The expansion of the estimated stability region plays an important role in the stability analysis of nonlinear systems.However,current literatures have not provided a complete mathematical description for this problem...The expansion of the estimated stability region plays an important role in the stability analysis of nonlinear systems.However,current literatures have not provided a complete mathematical description for this problem.This paper reveals that essentially the enlargement or the compression of the estimated stability region results directly from the diffeomorphism map,which is induced by the flow contained in the stability region.By proving that any integration algorithm with an order higher than one can approximately trace the flow of the system,a generalized methodology is proposed to construct various algorithms to realize the enlargement or the compression of the estimated stability region.With this methodology,two new algorithms based on symbolic calculation are suggested to reduce the computational burden.Furthermore,this methodology is applied to construct a scalable numerical algorithm to calculate the critical clearing time(CCT) of the power system for given faults.Tests on the IEEE 10-machine 39-bus system show that the computational results coincide well with the step-by-step simulation with high accuracy.展开更多
Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C...Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C++ and J++,do not support symbolic computation directly.Hence,it leads to difficulties in applying factorization in engineering fields.In this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients.The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library.In addition,the numerical computation part often only requires double precision and is easily parallelizable.展开更多
基金supported by the National Natural Science Foundation (Grant Nos 50525721, 50595411)
文摘The expansion of the estimated stability region plays an important role in the stability analysis of nonlinear systems.However,current literatures have not provided a complete mathematical description for this problem.This paper reveals that essentially the enlargement or the compression of the estimated stability region results directly from the diffeomorphism map,which is induced by the flow contained in the stability region.By proving that any integration algorithm with an order higher than one can approximately trace the flow of the system,a generalized methodology is proposed to construct various algorithms to realize the enlargement or the compression of the estimated stability region.With this methodology,two new algorithms based on symbolic calculation are suggested to reduce the computational burden.Furthermore,this methodology is applied to construct a scalable numerical algorithm to calculate the critical clearing time(CCT) of the power system for given faults.Tests on the IEEE 10-machine 39-bus system show that the computational results coincide well with the step-by-step simulation with high accuracy.
基金partly supported by the National Natural Science Foundation of China under Grant Nos.91118001 and 11170153the National Key Basic Research Project of China under Grant No.2011CB302400Chongqing Science and Technology Commission Project under Grant No.cstc2013jjys40001
文摘Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C++ and J++,do not support symbolic computation directly.Hence,it leads to difficulties in applying factorization in engineering fields.In this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients.The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library.In addition,the numerical computation part often only requires double precision and is easily parallelizable.
