In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th block.We study an approximation of the spectra of HSS preconditioned matrices and use these results to il...In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th block.We study an approximation of the spectra of HSS preconditioned matrices and use these results to illustrate and explain the spectra obtained from numerical examples,where the previous spectral analysis of HSS precon- ditioned matrices does not cover.展开更多
Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which...Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which increases the programming complexity of and limits the parallelizability of the whole simulation.In this paper,a new adaptive preconditioned Jacobian-free Newton-GMRES(m)method is proposed to be applied to dynamic simulations of power systems.This new method has totally Jacobian-free characteristics,which saves calculations and storages of Jacobian matrixes and features strong parallelizability.Moreover,several speedup strategies are introduced to enhance efficiency and parallelizability of overall computations.Numerical tests are carried out on IEEE standard test systems and results show that in series computing environment,simulations based on the proposed method have comparable speed to those based on classical Newton-Raphson methods.展开更多
The numerical solution of the differential-algebraic equations(DAEs) involved in time domain simulation(TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems.The use of ite...The numerical solution of the differential-algebraic equations(DAEs) involved in time domain simulation(TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems.The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems.The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS.As an improvement of dishonest preconditioner(DP) strategy,updating preconditioner strategy(UP) is introduced to the field of TDS for the first time.The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices.In order to make the linear system sequence in TDS suitable for UP strategy,a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating.The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China.Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%-61% the iteration count of the GMRES when compared with the DP method in all test cases.Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.展开更多
文摘In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th block.We study an approximation of the spectra of HSS preconditioned matrices and use these results to illustrate and explain the spectra obtained from numerical examples,where the previous spectral analysis of HSS precon- ditioned matrices does not cover.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51277104 and 51207076)the National High-Tech Research & Development Program of China ("863" Program) (Grant No.2012AA050217)+1 种基金the Postdoctoral Science Foundation of China (Grant No.2012M510441)Tsinghua University Initiative Scientific Research Program (Grant No. 20121087926)
文摘Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which increases the programming complexity of and limits the parallelizability of the whole simulation.In this paper,a new adaptive preconditioned Jacobian-free Newton-GMRES(m)method is proposed to be applied to dynamic simulations of power systems.This new method has totally Jacobian-free characteristics,which saves calculations and storages of Jacobian matrixes and features strong parallelizability.Moreover,several speedup strategies are introduced to enhance efficiency and parallelizability of overall computations.Numerical tests are carried out on IEEE standard test systems and results show that in series computing environment,simulations based on the proposed method have comparable speed to those based on classical Newton-Raphson methods.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60703055 and 60803019)the National High-Tech Research & Development Program of China ("863" Program) (Grant No. 2009AA01A129)+1 种基金State Key Development Program of Basic Research of China (Grant No. 2010CB951903)Tsinghua National Laboratory for Information Science and Technology (THList) Cross-discipline Foundation
文摘The numerical solution of the differential-algebraic equations(DAEs) involved in time domain simulation(TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems.The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems.The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS.As an improvement of dishonest preconditioner(DP) strategy,updating preconditioner strategy(UP) is introduced to the field of TDS for the first time.The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices.In order to make the linear system sequence in TDS suitable for UP strategy,a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating.The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China.Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%-61% the iteration count of the GMRES when compared with the DP method in all test cases.Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.
