A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs: With Application in Energy Production

This thesis is concerned with the development and implementation of an optimization method for the solution of multistage stochastic mixed-integer programs arising in energy production. Motivated by the strong increase in electricity produced from wind energy, we investigate the question of how energy storages may contribute to integrate the strongly fluctuating wind power into the electric power network. In order to study the economics of energy storages, we consider a power generation system which consists of conventional power plants, different types of energy storages, and an offshore wind park which supplies a region of certain dimension with electrical energy. On this basis, we aim at optimizing the commitment of the facilities over several days minimizing the overall costs. We formulate the problem as a mixed-integer optimization program concentrating on the combinatorial and stochastic aspects. The nonlinearities arising from partial load efficiencies of the units are approximated by piecewise linear functions. In order to account for the uncertainty regarding the fluctuations of the available wind power and of the prices for electricity purchased on the spot market, we describe the affected data via a scenario tree. Altogether, we obtain a stochastic multistage mixed-integer problem (SMIP) of high complexity whose solution is algorithmically and computationally challenging. The main focus of this thesis is on the development of a scenario tree-based decomposition approach combined with a branch-and-bound method (SDBB) for the solution of the SMIP described above. This novel method relies on the decomposition of the original formulation into several subproblems based on the splitting of the scenario tree into subtrees. Using a branchand-bound framework which we extend by Lagrangian relaxation, we can solve the problem to global optimality. In order to support the solution process, we investigate the polyhedral substructure which results from the description of switching processes in a scenario tree formulation yielding