A Probabilistic Approach to Small Signal Stability Analysis of Power Systems with Correlated Wind Sources

- Journal title : Journal of Electrical Engineering and Technology
- Volume 8, Issue 6, 2013, pp.1605-1614
- Publisher : The Korean Institute of Electrical Engineers
- DOI : 10.5370/JEET.2013.8.6.1605

Title & Authors

A Probabilistic Approach to Small Signal Stability Analysis of Power Systems with Correlated Wind Sources

Yue, Hao; Li, Gengyin; Zhou, Ming;

Yue, Hao; Li, Gengyin; Zhou, Ming;

Abstract

This paper presents a probabilistic methodology for small signal stability analysis of power system with correlated wind sources. The approach considers not only the stochastic characteristics of wind speeds which are treated as random variables with Weibull distributions, while also the wind speed spatial correlations which are characterized by a correlation matrix. The approach based on the 2m+1 point estimate method and Cornish Fisher expansion, the orthogonal transformation technique is used to deal with the correlation of wind farms. A case study is carried out on IEEE New England system and the probabilistic indexes for eigenvalue analysis are computed from the statistical processing of the obtained results. The accuracy and efficiency of the proposed method are confirmed by comparing with the results of Monte Carlo simulation. The numerical results indicate that the proposed method can actually capture the probabilistic characteristics of mode properties of the power systems with correlated wind sources and the consideration of spatial correlation has influence on the probability of system small signal stability.

Keywords

Small signal stability;Probabilistic analysis;Correlated wind sources;Point estimate method;

Language

English

Cited by

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References

1.

V. Akhmatov, "Analysis of dynamic behaviour of electric power systems with large amount of wind power," Electric Power Engineering, Orsted-DTU, Technical University of Denmark, Kgs. Lyngby, 2003.

2.

J. G. Slootweg and W. L. Kling, "The impact of large scale wind power generation on power system oscillations," Electric Power Systems Research, vol. 67, pp. 9-20, 2003.

3.

A. Mendonca and J. A. P. Lopes, "Impact of large scale wind power integration on small signal stability," in Future Power Systems, 2005 International Conference on, 2005, pp. 1-5.

4.

D. Gautam, V. Vittal, and T. Harbour, "Impact of Increased Penetration of DFIG-Based Wind Turbine Generators on Transient and Small Signal Stability of Power Systems," Power Systems, IEEE Transactions on, vol. 24, pp. 1426-1434, 2009.

5.

S. Q. Bu, W. Du, H. F. Wang, Z. Chen, L. Y. Xiao, and H. F. Li, "Probabilistic Analysis of Small-Signal Stability of Large-Scale Power Systems as Affected by Penetration of Wind Generation," Power Systems, IEEE Transactions on, vol. 27, pp. 1-9, 2011.

6.

J. M. Morales, L. Baringo, A. J. Conejo, and R. Minguez, "Probabilistic power flow with correlated wind sources," Generation, Transmission & Distribution, IET, vol. 4, pp. 641-651, 2010.

7.

B. Haibo and W. Hua, "A Stochastic Response Surface Method for Probabilistic Evaluation of the Voltage Stability Considering Wind Power," Proceedings of the CSEE, vol. 32, pp. 77-85,194, 2012.

8.

K. Xie and R. Billinton, "Considering wind speed correlation of WECS in reliability evaluation using the time-shifting technique," Electric Power Systems Research, vol. 79, pp. 687-693, 2009.

9.

B. Borkowska, "Probabilistic Load Flow," Power Apparatus and Systems, IEEE Transactions on, vol. PAS-93, pp. 752-759, 1974.

10.

R. C. Burchett and G. T. Heydt, "Probabilistic Methods For Power System Dynamic Stability Studies," Power Apparatus and Systems, IEEE Transactions on, vol. PAS-97, pp. 695-702, 1978.

11.

Z. Xu, Z. Y. Dong, and P. Zhang, "Probabilistic small signal analysis using Monte Carlo simulation," in Power Engineering Society General Meeting, 2005. IEEE, 2005, pp. 1658-1664 Vol. 2.

12.

C. Wang, L. Shi, L. Wang, and Y. Ni, "Modelling Analysis in Power System Small Signal Stability with Grid-connected Wind Farms of DFIG Type," Wind Engineering, vol. 32, pp. 243-264, 2008.

13.

J. L. Rueda, D. G. Colome, and I. Erlich, "Assessment and Enhancement of Small Signal Stability Considering Uncertainties," Power Systems, IEEE Transactions on, vol. 24, pp. 198-207, 2009.

14.

H. M. Zein El-Din and R. T. H. Alden, "Second order eigenvalue sensitivities applied to power system dynamics," Power Apparatus and Systems, IEEE Transactions on, vol. 96, pp. 1928-1936, 1977.

15.

E. Rosenblueth, "Point estimates for probability moments," in Proceedings of National Academy of Science of United States of America, 1975, pp. 3812-3814.

16.

M. E. Harr, "Probabilistic estimates for multivariate analyses," Applied Mathematical Modelling, vol. 13, pp. 313-318, 1989.

17.

H. H.P, "An efficient point estimate method for probabilistic analysis," Reliability Engineering and System Safety, vol. 59, pp. 261-267, 1998.

18.

J. M. Morales, and J. Perez-Ruiz, "Point Estimate Schemes to Solve the Probabilistic Power Flow," Power Systems, IEEE Transactions on, vol. 22, no. 4, pp. 1594-1601, 2007.

19.

P. Caramia, G. Carpinelli, and P. Varilone, "Point estimate schemes for probabilistic three-phase load flow," Electric Power Systems Research, vol. 80, no. 2, pp. 168-175, 2010.

20.

E. A. Cornish and R. A. Fisher, "Moments and cumulants in the specification of distributions," Revue de l'Institut International de Statistique, pp. 307-320, 1937.

21.

H. Holttinen, "Hourly wind power variations in the Nordic countries," WIND ENERGY, vol. 8, pp. 173-195, 2005.

22.

National Renewable Energy Laboratory (NERL). Wind Integration Datasets [Online]. Available: http://www.nrel.gov/wind/integrationdatasets/

23.

D. J. Vowles, C. Samarasinghe, M. J. Gibbard, and G. Ancell, "Effect of wind generation on small-signal stability - A New Zealand Example," in Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, 2008 IEEE, 2008, pp. 1-8.

24.

F. Milano, "An Open Source Power System Analysis Toolbox," Power Systems, IEEE Transactions on, vol. 20, pp. 1199-1206, 2005.

25.

M. Yamamoto and O. Motoyoshi, "Active and reactive power control for doubly-fed wound rotor induction generator," Power Electronics, IEEE Transactions on, vol. 6, pp. 624-629, 1991.

26.

J. Usaola, "Probabilistic load flow with wind production uncertainty using cumulants and Cornish-Fisher expansion," International Journal of Electrical Power & Energy Systems, vol. 31, pp. 474-481, 2009.

27.

M. A. Pai, Energy function analysis for power system stability, 1989.