Small Signal Parameter And Time Delay Stability Analysis Of Power System Based On Value Set Method

With the gradual establishment of modern large-scale interconnected power grid,the network structure and dynamic behavior of the system become increasingly complex.Adopting wide-area and remote control techniques for management is a necessary measure,which can theoretically enhance the stability of power system.However,the large-scale power system controllers based on wide-area measurement system(WAMS)will inevitably introduce hundreds of milliseconds time delays.Time delay phenomenon exists commonly not only in large power grid,but also in microgrid that clusters distributed generator(DGs),energy storages and local loads.These time delays are reflected in the feedback signals,which is expected to deteriorate the performance of controllers and even collapse the entire system.In addition,in the process of controller design considering the effect of time delays,the controller parameters to be optimized and adjusted are taken within a certain rang e,which can be regarded as the system has parameter uncertainty.At present,scholars at home and abroad have carried out extensive research on parameter uncertainty,but there is no complete theory for the stability analysis of power system considering both parameter and time delay uncertainties.Therefore,the study to the influence of uncertain parameters and time delays on small-signal stability of power system,is crucial to the development of advanced and excellent controllers that dampen the frequency oscillations and enhance the system stability.Based on the value set method of characteristic function,this paper carries out the research on small-signal stability of power system considering uncertain parameters and time delays.The main work and innovation achievements are described as follows:(1)A set of fast approximation techniques for constructing the characteristic function value set of uncertain power system is summarized.Firstly,the small-signal frequency domain model of the power system is established and its characteristic function expression onΓ stability region is calculated.Then,different techniques are adopted based on the structural classification of the characteristic function to quickly construct its value set.For the system with uncertain parameters,if the structure of the characteristic function is linear,select the edge theorem to draw its exact value set;If it is multilinear,select the mapping theorem to draw its external approximation;If it is polynomial,select the Bernstein transform technique to draw its external and internal approximations.While for the system with uncertain time delays,the structure of the characteristic function is quasi-polynomial,so its internal and external approximations can be drawn by utilizing the combination technique of Taylor transform and Bernstein transform.Finally,some case studies illustrate the construction process of value set.(2)A value set-based small-signal stability region algorithm for power system with uncertain parameters and time delays is proposed.Firstly,according to the value set theory in(1),the external and internal approximations of characteristic function value set of the system with uncertain parameters and time delays are constructed rapidly.Secondly,the four zero exclusion/inclusion discrimination conditions for the external and internal approximations of the value set are extracted from the zero-exclusion principle.Then,determine whether need to subdivide the uncertain space through the discrimination result of value set approximation until the stability boundary and region of the entire uncertain space are searched and traversed.Finally,some case studies verify the beneficial effect of space subdivision and the validity and accuracy of the proposed value set method.(3)An improved value set-based small-signal stability region algorithm for power system with uncertain time delays is proposed.First of all,from the two unique properties of crossing frequency and critical time delay,the delay tendency invariance property revealed by the cluster treatment of characteristic roots(CTCR)is deduced and confirmed,i.e.,the multiplication between frequency and delays(FDM)has a period of 2π.Secondly,the characteristic function of time-delay system is reconstructed in FDM space to improve the value set method.Then,the same zero exclusion/inclusion discrimination operation as the original value set method in(2)is adopted to subdivide and traverse the FDM kernel space,wo that its small-signal stability boundary can be obtained.In addition,the mapping process from the stability boundary in FDM kernel space to the one in large-scale time delay space is supplemented.Finally,some case studies show the excellent effect of the improved value set method,and its validity and accuracy are verified by simulation.