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Risk neutral and risk averse power optimization in electricity networks with dispersed generation

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Abstract

Models and algorithms for risk neutral and risk averse power optimization under uncertainty are presented. The approach differs from previous ones by incorporating the transmission network explicitly.

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References

  • Anderson EJ, Philpott AB (2002) Optimal offer construction in electricity markets. Math Oper Res 27: 82–100

    Article  MATH  MathSciNet  Google Scholar 

  • Anderson EJ, Xu H (2002) Necessary and sufficient conditions for optimal offers in electricity markets. SIAM J Control Optim 41: 1212–1228

    Article  MATH  MathSciNet  Google Scholar 

  • Andersson G (2004) Modelling and analysis of electric power systems. Lecture 227-0526-00, Power Systems Laboratory, ETH Zürich

  • CPLEX Interactive Optimizer 9.1.3, ILOG (1997–2005)

  • ddsip (2004) C package for the dual decomposition of stochastic programs with mixed-integer recourse. University of Duisburg-Essen, Department of Mathematics

  • Gollmer R, Nowak MP, Römisch W, Schultz R (2000) Unit commitment in power generation—a basic model and some extensions. Ann Oper Res 96: 167–189

    Article  MATH  Google Scholar 

  • Handschin E (1987) Elektrische Energieübertragungssysteme, vol 2. Hüthig-Verlag, Auflage

    Google Scholar 

  • Handschin E, Neise F, Neumann H, Schultz R (2006) Optimal operation of dispersed generation under uncertainty using mathematical programming. Int J Electrical Power Energy Syst 28: 618–626

    Article  Google Scholar 

  • Helmberg C, Kiwiel KC (2002) A spectral bundle method with bounds. Math Program 93: 173–194

    Article  MATH  MathSciNet  Google Scholar 

  • Müller A, Stoyan D (2002) Comparison methods for stochastic models and risks. Wiley, New York

    MATH  Google Scholar 

  • Nowak MP, Römisch W (2000) Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Ann Oper Res 100: 251–272

    Article  MATH  MathSciNet  Google Scholar 

  • Nowak MP, Schultz R, Westphalen M (2005) A stochastic integer programming model for incorporating day-ahead trading of electricity into hydro-thermal unit commitment. Optim Eng 6: 163–176

    Article  MATH  MathSciNet  Google Scholar 

  • Nürnberg R, Römisch W (2002) A two-stage planning model for power scheduling in a hydro-thermal system under uncertainty. Optim Eng 3: 355–378

    Article  MATH  MathSciNet  Google Scholar 

  • Philpott AB, Schultz R (2006) Unit commitment in electricity pool markets. Math Program 108: 313–337

    Article  MATH  MathSciNet  Google Scholar 

  • PowerWorld Simulator, PowerWorld Corporation, October 2005

  • Schultz R (2003) Stochastic programming with integer variables. Math Program 97: 285–309

    MATH  MathSciNet  Google Scholar 

  • Schultz R, Neise F (2007) Algorithms for mean-risk stochastic integer programs in energy. Rev Investig Oper 28: 4–16

    MathSciNet  Google Scholar 

  • Schultz R, Tiedemann S (2003) Risk aversion via excess probabilities in stochastic programs with mixed-integer recourse. SIAM J Optim 14: 115–138

    Article  MATH  MathSciNet  Google Scholar 

  • Schultz R, Tiedemann S (2006) Conditional value-at-risk in stochastic programs with mixed-integer recourse. Math Program 105: 365–386

    Article  MATH  MathSciNet  Google Scholar 

  • Sheble GB, Fahd GN (1996) Unit commitment literature synopsis. IEEE Trans Power Syst 11: 1497–1508

    Article  Google Scholar 

  • Takriti S, Birge JR, Long E (1996) A stochastic model for the unit commitment problem. IEEE Trans Power Syst 11: 1497–1508

    Article  Google Scholar 

  • Takriti S, Krasenbrink B, Wu LS-Y (2000) Incorporating fuel constraints and electricity spot prices into the stochastic unit commitment problem. Oper Res 48: 268–280

    Article  Google Scholar 

  • Wallace SW, Fleten S-E (2003) Stochastic programming models in energy. In: Ruszczyński A, Shapiro A(eds) Handbooks in operations research and management science. Stochastic programming, vol 10. Elsevier, Amsterdam, pp 637–688

    Google Scholar 

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Correspondence to Rüdiger Schultz.

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Kuhn, S., Schultz, R. Risk neutral and risk averse power optimization in electricity networks with dispersed generation. Math Meth Oper Res 69, 353–367 (2009). https://doi.org/10.1007/s00186-008-0264-3

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  • DOI: https://doi.org/10.1007/s00186-008-0264-3

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