Parallelized Analysis Methods For Critical Eigenvalues Of Large Scale Power Systems

Conventional methods for small signal stability analysis and control are challenged by high dimensionality of power system dynamic model,which is greatly expanded with interconnection of power grids and integration of numerous renewable generation units.In analysis of power system oscillation modes,high dimensionality would lower both efficiency and reliability of the eigenvalue-based methods.To address these problems,parallel computing techniques are utilized in our research on critical eigenvalue analysis methods,considering both high efficiency and reliability,for large scale power systems.In this thesis,subspace-based partial eigenvalue algorithms,reliability testing methods for critical eigenvalue computation,and sensitivity of critical eigenvalue with respect to power system operational parameters are included as the major research contents.Especially,parallel computing application covers the above three topics all-around.Firstly,spectral transformations for making power system critical eigenvalues dominant and construction of eigen-subspace are investigated.Then two methods suitable for computing critical eigenvalues of large scale power systems are proposed,which are parallelized Krylov-Schur method with improved restarting techniques and iterative Contour Integral Rayleigh Ritz(ICIRR)method.In the Krylov-Schur method,parallelization is applied based on the decoupled computation of critical eigenvalues by partitioning spectrum.Cayley and Shift-Invert transform are used in coordination to make eigenvalues in different spectrum partitions dominant.Restarting of Kryov-Schur algorithm is improved with a refined strategy for selecting silent subspace in Krylov-Schur contraction step.Well convergence property,computational efficiency and parallel speedup are obtained.For the ICIRR method,a contour integral based spectral transform(CIST)is proposed,which is able to make eigenvalues enclosed by a customized integral curve dominant equally.The equality on dominance of transformed eigenvalues is more capable in handling unknown eigenvalue distribution than Cayley and Shift-Invert transforms,and hence ensures well convergence of the wanted eigen-subspace.Numerical approach for evaluating contour integral is naturally parallelizable.Computational time for searching critical eigenvalues by ICIRR method is able to be much reduced by the applied parallel computing techniques.Next,a contour integral based method is proposed for testing and enhancing reliability of power system critical eigenvalue computation.The proposed method is able to calculate the number of eigenvalues in a given region on the complex plane,and then to find if any eigenvalue of interest is missed.Utilization of the sparsity property of augmented state matrix and parallel numerical integration make implementation of the proposed method very efficient.Meanwhile,eigenvalue distribution neighboring the integral curve could be approximated based on integral function values,which helps select shift points of spectral transforms and hence improve convergence of subspace based eigenvalue methods.Lastly,efficient method for computing sensitivity of critical eigenvalues with respect to power system operational parameters are investigated.Complexity analysis is performed on the existing analytical method and numerical perturbation method,which are found not applicable to large scale power systems due to their quadratic complexity.Based on the independence of state matrix sensitivity,a hybrid approach is proposed with state matrix sensitivity computed by numerical perturbation and eigenvalue sensitivity evaluated by closed formula.The complexity of the hybrid approach is reduced to be almost linearly correlated to system scale.Parallelization is easy to be adopted as sensitivity computation with respect to different parameters are decoupled.Well parallel speedup is achieved in the numerical experiment,especial for large scale power systems.