Energy Systems

, Volume 2, Issue 3, pp 209–242

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

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

DOI: 10.1007/s12667-011-0042-9

Cite this article as:
Jin, S., Ryan, S.M., Watson, JP. et al. Energy Syst (2011) 2: 209. doi:10.1007/s12667-011-0042-9

Abstract

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.

Keywords

Generation expansion planningStochastic programmingScenario generationMultiple replication procedureSolution stability

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Shan Jin
    • 1
  • Sarah M. Ryan
    • 1
  • 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