A Mean Field Control Method for Rapid Electrolysis Power Allocation of Green Hydrogen Production

This paper proposes a mean field control (MFC) method for rapid electrolysis power allocation to enhance the green hydrogen production efficiency of large-scale electrolyzer (EZ) array while improving the renewable energy utilization in renewable-dominated hydrogen production systems (RHPSs). Firstly, a hyper-box dynamic homogeneous particle partitioning model considering the safety electrolysis power fluctuation range and hydrogen production efficiency is formulated to reduce the control complexity. Secondly, an MFC strategy is designed for the EZ array to efficiently decompose the electrolysis power commands among a large number of EZ stacks, addressing uncertainties from random power fluctuations and cell failures through a linear-quadratic Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov (HJB-FPK) partial differential equations with Poisson jump processes. Additionally, a hybrid finite difference solution algorithm with convolutional neural network (CNN) acceleration is developed to numerically search for the mean field control equilibrium (MFCE), which can improve the high-order accuracy and computational efficiency. Finally, the stability, consistency and convergence of the solution algorithm are rigorously proven through the truncation error analysis rule and Lax equivalence theorem. Comparative case studies have validated the superiority of the proposed methodology on rapid electrolysis power allocation and green hydrogen production efficiency for large-scale EZ arrays.