Abstract
Renewable powered water electrolysis offers a promising strategy to decarbonize industrial sectors with high demand for hydrogen. Operational optimization of industrial electrolyzer systems is often formulated as mixed-integer linear programming (MILP) problems, where a constant hydrogen production to electrical power consumption ratio is assumed instead of the nonlinear relationship. Incorporating a nonlinear electrolyzer model into a linear optimal hydrogen dispatch framework remains a significant challenge. This study addresses this challenge by formulating the optimization problem in two ways. First, the model is solved as a nonlinear programming (NLP) problem by incorporating a nonlinear model of an alkaline electrolyzer (AEL) into the optimization framework. The binaries and integers are relaxed to continuous variables and associated penalty terms are added to the objective function to enforce integrality. The NLP is solved using the local nonlinear solver Interior Point OPTimizer (IPOPT) using a multi-start approach, where the solver is executed from random initial points and the minimum objective value is taken as the best guess for the global minimum. Second, a linearized model of the AEL is used in an MILP formulation. The univariate nonlinear terms within the model are approximated using three piecewise linearization techniques, i.e., convex combination, convex combination with SOS2 variables and a slope based big-M formulation. The bilinear terms are relaxed using the McCormick envelope. Results show that the MILP formulation achieves faster solution times, with varying accuracy depending on the linearization method, whereas the NLP approach more accurately captures the hydrogen production curve, albeit having longer convergence times.