Linear programming model predictive control for offshore wind-direct air capture system using battery storage

Direct air capture (DAC) of CO2 can entail mixed integer constrained optimization, when different aspects are simultaneously accounted: optimal electrical power schedule, maximization of captured CO2, satisfaction of predicted DAC load demands and fulfilment of system overall operational constraints. Motivated by the need of driving direct air capture systems via offshore wind-energy, in this paper we investigate how to optimally schedule the DAC system with the aim of capturing maximum CO2 by jointly considering renewable energy generation and the energy butter states. In particular, the energy storage system is integrated to supply smooth DAC loads during low wind hours. We also propose a lightweight, computationally inexpensive technique based on model predictive control (MPC) where a sequence of relaxed linear programming problems is solved to replace state of the art branch-and-bound or branch-and-cut techniques. Extensive simulations justify the effectiveness of the proposed approach.