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

Direct air capture (DAC) of CO
2
can entail mixed integer constrained optimization, when different aspects are simultaneously accounted: optimal electrical power schedule, maximization of captured CO
2
, 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 CO
2
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.