Stochastic Models and Algorithms for the Optimal Operation of a Dispersed Generation System under Uncertainty

Due to the impending renewal of generation capacities and present decisions concerning energy policy, dispersed generation systems become more and more important. The optimal operation of such a system and corresponding trading activities are substantially influenced by uncertainty and require powerful optimization techniques. We present expectation-based as well as risk-averse stochastic mixedinteger linear optimization models using risk measures and dominance constraints. Two case studies show the benefit of stochastic optimization in power generation and the superiority of tailored solution methods over standard solvers.

[1]  Rüdiger Schultz,et al.  On deviation measures in stochastic integer programming , 2005, Oper. Res. Lett..

[2]  J. Neumann,et al.  Theory of Games and Economic Behavior. , 1945 .

[3]  Rüdiger Schultz,et al.  Conditional Value-at-Risk in Stochastic Programs with Mixed-Integer Recourse , 2006, Math. Program..

[4]  N. Hatziargyriou,et al.  LESSONS LEARNED: EUROPEAN PILOT INSTALLATIONS FOR DISTRIBUTED GENERATION - AN OVERVIEW BY THE IRED CLUSTER , 2006 .

[5]  G. Gross,et al.  Short-term load forecasting , 1987, Proceedings of the IEEE.

[6]  Hendrik Neumann,et al.  Optimal operation of dispersed generation under uncertainty using mathematical programming , 2006 .

[7]  Rüdiger Schultz,et al.  Risk Aversion via Excess Probabilities in Stochastic Programs with Mixed-Integer Recourse , 2003, SIAM J. Optim..

[8]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[9]  Rüdiger Schultz,et al.  Stochastic programming with integer variables , 2003, Math. Program..

[10]  Rüdiger Schultz,et al.  Stochastic Programs with First-Order Dominance Constraints Induced by Mixed-Integer Linear Recourse , 2008, SIAM J. Optim..

[11]  René Henrion,et al.  Stability and Sensitivity of Optimization Problems with First Order Stochastic Dominance Constraints , 2007, SIAM J. Optim..

[12]  Frank Uphaus,et al.  Objektorientiertes Betriebsführungssystem zur Koordinierung dezentraler Energieumwandlungsanlagen , 2006 .

[13]  Darinka Dentcheva,et al.  Optimization with Stochastic Dominance Constraints , 2003, SIAM J. Optim..

[14]  J. Neumann,et al.  Theory of Games and Economic Behavior. , 1945 .

[15]  Josef Hadar,et al.  Rules for Ordering Uncertain Prospects , 1969 .

[16]  Rüdiger Schultz,et al.  Second-Order Stochastic Dominance Constraints Induced by Mixed-Integer Linear Recourse , 2007 .

[17]  Peter C. Fishburn,et al.  Utility theory for decision making , 1970 .

[18]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[19]  Gábor Rudolf,et al.  Relaxations of linear programming problems with first order stochastic dominance constraints , 2006, Oper. Res. Lett..

[20]  Christoph Helmberg,et al.  A spectral bundle method with bounds , 2002, Math. Program..

[21]  A. Ruszczynski,et al.  Portfolio optimization with stochastic dominance constraints , 2006 .