Global Topological Structure Analysis Of The Boundary Of The Transient Stability Region Of Power Systems

The safe operation of the power system is a guarantee for the steady development of the national economy.Facing the increasingly significant energy crisis and environmental problems,the theoretical research on the stability of modern power systems is still a challenging and important subject.Although lots of domestic and foreign scholars have conducted in-depth research on the nonlinear dynamic characteristics of power systems,especially the analysis and application of transient stability,there are still some important issues that have not been well resolved,such as the global structure of the boundary of transient stability region,and the geometric topology of the multi-dimensional manifolds,and how the renewable energy influent the boundary of the stability region,and the extended application of the stability boundary theory in transient stability analysis.It is urgent to find a more effective stability analysis theory and mathematical method.To solve these problems,this thesis studies from the perspective of “region”.Based on the theory of a nonlinear dynamic system,the transient stability of the power system is deeply discussed.The specific research results of the thesis are as follows:1)A manifold-based stability boundary theory is proposed and studied.This article expounds on the description of the manifold and sorts out the close relationship between the manifold and the stability boundary theory.Besides,the concept of the singularity at infinity is introduced,and the importance of the singularities at infinity in the process of global stability analysis is explained.Based on the global phase portraits of the planar dynamical systems,a shrinking-projection transformation method is proposed to study the global structure of high-dimensional nonlinear systems.Through this transformation,the trajectory of the system can be shrunk into a limited space,so that the distribution of the singularities at infinity and the shape of the stability boundary extending to infinity can be easily analyzed.Combining the geometric structure of the global manifold and the location distribution of the singularities at infinity,the integrity of the stability region is finally achieved.2)The boundary of the stability region of the one-machine system is studied.The manifold-based stability boundary theory is applied to study the transient stability of the one-machine system.Firstly,the mathematical model of the post-fault system is established in the projection space,and the local boundary of the stability region is estimated by using the union of the stable manifolds of the unstable equilibrium point.Using the union of stable manifolds of unstable equilibrium points,the local boundary of the stability region is estimated.Secondly,the global structure of the separatrix is studied by the proposed shrinking-projection transformation method.The singularity at infinity is used to supplement the starting point(or end point)of the separatrix,and the complete stability region of the one-machine system on the global angle-frequency phase plane is finally described.The mechanism of the change between the singularity at infinity and damping coefficient is revealed and the results are compared with the energy surface.The ability to restore stability and the transient process is visually and comprehensively displayed.3)The boundary of the stability region of the multi-machine system considering the singularity at infinity is studied.A new projection model is established by using the multimachine system equivalence processing technique and dimensionality reduction processing technique.The topology of the projection model is equivalent to the original multi-machine system model.Then the stability region of the projection model is used to directly reflect the stability of the original multi-machine system.According to the relationship between the distribution of the singularities at infinity and the size of the stability region,a new transient stability margin index of the power system is constructed,and the stability analysis of the multi-machine system under different fault conditions is studied.4)The differential topological properties and geometric characteristics of the global phase portraits in the high-dimensional space are deeply studied,and the issue of how to use the global phase portraits to describe the boundary of the stability region is discussed.A new algorithm based on the continuation method is proposed to display the structure of the global phase portraits in the “angle-frequency-frequency” phase space and the “anglefrequency-voltage” phase space,respectively.This algorithm can not only overcome the difficulty in describing the stability boundary in high dimensional phase space but also reduces the computational burden.5)The stability region of the power system with random disturbances is studied.Firstly,the stochastic differential equations of the power system are established by introducing stochastic terms,and the stability of the system is proved by the moment stability theory and It? integral.Secondly,the Euler-Maruyama numerical method is used to solve the stochastic differential equations,and the stability region with random disturbances is studied.The influence of random factors on the stability of the power angle,as well as the fluctuation characteristics and “jumping” phenomenon under random disturbances,are discussed.The correctness and effectiveness of the shrinking-projection transformation method in the stability analysis of power systems with random disturbances are verified.Based on the manifold theory,this thesis presents the entire stability region of the power system on the global phase plane and conducts an in-depth study on the global topological structure of the stability boundary.The global characteristics of the trajectories and the degree of stability based on the singularities at infinity are studied.The theoretical results will help promote the development of the direct method in transient stability analysis and provide technical support for the safe and stable economic operation and planning of the power system.