Nonlinear model predictive control of direct internal reforming solid oxide fuel cells via PDAE-constrained dynamic optimization

Direct internal reforming solid oxide fuel cells (DIR-SOFCs) are economically viable devices for power generation, while their reliability requires further improvement. Advanced process control can effectively facilitate the long-term operation of SOFCs with high efficiency and safety. DIR-SOFCs exhibit complex coupling effect and a high degree of nonlinearity, making it worthwhile to embed high-quality dynamic models including spatial distributions into nonlinear model predictive control (NMPC). A two-layer control architecture aiming for rapid load tracking and thermal management with high economic efficiency is designed for planar DIR-SOFCs, containing a set point optimizer and an NMPC controller based on the distributed parameter model expressed by partial differential–algebraic equations (PDAE). PDAE-constrained dynamic optimization problems are solved in the NMPC controller to seek optimal control strategies, considering safety constraints about the maximum temperature gradient and physical constraints of actuators. The high-fidelity one-dimensional PDAE model is validated through steady and dynamic simulations, and the optimal steady-state distributions are analyzed under three power demands. Behaviors of the closed-loop system under power demand step-up and step-down scenarios are investigated to demonstrate the effectiveness of the designed control scheme. The proposed NMPC controller can efficiently realize rapid load tracking, maintain good thermal management, and reduce the transition time, with minor steady-state errors and acceptable real-time performance.