Skip to main content

Advertisement

SpringerLink
Log in

An adaptive model with joint chance constraints for a hybrid wind-conventional generator system

  • Original Paper
  • Published:
Computational Management Science Aims and scope Submit manuscript

Abstract

We analyze scheduling a hybrid wind-conventional generator system to make it dispatchable, with the aim of profit maximization. Our models ensure that with high probability we satisfy the day-ahead power promised by the model, using combined output of the conventional and wind generators. We consider two scenarios, which differ in whether the conventional generator must commit to its schedule prior to observing the wind-power realizations or has the flexibility to adapt in near real-time to these realizations. We investigate the synergy between the conventional generator and wind farm in these two scenarios. Computationally, the non-adaptive model is relatively tractable, benefiting from a strong extended-variable formulation as an integer program. The adaptive model is a two-stage stochastic integer program with joint chance constraints. Such models have seen limited attention in the literature because of the computational challenges they pose. However, we develop an iterative regularization scheme in which we solve a sequence of sample average approximations under a growing sample size. This reduces computational effort dramatically, and our empirical results suggest that it heuristically achieves high-quality solutions. Using data from a wind farm in Texas, we demonstrate that the adaptive model significantly outperforms the non-adaptive model in terms of synergy between the conventional generator and the wind farm, with expected profit more than doubled.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Ahmed S, Shapiro A (2008) Solving chance-constrained stochastic programs via sampling and integer programming. Tutor Oper Res 10:261–269

    Google Scholar 

  • Arroyo JM, Conejo AJ (2000) Optimal response of a thermal unit to an electricity spot market. IEEE Trans Power Syst 15(3):1098–1104

    Article  Google Scholar 

  • Banos R, Manzano-Agugliaro F, Montoya F, Gil C, Alcayde A, Gómez J (2011) Optimization methods applied to renewable and sustainable energy: a review. Renew Sustain Energy Rev 15(4):1753–1766

    Article  Google Scholar 

  • Baring-Gould EI (2017) Wind/diesel power systems basics and examples. https://www.pembina.org/reports/wind-diesel-power-systems-basics.pdf. Accessed 15 Aug 2017

  • Baringo L, Conejo AJ (2016) Offering strategy of wind-power producer: a multi-stage risk-constrained approach. IEEE Trans Power Syst 31(2):1420–1429

    Article  Google Scholar 

  • Bayraksan G, Morton DP (2011) A sequential sampling procedure for stochastic programming. Oper Res 59:898–913

    Article  Google Scholar 

  • Bertsekas DP (1999) Nonlinear programming. Athena Scientific, Belmont

    Google Scholar 

  • Brown BG, Katz RW, Murphy AH (1984) Time series models to simulate and forecast wind speed and wind power. J Climate Appl Meteorol 23(8):1184–1195

    Article  Google Scholar 

  • Carrión M, Arroyo JM (2006) A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans Power Syst 21(3):1371–1378

    Article  Google Scholar 

  • Damcı-Kurt P, Küçükyavuz S, Rajan D, Atamtürk A (2016) A polyhedral study of production ramping. Math Program 158(1–2):175–205

    Article  Google Scholar 

  • DeMeo EA, Grant W, Milligan MR, Schuerger MJ (2005) Wind plant integration [wind power plants]. IEEE Power Energy Mag 3(6):38–46

    Article  Google Scholar 

  • Deshmukh MK, Deshmukh SS (2008) Modeling of hybrid renewable energy systems. Renew Sustain Energy Rev 12(1):235–249

    Article  Google Scholar 

  • Duran MJ, Cros D, Riquelme J (2007) Short-term wind power forecast based on ARX models. J Energy Eng 133(3):172–180

    Article  Google Scholar 

  • Electric Power Research Institute and Cooperative Research Network of the National Rural Electric Cooperation Association (2003) Costs of utility distributed generators, 1–10 MW: twenty-four case studies. http://www.publicpower.org/files/deed/finalreportcostsofutilitydistributedgenerators.pdf. Accessed 22 Aug 2017

  • Electric Reliability Council of Texas, Inc (2016) Market prices. http://www.ercot.com/mktinfo/prices. Accessed 17 Feb 2016

  • Energy Efficiency and Conservation Authority Energywise (2015) Stand alone power systems (SAPS). http://www.energywise.govt.nz/how-to-be-energy-efficient/generating-renewable-energy-at-home/stand-alone-power-systems. Accessed 22 Aug 2017

  • Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50:987–1007

    Article  Google Scholar 

  • GAMS—The Solver Manuals (2017) OSICPLEX, OSIGUROBI, OSIMOSEK, OSISOPLEX, OSIXPRESS. http://www.gams.com/help/topic/gams.doc/solvers/allsolvers.pdf. Accessed 22 Aug 2017

  • Global Wind Energy Council (GWEC) (2017) Wind in numbers. http://www.gwec.net/global-figures/wind-in-numbers/. Accessed 22 Aug 2017

  • González JS, Rodriguez AGG, Mora JC, Santos JR, Payan MB (2010) Optimization of wind farm turbines layout using an evolutive algorithm. Renew Energy 35(8):1671–1681

    Article  Google Scholar 

  • Halamay DA, Brekken TK, Simmons A, McArthur S (2011) Reserve requirement impacts of large-scale integration of wind, solar, and ocean wave power generation. IEEE Trans Sustain Energy 2(3):321–328

    Article  Google Scholar 

  • Harack B (2010) Electricity grid: Key terms and definitions. http://www.visionofearth.org/industry/electricity-grid-key-terms-and-definitions/#Forms_of_Power_Resources. Accessed 22 Aug 2017

  • Kamal L, Jafri YZ (1997) Time series models to simulate and forecast hourly averaged wind speed in Quetta, Pakistan. Sol Energy 61(1):23–32

    Article  Google Scholar 

  • Kargarian A, Fu Y, Wu H (2016) Chance-constrained system of systems based operation of power systems. IEEE Trans Power Syst 31(5):3404–3413

    Article  Google Scholar 

  • Klotz E, Newman AM (2013) Practical guidelines for solving difficult linear programs. Surv Oper Res Manag Sci 18(1):1–17

    Google Scholar 

  • Küçükyavuz S (2012) On mixing sets arising in chance-constrained programming. Math Program 132(1–2):31–56

    Article  Google Scholar 

  • Li S, Wunsch DC, O’Hair E, Giesselmann MG et al (2001) Using neural networks to estimate wind turbine power generation. IEEE Trans Energy Convers 16(3):276–282

    Article  Google Scholar 

  • Liu X, Küçükyavuz S, Luedtke J (2014) Decomposition algorithms for two-stage chance-constrained programs. Math Program 157:219–243

    Article  Google Scholar 

  • Ljung GM, Box GE (1978) On a measure of lack of fit in time series models. Biometrika 65(2):297–303

    Article  Google Scholar 

  • Luedtke J (2014) A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support. Math Program 146(1–2):219–244

    Article  Google Scholar 

  • Luedtke J, Ahmed S, Nemhauser G (2007) An integer programming approach for linear programs with probabilistic constraints. In: Integer programming and combinatorial optimization. Springer, pp 410–423

  • Miller AJ, Wolsey LA (2003) Tight formulations for some simple mixed integer programs and convex objective integer programs. Math Program 98(1–3):73–88

    Article  Google Scholar 

  • Milligan M, Schwartz M, Wan Y (2003) Statistical wind power forecasting models: results for US wind farms. http://www.nrel.gov/docs/fy03osti/33956.pdf. Accessed 10 Aug 2017

  • Morales JM, Conejo AJ, Pérez-Ruiz J (2010) Short-term trading for a wind power producer. IEEE Trans Power Syst 25(1):554–564

    Article  Google Scholar 

  • Morales-España G, Latorre JM, Ramos A (2013) Tight and compact MILP formulation for the thermal unit commitment problem. IEEE Trans Power Syst 28(4):4897–4908

    Article  Google Scholar 

  • Ostrowski J, Anjos MF, Vannelli A (2012) Tight mixed integer linear programming formulations for the unit commitment problem. IEEE Trans Power Syst 27(1):39–46

    Article  Google Scholar 

  • Ozturk UA, Mazumdar M, Norman B (2004) A solution to the stochastic unit commitment problem using chance constrained programming. IEEE Trans Power Syst 19(3):1589–1598

    Article  Google Scholar 

  • Pan K, Guan Y (2016) Strong formulations for multistage stochastic self-scheduling unit commitment. Oper Res 64(6):1482–1498

    Article  Google Scholar 

  • Pasupathy R (2010) On choosing parameters in retrospective-approximation algorithms for stochastic root finding and simulation optimization. Oper Res 58:889–901

    Article  Google Scholar 

  • Peterseim JH, White S, Tadros A, Hellwig U (2014) Concentrating solar power hybrid plants-enabling cost effective synergies. Renew Energy 67:178–185

    Article  Google Scholar 

  • Pozo D, Contreras J (2013) A chance-constrained unit commitment with an \(n-{K}\) security criterion and significant wind generation. IEEE Trans Power Syst 28(3):2842–2851

    Article  Google Scholar 

  • Prékopa A (1995) Stochastic programming. Kluwer Academic Publishers, Dordrecht

    Book  Google Scholar 

  • Rajan D, Takriti S (2005) Minimum up/down polytopes of the unit commitment problem with start-up costs. https://domino.research.ibm.com/library/cyberdig.nsf/1e4115aea78b6e7c85256b360066f0d4/cdcb02a7c809d89e8525702300502ac0. Accessed 11 Aug 2017

  • Royset JO, Szechtman R (2013) Optimal budget allocation for sample average approximation. Oper Res 61:762–776

    Article  Google Scholar 

  • Schölkopf B, Smola AJ (2002) Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT Press, Cambridge

    Google Scholar 

  • Sen S, Kothari DP (1998) Optimal thermal generating unit commitment: a review. Int J Electr Power Energy Syst 20(7):443–451

    Article  Google Scholar 

  • Tikhonov A (1963) Solution of incorrectly formulated problems and the regularization method. Sov Math Doklady 5:1035–1038

    Google Scholar 

  • Ummels BC, Gibescu M, Pelgrum E, Kling WL, Brand AJ (2007) Impacts of wind power on thermal generation unit commitment and dispatch. IEEE Trans Energy Convers 22(1):44–51

    Article  Google Scholar 

  • Vick BD, Moss TA (2013) Adding concentrated solar power plants to wind farms to achieve a good utility electrical load match. Sol Energy 92:298–312

    Article  Google Scholar 

  • Vrakopoulou M, Margellos K, Lygeros J, Andersson G (2013) A probabilistic framework for reserve scheduling and \({N}-1\) security assessment of systems with high wind power penetration. IEEE Trans Power Syst 28(4):3885–3896

    Article  Google Scholar 

  • Wang Q, Guan Y, Wang J (2012) A chance-constrained two-stage stochastic program for unit commitment with uncertain wind power output. IEEE Trans Power Syst 27(1):206–215

    Article  Google Scholar 

  • Wu H, Shahidehpour M, Li Z, Tian W (2014) Chance-constrained day-ahead scheduling in stochastic power system operation. IEEE Trans Power Syst 29(4):1583–1591

    Article  Google Scholar 

  • Wu L (2011) A tighter piecewise linear approximation of quadratic cost curves for unit commitment problems. IEEE Trans Power Syst 26(4):2581–2583

    Article  Google Scholar 

  • Zhang M, Küçükyavuz S, Goel S (2014) A branch-and-cut method for dynamic decision making under joint chance constraints. Manage Sci 60(5):1317–1333

    Article  Google Scholar 

  • Zhang Y, Wang J, Zeng B, Hu Z (2017) Chance-constrained two-stage unit commitment under uncertain load and wind power output using bilinear benders decomposition. IEEE Trans Power Syst 32:3637–3647

    Article  Google Scholar 

  • Zhao C, Wang Q, Wang J, Guan Y (2014) Expected value and chance constrained stochastic unit commitment ensuring wind power utilization. IEEE Trans Power Syst 29(6):2696–2705

    Article  Google Scholar 

Download references

Acknowledgements

The authors were supported, in part, by the National Science Foundation under ECCS Grant #1162328.

Author information

Authors and Affiliations

  1. Graduate Program in Operations Research and Industrial Engineering, The University of Texas at Austin, Austin, TX, 78712, USA

    Bismark Singh

  2. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, 60208, USA

    David P. Morton

  3. Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, 78701, USA

    Surya Santoso

Authors
  1. Bismark Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David P. Morton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Surya Santoso
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bismark Singh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, B., Morton, D.P. & Santoso, S. An adaptive model with joint chance constraints for a hybrid wind-conventional generator system. Comput Manag Sci 15, 563–582 (2018). https://doi.org/10.1007/s10287-018-0309-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10287-018-0309-x

Keywords

Search

Navigation