On the Fokker-Planck equation for stochastic hybrid systems: Application to a wind turbine model

2006 9th International Conference on Probabilistic Methods Applied to Power Systems, PMAPS

Volumn , Issue , 2006, Pages

  Bect, Julien ^a,b   Phulpin, Yannick ^a,b   Baili, Hana ^a,b   Fleury, Gilles ^a,b  

^a Dept of Signal Processing and Electronic Systems ^*  (France)

^b SUPELEC   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS TIME SYSTEMS; HYBRID SYSTEMS; MARKOV PROCESSES; PROBABILITY DENSITY FUNCTION; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; WHITE NOISE; WIND; WIND TURBINES;

CONTINUOUS TIME MARKOV PROCESS; DYNAMICAL ANALYSIS; GAUSSIAN WHITE NOISE; STATIONARY DISTRIBUTION; STOCHASTIC HYBRID SYSTEMS; SWITCHING CONTROLLERS; VARIABLE-SPEED WIND TURBINE; WIND TURBINE MODELING;

FOKKER PLANCK EQUATION;

EID: 46149111923     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/PMAPS.2006.360298     Document Type: Conference Paper

References (21)

1. A. J. van der Schaft and H. Schumacher, An Introduction to Hybrid Dynamical Systems, ser. LNCIS. Springer-Verlag, 2000, vol. 251.
2. I. A. Hiskens and M. A. Pai, "Hybrid systems view of power system modelling," in IEEE International Symposium on Circuits and Systems, ISCAS 2000, Geneva, Switzerland, May 2000.
3. G. Labinaz, M. M. Bayoumi, and K. Rudie, "A survey of modeling and control of hybrid systems," Annual Reviews in Control, vol. 21, pp. 79-92, 1997.
4. G. Pola, M. Bujorianu, J. Lygeros, and M. D. Benedetto, "Stochastic hybrid models: an overview," in IFAC Conference on the Analysis and Design of Hybrid Systems, June 2003.
5. J. Hu, J.Lygeros, and S. Sastry, "Towards a theory of stochastic hybrid systems," in Hybrid Systems: Computation and Control, Third International Workshop, HSCC 2000, ser. LNCS, N. Lynch and B. H. Krogh, Eds. Springer-Verlag, 2000, pp. 160-173.
6. B. Oksendal, Stochastic Differential Equations. Springer-Verlag, 1985.
7. L. H. R. Alvarez, "Stochastic forest stand value and optimal timber harvesting," SIAM Journal on Control and Optimization, vol. 42, pp. 1972-1993, 2004.
8. A. Dixit, "Entry and exit decisions under uncertainty," Journal of Political Economy, vol. 97, pp. 620-638, 1989.
9. Y. Xu and J. Hespanha, "Communication logics for networked control systems," in Proceedings of the 2004 American Control Conference, June 2004, pp. 572-577.
10. C. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Berlin: Springer-Verlag, 1985.
11. R. Malhamé and C-Y. Chong, "Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system," IEEE Trans. Automat. Contr., vol. 30, no. 9, pp. 854-860, September 1985.
12. J. Beet, H. Baili, and G. Fleury, "Generalized Fokker-Planck equation for piecewise-diffusion processes with boundary hitting resets," 2005, submitted to the 17th International Symposium on the Mathematical Theory of Networks and Systems (MTNS 2006).
13. J. G. Slootweg, H. Polinder, and W. L. Kling, "Representing wind turbine electrical generating systems in fundamental frequency simulations," IEEE Transactions on Energy Conversion, vol. 18, no. 4, pp. 516-524, December 2003.
14. E. Muljadi and C. P. Butterfield, "Pitch-controlled variable-speed wind turbine generation," IEEE Transactions on Industry Applications, vol. 37, pp. 240-246, 2001.
15. C. Nichita, D. Luca, B. Dakyo, and E. Ceanga, "Large band simulation of the wind speed for real time wind turbine simulators," IEEE Transactions on Energy Conversion, vol. 17, no. 4, pp. 523-529, December 2002.
16. E. Welfonder, R. Neifer, and M. Spanner, "Development and experimental identification of dynamic models for wind turbines," Control Engineering Practice, vol. 5, no. 1, pp. 63-73, 1997.
17. P. S. Veers, "Three-dimensional wind simulation," Sandia National Laboratories, Albuquerque, Tech. Rep. SAND88-0152, March 1988.
18. T. Ekelund, "Speed control of wind turbines in the stall region," in Proceedings of the Third IEEE Conference on Control Applications, Glasgow, UK, 1994, pp. 227-232.
19. C. Schütte, W. Huisinga, and S. P. Meyn, "Metastability of diffusion processes," in Proceeding of the IUTAM Symposium on Nonlinear Stochastic Dynamics, 2003.
20. R. Eymard, T. Gallouät, and R. Herbin, Handbook of Numerical Analysis, Vol. VII. North-Holland /Elsevier, 2000, ch. Finite volume methods, pp. 713-1020.
21. R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK User's Guide - Solution of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, ser. SIAM series in software, environments and tools. SIAM, 1998, no. ISBN 0-89871-407-9.