Mixed integer linear programming is frequently applied to identify promising design solutions of energy supply systems. However, application-relevant optimization models are often associated with complicating model features, e.g. numerous discrete design candidates or a large time horizon of the optimization. So, even state-of-the-art solvers may be confronted with major challenges to find satisfying solutions within reasonable time. In this paper a systematic multi-stage optimization approach is proposed that is intended to support the available algorithms in solving these complex problems. The basic idea of the approach is the distribution of the original problem into two major levels. On the first level, promising design candidates are generated using simplified optimization models. These simplifications are achieved through time series aggregation and the relaxation of operational binary variables. In the second stage, the objective values of the design candidates for the original problem are determined. The division of the problem into two stages leads to a significant reduction in required optimization time but simultaneously leads to an uncertainty regarding the quality of the found solution. Therefore, in a subsequent step, it is checked whether the objective value is within an acceptable distance from the theoretically best solution. If this is not the case, the first two steps are iteratively repeated. The proposed multi-stage approach is applied to the optimization of an energy supply system located in Germany. The results show a superior performance regarding required optimization time over conventional methods.

Energy system optimization models are typically large models which combine sub-models which range from linear to very nonlinear. Column generation (CG) is a classical tool to generate feasible solutions of sub-models, defining columns of global master problems, which are used to steer the search for a global solution. In this paper, we present a new inner approximation method for solving energy system MINLP models. The approach is based on combining CG and the Frank Wolfe algorithm for generating an inner approximation of a convex relaxation and a primal heuristic for computing solution candidates. The features of this approach are: (i) no global branch-and-bound tree is used, (ii) sub-problems can be solved in parallel to generate columns, which do not have to be optimal, nor become available at the same time to synchronize the solution, (iii) an arbitrary solver can be used to solve sub-models, (iv) the approach (and the implementation) is generic and can be used to solve other nonconvex MINLP models. We perform experiments with decentralized energy supply system models with more than 3000 variables. The numerical results show that the new decomposition method is able to compute high-quality solutions and has the potential to outperform state-of-the-art MINLP solvers.