Original Paper

Energy Systems

, Volume 2, Issue 3, pp 209-242

First online:

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

  • Shan JinAffiliated withDepartment of Industrial and Manufacturing Systems Engineering, Iowa State University
  • , Sarah M. RyanAffiliated withDepartment of Industrial and Manufacturing Systems Engineering, Iowa State University Email author 
  • , Jean-Paul WatsonAffiliated withDiscrete Math and Complex Systems Department, Sandia National Laboratories
  • , David L. WoodruffAffiliated withGraduate School of Management, University of California Davis

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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