Analysis Of Power System Dynamics Based On Trajectory Section Eigenvalues

Accurate analysis of power system dynamics is of great significance for the security and stability evaluation of power systems.Existing methodologies can be categorized into two types:model-based method and trajectory-based method.The former one solves the characteristic equations of power systems at the equilibrium point,whereas the latter one extracts oscillation characteristics from the time responses.However,the oscillation characteristics of a nonlinear and time-varying power system usually vary with time.The model-based method can hardly consider the nonlinear factors,whereas the trajectory-based method lacks structural information on power systems.For the sake of objectively describing the dynamic behaviors and deeply exploring the mechanisms of complex phenomena,emphases are put on the extraction of instantaneous oscillation features and the evolvements of eigenmodes.As a consequence,the researches on instantaneous features,eigenmode evolvements,and mode interactions are carried out by this dissertation.Based on the trajectory section eigenvalue(TSE)theory,a framework is proposed to analyze the time-varying dynamic characteristics of power systems.The corresponding theoretical derivations and simulation results are put forward to verify the effectiveness and superiority of the proposed method and framework.The explorations on engineering problems urge the TSE theory from the theoretical stage to practical applications.The main innovative contributions of the dissertation are summarized as follows.(1)A novel idea is proposed to study the dynamic behaviors of power systems,integrating model-based and trajectory-based methods.According to the classification of power system stability(IEEE/CIGRE 2004)and the industry-standard(China DL 755-2001),the research objects of this dissertation include small-disturbance dynamic stability and large-disturbance dynamic stability.When it comes to the dynamic process of a power system after disturbed,the key elements of analysis usually consist of dynamic models,disturb scenarios,and trajectories.(2)A theoretical system of TSE is built to demonstrate the limitation of piecewise linearization and the physical meaning of TSEs.The assumptions of piecewise linearization are discussed,and the state variables are reconstructed based on TSEs.Thus,the reconstructed state variables can be decoupled into multi-components varying with time.By comparing the expression of the reconstructed variables and the extrapolation formula of numerical integration,the local truncation error of the TSEs in one integration step is analyzed.Furthermore,a new system is structured to approach the trajectories of the state variables,explaining the physical meaning of the TSEs Therefore,the application scope of the TSE theory is clearly defined,and several doubts in academia are clarified,which strongly support further researches in related fields.(3)A method is proposed to extract the instantaneous oscillation features,and a framework is designed to analyze the time-varying dynamic behavior of a power system.Firstly,the time response of the system is obtained by numerical simulation in a given fault scenario.Secondly,the TSEs and instantaneous damping/frequency are solved by substituting the algebraic variables to the differential-algebraic equations and linearizing the nonlinear components of the equations along the trajectory.Thirdly,the state variables are reconstructed with the initial values,extracting features to describe the degree of eigenmode excitation.Fourthly,the evolvements of critical eigenmodes are analyzed by the above instantaneous oscillation features.Moreover,the electro-mechanical-correlation-ratio of the critical eigenmode and the participation factors are further extracted.The effectiveness and the superiority of the proposed method and framework are verified in the IEEE 3G9N system and the IEEE 10G39N system.(4)The effects of mode interactions and generator shedding are investigated.In the aspect of small-disturbance dynamic analysis,the interactions of eigenmodes are analyzed in ultra-low frequency oscillation(ULFO),based on the reconstruction of state variables.The mechanisms of two complex phenomena,such as undamped oscillation and eigenmode re-excitation,are revealed in the time domain and the frequency domain.In the aspect of large-disturbance dynamic analysis,in order to research the potential oscillation risk of generator shedding,the instantaneous damping feature of critical eigenmode is derived.The instantaneous oscillation features describe the changes in structural characteristics and dynamic behaviors.The above applications further demonstrate that the TSE theory can not only analyze the mode interactions in small-disturbance dynamic fields,but also take time-varying oscillation characteristics into account in large-disturbance dynamic fields.Thus,the current analyzing framework of power system stability is improved by the proposed method.(5)In order to solve two engineering problems,the TSE method is further developed to achieve eigenmodes matching and fast eigenvalues calculation along the trajectory.The former method mathematically analyzes the inheritance relationship of eigenmodes in adjacent time sections,while the latter one mechanically discusses the inner links between eigenmodes and oscillation modes.The effectiveness of the proposed mode matching method is verified in the IEEE 10G39N system,and the matching error is reduced by at least one order of magnitude.The fast calculation method achieves accurate features extraction in a provincial system(500-order)of China.Compared with the QR method,the computation can almost be ignored.This dissertation discusses the application scope of the TSE theory,clearing the obstacles of further researches theoretically.By extracting the instantaneous oscillation features along the trajectory,a framework is proposed to analyze the time-varying dynamic characteristics of power systems.As an effective analyzing technique,the TSE theory is utilized to research the mode interactions in the time domain and the frequency domain.The mechanisms of some complex phenomena are revealed,while the evolvements of medium to long process after disturbances are illuminated.By further exploring the correlation between TSEs and transient instability,further work can be made to build a comprehensive framework of dynamic stability estimation.Besides,more engineering researches help strike the right balance between the accuracy and the speed of eigenvalues calculation.