This paper presents a framework for parameter estimation of Solid Oxide Electrolyzer Stack (SOES) model. The complexity of multi-physics in SOES models poses a unique challenge for parameter identification due to the presence of nonlinearities, the large number of parameters, and few available measurements. Consequently, this study presents an enhanced method of parameter estimation, based on the Gauss- Newton optimization algorithm, incorporating a truncated Sin- gular Value Decompostion (SVD) of a normalized sensitivity matrix. This modification prioritizes the update of parameters in the directions of high sensitivity while limiting the condition number of the matrix inverted to choose the step size, thus attenuating the adverse effects of noise and model errors unavoidable in the estimation process. This departure from the conventional approaches, allows a more nuanced and effective identification strategy tailored to the intricacies of SOESs. The proposed method is validated using data from an experimental test bench and compared to other identification methods.