Time Integration Partial Spectral Discretization-Based Stability Analysis Of Delayed Cyber-Physical Power System

The stability and security of the weakly interconnected power systems are usually constrained by low frequency inter-area oscillations.With the high integration of infor-mation technologies and modern power system,wide-area damping control based on wide-area measurement systems(WAMS)provides a new way for limiting the harm of low frequency oscillations.However,inevitable time delays are introduced in damping controlling through transmitting and processing remote signals,depending on different communication infrastructures.Time delays will deteriorate the performance of con-troller and system's small signal stability.Thus,challenges posed by time delays in the safe and stability operation of power system reveal the need of deep and extensive researches.Aiming at resolving the system's stability problem,a series of eigen-analysis meth-ods of large delayed power system by time integration-based partial spectral discretiza-tion are studied in this thesis.The major work and contributions are summarized as follows.(1)The eigen-analysis methods based on linear multistep and implicit Runge-Kutta discretization of infinitesimal generator(IGD-LMS/IRK)are presented for large de-layed power system.First,based on the delay differential equation(DDE)modeling and piecewise discretization idea,the infinitesimal generator is discretized by time in-tegration methods,resulting in highly structured and sparse discretization matrices.Then,the shift-invert technique and sparse eigenvalue computation are used to guaran-tee the scalability of IGD-LMS/IRK in dealing with large delayed power system.Fi-nally,numerical results on the two-area four-machine test system and Shandong power grid validate the effectiveness of proposed methods.It shows that IGD-LMS/IRK are more efficient than infinitesimal generator pseudo-spectral discretization(IGD-PS)method.Besides,compared with solution operator discretization with LMS and IRK(SOD-LMS/IRK)methods and the Pade approximation-based eigenvalue computation method,IGD-LMS/IRK methods are obviously more accurate especially for large sys-tem with large time delays(e.g.,400-500 ms or more).(2)By improving the original IGD-LMS/IRK methods,the eigen-analysis meth-ods based on partial IGD-LMS/IRK(PIGD-LMS/IRK)are proposed for large delayed power system.They are capable of computing eigenvalues with high efficiency no matter what type of feedback signals in wide-area damping control.Firstly,delay differential-algebraic equation(DDAE)modeling are adopted and system variables are partitioned into two parts:delay-free variables and retarded variables.Secondly,ac-cording to the idea of partial spectral discretization,only retarded variables are dis-cretized by time integration methods,leading to approximate matrices to infinitesi-mal generator,which is the Schur complement of the admittance matrix.Thirdly,the shift-invert technique and sparse eigenvalue computation free from iterative calculation of matrix-inversion-vector products(MIVP)allow PIGD-LMS/IRK to compute criti-cal eigenvalues of large system.Finally,PIGD-LMS/IRK methods are validated on the two-area four-machine system and Shandong grid as well as North China-Central China interconnected grid.Compared with IGD-LMS/IRK methods,PIGD-LMS/IRK can dramatically improve the computation efficiency while ensuring the accuracy.Es-pecially for large delayed power system,the efficiency can be enhanced by around 103?104 times,which is close to the efficiency of eigenvalue computation for system without any time delay.(3)The eigen-analysis methods based on partial SOD-IRK(PIGD-IRK)are pre-sented for large delayed power system.PSOD-IRK can obtain the eigenvalues with damping ratios smaller than a given value by one calculation and ensure its high-efficiency under any type of feedback signals.Firstly,the definition of solution op-erator and basic strategies of PIGD-IRK method under the DDAE modeling are illu-minated.Secondly,partial spectral discretization with Radau IIA method is exploited to solution operator,which results in the discretization matrix with low order.Thirdly,PSOD-IRK is endowed with scalability in analyzing large delayed power system by the shift-invert technique and sparse eigenvalue computation without iterative MIVP cal-culation involved.Finally,numerical simulations on the two-area four-machine system and Shandong grid as well as North China-Central China interconnected grid validated the accuracy and well higher efficiency of PSOD-IRK method.It consumed almost 1/10 of computational time in SOD-IRK method while ensuring its accuracy.The proposed methods in this thesis inherit computational frameworks of spectral discretization methods,and then improve the original methods by various ways for instance changing the system modeling,order reduction of discretization matrices and eliminating time-consuming iteration computation.The purpose of these researches is to enrich the family of spectral discretization methods and provide eigen-analysis methods of large delayed power system with higher efficiency and wider applicability.