Optimizing Annual-Coupled Energy Systems with Sequential Time Dependencies in a Two-Stage Algorithm

Abstract

The use of mathematical methods in simulation and optimization models is widely spread to solve the current and future problems of an efficient and sustainable energy supply. Especially MILP is commonly used for industrial and municipal energy systems, where hourly resolved demand profiles are addressed in the time frame of one year in a quasi-stationary optimization. Certain technical or regulatory circumstances make necessitate considering all time steps in one coupled optimization problem. This results in a level of model complexity where today's solvers often struggle to find a solution within a reasonable timeframe. Application examples are annual maximum runtime restrictions or finding the optimum loading strategy of a seasonal storage. Regulatory examples in Germany include the full-load hour restricted CHP-surcharge, the high-efficiency-criterion or the maximum emission of a CO2-Budget which lead to an annual integral limitation. In this work, we present a two-stage approach with a simplified year-round-coupled first stage and a fully resolved second stage with a rolling horizon. To compress the input data in the simplified first stage while maintaining the order of the time sequence, we use different resolutions of downsampling and LP-relaxation. For the second stage, we derive corresponding additional boundary conditions and evaluate these in this study.Various use-cases involving both MILP and MIQCP models are evaluated using different compression parameters. The aim is to achieve high accuracy while saving computation time and furthermore enabling the solution of problems that would otherwise be computationally unsolvable without this method.