Invited Session Mon.3.MA 550

Monday, 15:15 - 16:45 h, Room: MA 550

Cluster 18: Optimization in energy systems [...]

Stochastic optimization for electricity production and trading


Chair: Raimund M. Kovacevic



Monday, 15:15 - 15:40 h, Room: MA 550, Talk 1

Densing Martin
Multistage stochastic optimization of power dispatch and multiperiod duality of CVaR

Coauthor: János Mayer


We consider cost-optimization models of power production in the context of mean-risk multi-stage stochastic optimization problems. We introduce the concept of occupation times to reduce the size of the scenario tree in a finite setting in time and states. In terms of financial risk measurement, we apply multiperiod extensions of the risk measure Conditional-Value-at-Risk (CVaR), which is widely used in applications due to its coherency properties. We show a time-consistent generalization to multiple periods that applies CVaR-like measures recursively over the time periods and compare with other extensions. In terms of modeling, we discuss how financial futures may reduce risk and how demand can be incorporated in the proposed framework. Numerical results are presented.
%This is a joint work with János Mayer, Department of Business Administration, University of Zurich.



Monday, 15:45 - 16:10 h, Room: MA 550, Talk 2

Georg Pflug
Stochastic bilevel programs with applications to electricity contracts

Coauthor: Raimund Kovacevic


We describe a typical contracting situation for flexible energy contracts as a bilevel stochastic program: The upper level sets the price and the lower level sets the execution pattern.
Bilevel programs are hard nonconvex global problems and typically no polynomial algorithms exist. We present however some solution algorithms, including stochastic quasigradient methods, penalty methods and line search methods.
We give illustrative examples for electricity swing option pricing, but remark that the very same type of problems appears in insurance pricing (adverse selection and moral hazard) as well as in terrorism modeling.



Monday, 16:15 - 16:40 h, Room: MA 550, Talk 3

Bita Analui
Multistage stochastic optimization problems under model ambiguity


A multistage stochastic optimization problem with uncertainty about the underlying model is considered. In this paper and for the first time we introduce and develop an approach that explicitly takes into account the ambiguity in probability model for the real world class of multistage stochastic optimization problems where the robustness of the decisions are highly expected. This is done by developing the concept of ambiguity of dynamic trees for multistage stochastic optimization problems incorporating the results from multistage distance. In the presence model ambiguity one approach is to study a set of possible models in which the true model sits. In this line, we define this set as an ε-radius (for the given ε) ball around a reference measure P with respect to a multistage distance d and therefore robustify the original problem by a worst case approach with respect to this ambiguity neighborhood. This way we analyze the sensitivity with respect to model changes. For implementation, we consider an optimization horizon with weekly discretization, the uncertainty is the random behavior of electricity spot prices.


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