This paper models a hydro turbine based on the dynamic description of the hydraulic system having a surge tank and elastic water hammer. The dynamic of the hydraulic system is transformed from transfer function form into the differential equation model in relative value. This model is then combined with the motion equation of the main servomotor to form the nonlinear model of the hydro turbine, in which the power of the hydro turbine is calculated using algebraic equation. A new control model is thus proposed in which the dynamic of the surge tank is taken as an additional input of control items. As such, the complex hydraulic system is decomposed into a classical one penstock and one machine model with an additional input control. Therefore, the order of the system is descended. As a result, the feasibility of the system is largely improved. The simulated results show that the additional input of the surge tank is effective and the proposed method is realizable.

This paper presents the result and analysis of the composition of energy loss occurring in the hydro turbine. Two new types of energy losses, namely the hydraulic loss in the flow channel and the impact loss, are defined. All losses within the hydro turbine are divided into four types and the loss coefficients are defined accordingly. Expressions or characteristic descriptions of these losses as well as the calibration method of the loss coefficients are presented. Furthermore, the torque model of the hydro turbine where the inner energy loss takes place is established. The developed model has been used to calculate the power loss due to the mechanical friction generated by the units' rotation to solve the difficulty of measurements of the mechanical friction loss in the hydro turbine. The definition of the impact loss explains the phenomenon that the loss of no-load is greater than that of the rated operation. A set of conversion coefficients are defined using the characteristic parameters at the rated operation, which are used to transform the parameters in the torque model into those that are easily measured. Therefore, the expression of the hydro turbine power is converted into a function that has the main servomotor displacement as its single variable. This makes the proposed model be convenient to use. Finally, the proposed model and methods are calibrated and verified using the measured data of a hydropower plant. Good agreement between the modeled results and the measurements indicates that the proposed model can represent the inner energy loss characteristics of the hydro turbine.hydraulic loss in flow channel, impact loss, loss coefficients, conversion coefficients Citation:Zeng Y, Guo Y K, Zhang L X, et al. Torque model of hydro turbine with inner energy loss characteristics.

The structure of dynamic models of nonlinear hydro turbine with elastic water column is studied in this paper. The nonlinear differential equations for hydraulic system (NDE-HS) are derived based on transfer function model of it. The dynamic model I of hydro turbine is built by combining NDE-HS with the algebraic equation of hydro turbine torque. By means of except of transfer coefficient, the differential equation of hydro turbine torque is derived and combines with NDE-HS, the dynamic model II is built. Simulation is done with actual hydroelectric plant, simulation results show that dynamic responses of two type models are almost same, and the dynamic of hydro turbine is determined by hydraulic system. Furthermore, the nonlinear differential-algebraic model for hydro turbine is given, which is a reduce-order system and includes inner energy loss characteristic. Keywordshydro turbine; elastic water column; dynamic model; inner energy loss; transfer coefficientI.978-1-4244-4813-5/10/$25.00 ©2010 IEEE

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To bring the hydro turbine and hydraulic system into the theory frame of the generalized Hamiltonian and study the dynamic mechanism of its operation and control, the model of its Hamiltonian system is studied in this paper. Based on the differential equation model of hydro turbine decomposed hydraulic dynamics with sharing common conduit, by constructing the Hamiltonian function of hydraulic turbine, the nonlinear model of hydro turbine is converted to Hamiltonian system by adopting orthogonal decomposition realization, and it is realized into Hamiltonian dissipative forms by decomposing the structure matrix and designing the dissipative feedback. The variation of dissipative structure, feedback equivalence and energy flow in built Hamiltonian model are studied, the energy flows of Hamiltonian are consistent with actual system in description of generalized energy. Simulation indicates that the Hamiltonian function contains detailed main information of energy change of hydraulic turbine in transient, and is feasible.