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The aim of this article is to develop a simplified equivalent dynamic model capable to capture the transient behavior of a gas-fueled co-generator. To comply with this exigency, an online identification methodology based on the sensitivity theory in conjunction with the Lyapunov function is adopted. By this methodology, stable solutions can be achieved in the online environment, renewing the parameters of the model at every change occurring on the physical system. In order to investigate the effectiveness of the proposed methodology in deriving a simplified dynamic model, several simulations and experimental tests were performed on the Prince Lab microgrid located at the Polytechnic University of Bari. [ABSTRACT FROM AUTHOR]