Multivariable Linear Regression for SOFC Stack Temperature Estimation under Degradation Effects

Multivariable linear regression (MLR) models are developed for the estimation of the maximum temperature and the temperature difference over a cell inside a solid oxide fuel cell (SOFC) stack. Empirical test data from both long-term tests (3500 hours) and a full three-factor designed experiment on a 10 kW SOFC system are utilized in the work. It is shown that accurate estimation can be carried out effectively based on systematic short-term experiments and by using simple and reliable measurements even under the effects of stack performance degradation. After proper data is obtained, selection of suitable MLR model regressors is crucial to obtaining good estimates. The cathode outlet temperature was found useful for the estimation of the stack maximum temperature and the stack voltage for the estimation of the temperature difference over a cell. Also, analysis of the measurement data shows that the experiment design can be considerably reduced without significant reduction in obtained information. The importance of using both long-term testing data as well as short-term designed experiments from an invariant system as the basis for modeling is underlined.