Dual-timescale frequency-domain multi-energy circuit method for dynamic modeling and analysis of SOFC stacks

Solid oxide fuel cells (SOFCs) are exceptionally suitable to meet flexibility requirement of power grids due to their outstanding regulation capability. However, their applications are hindered, because conventional time-domain analysis methods encounter difficulties in resolving multi-timescale dynamics of SOFCs accurately within a reasonable computation time. This study applies Fourier transform and perturbation-decomposition method to construct the frequency-domain multi-energy circuit model for SOFC stacks to tackle this challenge, enabling the isomorphic representation of mass and electrical/chemical/thermal energies. By decomposing the nonlinear governing equations into linear baseline part and nonlinear perturbation part and treat them with corresponding algorithms, a solution method that covers both global and local periods with corresponding timescales is proposed to solve the frequency-domain model of SOFCs, enabling their cross-timescale simulations. The proposed frequency-domain approach captures dynamic characteristics of physical processes in the stack across timescales of interest through spatial integration and the analytical solution, reducing both computation time and relative error to approximately 1/4 in global period solutions and 1/3 in refined period solutions compared to time-domain methods, and the speed can be further improved via parallel computing. Besides, the cross-timescale simulation of SOFC under a complex operation profile shows that SOFC can exhibit different responses to the same control signal, which can be attributed to their cross-timescale dynamics and different operation histories. This highlights the importance of accurately considering the multi-timescale characteristics of SOFCs in the regulation capabilities required for power grid stability.