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Several types of power-split hybrid transmissions are outlined and the strengths and weaknesses of typical compound power-split prototype designs are summarized in this paper. Based on an modified Ravigneaux gear set, a novel compound power-split hybrid transmission with compact mechanical structure is presented, its dynamic and kinematic characteristics in equations and operating modes are described, and then equivalent lever diagrams are used to investigate the proposed compound power-split device. Control strategies in different operating modes are discussed with the simplified combined lever diagram, and a global optimization method is implemented to find the optimum operation point for the hybrid powertrain. To evaluate the fuel economy of a hybrid car equipped with this hybrid transmission, a forward powertrain simulation model is developed and real vehicle performance tests are conducted in the chassis dynamometer.