Economic operation optimization for large electrolyzer systems using economic multilinear model predictive control

Large-scale multi-stack proton exchange membrane water electrolyzers require scalable and economically efficient supervisory control strategies to make use of renewable power supply under modular system constraints. This paper presents an economic multilinear model predictive control (EMMPC) approach for the joint optimization of switching decisions and power allocation in multi-stack electrolyzer plants with up to 100 controllable single-stack units. The method is based on a discrete-time hybrid implicit multilinear time-invariant (iMTI) electrolyzer model, which is successively linearized and transformed into a lifted linear system representation. An extended degradation model is developed that captures calendric aging, continuous operation-dependent aging, and switching-induced degradation simultaneously within both the electrochemical model and the economic cost function. The resulting two-stage optimization problem is formulated as a mixed-integer nonlinear program for the switching stage and a quadratic program for the power allocation stage. Computational performance is evaluated, demonstrating a non-exponential scaling behavior, while the problem structure indicates theoretical real-time capability. The EMMPC approach is benchmarked against the rule-based Equal and Daisy Chain strategies using a one-month wind power time series from Bremerhaven, Germany, for a 20-stack plant. Under the assumed economic and degradation parameters, the proposed controller improves total earnings by 12.80% compared to Equal and by 14.15% compared to Daisy Chain by identifying an economically favorable trade-off between hydrogen production and stack degradation. Two sensitivity studies confirm the robustness of the approach across varying initial degradation states and parameters.