1. Stabilization of Multimachine Power Systems by Decentralized Feedback Control Zhi-Cheng Huang Department of Communications, Navigation and Control Engineering National Taiwan Ocean University 1

2. Outline Introduction Decentralized controller design Illustrative example Conclusions 2

3. Introduction State-dependent impulse disturbance will be investigated Direct feedback linearization compensator will be proposed Boundedness of the system states will be guaranteed within the derived impulse intervals 3

4. Decentralized controller design n synchronous machines Mechanical equations 4

5. Decentralized controller design Salient-pole synchronous generator Generator electrical dynamics 5

6. Decentralized controller design Electrical equations 6

7. The compensated multimachine power system model where 7 Decentralized controller design

8. DFL compensating law except for the point (which is not in the normal working region for a generator) where 8

9. Generalized uncertain DFL compensated model where known real constant matrices and controllable real time-varying parameter uncertainties interaction terms unknown nonlinearity constant with values either 1 or 0 9 Decentralized controller design

10. Assumption 1. (System Matrix Uncertainties) with Lebesgue measurable element 10

11. Decentralized controller design Assumption 2. (Interaction functions) with Lebesgue measurable element 11

12. Assumption 3. (impulse disturbance) where the effect of state changing with 12 Decentralized controller design

13. An Illustrative Example A three-machine example system is chosen to demonstrate the effectiveness of the proposed nonlinear decentralized controller 13

14. An Illustrative Example The excitation control input limitations The generator #3 is an infinite bus and use the generator as the reference 14

15. System parameters G1G2 1.8632.36 0.2570.319 0.1290.110.55 1.712 0.53 6.97.960.6 H (s)45.1314.159 53 11 15 An Illustrative Example

16. A three-machine power system 16

17. An Illustrative Example The DFL compensated model for the generators #1 and #2 17

18. An Illustrative Example with 18

19. An Illustrative Example Assume 19

20. An Illustrative Example the DFL compensated power system model will be globally asymptotically stable by the linear local state feedback 20

21. 21 An Illustrative Example

22. Fig. 1. The state responses with finite number of impulse disturbances 22

23. An Illustrative Example 23

24. An Illustrative Example 24

25. Conclusions The problem of decentralized control of multimachine power systems with state-jump disturbances has been explored A new synthesis algorithm for the direct feedback linearization compensator has been proposed Sufficient conditions have been derived such that the decentralized practical stability can be guaranteed The states of the uncertain multimachine power systems with equidistant or periodic impulse disturbance will attract into a bounded ball 25

26. Q&A

27. The End Thanks for your Attention 27