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Statistical reliability of wind power scenarios and stochastic unit commitment cost

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Abstract

Probabilistic wind power scenarios constitute a crucial input for stochastic day-ahead unit commitment in power systems with deep penetration of wind generation. To minimize the cost of implemented solutions, the scenario time series of wind power amounts available should accurately represent the stochastic process for available wind power as it is estimated on the day ahead. The high computational demands of stochastic programming motivate a search for ways to evaluate scenarios without extensively simulating the stochastic unit commitment procedure. The statistical reliability of wind power scenario sets can be assessed by approaches extended from ensemble forecast verification. We examine the relationship between the statistical reliability metrics and the results of stochastic unit commitment when implemented solutions encounter the observed available wind power. Lack of uniformity in a mass transportation distance rank histogram can eliminate scenario sets that might lead to either excessive no-load costs of committed units or high penalty costs for violating energy balance when the committed units are dispatched. Event-based metrics can help to predict results of implementing solutions found with the remaining scenario sets.

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References

  1. Zheng, Q.P.P., Wang, J.H., Liu, A.L.: Stochastic optimization for unit commitment—a review. IEEE Trans. Power Syst. 30(4), 1913–1924 (2015)

    Article  Google Scholar 

  2. Gneiting, T., Balabdaoui, F., Raftery, A.E.: Probabilistic forecasts, calibration and sharpness. J. R. Stat. Soc. B 69, 243–268 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hsu, W.R., Murphy, A.H.: The attributes diagram—a geometrical framework for assessing the quality of probability forecasts. Int. J. Forecast. 2(3), 285–293 (1986). doi:10.1016/0169-2070(86)90048-8

    Article  Google Scholar 

  4. Sari, D., Lee, Y., Ryan, S., Woodruff, D.: Statistical metrics for assessing the quality of wind power scenarios for stochastic unit commitment. Wind Energy 19(5), 873–893 (2016)

    Article  Google Scholar 

  5. Ortega-Vazquez, M.A., Kirschen, D.S.: Assessing the impact of wind power generation on operating costs. IEEE Trans. Smart Grid 1(3), 295–301 (2010)

    Article  Google Scholar 

  6. Ummels, B.C., Gibescu, M., Pelgrum, E., Kling, W.L., Brand, A.J.: Impacts of wind power on thermal generation unit commitment and dispatch. IEEE Trans. Energy Convers. 22(1), 44–51 (2007)

    Article  Google Scholar 

  7. Tuohy, A., Meibom, P., Denny, E., O’Malley, M.: Unit commitment for systems with significant wind penetration. IEEE Trans. Power Syst. 24(2), 592–601 (2009)

    Article  Google Scholar 

  8. Yang, Y.C., Wang, J.H., Guan, X.H., Zhai, Q.Z.: Subhourly unit commitment with feasible energy delivery constraints. Appl. Energ. 96, 245–252 (2012)

    Article  Google Scholar 

  9. Osorio, G.J., Lujano-Rojas, J.M., Matias, J.C.O., Catalao, J.P.S.: A probabilistic approach to solve the economic dispatch problem with intermittent renewable energy sources. Energy 82, 949–959 (2015)

    Article  Google Scholar 

  10. Ortega-Vazquez, M.A., Kirschen, D.S.: Optimizing the spinning reserve requirements using a cost/benefit analysis. IEEE Trans. Power Syst. 22(1), 24–33 (2007)

    Article  Google Scholar 

  11. Ela, E., O’Malley, M.: Studying the variability and uncertainty impacts of variable generation at multiple timescales. IEEE Trans. Power Syst. 27(3), 1324–1333 (2012)

    Article  Google Scholar 

  12. Zhou, Z., Botterud, A., Wang, J., Bessa, R.J., Keko, H., Sumaili, J., Miranda, V.: Application of probabilistic wind power forecasting in electricity markets. Wind Energy 16(3), 321–338 (2013)

    Article  Google Scholar 

  13. Takriti, S., Birge, J.R., Long, E.: A stochastic model for the unit commitment problem. IEEE Trans. Power Syst. 11(3), 1497–1506 (1996)

    Article  Google Scholar 

  14. Bakirtzis, E.A., Biskas, P.N., Labridis, D.P., Bakirtzis, A.G.: Multiple time resolution unit commitment for short-term operations scheduling under high renewable penetration. IEEE Trans. Power Syst. 29(1), 149–159 (2014)

    Article  Google Scholar 

  15. Papavasiliou, A., Oren, S.S.: Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network. Oper. Res. 61(3), 578–592 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wu, H.Y., Shahidehpour, M.: Stochastic SCUC solution with variable wind energy using constrained ordinal optimization. IEEE Trans. Sustain. Energy 5(2), 379–388 (2014)

    Article  Google Scholar 

  17. Madaeni, S.H., Sioshansi, R.: The impacts of stochastic programming and demand response on wind integration. Energy Syst. 4(2), 109–124 (2013). doi:10.1007/s12667-012-0068-7

    Article  Google Scholar 

  18. Bouffard, F., Galiana, F.D.: Stochastic security for operations planning with significant wind power generation. IEEE Trans. Power Syst. 23(2), 306–316 (2008)

    Article  Google Scholar 

  19. Ruiz, P.A., Philbrick, C.R., Zak, E., Cheung, K.W., Sauer, P.W.: Uncertainty management in the unit commitment problem. IEEE Trans. Power Syst. 24(2), 642–651 (2009)

    Article  Google Scholar 

  20. Wang, J.D., Wang, J.H., Liu, C., Ruiz, J.P.: Stochastic unit commitment with sub-hourly dispatch constraints. Appl. Energy 105, 418–422 (2013)

    Article  Google Scholar 

  21. Quan, H., Srinivasan, D., Khambadkone, A.M., Khosravi, A.: A computational framework for uncertainty integration in stochastic unit commitment with intermittent renewable energy sources. Appl. Energy 152, 71–82 (2015)

    Article  Google Scholar 

  22. Ela, E., Milligan, M., O’Malley, M.: A flexible power system operations simulation model for assessing wind integration. In: IEEE Power and Energy Society General Meeting, pp. 1–8. San Diego, CA (2011)

  23. Papavasiliou, A., Oren, S.S., O’Neill, R.P.: Reserve requirements for wind power integration: a scenario-based stochastic programming framework. IEEE Trans. Power Syst. 26(4), 2197–2206 (2011)

    Article  Google Scholar 

  24. Wang, J., Botterud, A., Bessa, R., Keko, H., Carvalho, L., Issicaba, D., Sumaili, J., Miranda, V.: Wind power forecasting uncertainty and unit commitment. Appl. Energy 88(11), 4014–4023 (2011)

    Article  Google Scholar 

  25. Morales, J.M., Minguez, R., Conejo, A.J.: A methodology to generate statistically dependent wind speed scenarios. Appl. Energy 87(3), 843–855 (2010)

    Article  Google Scholar 

  26. Pinson, P., Madsen, H., Nielsen, H.A., Papaefthymiou, G., Klockl, B.: From probabilistic forecasts to statistical scenarios of short-term wind power production. Wind Energy 12(1), 51–62 (2009)

    Article  Google Scholar 

  27. Pinson, P., Girard, R.: Evaluating the quality of scenarios of short-term wind power generation. Appl. Energy 96, 12–20 (2012)

    Article  Google Scholar 

  28. Gneiting, T., Stanberry, L.I., Grimit, E.P., Held, L., Johnson, N.A.: Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds. Test 17(2), 211–235 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  29. Wilks, D.S.: The minimum spanning tree histogram as a verification tool for multidimensional ensemble forecasts. Mon. Weather Rev. 132(6), 1329–1340 (2004)

    Article  Google Scholar 

  30. Gombos, D., Hansen, J.A., Du, J., McQueen, J.: Theory and applications of the minimum spanning tree rank histogram. Mon. Weather Rev. 135(4), 1490–1505 (2007)

    Article  Google Scholar 

  31. Brier, G.W.: Verification of forecasts expressed in terms of probability. Mon. Weather Rev. 78(1), 1–3 (1950). doi:10.1175/1520-0493(1950)078<0001:VOFEIT>2.0.CO;2

    Article  Google Scholar 

  32. Bruninx, K., Dvorkin, Y., Delarue, E., Pandzic, H., D’haeseleer, W., Kirschen, D.S.: Coupling pumped hydro energy storage with unit commitment. IEEE Trans. Sustain. Energy 7(2), 786–796 (2016)

    Article  Google Scholar 

  33. Siface, D., Vespucci, M.T., Gelmini, A.: Solution of the mixed integer large scale unit commitment problem by means of a continuous Stochastic linear programming model. Energy Syst. 5(2), 269–284 (2014). doi:10.1007/s12667-013-0107-z

    Article  Google Scholar 

  34. Bruninx, K.: Bergh, KVd, Delarue, E., D’haeseleer, W.: Optimization and allocation of spinning reserves in a low-carbon framework. IEEE Trans. Power Syst. 31(2), 872–882 (2016). doi:10.1109/TPWRS.2015.2430282

    Article  Google Scholar 

  35. Shukla, A., Singh, S.N.: Clustering based unit commitment with wind power uncertainty. Energy Convers. Manag. 111, 89–102 (2016)

    Article  Google Scholar 

  36. Feng, Y., Ryan, S.M.: Solution sensitivity-based scenario reduction for stochastic unit commitment. CMS 13(1), 29–62 (2016). doi:10.1007/s10287-014-0220-z

    Article  MathSciNet  Google Scholar 

  37. Ji, B., Yuan, X.H., Chen, Z.H., Tian, H.: Improved gravitational search algorithm for unit commitment considering uncertainty of wind power. Energy 67, 52–62 (2014)

    Article  Google Scholar 

  38. Nasri, A., Kazempour, S.J., Conejo, A.J., Ghandhari, M.: Network-constrained AC unit commitment under uncertainty: a Benders’ decomposition approach. IEEE Trans. Power Syst. 31(1), 412–422 (2016)

    Article  Google Scholar 

  39. Cheung, K., Gade, D., Silva-Monroy, C., Ryan, S.M., Watson, J.P., Wets, R.J.B., Woodruff, D.L.: Toward scalable stochastic unit commitment Part 2: solver configuration and performance assessment. Energy Syst. 6(3), 417–438 (2015). doi:10.1007/s12667-015-0148-6

    Article  Google Scholar 

  40. Thorarinsdottir, T.L., Scheuerer, M., Heinz, C.: Assessing the calibration of high-dimensional ensemble forecasts using rank histograms. J. Comput. Graph. Stat. 25(1), 105–122 (2016). doi:10.1080/10618600.2014.977447

    Article  MathSciNet  Google Scholar 

  41. Dupacova, J., Gröwe-Kuska, N., Römisch, W.: Scenario reduction in stochastic programming: an approach using probability metrics. Math. Program. 95(3), 493–511 (2003). doi:10.1007/s10107-002-0331-0

    Article  MathSciNet  MATH  Google Scholar 

  42. Rachev, S.T.: Probability Metrics and the Stability of Stochastic Models. Wiley, New York (1991)

    MATH  Google Scholar 

  43. Rachev, S.T., Rüschendorf, L.: Mass Transportation Problems. Probability and its Applications. Springer, Berlin (1998)

    MATH  Google Scholar 

  44. Feng, Y.H., Rios, I., Ryan, S.M., Spurkel, K., Watson, J.P., Wets, R.J.B., Woodruff, D.L.: Toward scalable stochastic unit commitment. Part 1: load scenario generation. Energy Syst. 6(3), 309–329 (2015). doi:10.1007/s12667-015-0146-8

    Article  Google Scholar 

  45. Bonneville Power Administration: Wind generation and total load in the BPA balancing authority. http://transmission.bpa.gov/Business/Operations/Wind/default.aspx. Accessed 11 Oct 2017

  46. Bonneville Power Administration: Wind power forecasting data. http://www.bpa.gov/Projects/Initiatives/Wind/Pages/Wind-Power-Forecasting-Data.aspx. Accessed 11 Oct 2017

  47. ISO-New England: Zonal information. http://www.iso-ne.com/isoexpress/web/reports/pricing/-/tree/zone-info. Accessed 11 Oct 2017

  48. Royset JO, Wets, R.B.: Nonparametric density estimation via exponential epi-eplines: fusion of soft and hard information (2013). https://www.math.ucdavis.edu/~rjbw/mypage/Statistics_files/RstW13_xspl.pdf

  49. Rios, I., Wets, R.J.-B., Woodruff, D.L.: Multi-period forecasting and scenario generation with limited data. CMS 12(2), 267–295 (2015). doi:10.1007/s10287-015-0230-5

    Article  MathSciNet  MATH  Google Scholar 

  50. Watson, J.-P, Woodruff, D. L.: PYSP user documentation. https://software.sandia.gov/trac/coopr/wiki/PySP. Accessed 11 Oct 2017

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Acknowledgements

This manuscript was prepared under award OG-14-014 from the Iowa Energy Center.

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  1. Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA, 50011-2164, USA

    Didem Sari & Sarah M. Ryan

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  1. Didem Sari
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Correspondence to Sarah M. Ryan.

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Sari, D., Ryan, S.M. Statistical reliability of wind power scenarios and stochastic unit commitment cost. Energy Syst 9, 873–898 (2018). https://doi.org/10.1007/s12667-017-0255-7

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