Small Signal Stability Aaron Cowan Electrical Engineering Power - PowerPoint PPT Presentation

Masters of Engineering Small Signal Stability Aaron Cowan Electrical Engineering Power

Small Signal Stability • Exciter – Field current Field current – Terminal voltage • Power System Stabilizer P S t St bili – Enhance stability – Rotor angle • Equal Area Criterion (Fig 13.5, Kundur) g – A a < A d – A a > A d a d

SMIB Example v _s delta_wr PSS K_4 delta _Tm v_s delta _Psi_fd delta _Te delta _delta 1 K_3 1 V ref V_ref K A K_A K 2 K_2 s T_3.s+1 2*Hs+K_D delta _wr Exciter w_0/s V_ref Field Circuit v_1 K_6 K_1 delta _E_t 1 K_5 T_R.s+1 Voltage Transducer Problem details in section 12.3 of Power System Stability and Control , Kundur

Results Kundur Matlab ω d = 1.05Hz ω d 1.05Hz ω d = 1.21Hz ω d 1.21Hz State Matrix and d ξ = 0.15 ξ = 0.1447 eigenvalues agree K S = 0.829 K S = 1.1062 K D = 14.08 K 14 08 K K D = 15.6306 15 6306 A �

Power World Transient Stability Bus 7 Bus 8 Bus 9 Bus 3 Bus 2 1.016 pu 163 MW 163 MW 85 MW 85 MW 1.025 pu 1.026 pu 1.032 pu 1.025 pu 7 Mvar -11 Mvar 100 MW Bus 5 0.996 pu Bus 6 1.013 pu 35 Mvar 125 MW 50 Mvar 90 MW Bus 4 1.026 pu 30 Mvar Bus1 1.040 pu 72 MW slack 27 Mvar WECC equivalent in Power World

Exciter Models

Exciter Models

Exciter Models

PSS Model

IEEE 421.2

SMIB – Power World { { • Eigenvalues { • Equivalent SMIB l • State Matrix • Eigenvalues

Power World Transient Stability Bus 7 Bus 8 Bus 9 Bus 3 Bus 2 1.016 pu 163 MW 163 MW 85 MW 85 MW 1.025 pu 1.026 pu 1.032 pu 1.025 pu 7 Mvar -11 Mvar 100 MW Bus 5 0.996 pu Bus 6 1.013 pu 35 Mvar 125 MW 50 Mvar 90 MW Bus 4 1.026 pu 30 Mvar Bus1 1.040 pu 72 MW slack 27 Mvar WECC equivalent in Power World

Stability Simulation • Default values used – Did change T R to 0.02 in all cases Did change T to 0 02 in all cases • SEXS_GE and STAB1 ↔ Fig 17.5, Kundur • Set all generator stability models equal – Innumerable permutations

Stability Simulation • Fault on line 7-5 – Both breakers open Both breakers open – Cleared in 0.07 sec • Three cases for each Exciter Th f h E it – Each generator • Three cases for each Exciter+PSS – Each generator

Generator 1

Generator 1: ESAC1A MW vs. Rotor Angle Generator 1 MW vs. Rotor Angle Generator 1 240 220 220 200 200 200 180 180 160 160 140 140 120 120 100 100 80 80 60 60 40 40 20 20 0 0 -20 -20 20 -40 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 g b c f d e MW Terminal_Gen '1' '1' b c d e f g MW Terminal_Gen '1' '1'

Generator 2

Generator 2: ESDC1A MW vs. Rotor Angle Generator 2 MW vs. Rotor Angle Generator 2 210 220 200 210 190 190 200 200 190 180 180 170 170 160 160 150 150 140 140 130 130 120 120 110 110 110 100 100 100 90 90 80 80 70 70 60 60 50 50 40 40 30 30 20 20 10 10 0 0 55 60 65 70 75 80 85 90 95 100 55 60 65 70 75 80 85 90 95 100 d c g f e b MW Terminal_Gen '2' '1' b c d e g f MW Terminal_Gen '2' '1'

Generator 3

Generator 3: SEXS_GE MW vs. Rotor Angle Generator 3 MW vs. Rotor Angle Generator 3 100 95 95 90 90 85 85 80 80 75 75 70 70 70 65 65 60 60 55 55 50 50 45 45 45 47 48 49 50 51 52 53 54 55 56 57 58 59 60 49 50 51 52 53 54 55 56 57 58 59 c b g d f e MW Terminal_Gen '3' '1' c d e f g b MW Terminal_Gen '3' '1'

Summary • Power World Transient Stability – Block Diagrams Block Diagrams – SMIB Eigenvalues • ESDC1A without PSS ESDC1A ith t PSS • SEXS_GE with PSS • PSS stability enhancement

Questions? Small Signal Stability

Generator 1: ESDC1A MW vs. Rotor Angle Generator 1 MW vs Rotor Angle Generator 1 MW vs Rotor Angle Generator 1 MW vs. Rotor Angle Generator 1 200 170 160 180 150 160 140 130 140 120 110 120 100 90 100 80 70 80 60 50 60 40 40 30 20 20 10 0 0 0 -10 -20 -20 -30 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 c b d g f e MW Terminal_Gen '1' '1' b c d e f g MW Terminal_Gen '1' '1'

Generator 1: SEXS_GE MW vs. Rotor Angle Generator 1 MW vs Rotor Angle Generator 1 MW vs. Rotor Angle Generator 1 MW vs Rotor Angle Generator 1 170 180 160 150 160 140 130 140 120 110 120 100 100 100 90 80 80 70 60 60 50 40 40 30 20 20 10 0 0 -10 -20 -20 -30 -25 -20 -15 -10 -5 0 5 10 15 20 -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 g f c d e b MW Terminal_Gen '1' '1' f e d c b g MW Terminal_Gen '1' '1'

Generator 2: ESAC1A MW vs. Rotor Angle Generator 2 MW vs Rotor Angle Generator 2 MW vs Rotor Angle Generator 2 MW vs. Rotor Angle Generator 2 210 220 200 210 200 190 190 180 180 170 170 160 160 150 150 140 140 140 130 130 130 120 120 110 110 100 100 90 90 80 80 70 70 60 60 50 50 40 40 40 40 30 30 20 20 10 10 0 0 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 50 55 60 65 70 75 80 85 90 95 c d e f g b MW Terminal_Gen '2' '1' b c d e f g MW Terminal_Gen '2' '1'

Generator 2: SEXS_GE MW vs. Rotor Angle Generator 2 MW vs. Rotor Angle Generator 2 220 200 210 190 200 180 190 170 180 160 170 150 160 140 150 130 140 130 120 120 110 110 100 100 90 90 80 80 70 70 60 60 50 50 50 40 40 30 30 20 20 10 10 0 0 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 MW Terminal_Gen '2' '1' MW Terminal_Gen '2' '1' b g f e d c g f e c b d

Generator 3: ESDC1A MW vs. Rotor Angle Generator 3 MW vs Rotor Angle Generator 3 MW vs Rotor Angle Generator 3 MW vs. Rotor Angle Generator 3 105 100 100 95 95 90 90 85 85 80 80 80 75 75 70 70 65 65 60 60 55 55 50 50 45 45 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 d c g f e b MW Terminal_Gen '3' '1' b c d f g e MW Terminal_Gen '3' '1'

Generator 3: ESAC1A MW vs. Rotor Angle Generator 3 MW vs. Rotor Angle Generator 3 100 105 95 100 90 95 85 90 85 80 80 80 75 75 70 70 65 65 60 60 55 55 50 50 50 45 45 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 d c g f e b MW Terminal_Gen '3' '1' b c d e f g MW Terminal_Gen '3' '1'