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

Bismark Singh*, David P. Morton, Surya Santoso

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)563-582
Number of pages20
JournalComputational Management Science
Issue number3-4
StatePublished - Oct 1 2018


  • Chance-constrained optimization
  • Hybrid renewable system
  • Stochastic integer programming
  • Wind power

ASJC Scopus subject areas

  • Business, Management and Accounting (miscellaneous)
  • Management Information Systems
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research


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