A Multi-Stage Optimization Approach for Energy Supply Systems With Discrete Design Decisions

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.