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

SLIDE 1

Masters of Engineering

Small Signal Stability

Aaron Cowan Electrical Engineering Power

SLIDE 2

Small Signal Stability

Exciter

Field current – Field current – Terminal voltage

P S t St bili

Power System Stabilizer

– Enhance stability – Rotor angle

Equal Area Criterion (Fig 13.5, Kundur)

g

– Aa < Ad – Aa > Ad

a d

SLIDE 3

SMIB Example

PSS delta_wr v _s delta _delta delta _Te delta _Psi_fd v_s 1 K_4 K 2 1 K_3 K A V ref delta _Tm delta _wr v_1 V_ref w_0/s 2*Hs+K_D K_6 K_2 K_1 s Field Circuit T_3.s+1 Exciter K_A V_ref delta _E_t Voltage Transducer 1 T_R.s+1 K_5

Problem details in section 12.3 of Power System Stability and Control, Kundur

SLIDE 4

Results

Matlab ωd = 1.21Hz Kundur ωd = 1.05Hz d ωd 1.21Hz ξ = 0.1447 KS = 1.1062 K 15 6306 ωd 1.05Hz ξ = 0.15 KS = 0.829 K 14 08 State Matrix and eigenvalues agree KD = 15.6306 KD = 14.08 A

SLIDE 5

Power World Transient Stability

Bus 2 163 MW Bus 7 Bus 8 Bus 9 Bus 3 85 MW 1.016 pu Bus 5 163 MW 7 Mvar 85 MW

11 Mvar

100 MW 35 Mvar Bus 6 1.026 pu 1.025 pu 0.996 pu 1.032 pu 1.025 pu 1.013 pu Bus 4 125 MW 50 Mvar 90 MW 30 Mvar 1.026 pu slack Bus1 72 MW 27 Mvar 1.040 pu

WECC equivalent in Power World

SLIDE 6

Exciter Models

SLIDE 7

Exciter Models

SLIDE 8

Exciter Models

SLIDE 9

PSS Model

SLIDE 10

IEEE 421.2

SLIDE 11

SMIB – Power World

l

{

Equivalent SMIB
State Matrix
Eigenvalues

{• Eigenvalues {

SLIDE 12

Power World Transient Stability

Bus 2 163 MW Bus 7 Bus 8 Bus 9 Bus 3 85 MW 1.016 pu Bus 5 163 MW 7 Mvar 85 MW

11 Mvar

100 MW 35 Mvar Bus 6 1.026 pu 1.025 pu 0.996 pu 1.032 pu 1.025 pu 1.013 pu Bus 4 125 MW 50 Mvar 90 MW 30 Mvar 1.026 pu slack Bus1 72 MW 27 Mvar 1.040 pu

WECC equivalent in Power World

SLIDE 13

Stability Simulation

Default values used

Did change T to 0 02 in all cases – Did change TR to 0.02 in all cases

SEXS_GE and STAB1 ↔ Fig 17.5, Kundur
Set all generator stability models equal

– Innumerable permutations

SLIDE 14

Stability Simulation

Fault on line 7-5

Both breakers open – Both breakers open – Cleared in 0.07 sec

Th f h E it

Three cases for each Exciter

– Each generator

Three cases for each Exciter+PSS

– Each generator

SLIDE 15

Generator 1

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Generator 1: ESAC1A

MW vs. Rotor Angle Generator 1 220 200 MW vs. Rotor Angle Generator 1 240 220 200 180 160 140 120 100 200 180 160 140 120 100 80 60 40 20

20

80 60 40 20

20

MW Terminal_Gen '1' '1' g f e d c b 25 20 15 10 5

5
10
15
20
25
30
35
40
40

MW Terminal_Gen '1' '1' g f e d c b 20 15 10 5

5
10
15
20
25
30
35
40

20

SLIDE 17

Generator 2

SLIDE 18

Generator 2: ESDC1A

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

SLIDE 19

Generator 3

SLIDE 20

Generator 3: SEXS_GE

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

SLIDE 21

Summary

Power World Transient Stability

Block Diagrams – Block Diagrams – SMIB Eigenvalues

ESDC1A ith t PSS

ESDC1A without PSS
SEXS_GE with PSS
PSS stability enhancement

SLIDE 22

Small Signal Stability

Questions?

SLIDE 23

Generator 1: ESDC1A

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

5
10
15
20
25
30
35
40
45
10
20
30

MW Terminal_Gen '1' '1' g f e d c b 15 10 5

5
10
15
20
25
30
35
40
45
20

SLIDE 24

Generator 1: SEXS_GE

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

5
10
15
20
25
30
20

MW Terminal_Gen '1' '1' g f e d c b 16 14 12 10 8 6 4 2

2
4
6
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10
12
14
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28
30

10

10
20

SLIDE 25

Generator 2: ESAC1A

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

SLIDE 26

Generator 2: SEXS_GE

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

SLIDE 27

Generator 3: ESDC1A

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

SLIDE 28

Generator 3: ESAC1A

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