Properties Of H-Matrices In Hamiltonian Realization And Its Application In Power System

The power system is a typical high-dimensional nonlinear dynamic system,which constantly suffers from various disturbances during normal operation.Therefore,the security and stability and economic operation of the power system is very important.Generalized Hamiltonian system theory is one of the important methods to study the nonlinear system at present.Actually,it is widely used in multi-machine system stability control.In this paper,we get the new criteria for judging the positive defi-niteness of Hessian matrix of the Hamiltonian function by applying block matrix technology and generalized(?-block)H-matrix method and us-ing matrix singularity decomposition,which is applied in excitation con-trol for multi machine power system.In chapter one,some background knowledge and recent works for generalized hamiltonian system theory and its application in power sys-tem,and some basic symbols and lemmas used in this paper are intro-duced.In chapter two,it is noted that the energy-based Lyapunov candi-dates is selected from the Hamiltonian function of generalized Hamiltoni-an system.Therefore,if the Hamiltonian function achieves a strict local minimum at the equilibrium point,then it is used as a Lyapunov func-tion to analyze the stability or stability controller design of the system in a vicinity of the equilibrium point.Further,we know that the strict minimum property of Hamiltonian function at equilibrium point is deter-mined by judging the positive definiteness of its corresponding Hessian matrix.For this reason,by using block matrix technology and matrix singularity decomposition,the judgement of the positive definiteness of a Large-scale block symmetric matrix is converted into judging gener-alized(?-block)H-matrix.Furthermore,we also get the new criteria for judging generalized(?-block)H-matrix.Finally,corresponding nu-merical examples are given to illustrate the effectiveness of the proposed method.In chapter three,by using generalized(?-block)H-matrix method,the new criteria for judging the positive definiteness of Hessian matrix of the energy function for multi machine power system considering uncer-tainties are given.Further,for a given penalty signal,a robust excitation controller with L2 disturbance attenuation criteria is proposed.In chapter four,an example is given for three machine system to illustrate the effectiveness of the proposed method in chapter three.