This work focuses on calculating the amount of control reserve, which can be provided by a pool of renewable power plants on the next day. The power forecast of wind and solar power plants depends on the weather forecast, which always contains errors. A merger of individual plants at different locations is advantageous in order to reduce the overall forecast error. Still, the amount of control reserve needs to be determined with a high level of reliability. For the calculation, a probabilistic approach based on historical and current weather data is chosen. In order to model the spatial dependencies of the forecast errors between individual plants, R-vine copulas are used. In the copula theory, R-vine copulas provide high accuracy in modelling the dependency of stochastic variables. The methodology is validated and compared to three alternative approaches with a use case of 32 wind and solar plants. The calculated amount of control reserve provided and the achieved reliability proves to be superior to alternative approaches. Additionally, the required reliability level is varied to investigate the impact on the amount of control reserve, which can be offered with the pool.

References

1. 1)
  - 9. Díaz, G., Casielles, P.G., Coto, J.: ‘Simulation of spatially correlated wind power in small geographic areas – sampling methods and evaluation’, Int. J. Electr. Power Energy Syst., 2014, 63, pp. 513–522.
2. 2)
  - 7. Hagspiel, S., Papaemannouil, A., Schmid, M., et al: ‘Copula-based modeling of stochastic wind power in Europe and implications for the Swiss power grid’, Appl. Energy, 2012, 96, pp. 33–44.
3. 3)
  - 1. Katzenstein, W., Fertig, E., Apt, J.: ‘The variability of interconnected wind plants’, Energy. Policy, 2010, 38, (8), pp. 4400–4410.
4. 4)
  - 10. Díaz, G.: ‘A note on the multivariate Archimedean dependence structure in small wind generation sites’, Wind Energy, 2014, 17, (8), pp. 1287–1295.
5. 5)
  - 27. Aas, K., Czado, C., Frigessi, A., et al: ‘Pair-copula constructions of multiple dependence’, Insur.: Math. Econ., 2009, 44, (2), pp. 182–198.
6. 6)
  - 21. Wang, S., Zhang, X., Liu, L.: ‘Multiple stochastic correlations modeling for microgrid reliability and economic evaluation using pair-copula function’, Int. J. Electr. Power Energy Syst., 2016, 76, pp. 44–52.
7. 7)
  - 6. Papaefthymiou, G., Kurowicka, D.: ‘Using copulas for modeling stochastic dependence in power system uncertainty analysis’, Trans. Power Syst., 2009, 24, (1), pp. 40–49.
8. 8)
  - 31. Genest, C., Favre, A.-C.: ‘Everything you always wanted to know about copula modeling but were afraid to ask’, J. Hydrol. Eng., 2007, 12, (4), pp. 347–368.
9. 9)
  - 8. Louie, H.: ‘Evaluation of bivariate Archimedean and elliptical copulas to model wind power dependency structures’, Wind Energy, 2014, 17, (2), pp. 225–240.
10. 10)
  - 16. Grothe, E.O., Schnieders, J.: ‘Spatial dependence in wind and optimal wind power allocation: a copula-based analysis’, Energy. Policy., 2011, 39, (9), pp. 4742–4754.
11. 11)
  - 2. Juban, J., Siebert, N., Kariniotakis, G.N.: ‘Probabilistic short-term wind power forecasting for the optimal management of wind generation’. IEEE Lausanne Power Tech, Lausanne, 2007, pp. 683–688.
12. 12)
  - 11. Li, Y., Li, W., Xie, K.: ‘Modelling wind speed dependence in system reliability assessment using copulas’, IET Renew. Power Gener., 2012, 6, (6), pp. 392–399.
13. 13)
  - 32. Kendall, M.G.: ‘Rank correlation methods’ (Hafner Publishing Co., Oxford, England, 1955, 2nd edn.).
14. 14)
  - 22. Wu, W., Wang, K., Han, B., et al: ‘A versatile probability model of photovoltaic generation using pair copula construction’, IEEE Trans. Sustain. Energy, 2015, 6, (4), pp. 1337–1345.
15. 15)
  - 25. Ohsenbrügge, A.: ‘Dynamic strategies for amount and reliability of control reserve in future smart grids’. 27th International Conference on Environmental Informatics for Environmental Protection, Sustainable Development and Risk Management, EnviroInfo 2013, Hamburg, Germany, September 2–4, 2013, pp. 230–236.
16. 16)
  - 18. Wang, Z., Shen, C., Liu, F.: ‘A conditional model of wind power forecast errors and its application in scenario generation’, Appl. Energy, 2018, 212, pp. 771–785.
17. 17)
  - 19. Wang, Z., Wang, W., Liu, C., et al: ‘Probabilistic forecast for multiple wind farms based on regular vine copulas’, IEEE Trans. Power Syst., 2018, 33, (1), pp. 578–589.
18. 18)
  - 14. Hu, W., Min, Y., Zhou, Y., et al: ‘Wind power forecasting errors modelling approach considering temporal and spatial dependence’, J. Mod. Power Syst. Clean Energy, 2017, 5, (3), pp. 489–498.
19. 19)
  - 12. Li, Y., Xie, K., Hu, B.: ‘Copula-ARMA model for multivariate wind speed and its applications in reliability assessment of generating systems’, J. Electr. Eng. Technol., 2013, 8, (3), pp. 421–427.
20. 20)
  - 23. Vasilj, J., Sarajcev, P., Jakus, D.: ‘Estimating future balancing power requirements in wind–PV power system’, Renew. Energy, 2016, 99, (C), pp. 369–378.
21. 21)
  - 24. Hu, B., Li, Y., Yang, H., et al: ‘Wind speed model based on kernel density estimation and its application in reliability assessment of generating systems’, J. Modern Power Syst. Clean Energy, 2017, 5, (2), pp. 220–227.
22. 22)
  - 34. Jacovides, C., Tymvios, F., Assimakopoulos, V., et al: ‘Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation’, Renew. Energy, 2006, 31, (15), pp. 2492–2504.
23. 23)
  - 5. Papaefthymiou, G., Pinson, P.: ‘Modeling of spatial dependence in wind power forecast uncertainty’. Proc. of the 10th Int. Conf. on Probablistic Methods Applied to Power Systems, Rincon, 2008, pp. 1–9.
24. 24)
  - 30. Huang, Y., Xu, Q., Jiang, X., et al: ‘Modelling correlated forecast error for wind power in probabilistic load flow’, Elektron. Elektrotech., 2017, 23, (5), pp. 61–66.
25. 25)
  - 3. Doherty, R., O'Malley, M.: ‘A new approach to quantify reserve demand in systems with significant installed wind capacity’, IEEE Trans. Power Syst., 2005, 20, (2), pp. 587–595.
26. 26)
  - 28. Juban, J., Fugon, L., Kariniotakis, G.N.: ‘Probabilistic short-term wind power forecasting based on kernel density estimators’. European Wind Energy Conf. and Exhibition, EWEC, Milan, Italy, 2007.
27. 27)
  - 17. Wang, Y., Zhang, N., Kang, C., et al: ‘An efficient approach to power system uncertainty analysis with high-dimensional dependencies’, IEEE Trans. Power Syst., 2018, 33, (3), pp. 2984–2994.
28. 28)
  - 29. Baldauf, M., Förstner, J.: ‘Kurze beschreibung des lokal-modells kürzestfrist COSMO-DE (LMK) und seiner datenbanken auf dem datenserver des DWD’ (Deutscher Wetterdienst, Offenbach, 2016). Available at https://www.dwd.de/SharedDocs/downloads/DE/modelldokumentationen/nwv/cosmo_de/cosmo_de_dbbeschr_version_2_4_161124.pdf?__blob=publicationFile&v=4.
29. 29)
  - 33. Klucher, T.M.: ‘Evaluation of models to predict insolation on tilted surfaces’, Sol. Energy, 1979, 23, (2), pp. 111–114.
30. 30)
  - 4. Zhang, N., Kang, C., Xia, Q., et al: ‘Modeling conditional forecast error for wind power in generation scheduling’, IEEE Trans. Power Syst., 2014, 29, (3), pp. 1316–1324.
31. 31)
  - 15. Valizadeh Haghi, H., Lotfifard, S.: ‘Spatiotemporal modeling of wind generation for optimal energy storage sizing’, IEEE Trans. Sustain. Energy, 2015, 6, (1), pp. 113–121.
32. 32)
  - 26. Nelson, R.: ‘An Introduction to copulas’ (Ser. Springer Series in Statistics, Springer, 2006).
33. 33)
  - 20. Munkhammar, J., Widén, J.: ‘Copula correlation modeling of aggregate solar irradiance in spatial networks’. 6th Solar Integration Workshop, Vienna, Austria, November 2016.
34. 34)
  - 13. Cao, J., Yan, Z.: ‘Probabilistic optimal power flow considering dependences of wind speed among wind farms by pair-copula method’, Int. J. Electr. Power Energy Syst., 2017, 84, pp. 296–307.

Probabilistic power forecast of renewable distributed generation for provision of control reserve using vine copulas

References

Related content