Soft sensor design for estimation of SOFC stack temperatures and axygen-to-barbon ratio

The life span of a solid oxide fuel cell (SOFC) stack depends on several factors, such as internal stack temperature and temperature gradients as well as the fuel gas oxygen-to-carbon (O/C) ratio. An excessive stack temperature generally accelerates the degradation, while large temperature gradients across the stack cause thermal stress, which leads to delamination. Too low O/C ratio inflicts carbon deposition, which quickly leads to stack breakage. Therefore, monitoring of these variables is of vital importance. Although direct sensing of temperatures within the stack as well as fuel gas composition in fuel stream is feasible, it is not desirable due to increased equipment cost. In this paper a data-driven design of soft sensors for minimal and maximal stack temperatures as well as the O/C ratio is presented. Dynamic and static models for stack temperature are identified from data and their performance is compared. The dynamic model is derived by means of the subspace identification, which results in a causal state-space model. The non-causal static model assumes that a combination of process variables at the stack inlet and outlet describe its internal condition. The estimator of O/C ratio is based on static relationships. The soft sensors are designed in such a way that adding extra inputs to the model yields no further increase in accuracy of the estimates. The empirical data required for modelling were obtained from a SOFC power generating unit. The results show that the reconstruction of all the relevant variables can be accomplished by simple linear regression models.