Operation planning with thermal storage units using MILP: Comparison of heuristics for approximating non-linear operating behavior

Abstract

For operation planning in industrial energy systems mixed integer linear programming (MILP) is the go-to method because of its reliability and the huge advances in MILP algorithms in recent years. MILP is especially well suited for planning the use of storage units, even if including the non-linear operating behavior of thermal storages is still a big challenge ± especially if partial load cycles are considered. To model the storage behavior, a multi-variate non-linear function has to be linearized and incorporated into the MILP model. The key for good performance in MILP is using as few linear pieces as possible to achieve the required accuracy. We consider two types of piecewise-linear models: triangulation on a grid and general triangulation. In this paper, we present different heuristics for computing efficient piecewise-linear approximations of nonlinear functions. As a use case we consider the behavior of a thermal storage unit. We apply the heuristics to compute piecewise-linear approximation of the non-linear operating behavior and discuss the results. We then compare the performance of the models in a MILP model for the operation planning of an energy system. For translating the piecewise-linear function to MILP we consider state-of-the-art approaches with a logarithmic number of binary variables. Our results show that gridded triangulation models in combination with logarithmic MILP formulations can be used for data-driven modeling of non-linear operating behavior of devices. We highlight the potential of this approach for realizing adaptable operation optimization of energy systems.