Model predictive supervisory control for multi-stack electrolyzers using multilinear modeling

Offshore green hydrogen production lacks of flexible and scalable supervisory control approaches for multi-stack electrolyzers, raising the need for extendable and high-performance solutions. This work presents a two-stage nonlinear model predictive control (MPC) method. First, an MPC stage generates a discrete on-off electrolyzer switching decision through algebraic relaxation of a Boolean signal. The second MPC stage receives the stack's on-off operation decision and optimizes hydrogen production. This is a novel approach for solving a mixed-integer nonlinear program (MINP) in multi-stack electrolyzer control applications. In order to realize the MPC, the advantages of the implicit multilinear time-invariant (iMTI) model class are exploited for the first time for proton exchange membrane (PEM) electrolyzer models. A modular, flexible, and scalable framework in MATLAB is built. The tensor based iMTI model, in canonical polyadic (CP) decomposed form, breaks the curse of dimensionality and enables effective model composition for electrolyzers. Simulation results show an appropriate multilinear model representation of the nonlinear system dynamics in the operation region. A sensitivity analysis identified three numeric factors as decisive for the effectiveness of the MPC approach. The classic rule-based control methods Daisy Chain and Equal serve as reference. Over two weeks and under a wind power input profile, the MPC strategy performs better regarding the objective of hydrogen production compared to the Daisy Chain (4.60 %) and Equal (0.43 %) power distribution controllers. As a side effect of the optimization, a convergence of the degradation states is observed.