Multivariable model predictive control of PEM electrolysis system based on improved gray wolf optimization algorithm

To overcome the limitations of low hydrogen production efficiency in conventional control approaches for proton exchange membrane (PEM) electrolysis systems, a novel multivariable model predictive control (MPC) strategy integrated with an improved gray wolf optimization (IGWO) algorithm is proposed in this paper. First, a comprehensive mathematical model of the PEM electrolysis system is established, incorporating a dynamic coupling model that captures the complex interactions among current density, operating temperature, system pressure, and hydrogen production efficiency. Second, the nonlinear efficiency model is linearized through a robust weighted least squares approach, incorporating operational constraints for temperature and pressure. This linearized framework facilitates the development of a state-space model with current density, temperature, and pressure as manipulated variables, targeting hydrogen production efficiency as the controlled output. Third, the optimization problem of hydrogen production efficiency is transformed into a quadratic programming problem through the MPC framework enhancement. An upgraded gray wolf optimization algorithm featuring a dynamic convergence factor adjustment mechanism that improves computational efficiency of weight matrix optimization in MPC is proposed. The integration of the IGWO algorithm with the MPC framework establishes a dual-loop collaborative control architecture (IGWO-MPC) that synergistically combines predictive modeling with intelligent optimization. Finally, the performance improvements are validated by simulation experiments. Compared to conventional proportional-integral-derivative control, the IGWO-MPC architecture achieves 4.6% higher hydrogen production power, 5.3% reduction in thermal power loss, 5.3% efficiency enhancement over 24 h, and a 6.7% increase in daily hydrogen yield. When benchmarked against traditional MPC, IGWO-MPC maintains superior performance with 1.9% greater hydrogen production power, 2.1% lower thermal losses, 2.4% efficiency improvement, and 4.89% higher daily output.