eeh power systemslaboratory

In the present master thesis, three different algorithms, for optimizing a medium-term hydro-power planning problem with consideration of stochastic values, are presented and compared. The uncertainty arises due to varying water inflows and uncertain evolution of prices. The solution methods yield robust control strategies, which indicate for every time step, e.g. every month in one year, the optimal amount of energy to turbine and pump. A power plant with a single reservoir, that is able to turbine and pump, is considered. The stochastic processes are modelled using samples from estimated probability density functions for every time step. The stochastic linear programming, represents the stochastics in a scenario tree, consisting of a selection of possible stochastic evolutions with corresponding probabilities, and optimizes it using a standard solver for linear programs. The other two methods stochastic dynamic programming and stochastic dual dynamic programming are based on the principle of optimality by Bellman. The maximization problem is reformulated into a recursive form which results in a problem of finding so called profit-to-go functions. It is shown, that stochastic dynamic programming and stochastic linear programming are subject to the curse of dimensionality, so for multi-reservoir systems, the method stochastic dual dynamic programming is more suitable, since it approximates the profit-to-go functions using dual solutions. The methods are compared in different case studies. Exemplarily, the robustness of the optimizations is demonstrated. The results of all methods seem plausible and show only little deviation from the solution with perfect information. However, for more complex systems, the methods based on dynamic programming are clearly superior, both in run-time and the possibilities of inclusion of the stochastic processes. Furthermore, it is shown that control reserves are easily integrated in an optimization if they are expressed as a dynamic program and it is explained why the results from stochastic dual dynamic programming are inaccurate. The stochastic dynamic programming however yields good results. In the concluding chapter, the most important advantages and drawbacks of the methods are listed.