1. Masters of Engineering
Small Signal Stability
Aaron Cowan
Electrical Engineering
Power

2. Small Signal Stability
Exciter
Field current
Terminal voltage
Power System Stabilizer
Enhance stability
Rotor angle
Equal Area Criterion (Fig 13.5, Kundur)
Aa < Ad
Aa > Ad

3. SMIB Example
Problem details in section 12.3 of Power System Stability and Control, Kundur

4. Results Kundur ωd = 1.05Hz ξ = 0.15 KS = 0.829 KD = 14.08 Matlab
ξ =
KS =
KD =
State Matrix and eigenvalues agree
0 −0.109 − −0.193 − − − − −1.037 − − −4.840 − −30.303
Δ𝜔𝑟 Δ𝛿 Δ𝜓𝑓𝑑 Δ𝜈1 Δ𝜈2 Δ𝜈𝑠
A =
𝜆2=0.504+𝑗7.23 ←𝑒𝑖𝑔𝑒𝑛𝑣𝑎𝑙𝑢𝑒 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑟𝑜𝑡𝑜𝑟 𝑎𝑛𝑔𝑙𝑒

5. Power World Transient Stability
WECC equivalent in Power World

6. Exciter Models

7. Exciter Models

8. Exciter Models

9. PSS Model

10. IEEE 421.2

11. SMIB – Power World {
Equivalent SMIB
State Matrix
Eigenvalues

12. Power World Transient Stability
WECC equivalent in Power World

13. Stability Simulation Default values used
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

14. Stability Simulation Fault on line 7-5 Three cases for each Exciter
Both breakers open
Cleared in 0.07 sec
Three cases for each Exciter
Each generator
Three cases for each Exciter+PSS

15. Generator 1

16. Generator 1: ESAC1A
𝑀𝑊0=71.6
𝛿0=3.5°
𝑀𝑊𝑐𝑙𝑒𝑎𝑟=70.6
𝛿𝑐𝑙𝑒𝑎𝑟=−5.3°

17. Generator 2

18. Generator 2: ESDC1A
𝑀𝑊0=163
𝛿0=61.1°
𝑀𝑊𝑐𝑙𝑒𝑎𝑟=163
𝛿𝑐𝑙𝑒𝑎𝑟=70.7°

19. Generator 3

20. Generator 3: SEXS_GE
𝑀𝑊0=85
𝛿0=54.1°
𝑀𝑊𝑐𝑙𝑒𝑎𝑟=85
𝛿𝑐𝑙𝑒𝑎𝑟=51.9°

21. Summary Power World Transient Stability ESDC1A without PSS
Block Diagrams
SMIB Eigenvalues
ESDC1A without PSS
SEXS_GE with PSS
PSS stability enhancement

22. Small Signal Stability
Questions?

23. Generator 1: ESDC1A

24. Generator 1: SEXS_GE

25. Generator 2: ESAC1A

26. Generator 2: SEXS_GE

27. Generator 3: ESDC1A

28. Generator 3: ESAC1A