A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the s...A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.展开更多
A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt, New...A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt, Newton method, and so on, can be used to solve crystal field parameters by fitting to experimental energy levels. With the numerical eigenvalue derivative, a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described. This method is used to compute the crystal parameters of Yb^3＋ in Sc2O3 crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method. By fitting on the parameters of a simple overlap model of crystal field, the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.展开更多
With the rapid integration of renewable energy,wide-band oscillations caused by interactions between power electronic equipment and grids have emerged as one of the most critical stability issues.Existing methods are ...With the rapid integration of renewable energy,wide-band oscillations caused by interactions between power electronic equipment and grids have emerged as one of the most critical stability issues.Existing methods are usually studied for local power systems with around one hundred nodes.However,for a large-scale power system with tens of thousands of nodes,the dimension of transfer function matrix or the order of characteristic equation is much higher.In this case,the existing methods such as eigenvalue analysis method and impedance-based method have difficulty in computation and are thus hard to utilize in practice.To fill this gap,this paper proposes a novel method named the smallest eigenvalues based logarithmic derivative(SELD)method.It obtains the dominant oscillation modes by the logarithmic derivative of the k-smallest eigenvalue curves of the sparse extended nodal admittance matrix(NAM).An oscillatory stability analysis tool is further developed based on this method.The effectiveness of the method and the tool is validated through a local power system as well as a large-scale power system.展开更多
基金Project supported by the Mathematical Tianyuan Foundation of China (No. 10626019)
文摘A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50772112 and 50872135)the Natural Science Foundation of Anhui Province of China(Grant No.08040106820)the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No.YYYJ-1002)
文摘A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt, Newton method, and so on, can be used to solve crystal field parameters by fitting to experimental energy levels. With the numerical eigenvalue derivative, a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described. This method is used to compute the crystal parameters of Yb^3＋ in Sc2O3 crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method. By fitting on the parameters of a simple overlap model of crystal field, the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.
基金supported by the National Natural Science Foundation of China(No.52321004)the Delta Power Electronics Science and Education Development Program of Delta Group.
文摘With the rapid integration of renewable energy,wide-band oscillations caused by interactions between power electronic equipment and grids have emerged as one of the most critical stability issues.Existing methods are usually studied for local power systems with around one hundred nodes.However,for a large-scale power system with tens of thousands of nodes,the dimension of transfer function matrix or the order of characteristic equation is much higher.In this case,the existing methods such as eigenvalue analysis method and impedance-based method have difficulty in computation and are thus hard to utilize in practice.To fill this gap,this paper proposes a novel method named the smallest eigenvalues based logarithmic derivative(SELD)method.It obtains the dominant oscillation modes by the logarithmic derivative of the k-smallest eigenvalue curves of the sparse extended nodal admittance matrix(NAM).An oscillatory stability analysis tool is further developed based on this method.The effectiveness of the method and the tool is validated through a local power system as well as a large-scale power system.
