact of Interactions Among Power System Controls TEST SYSTEM Simplified representation of the Brazilian Southern system Characteristics: Southeastern region represented by an infinite bus Static exciters with high gain (Ka = 100, Ta = 0.05 s) Itaipu Southeast ~ Foz do Areia Salto Santiago ~ ~ Salto Segredo ~ 35 Impact of Interactions Among Power System Controls South CRITICAL OSCILLATORY MODES Critical electromechanical modes of oscillation Real Imag. Freq. (Hz) Damping 1 +0.15309 5.9138 0.94121 -2.59% 2 +0.17408 4.6435 0.73904 -3.75% Nature Local Mod Itaipu x Sys Inter-area M South x Sout Parameters related to the phase tuning of the PSSs Number of lead blocks 2 36 Tw (s) 3 Impact of Interactions Among Power System Controls Tn (s) 0.100 Td (s) 0.010 CRITICAL OSCILLATORY MODES 1 : Itaipu x (South + Southeast) 1 = + 0.15 j 5.91 Itaipu Southeast ~ Foz do Areia Salto Santiago ~ ~ Salto Segredo ~ 37 Impact of Interactions Among Power System Controls South CRITICAL OSCILLATORY MODES 2 : Southeast x (Itaipu + South) Itaipu 2 = + 0.17 j 4.64 Southeast ~ Foz do Areia Salto Santiago ~ ~ Salto Segredo ~ 38 Impact of Interactions Among Power System Controls South CONTRIBUTION OF EACH PSS TO THE SHIFT A change in the gain vector DK 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 1 and three PSSs: DV DVPSS3 DK DVPSS2 PSS 1 1 , 1 R , 1 R , 1 Re R Re D1 DVREF1 DVREF2 DVREF3 DK 2 = DVPSS3 DVPSS2 ImD1 DVPSS1 Im R , 1 R , 1 R , 1 DK DVREF1 DVREF2 DVREF3 3 39 Impact of Interactions Among Power System Controls CONTRIBUTION OF EACH PSS TO THE SHIFT Normalized contribution of each PSS to the shifts of the real and imaginary parts of the two critical eigenvalues Re[Res(Vpss/Vref)] 0.5 1.5 1 – Itaipu mode I II III 2 2.5 Oscillatory Modes I II III 1 -1 -0.5 0 2 – Southern mode 0.5 1 PSS Location Im[Res(Vpss/Vref)] 0.5 1 II III 1.5 40 -1 -0.5 0 – Itaipu II – S. Segredo I II III 2 2.5 I I III – Foz do Areia 0.5 Impact of Interactions Among Power System Controls 1 POLE-ZERO MAP OF [Dw/DVREF] Map of poles and zeros for the matrix transfer function [Dw/DVREF] considering only a PSS in Itaipu 15. 15.0% 10.0% 5.0% 11.2 7.5 3.7 -0.1 -4. 41 -2.88 -1.75 Real Impact of Interactions Among Power System Controls -0.63 0.5 ROOT LOCUS WHEN INCREASING THE GAIN OF THE PSS AT ITAIPU Inadequate damping of electromechanical mode; destabilization of the exciter mode Exciter Mode 15. 11.2 Electromechanical Modes 7.5 3.7 -0.1 -4. 42 -2.88 -1.75 Real Impact of Interactions Among Power System Controls -0.63 0.5 POLE PLACEMENT – 2 MODES AND 2 PSSS Improve the damping factors of two critical oscillatory modes by the use of two PSSs installed in: Itaipu The gains of the PSSs are computed for a desired shift in the real part of the eigenvalues Gain vector DK will be calculated at each Newton iteration using the following relation: DK1 DK 2 43 and Salto Segredo DV DVPSS2 PSS 1 , 1 R , 1 Re R DVREF1 DVREF 2 = DVPSS1 D V Re R R PSS2 , 2 , 2 DV DVREF1 REF 2 Impact of Interactions Among Power System Controls 1 D1 Re D2 POLE-ZERO MAP OF [Dw/DVREF]2x2 Map of poles and zeros for the matrix transfer function [Dw/DVREF]2x2 with PSSs in Itaipu and S. Segredo 15. 15.0% 10.0% 5.0% 11.2 7.5 3.7 -0.1 -4. 44 -2.88 -1.75 Real Impact of Interactions Among Power System Controls -0.63 0.5 POLE PLACEMENT – 2 MODES AND 2 PSSS 35. 10.0% 28. KItaipu 5.0% 15.0% =5 KS.Segredo = 91 20.9 z1 = 10.4 % 13.9 z2 = 10.9 % 6.8 -0.2 -4. 27. -2.75 15.0% -1.5 Real 10.0% -0.25 1. 5.0% KItaipu 21.6 KS.Segredo = 29 16.1 z1 = 22.0 % 10.7 5.2 -0.2 -4. 45 = 14 z2 = 13.5 % -2.92 -1.85 Real -0.78 Impact of Interactions Among Power System Controls 0.3 POLE PLACEMENT – 2 MODES AND 2 PSSS 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 the pole placement more convenient pole-zero map Facilitates Number of PSSs differs from the number of poles to be placed pseudo-inverse of a non-square matrix must be computed Algorithm 46 must be modified Impact of Interactions Among Power System Controls PSEUDO-INVERSE ALGORITHM Problems without unique solution pseudo-inverse algorithm Re R m xn DK nx1 = Re D m x1 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 DK 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 ReRDK ReD 47 Impact of Interactions Among Power System Controls POLE PLACEMENT – 2 MODES AND 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 DK 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: DK1 Re R DVPSS1 , R DVPSS2 , R DVPSS3 , 1 1 DV DV DVREF1 1 REF2 REF3 DK 2 = DVPSS3 DVPSS2 DVPSS1 , 2 R , 2 R , 2 DK 3 Re R DVREF2 DVREF3 DVREF1 48 Impact of Interactions Among Power System Controls + D1 Re D2 POLE-ZERO MAP OF [Dw/DVREF]3x3 Map of poles and zeros for the matrix transfer function [Dw/DVREF]3x3 with PSSs in Itaipu, S. Segredo and Foz do Areia 15. 15.0% 10.0% 5.0% 11.2 7.5 3.7 -0.1 -4. 49 -2.88 -1.75 Real Impact of Interactions Among Power System Controls -0.63 0.5 POLE PLACEMENT – 2 MODES AND 3 PSSS 20. 20.0% 15.0% 10.0% 5.0% 15.9 KItaipu = 8.1 KS.Segredo = 11.9 11.9 KFoz do Areia = 12.0 7.9 z1 = 15.9 % 3.8 -0.2 -4. 20. 20.0% -2.92 15.0% -1.85 Real 10.0% -0.77 0.3 5.0% 16. 11.9 = 10.4 KS.Segredo = 16.3 z1 = 22.0 % 3.8 50 KItaipu KFoz do Areia = 16.3 7.9 -0.2 -4. z2 = 15.9 % -2.92 -1.85 Real -0.78 Impact of Interactions Among Power System Controls 0.3 z2 = 21.4 % 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 Practical difficulties with pole placement method Selected locations for the poles may inadvertantly impose severe constraints may not be feasible pole placement may require excessively high values for the PSS gains Results 51 Impact of Interactions Among Power System Controls IMPACT OF INTERACTIONS AMONG POWER SYSTEM CONTROLS SECONDARY VOLTAGE REGULATION: PRELIMINARY STUDY IN THE RIO AREA Coordinated Voltage Control Optimal Vp TVC Vrba Vp SVR PVC Vrbb JVC AVR Pilot Bus Vt E fd bb ba E fd AVR Vt System Time Constants 53 Impact of Interactions Among Power System Controls SCADA SVR: Preliminary Study in Rio Area Participating Power Plants Angra I, Furnas, Santa Cruz, Grajau Pilot Bus JACAREP-138 kV , regulated at 1.0 pu The High Side Voltage Control implemented in more distant plants Marimbondo-500 54 strategy kV, regulated at 1.03 pu Impact of Interactions Among Power System Controls was SVR: Preliminary Study in Rio Area Load Curve for a part of the Rio Area 1050 890 730 570 410 250 55 0 3 6 9 12 15 Time (h) Impact of Interactions Among Power System Controls 18 21 24 SVR: Preliminary Study in Rio Area Voltage profiles for generation and load (pilot) buses 1.06 1.04 1.02 1.00 0.98 0.96 0.94 0.92 0.90 56 0 3 6 VOLT 10 ANGRA----1MQ VOLT 30 SCRUZ19--1MQ VOLT 16 FURNAS---7MQ VOLT 44 GRAJAU---2MQ VOLT 20 MARIMBON-8MQ VOLT 180 JACAREP--138 9 12 15 Time (h) Impact of Interactions Among Power System Controls 18 21 24 FINAL REMARKS Important developments and increased use of modal analysis in power system studies Large-scale, Much room for further improvements Advantages 57 control-oriented eigenanalysis of coordinated voltage control Impact of Interactions Among Power System Controls