Data reduction for mixed integer linear programming in complex energy systems

The task of optimally designing and scheduling energy systems with a high share of renewable energies is complex and computationally demanding. A widespread method for tackling this task is to apply mixed integer linear programming (MILP). Even though the branch-and-bound algorithms used for solving these programs have seen significant improvements in the last years, many problems cannot be solved without further time series aggregation (TSA) methods. State of the art approaches tackle TSA by using well known machine learning techniques to cluster yearly input data to typical periods. However, latter algorithms are usually evaluated by indicators on the performance of the algorithms themselves rather than the MILP optimization model. Furthermore, the selection of the optimal number of typical periods is commonly a subjective imposition of thresholds on these performance indicators. The issue of computational effort is eased by this generally accepted algorithm, but is still limited by the size of the problem, especially the number of integer decisions. This paper aims at proposing a algorithm for systematically reducing the input data for MILP optimization models and choosing the appropriate size. Contrary to most existing studies, the focus is on the impact on the objective function as well as the integer decision rather than on the quality of the clustering algorithm. The subject is addressed by exploiting the two-stage character of optimal design and scheduling of the system by sequentially performing k-medoids clustering. The demonstration of the algorithm on two case studies shows that a few typical periods are sufficient to achieve near optimal decisions. Multi objective optimization (MOO) is performed to assess the quality of the data reduction. The proposed approach is outperforming state of the art algorithms for TSA by reducing CPU time of more than 40%. The case study furthermore reveals that the runtime of the MOO can be reduced by approximately 90% while diverting less than 2 % on Pareto optimal solutions.