# Methodological Concepts for Stochastic Optimization of Electric Power System Operation

Alfred Kalliauer^{*}

The task for optimizing the operation of electric power systems under stochastic parameters often results into a complex mathematical and computational task. Systems consisting of hydro or gas storages or integral contracts belong to stochastic models of general resource allocation under stochastics subject to market price and uncertainty of fuel price and inflow. As an introduction to the Minisymposium an overview of different methodological concepts will be given ranging between LP- and DP-oriented approaches, highlighting the computational aspects. \newline For limitation of the computational effort to a practicable size the complexity of such multidimensional problems is usually treated by approximate solution techniques, whereas approximation is done either in the uncertainty space of the inputs or in the state space of the decisions. At LP-oriented methods this yields the usage of scenario reduction techniques to simplify the nested staircase-like structure of the deterministic equivalent problem, or in case of DP-oriented approaches usually results into Dual-DP-techniques where some kind of approximate representation of the state space, e.g. by “cuts” is used. The comparison of methodological concepts is done in view of their applicability to these special mathematical circumstances and requirements.

Mathematics Subject Classification: 90C15 86C08

Keywords: Stochastic Programming; Energy Systems

Minisymposion: Stochastic Models for Optimization of Electric Power Systems