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
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)
Gneiting, T., Balabdaoui, F., Raftery, A.E.: Probabilistic forecasts, calibration and sharpness. J. R. Stat. Soc. B 69, 243–268 (2007)
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
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)
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)
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)
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)
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)
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)
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)
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)
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)
Takriti, S., Birge, J.R., Long, E.: A stochastic model for the unit commitment problem. IEEE Trans. Power Syst. 11(3), 1497–1506 (1996)
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)
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)
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)
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
Bouffard, F., Galiana, F.D.: Stochastic security for operations planning with significant wind power generation. IEEE Trans. Power Syst. 23(2), 306–316 (2008)
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)
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)
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)
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)
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)
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)
Morales, J.M., Minguez, R., Conejo, A.J.: A methodology to generate statistically dependent wind speed scenarios. Appl. Energy 87(3), 843–855 (2010)
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)
Pinson, P., Girard, R.: Evaluating the quality of scenarios of short-term wind power generation. Appl. Energy 96, 12–20 (2012)
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)
Wilks, D.S.: The minimum spanning tree histogram as a verification tool for multidimensional ensemble forecasts. Mon. Weather Rev. 132(6), 1329–1340 (2004)
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)
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
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)
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
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
Shukla, A., Singh, S.N.: Clustering based unit commitment with wind power uncertainty. Energy Convers. Manag. 111, 89–102 (2016)
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
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)
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)
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
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
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
Rachev, S.T.: Probability Metrics and the Stability of Stochastic Models. Wiley, New York (1991)
Rachev, S.T., Rüschendorf, L.: Mass Transportation Problems. Probability and its Applications. Springer, Berlin (1998)
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
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
Bonneville Power Administration: Wind power forecasting data. http://www.bpa.gov/Projects/Initiatives/Wind/Pages/Wind-Power-Forecasting-Data.aspx. Accessed 11 Oct 2017
ISO-New England: Zonal information. http://www.iso-ne.com/isoexpress/web/reports/pricing/-/tree/zone-info. Accessed 11 Oct 2017
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
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
Watson, J.-P, Woodruff, D. L.: PYSP user documentation. https://software.sandia.gov/trac/coopr/wiki/PySP. Accessed 11 Oct 2017
Acknowledgements
This manuscript was prepared under award OG-14-014 from the Iowa Energy Center.
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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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DOI: https://doi.org/10.1007/s12667-017-0255-7
Keywords
- Wind power scenarios
- Stochastic unit commitment
- Reliability
- Scenario generation