Model predictive control for spatial–temporal temperature gradient constrained dynamic operation of a marine SOFC system

The use of solid oxide fuel cells (SOFC) offers an alternative energy-conversion technology for the maritime sector, supporting the transition to renewable fuels. However, operating SOFCs for onboard power generation requires them to accommodate dynamic load changes, which introduces thermal stress, accelerates degradation, and reduces their operational lifetime. This work introduces a set of load-tracking model predictive control (MPC) strategies that reduce thermal stress by introducing spatial temperature gradient constraints (STGC), temporal temperature gradient constraints (TTGC) and temporal temperature gradient cost (TTGQ) components. The development of a spatially resolved one-dimensional prediction model for the SOFC stack is essential for incorporating these components into MPC strategies. The strategies are evaluated via simulations across multiple scenarios using key performance indicators (KPIs) for thermal stress, load-tracking performance and electrical efficiency, and benchmarked against a baseline MPC and a current-ramping-limit (CRL) approach. The results show that the STGC effectively reduces and constrains the spatial temperature gradient while maximising electrical efficiency. Furthermore, the TTGC and TTGQ strategies improve dynamic load-tracking response while resulting in lower temporal temperature gradients than a CRL.