Pushing computational boundaries: Solving integrated investment planning problems for large-scale energy systems with PIPS-IPM+

Abstract

Energy policies for setting the course of future energy supply often rely on models of energy systems with increasing interdependencies. On the mathematical side this translates into linking variables and constraints in the structure of optimization problems. Challenges concerning limited computing resources are often tackled from the applied side since generic parallel solvers are not available. This means that modelers today aim to simplify real-world models when implementing new features, despite of lots of effort spent for improving them before. This prevents accurately modeling of all system components. We tackle this challenge by combining both domain knowledge from the application side and the solver side and demonstrate our solution for a real-world model which is practically not solvable with existing methods. Therefore, we parameterize instances of the energy system optimization model REMix having more than 700 Mio. non-zeros. For the first time, these model instances incorporate both the optimization of a full hourly operational time horizon and path-dependent long-term investment planning for the German power system. These instances are annotated in a way, that the corresponding linear problems (LPs) decompose into blocks of similar size. To solve the annotated LPs, the new interior-point solver PIPS-IPM++ is applied. It treats large numbers of linking variables and constraints using a hierarchical algorithm and enables efficient scaling on parallel hardware. In this sense, we expand the boundaries of what is computationally possible when solving LPs in energy systems analysis. Accordingly, using the best possible real-world models becomes practicable, which enables the calibration of simplified models in a domain where validation is difficult.