Abstract
In minimization problems with uncertain parameters, cost savings can be achieved by solving stochastic programming (SP) formulations instead of using expected parameter values in a deterministic formulation. To obtain such savings, it is crucial to employ scenarios of high quality. An appealing way to assess the quality of scenarios produced by a given method is to conduct a re-enactment of historical instances in which the scenarios produced are used when solving the SP problem and the costs are assessed under the observed values of the uncertain parameters. Such studies are computationally very demanding. We propose two approaches for assessment of scenario generation methods using past instances that do not require solving SP instances. Instead of comparing scenarios to observations directly, these approaches consider the impact of each scenario in the SP problem. The methods are tested in simulation studies of server location and unit commitment, and then demonstrated in a case study of unit commitment with uncertain variable renewable energy generation.
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References
Ahmed S, Garcia R, Kong N, Ntaimo L, Parija G, Qiu F, Sen S (2015) SIPLIB: a stochastic integer programming test problem library. http://www.isye.gatech.edu/~sahmed/siplib. Accessed 10 Jan 2019
Bakirtzis EA, Biskas PN, Labridis DP, Bakirtzis AG (2014) Multiple time resolution unit commitment for short-term operations scheduling under high renewable penetration. IEEE Trans Power Syst 29:149–159
Bayraksan G, Morton DP (2006) Assessing solution quality in stochastic programs. Math Program 108:495–514. https://doi.org/10.1007/s10107-006-0720-x
Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer series in operations research. Springer, New York
Bruninx K, Delarue E, D‘haeseleer W (2014) A practical approach on scenario generation and reduction algorithms for wind power forecast error scenarios. https://www.mech.kuleuven.be/en/tme/research/energy_environment/Pdf/wp2014-15b.pdf. Accessed 8 Mar 2019
Bruninx K, Bergh KVd, Delarue E, D‘haeseleer W (2016a) Optimization and allocation of spinning reserves in a low-carbon framework. IEEE Trans Power Syst 31:872–882. https://doi.org/10.1109/TPWRS.2015.2430282
Bruninx K, Dvorkin Y, Delarue E, Pandžić H, D’haeseleer W, Kirschen DS (2016b) Coupling pumped hydro energy storage with unit commitment. IEEE Trans Sustain Energy 7:786–796. https://doi.org/10.1109/TSTE.2015.2498555
Du E, Zhang N, Kang C, Xia Q (2018) Scenario map-based stochastic unit commitment. IEEE Trans Power Syst PP:1. https://doi.org/10.1109/tpwrs.2018.2799954
Dupacova J, Gröwe-Kuska N, Römisch W (2003) Scenario reduction in stochastic programming: an approach using probability metrics. Math Program 95:493–511. https://doi.org/10.1007/s10107-002-0331-0
Feng Y, Ryan SM (2016) Solution sensitivity-based scenario reduction for stochastic unit commitment. CMS 13:29–62. https://doi.org/10.1007/s10287-014-0220-z
Feng YH, Rios I, Ryan SM, Spurkel K, Watson JP, Wets RJB, Woodruff DL (2015) Toward scalable stochastic unit commitment. Part 1: load scenario generation. Energy Syst 6:309–329. https://doi.org/10.1007/s12667-015-0146-8
Heitsch H, Römisch W (2003) Scenario reduction algorithms in stochastic programming. Comput Optim Appl 24:187–206. https://doi.org/10.1023/a:1021805924152
Heitsch H, Römisch W (2007) A note on scenario reduction for two-stage stochastic programs. Oper Res Lett 35:731–738. https://doi.org/10.1016/j.orl.2006.12.008
Kaut M, Wallace SW (2007) Evaluation of scenario-generation methods for stochastic programming. Pac J Optim 3:257–271
Lunn AD, Davies SJ (1998) A note on generating correlated binary variables. Biometrika 85:487–490. https://doi.org/10.1093/biomet/85.2.487
Morales JM, Pineda S, Conejo AJ, Carrion M (2009) Scenario reduction for futures market trading in electricity markets. IEEE Trans Power Syst 24:878–888. https://doi.org/10.1109/TPWRS.2009.2016072
Ntaimo L, Sen S (2005) The million-variable “march” for stochastic combinatorial optimization. J Glob Optim 32:385–400. https://doi.org/10.1007/s10898-004-5910-6
Papavasiliou A, Oren SS (2013) Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network. Oper Res 61:578–592
Pinson P, Girard R (2012) Evaluating the quality of scenarios of short-term wind power generation. Appl Energy 96:12–20. https://doi.org/10.1016/j.apenergy.2011.11.004
Pinson P, Madsen H, Nielsen HA, Papaefthymiou G, Klockl B (2009) From probabilistic forecasts to statistical scenarios of short-term wind power production. Wind Energy 12:51–62
Rachev ST (1991) Probability metrics and the stability of stochastic models. Wiley series in probability and mathematical statistics. Applied probability and statistics. Wiley, Chichester
Rios I, Wets RJB, Woodruff DL (2015) Multi-period forecasting and scenario generation with limited data. CMS 12:267–295. https://doi.org/10.1007/s10287-015-0230-5
Sarı D, Ryan S (2016) MTDrh: mass transportation distance rank histogram. https://cran.r-project.org/web/packages/MTDrh/index.html. Accessed 8 Mar 2019
Sarı D, Ryan S (2017) Statistical reliability of wind power scenarios and stochastic unit commitment cost. Energy Syst. https://doi.org/10.1007/s12667-017-0255-7
Sarı D, Lee Y, Ryan S, Woodruff D (2016) Statistical metrics for assessing the quality of wind power scenarios for stochastic unit commitment. Wind Energy 19:873–893
Staid A, Watson J-P, Wets RJB, Woodruff DL (2017) Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators. Wind Energy 20:1911–1925. https://doi.org/10.1002/we.2129
Takriti S, Birge JR, Long E (1996) A stochastic model for the unit commitment problem. IEEE Trans Power Syst 11:1497–1508. https://doi.org/10.1109/59.535691
Wu H, Shahidehpour M (2014) Stochastic SCUC solution with variable wind energy using constrained ordinal optimization. IEEE Trans Sustain Energy 5:379–388. https://doi.org/10.1109/TSTE.2013.2289853
Zheng QPP, Wang JH, Liu AL (2015) Stochastic optimization for unit commitment—a review. IEEE Trans Power Syst 30:1913–1924
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Sarı Ay, D., Ryan, S.M. Observational data-based quality assessment of scenario generation for stochastic programs. Comput Manag Sci 16, 521–540 (2019). https://doi.org/10.1007/s10287-019-00349-1
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DOI: https://doi.org/10.1007/s10287-019-00349-1