Power System Stability

1. Power System Stability

4. ¢ X d I + ¢¢Ð d V =| | EE

5. Fig 12- 4

6. I I 1 2 1 2 + E' E' 1 2 r r

7. P e P max D +) (PP ee 0 Generator Q 0 P e 0 –180º –90º d 90º 180º d 0 d Dd + 0 Motor

12. Fig. 12.11

14. P e d 1.79 sin 1.79 d 1.265 sin 1.265 =1.0 P d 0.694 sin m P 0.694 Q 0 d 33.9º 90º

15. Infinite ¢ X X bus d e + P e ¢ Ðd || E Ð ||0º V

17. Fig 12-16

19. Unstable d d = 0 d t d max Stable 0 t

21. P e c A 2 b P m 1 A 1 a P m 0 p d d d d 0 1 2 w w w w s s > s w w < s

22. P e A 2 b c P m 1 A 1 P a m 0 p d d d d 0 0 1 2

26. Infinite bus P Ð m ||0º V (a) X 1 Ðd ¢ || E ¢ X d Ð Switched off ||0º V P m X 2 (b)

27. P e (both lines in) P e I A 2 d a P m c (line 2 out) P e II b A 1 d d d p d 0 0 1 2

28. X 1 ¢ Ðd || E ¢ X Infinite d bus P Ð m ||0º V X 2 (a) X 1 ¢ Ðd || E ¢ X d P Ð ||0º V m X 2 (b)

30. Fig. 12-29

31. P e P, prefault (2 lines) e I P, postfault (1 line) e III A 2 P m P, during fault e II A 1 p d d d d d 0 0 c 2 max

32. P e , prefault (2 lines) P I e , postfault (1 line) P III e A 2 P m , during fault P II e A 1 d d dd p d 0 = 0 cr 2 max Critical clearing angle

33. P e P e I P A e II 2 P m A P 1 e III d rc d d d d d p 0 max 0 c 2 (Clearing angle) (Angle of reclosure )

34. Fig. 12-33

35. Fig. 12-34

36. Fig. 12-35

37. Fig. 12-36

42. Fig. 12-41

43. Machine 1 is reference (Infinite bus) Machine 2 50º 40º r g e d 30º Machine 3 * 20º 10º 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (0.275s fault cleared at) seconds s e e

46. Fig. 12-45

47. 00915 · ||=12 · =0246 · ||=10 · E V 0154 · P 04 · 04 ·

48. X 12