Energy Systems

, Volume 2, Issue 3–4, pp 209–242 | Cite as

Modeling and solving a large-scale generation expansion planning problem under uncertainty

  • Shan Jin
  • Sarah M. RyanEmail author
  • Jean-Paul Watson
  • David L. Woodruff
Original Paper


We formulate a generation expansion planning problem to determine the type and quantity of power plants to be constructed over each year of an extended planning horizon, considering uncertainty regarding future demand and fuel prices. Our model is expressed as a two-stage stochastic mixed-integer program, which we use to compute solutions independently minimizing the expected cost and the Conditional Value-at-Risk; i.e., the risk of significantly larger-than-expected operational costs. We introduce stochastic process models to capture demand and fuel price uncertainty, which are in turn used to generate trees that accurately represent the uncertainty space. Using a realistic problem instance based on the Midwest US, we explore two fundamental, unexplored issues that arise when solving any stochastic generation expansion model. First, we introduce and discuss the use of an algorithm for computing confidence intervals on obtained solution costs, to account for the fact that a finite sample of scenarios was used to obtain a particular solution. Second, we analyze the nature of solutions obtained under different parameterizations of this method, to assess whether the recommended solutions themselves are invariant to changes in costs. The issues are critical for decision makers who seek truly robust recommendations for generation expansion planning.


Generation expansion planning Stochastic programming Scenario generation Multiple replication procedure Solution stability 



Support for this work at Iowa State University was provided by its Electric Power Research Center. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94-AL85000. The Sandia and University of California Davis authors were funded in part by the Department of Energy’s Office of Science.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Shan Jin
    • 1
  • Sarah M. Ryan
    • 1
    Email author
  • Jean-Paul Watson
    • 2
  • David L. Woodruff
    • 3
  1. 1.Department of Industrial and Manufacturing Systems EngineeringIowa State UniversityAmesUSA
  2. 2.Discrete Math and Complex Systems DepartmentSandia National LaboratoriesAlbuquerqueUSA
  3. 3.Graduate School of ManagementUniversity of California DavisDavisUSA

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