Study Of Hamiltonian System Based On Differential Algebraic Equations And Its Application In Power System Stability Control

With the development of electric power systems, the complexity of network structures and operation conditions have been increasing, which has brought new challenge to the security and stability of power systems. The appearance of flexible ac transmission system (FACTS) offers more controllable resources. How to realize the coordinated control of various devices to improve the operation condition of power system is significant in both theory and practice. The power system models described by a set of differential algebraic equations can combine various device models together, which provide a convenient way to study the coordinated control. So the study on differential algebraic equations and control strategies has become an active research issue all over the world.Energy based generalized Hamiltonian system theory has attracted the attention of many scholars on system stability analysis, system stabilization and other issues. This dissertation focuses on the study of Hamiltonian system theory based on differential algebraic equations and its application in power system stability. The results achieved in the paper are as following:1,Based on the summary of power system models and current Hamiltonian realization formulations of differential algebraic equations, a new Hamiltonian realization formulation of differential algebraic equations is proposed which is easier for realization and more suitable for power system research. Also the construction method of Hamiltonian function is presented.2,With the proposed Hamiltonian realization formulation of differential algebraic equations, a feedback controller is presented to ensure asymptotical stability. And interconnection and damping assignment passivity-based control (IDA-PBC) (energy-shaping method) is extended into nonlinear differential algebraic system to reassign the structure matrix for the improvement of stability and the dynamic performance. Considering the uncertainties in the system, the L2 -gain disturbance attenuation problem of differential algebraic system is studied and relevant controller is proposed to reduce the influence of disturbances. The close-loop system is asymptotically stable and robust in the meaning of L2 -gain.3,Based on the analysis of power system structure preserving model which described by a set of differential algebraic equations, Hamiltonian realization of multi-machine power system with nonlinear load is finished. This Hamiltonian system has physical meaning and expresses the interconnection structure of system clearly. Because Hamiltonian function can be regarded as an energy function, the influence of Eq′on transient stability is studied by the energy function method. Through the analysis of structure matrix, the proposed IDA-PBC method is used to design excitation controllers. The structure matrix is reassigned and electromechanical coupling item is introduced to shape the system energy. The excitation controllers are helpful for improving the transient stability of the power system with nonlinear load.4,In order to overcome the negative interactions among multiple controllable devices, the coordinated control of excitation and static var compensators (SVC) is studied. Via IDA-PBC method, the coordinated controllers of excitation and SVC are presented based on the Hamiltonian realization of multi-machine power system with SVC. The transient stability and damping characteristic are enhanced. Meanwhile, the voltage stability is ensured. The simulation results show the effectiveness of the proposed method.5,Considering that the power system is susceptible to many disturbances, coordinated controllers of excitation and static synchronous compensators (STATCOM) are offered by the previously mentioned design method of L2 -gain disturbance attenuation control of differential algebraic equations. The simulation results show the coordinated control law not only ensures the asymptotic stability but also restrains the disturbance effectively.Finally, a systematical summary and future study are given.