A Comprehensive Approach for an Approximative Integration of Nonlinear-Bivariate Functions in Mixed-Integer Linear Programming Models

As decentralized energy supply units, microgrids can make a decisive contribution to achieving climate targets. In this context, it is particularly important determine the optimal size of components contained in and their operating schedule. Hence, mathematical optimization methods are often used association with such tasks. particular, mixed-integer linear programming (MILP) has proven be useful tool. Due versatility different energetic (e.g., storages, solar modules) special technical characteristics, relationships only inadequately describe real processes. order take advantage solution techniques but at same time better represent these real-world processes, accurate efficient approximation need applied system modeling. nonlinear-bivariate functions major challenge, which why paper derives implements method that addresses issue. The any bivariate nonlinear (MINLP) formulation transformed into MILP using comprehensive method. For performance comparison, quadratic constrained (MIQCP) model—as an MINLP case—is MILP, problem compared one MIQCP. Since there good off-the-shelf solvers for MIQCP problems available, comparison conservative. results exemplary microgrid sizing task show delivers strong performance, both terms error (0.08%) computation time. its implementation serve as general user-tool also basis further methodological developments research.