Hamiltonian formulation and analysis for transient dynamics of multi-unit hydropower system

This paper focuses on the implementation of a Hamiltonian model of multi-unit hydropower systems (MUHSs). First, a nonlinear mathematical model of the MUHS is established considering the occurrence of water hammer during the transient process. From the point of view of the energy transmission and dissipation of the system, a novel Hamiltonian model of the MUHS is proposed. Moreover, numerical simulations are carried out to further investigate the effectiveness and consistency of the implemented model. Finally, a comparative analysis is performed to validate the proposed approach against existing methods. The results demonstrate that the proposed Hamiltonian function not only reflects the energy change but also describes the complex dynamic evolution of MUHSs in transient processes. It is also found that the transient dynamic behavior of the system is influenced by the coupled effect of common penstock and the interaction of basic system variables. This study provides theoretical basis for the safe and stable operation of hydropower stations during transient processes.