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This paper addresses the Hamiltonian mathematical modeling and dynamic analysis of a hydro-energy generation system in the transient of sudden load increasing. First, six dynamic transfer coefficients of the hydro-turbine for the transient of sudden load increasing are innovatively introduced into the hydro-energy generation system. Considering the elastic water-hammer model of the penstock and third-order model of the generator, we established a dynamic mathematical model of the hydro-energy generation system in the transient of sudden load increasing. Moreover, from the point of view of the transmission and dissipation of energy of the system, we propose the hydro-energy generation system into the theory frame of the generalized Hamiltonian system. A novel Hamiltonian model of the hydro-energy generation system is established utilizing the method of orthogonal decomposition. Finally, based on the data of a real hydropower plant, numerical simulations and

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