Having especially in view application to fuel cell systems, we study in this paper the reduced modeling of impedance networks. The networks under study are constituted by a set of approximately identical (sub-)cells, coupled by series-parallel electrical links. In order to detect and diagnose the appearance of disparities in the behavior of the latter (coming, say, from aging or degradations), the description of the electrical behavior of the whole system by a ''mean cell'' is not sufficient. The main contribution of the paper is to provide a more involved approximation of the global network impedance function, including corrective terms characterizing the dispersion with respect to the average behavior. It is then natural an attempt to identify quantities able to describe the average behavior and the dispersion, in order to use them as alert data for supervision and diagnosis. As an illustrative example, the corresponding identification problem for the reduced model is studied in more details in the case where the individual impedance functions are first-order transfers.