Journal of Electrical Engineering and Technology

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지
DOI QR코드

DOI QR Code

Copula-ARMA Model for Multivariate Wind Speed and Its Applications in Reliability Assessment of Generating Systems

  • Li, Yudun (School of Electrical Engineering, Chongqing University) ;
  • Xie, Kaigui (State Key Laboratory of Power Transmission Equipment & System Security, School of Electrical Engineering, Chongqing University) ;
  • Hu, Bo (School of Electrical Engineering, Chongqing University)
  • Received : 2012.06.18
  • Accepted : 2012.10.23
  • Published : 2013.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

The dependence between wind speeds in multiple wind sites has a considerable impact on the reliability of power systems containing wind energy. This paper presents a new method to generate dependent wind speed time series (WSTS) based on copulas theory. The basic feature of the method lies in separating multivariate WSTS into dependence structure and univariate time series. The dependence structure is modeled through the use of copulas, which, unlike the cross-correlation matrix, give a complete description of the joint distribution. An autoregressive moving average (ARMA) model is applied to represent univariate time series of wind speed. The proposed model is illustrated using wind data from two sites in Canada. The IEEE Reliability Test System (IEEE-RTS) is used to examine the proposed model and the impact of wind speed dependence between different wind regimes on the generation system reliability. The results confirm that the wind speed dependence has a negative effect on the generation system reliability.

Keywords

References

  1. F. C. Sayas and R. N. Allan, "Generation Availability Assessment of Wind Farms," IEE Proc. Generation, Transmission, and Distribution, Vol. 143, No. 5, pp. 507-518, Sep. 1996 https://doi.org/10.1049/ip-gtd:19960488
  2. S. H. Karaki, B. A. Salim, and R. B. Chedid, "Probabilistic Model of A Two-Site Wind Energy Conversion System," IEEE Trans. on Energy Conversion, Vol. 17, No. 4, pp. 530-536, Dec. 2002 https://doi.org/10.1109/TEC.2002.805215
  3. L. Wu, J. Park, J. Choi, and A. A. EI-Keib, "Probabilistic Reliability Evaluation of Power Systems Including Wind Turbine Generators Considering Wind Speed Correlation," Journal of Electrical Engineering & Technology, Vol. 4, No. 4, pp. 485- 491, Sep. 2009 https://doi.org/10.5370/JEET.2009.4.4.485
  4. W. Wangdee, R. Billinton, "Considering Load-Carrying Capability and Wind Speed Correlation of WECS in Generation Adequacy Assessment," IEEE Trans. on Energy Conversion, Vol. 21, No, 3, pp. 734-741, Sep. 2006 https://doi.org/10.1109/TEC.2006.875475
  5. R. Billinton, Y. Gao, and R.Karki, "Composite System adequacy Assessment Incorporating Large-Scale Wind Energy Conversion Systems Considering Wind Speed Correlation," IEEE Trans. on Power Systems, Vol. 24, No. 3, pp.1375-1382, Aug. 2009. https://doi.org/10.1109/TPWRS.2009.2023263
  6. Y. Gao and R. Billinton, "Adequacy Assessment of Generating Systems Containing Wind Power Considering Wind Speed Correlation," IET Renewable. Power Generation, Vol. 3, No. 2, pp. 217-226. Jun. 2009. https://doi.org/10.1049/iet-rpg:20080036
  7. K. Xie and R. Billiton, "Considering Wind Speed Correlation of WECS in Reliability Evaluation Using the Time-Shifting Technique," Electric Power System Research, Vol. 79, No. 4, pp. 687-693, Dec. 2009. https://doi.org/10.1016/j.epsr.2008.10.013
  8. U. Cherubini, E. Luciano, and W. Vecchiato, Copula Methods in Finance. England: John Wiley & Sons Ltd., 2004.
  9. J. Crook and F. Moreira, "Checking for Asymmetric Default Dependence in A Credit Card Portfolio-A Copula Approach," Journal of Empirical Finance, Vol. 18, No. 4, pp.728-742, Sep.2011. https://doi.org/10.1016/j.jempfin.2011.05.005
  10. S. Grimaldia and F. Serinaldi, "Asymmetric Copula in Multivariate Flood Frequency Analysis," Advances in Water Resources, Vol. 29, No. 8, pp. 1155-1167, Aug. 2006. https://doi.org/10.1016/j.advwatres.2005.09.005
  11. B. Klein, M. Pahlow, Y. Hundecha, and A. Schumann, "Probability Analysis of Hydrological Loads for The Design of Flood Control Systems Using Copulas," Journal of Hydrologic Engineering, Vol. 15, No. 5, pp. 360-369, May.2010. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000204
  12. B. Stephen, S. J. Galloway, D. McMillan, D. C. Hill, and D. G. Infield ,"A Copula Model of Wind Turbine Performance," IEEE Trans. on Power Systems, Vol. 26, No. 2, pp. 965-966, May. 2011. https://doi.org/10.1109/TPWRS.2010.2073550
  13. S. Gill, B. Stephen, and S. Galloway, "Wind Turbine Condition Assessment Through Power Curve Copula Modeling, " IEEE Trans. on Sustainable Energy, Vol. 3, No. 1, pp. 94-101, Jan. 2012. https://doi.org/10.1109/TSTE.2011.2167164
  14. Reliability Test System Task Force of the Application of Probability Methods Subcommittee, "A reliability test system," IEEE Trans. on Power Apparatus and Systems, Vol. 98, No. 6, pp. 2047-2054, Nov. 1979.
  15. R. Billinton and W. Li, Reliability assessment of electrical power systems using Monte Carlo methods. New York and London: Plenum, 1994
  16. R. B. Nelsen, "An Introduction to Copulas, 2nd Ed. New York: Springer Science & Business Media Inc, 2006.
  17. H. Joe, Multivariate Models and Dependence Concepts. New York and London :Chapman & Hall, 1997.
  18. R. Billinton, H. Chen, and R. Ghajar, "Time-Series Models for Reliability Evaluation of Power Systems Including Wind Energy," Microelectronics Reliability, Vol. 36, No. 9, pp. 1253-1261, May. 1996. https://doi.org/10.1016/0026-2714(95)00154-9

Cited by

  1. Residual-based copula parameter estimation vol.29, pp.1, 2016, https://doi.org/10.5351/KJAS.2016.29.1.267
  2. Correlation Characteristic Analysis for Wind Speed in Different Geographical Hierarchies vol.10, pp.2, 2017, https://doi.org/10.3390/en10020237
  3. Reliability models of wind farms considering wind speed correlation and WTG outage vol.119, 2015, https://doi.org/10.1016/j.epsr.2014.10.016
  4. Ordinal Optimization Theory Based Planning for Clustered Wind Farms Considering the Capacity Credit vol.10, pp.5, 2015, https://doi.org/10.5370/JEET.2015.10.5.1930
  5. Variability assessment and forecasting of renewables: A review for solar, wind, wave and tidal resources vol.44, 2015, https://doi.org/10.1016/j.rser.2014.12.019
  6. Estimation for the Capacity Value of PV and Wind Plants Considering Output Correlation vol.141, 2017, https://doi.org/10.1016/j.egypro.2017.11.011
  7. Stochastic Model for Estimating Extreme Water Level in Port and Coastal Engineering Design vol.17, pp.4, 2018, https://doi.org/10.1007/s11802-018-3558-y
  8. Power system security assessment with high wind penetration using the farms models based on their correlation vol.12, pp.8, 2018, https://doi.org/10.1049/iet-rpg.2017.0386