Multi-objective optimization of a power-to-hydrogen system for mobility via two-stage stochastic programming

A systematic way for the optimal design of renewable-based hydrogen refuelling stations in the presence of uncertainty in the hydrogen demand is presented. A two-stage stochastic programming approach is used to simultaneously minimize the total annual cost and the CO 2 footprint due to the electricity generation sources. The first-stage (design) variables correspond to the sizing of the devices, while the second-stage (operation) variables correspond to the scheduling of the installed system that is affected by uncertainties. The demand of a fleet of fuel cell vehicles is synthesized by means of a Poisson distribution and different scenarios are generated by random sampling. We formulate our problem as a large-scale mixed-integer linear program and we rely on a two-level approximation scheme to keep the problem computationally tractable. A solely deterministic setting which does not take into account uncertainties leads to underestimated device sizes, resulting in a significant fraction of demand remaining unserved with a consequent loss in revenue. The multi-objective optimization produces a convex Pareto front, showing that a reduction in carbon footprint comes with increasing costs and thus diminishing profit.