Application Of Eigenvalues Of Differential Algebraic Equations In Power Grid Evaluation

The balance progress between the power generation(source)and electricity consumption(load)through the power grid(network)during power system operation is an uncertain nonlinear process.The integration of renewable energy enhances the uncertainty of this nonlinear process and the disturbances that the system faces.How to evaluate its anti-disturbance ability is a fundamental problem in power grid operation,control and planning.In this paper,based on linearization,the uncertain nonlinear power system operation process is deduced into a progressive dynamic(differential equation)and static(algebraic equations)part.Its dynamic and static capabilities are evaluated through the eigenvalue analysis in order to provide a basis for power grid operation and planning.Most of the research on this issue is based on traversing all the source-net-load scenarios to optimize and analysis,and then to make an evaluation,which has its complexity.The research idea of this paper is to explore the essence of the progress.Based on the eigenvalue analysis of linear differential equations and algebraic equations in some steady state,the direct evaluation method is sought to achieve the purpose of rapid analysis.Following displays the main research works in this paper:Firstly,the operation process of uncertain and nonlinear power system is summarized as dynamic and static progress.At the same time,the static characteristics,dynamic characteristics and the dialectical relationship between them are analyzed.Then,the linear differential algebraic equations of dynamic and static characteristics are obtained under small disturbances.The analysis of the eigenvalues and the relationship between the eigenvalues and the evaluation on the power grid characteristics are executed,which sets up the foundation for the research.Secondly,as for the dynamic characteristics,the double fed induction generation is taken as an example,based on the establishment of its nonlinear dynamic model,the differential equation is linearized in a certain operating state.The small signal stability is evaluated by the corresponding eigenvalues.As for the static characteristics,based on the network equations and the power flow equations,the eigenvalues and condition numbers of the node admittance matrix and the Jacobian matrix are used to evaluate the network structure,which denotes the strength and weakness of each node.Finally,the active distribution system is taken as an example,based on the relationship between the power system dynamics and statics,a dynamic model of active distribution system considering the distributed generations is established.The small signal stability of the distributed generations in different positions is analyzed.A distribution network reconfiguration model that takes into account the small signal stability of the distributed generations is established.Aiming at solving the problem of linearization of small signal stability constraints,the genetic algorithm is used to solve the model.Aiming at a large number of infeasible solutions are generated by this method,a genetic algorithm based on topology evaluation is proposed to improve the computational efficiency.