Generation of multivariate scenario trees to model stochasticity in power management

2005 IEEE Russia Power Tech, PowerTech

Volumn , Issue , 2005, Pages

  Heitsch, Holger ^a   Römisch, Werner ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Power management; Scenario reduction; Scenario tree construction; Stochastic programming

Indexed keywords

DECISION TREES; ELECTRICITY; ENERGY MANAGEMENT; PROBABILITY; PROBABILITY DISTRIBUTIONS; RISK ANALYSIS; RISK MANAGEMENT; SET THEORY; STOCHASTIC MODELS; STREAM FLOW;

POWER MANAGEMENT; SCENARIO REDUCTION; SCENARIO TREE CONSTRUCTION; SCENARIO TREES;

STOCHASTIC PROGRAMMING;

EID: 51549100420     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/PTC.2005.4524696     Document Type: Conference Paper

References (34)

1. Bacaud, L., Lemaŕechal, C., Renaud, A., Sagastiźabal, C.: Bundle methods in stochastic optimal power management: A disaggregated approach using preconditioners. Computational Optimization and Applications 20 (2001), 227-244.
2. Chiralaksanakul, A., Morton, D.P.: Assessing policy quality in multistage stochastic programming, Manuscript, University of Texas at Austin, 2003.
3. Carpentier, P., Cohen, G., Culioli, J.-C., Renaud, A.: Stochastic optimization of unit commitment: a new decomposition framework, IEEE Transactions on Power Systems 11 (1996), 1067-1073.
4. Casey, M., Sen, S.: The scenario generation algorithm for multistage stochastic linear programming, Mathematics of Operations Research (to appear).
5. Consigli, G.; Dempster, M.A.H.: Dynamic stochastic programming for dynamic asset-liability management, Annals of Operations Research 81 (1998), 131-161.
6. Dupačov́a, J., Consigli, G., Wallace, S.W.: Scenarios for multistage stochastic programs, Annals of Operations Research 100 (2000), 25-53.
7. Dupačov́a, J., Gr̈owe-Kuska, N., R̈omisch, W.: Scenario reduction in stochastic programming: An approach using probability metrics, Mathematical Programming Ser. A 95 (2003), 493-511.
8. Edirisinghe, N.: Bounds-based approximations in multistage stochastic programming, Annals of Operations Research 85 (1999), 103-127.
9. Escudero, L.F., de la Fuente, J.L., Garcia, C., Prieto, F.J.: Hydropower generation management under uncertainty via scenario analysis and parallel computation, IEEE Transactions on Power Systems 11 (1996), 683-689.
10. S.-E. Fleten, S.W. Wallace and W.T. Ziemba: Hedging electricity portfolios via stochastic programming, in [12], pp. 71-94.
11. Frauendorfer, K.: Barycentric scenario trees in convex multistage stochastic programming, Mathematical Programming Ser. B, 75 (1996), 277-293.
12. Greenberg, C., Ruszczýnski, A., eds., Decision Making Under Uncertainty. Energy and Power, IMA Volumes in Mathematics and its Applications Vol. 128, Springer, New York 2002.
13. Gr̈owe-Kuska, N., Heitsch, H., R̈omisch, W.: Scenario reduction and scenario tree construction for power management problems, IEEE Bologna Power Tech Proceedings (A. Borghetti, C.A. Nucci, M. Paolone eds.), 2003.
14. Gr̈owe-Kuska, N., R̈omisch, W.: Stochastic unit commitment in hydrothermal power production planning, in: Applications of Stochastic Programming (S.W.Wallace, W.T. Ziemba eds.), MPS-SIAM Series in Optimization (to appear).
15. Heitsch, H., R̈omisch, W.: Scenario reduction algorithms in stochastic programming, Computational Optimization and Applications 24 (2003), 187-206.
16. Heitsch, H., R̈omisch, W.: Scenario tree modelling for multistage stochastic programs, in preparation.
17. Heitsch, H., R̈omisch,W., Strugarek, S.: Stability of multistage stochastic programs, Preprint, Humboldt-University Berlin, 2005.
18. Hochreiter, R., Pflug, G.: Scenario tree generation as a multidimensional facility location problem, AURORA Technical Report, Department of Statistics, University of Vienna, 2002.
19. Høyland, K., Wallace, S.W.: Generating scenario trees for multi-stage decision problems, Management Science 47 (2001), 295-307.
20. Høyland, K., Kaut, M., Wallace, S.W.: A heuristic for moment-matching scenario generation, Computational Optimization and Applications 24 (2003), 169-185.
21. Infanger, G.: Planning under uncertainty: Solving large-scale stochastic linear programs, Boyd & Fraser Publishing company, 1994.
22. Kaut, M., Wallace, S.W.: Evaluation of scenario-generation methods for stochastic programming, Stochastic Programming E-Print Series 14-2003 (〈www.speps.info〉).
23. Pennanen, T.: Epi-convergent discretizations of multistage stochastic programs via integration quadratures, Stochastic Programming E-Print Series 19-2004 (〈www.speps.info〉).
24. M.V.F. Pereira and L.M.V.G. Pinto: Multi-stage stochastic optimization applied to energy planning, Mathematical Programming 52 (1991), 359-375.
25. Pflug, G.: Scenario tree generation for multiperiod financial optimization by optimal discretization, Mathematical Programming, Ser. B 89 (2001), 251-271.
26. Philpott, A.B., Craddock, M., Waterer, H.: Hydro-electric unit commitment subject to uncertain demand, European Journal of Operational Research 125 (2000), 410-424.
27. Rachev, S. T., R̈uschendorf, L.: Mass Transportation Problems, Vol. I and II, Springer, Berlin 1998.
28. R̈omisch, W.: Stability of stochastic programming problems, Chapter 8 in [29], 483-554.
29. Ruszczýnski, A., Shapiro, A., eds.: Stochastic Programming, Handbooks of Operations Research and Management Science, Vol. 10, Elsevier, Amsterdam, 2003.
30. Schm̈oller, H.: Modellierung von Unsicherheiten bei der mittelfristigen Stromerzeugungs- und Handelsplanung, Dissertation, RWTH Aachen, 2005.
31. Shapiro, A.: Inference of statistical bounds for multistage stochastic programming problems, Mathematical Methods of Operations Research 58 (2003), 57-68.
32. Takriti, S., Birge, J.R., Long, E.: A stochastic model for the unit commitment problem, IEEE Transactions on Power Systems 11 (1996), 1497-1508.
33. Wallace, S.W., Fleten, S.-E.: Stochastic programming models in energy, Chapter 10 in [29], 637-677.
34. Weber, C.: Uncertainty in the electric power industry: Methods and models for decision support, Springer, New York, 2004.