Using copulas for modeling stochastic dependence in power system uncertainty analysis

IEEE Transactions on Power Systems

Volumn 24, Issue 1, 2009, Pages 40-49

  Papaefthymiou, George ^a,b   Kurowicka, Dorota ^c  

^a Delft University of Technology ^*  (Netherlands)

^b Ecofys Germany   (Germany)

^c DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Copula; Correlation; Monte Carlo simulation; Stochastic dependence; Stochastic generation; Uncertainty analysis; Wind power

Indexed keywords

ELECTRIC NETWORK ANALYSIS; ELECTRIC POWER TRANSMISSION NETWORKS; MONTE CARLO METHODS; MULTIVARIANT ANALYSIS; POWER TRANSMISSION; RANDOM PROCESSES; RANDOM VARIABLES; RENEWABLE ENERGY RESOURCES; STOCHASTIC SYSTEMS; WIND POWER;

COPULA; CORRELATION; MONTE CARLO SIMULATION; STOCHASTIC DEPENDENCE; STOCHASTIC GENERATION;

UNCERTAINTY ANALYSIS;

EID: 60149085866     PISSN: 08858950     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPWRS.2008.2004728     Document Type: Article

References (21)

1. G. Papaefthymiou, "Integration of stochastic generation in power systems" Ph.D. dissertation, Electrical Power Systems Group (EPS), Delft Univ. Technol., Delft, The Netherlands, 2007. [Online]. Available: http://www.library.tudelft.nl/ws/search/publications/index.htm.
2. G. Papaefthymiou, P. H. Schavemaker, L. van der Sluis, W. L. Kling, D. Kurowicka, and R. M. Cooke, "Integration of stochastic generation in power systems," Elect. Power Energy Syst., vol. 28, pp. 655-667, 2006.
3. G. Giebel, G. Kariniotakis, and R. Brownsword, State of the Art on Short-Term Wind Power Prediction, ANEMOS, Deliverable Report D1.1, 2003. [Online]. Available: http://anemos.cma.fr.
4. P. Pinson, "Estimation of the uncertainty in wind power forecasting" Ph.D. dissertation, Ecole des Mines de Paris, Paris, France, 2006. [Online]. Available: http://pastel.paristech.org/.
5. P. Pinson, G. Papaefthymiou, B. Klöckl, and H. A. Nielsen, "Generation of statistical scenarios of short-term wind power production," in Proc. PowerTech 2007 Conf., Lausanne, Switzerland, Jul. 1-5, 2007.
6. G. Papaefthymiou and P. Pinson, "Modeling of spatial dependence in wind power forecast uncertainty," in Proc. 10th Int. Conf. Probabilistic Methods Applied to Power Systems (PMAPS), Rincon, Puerto Rico, May 25-29, 2008.
7. C. Singh and Y. Kim, "An efficient technique for reliability analysis of power systems including time dependent sources," IEEE Trans. Power Syst., vol. 3, no. 3, pp. 1090-1096, Aug. 1988.
8. A. M. L. da Silva, V. L. Arienti, and R. N. Allan, "Probabilistic load flow considering dependence between input nodal powers," IEEE Trans. Power App. Syst., vol. PAS-103, no. 6, pp. 1524-1530, Jun. 1984.
9. R. N. Allan, A. M. L. da Silva, and R. C. Burchett, "Evaluation methods and accuracy in probabilistic load flow solutions," IEEE Trans. Power App. Syst., vol. PAS-100, no. 5, pp. 2539-2546, May 1981.
10. M. C. Caramanis, R. D. Tabors, K. S. Nochur, and F. C. Schweppe, "The introduction of non-dispatchable technologies as decision variables in long-term generation expansion models," IEEE Trans. Power App. Syst. vol. PAS-101, no. 8, pp. 2658-2666, Aug. 1982.
11. J. A. Bloom, "Probabilistic production costing with dependent generating sources," IEEE Trans. Power App. Syst., vol. PAS-104, no. 8, pp. 2064-2070, Aug. 1985.
12. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, ser. Electrical and Computer Engineering, 4th ed. New York: McGraw-Hill, 2002.
13. R. B. Nelsen, An Introduction to Copulas. New York: Springer, 1999.
14. A. Sklar, "Fonctions de répartition á n dimensions et leurs marges," Publications de l'Institut de Statistique de L'Université de Paris, vol. 8, pp. 229-231, 1959.
15. H. Joe, Multivariate Models and Dependence Concepts. London, U.K.: Chapman & Hall, 1997.
16. D. Kurowicka and R. M. Cooke, Uncertainty Analysis With High Dimensional Dependence Modelling, ser. Probability and Statistics. New York: Wiley, 2006.
17. S. Ghosh and S. Henderson, "Properties of the notra method in higher dimensions," in Proc. 2002 Winter Simulation Conf., 2002, pp. 263-269.
18. R. Rebonato and P. Jäckel, "The most general methodology to create a valid correlation matrix for risk management and option pricing purposes," J. Risk, vol. 2, no. 2, pp. 17-28, 1999.
19. P. Embrechts, A. McNeil, and D. Straumann, "Correlation and dependence in risk management: Properties and pitfalls," Risk Manage.: Value at Risk and Beyond, pp. 176-223, 2002.
20. Royal Netherlands Meteorological Institute (KNMI), HYDRA Project: Wind Climate Assessment of The Netherlands, 2006. [Online]. Available: http:// www.knmi.nl/samenw/hydra.
21. P. Nørgaard and H. Holttinen, "A multi-turbine power curve approach,: in Proc. Nordic Wind Power Conf. (NWPC2004), Gothenburg, Sweden, Mar. 1-2, 2004.