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International audience; The hybridization of the conventional thermal vehicles nowadays constitutes a paramount importance for car manufacturers, facing the challenge of minimizing the consumption of the road transport. Although hybrid power train technologies did not converge towards a single solution, series/parallel power trains with power-split electromechanical transmissions prove to be the most promising hybrid technology. In fact, these power trains show maximum power train overall efficiency and maximum fuel reduction in almost all driving conditions compared to the conventional and other hybrid power trains. This paper addresses the model and design of the electro-mechanical configuration of one of the most effective HEV power trains: case study of the 2nd generation Prius. It presents the simulation work of the overall operation of the Toyota Hybrid System (THS-II) of the Prius, and explores not only its power-split eCVT innovative transmission system but also its overall supervision controller for energy management. The kinematic and dynamic behaviors of the THS-II power train are explained based on the power-split aspect of its transmission through a planetary gear train. Then, the possible regular driving functionalities that result from its eCVT operation and the energy flow within its power train are outlined. A feed-forward dynamic model of the studied power train is next proposed, supervised by a rule-based engineering intuition controller. The energy consumption of the THS-II proposed model has been validated by comparing simulation results to published results on European, American and Japanese regulatory driving cycles.