# Applying Mixed Integer Linear Programming to Stochastic Medium Term Optimization of Thermal and Hydro Power Systems

Walter Reinisch^{*} and Willibald Kritscha

With the rising uncertainty in renewable electricity production the necessity rises to consider these uncertainties in the medium term planning process of electric power systems. The main hurdle to take is the trade-off between calculation effort and accuracy of the mathematical model with respect to the level of detail of the technical power system constraints as well as the number of scenarios used to describe the uncertainties. \newline In this work a solution for stochastic optimization is presented, which employs Mixed Integer Linear Programming for modeling the power systemâ€™s technical constraints. The solution covers the entire workflow of the optimization procedure, starting with scenario generation of independent or correlated scenarios. These scenarios are further converted to a scenario tree, which is the base for the stochastic MILP optimization. This MILP optimization is then tuned for the trade-off between calculation performance and model accuracy. \newline Since this trade-off very much depends on the respective power system, two real-world examples are considered to analyze the limits of applicability of the MILP approach. A hydraulic power system and a thermal power system is examined with consideration of those constraints that are of particular interest in power system operation, like minimum power or minimum up-time of thermal units.

Mathematics Subject Classification: 90C15

Keywords: stochastic optimization; mixed integer linear programming; electric power systems

Minisymposion: Stochastic Models for Optimization of Electric Power Systems