In this paper, an online energy management control strategy is proposed based on a novel fractional-order extremum seeking (ES) method. The proposed method is an online adaptive optimization algorithm, which can be effectively used in the applications of fuel cell hybrid electric vehicles. Compared with the traditional integer-order ES method, the presented method uses Oustaloup approximation based fractional-order calculus in order to achieve faster convergence speed and higher robustness. A detailed mathematical analysis of the proposed method is presented to give a stability proof and shows how the fractional-order calculus improves the integer-order ES method. In order to support the stability analysis results and demonstrate the effectiveness and robustness of the proposed method, a hardware-in-the-loop test bench is developed to provide two experimental case studies. Experimental results show that, by using the presented fractional-order ES approach, the operation points of a proton exchange membrane fuel cell stack system can be effectively controlled in its maximum efficiency area. In addition, the fuel cell system durability can be improved.

In this paper, a novel degradation prediction model for proton-exchange-membrane fuel cell (PEMFC) performance is proposed based on a multiphysical aging model with particle filter (PF) and extrapolation approach. The proposed multiphysical aging model considers major internal physical aging phenomena of fuel cells, including fuel cell ohmic losses, reaction activity losses, and reactants mass transfer losses. Furthermore, in order to obtain accurate values of electrochemical activation losses under a variable load profile, a bisection solver is presented to solve the implicit Butler-Volmer equation. The proposed aging model is initialized at first by fitting the PEMFC polarization curve at the beginning of lifetime. During the prediction process, the aging dataset is then divided into two parts, learning and prediction phases. The PF framework is used to study the degradation characteristics and update the aging parameters during the learning phase. The suitable fitting curve functions are then selected to satisfy the degradation trends of trained aging parameters, and used to further extrapolate the future values of aging parameters in the prediction phase. By using these extrapolated aging parameters, the prediction results are thus obtained from the proposed aging model. Three experimental validations with different aging testing profiles have been performed. The results demonstrate the robustness and advantages of the proposed prediction method.