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
In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithm...In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.展开更多
The model of the universal Teichmller space by the derivatives of logarithm is the union of infinite disconnected components. In this paper, the fact that each component is not starlike with respect to its center is ...The model of the universal Teichmller space by the derivatives of logarithm is the union of infinite disconnected components. In this paper, the fact that each component is not starlike with respect to its center is proved, and the outer radius of the space with respect to each center is obtained.展开更多
The model of the universal Teichmuller union of infinite disconnected components. between different components is 0, and the every other component is 2. space by the derivatives of logarithm is the In this paper, it i...The model of the universal Teichmuller union of infinite disconnected components. between different components is 0, and the every other component is 2. space by the derivatives of logarithm is the In this paper, it is proved that the distance distance from the center of a component to展开更多
Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible c...Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.展开更多
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.
基金partially supported by the National Nature Science Foundation of China(12061033)。
文摘In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.
文摘The model of the universal Teichmller space by the derivatives of logarithm is the union of infinite disconnected components. In this paper, the fact that each component is not starlike with respect to its center is proved, and the outer radius of the space with respect to each center is obtained.
基金Project supported by the National Natural Science Foundation of China (No.10271029).
文摘The model of the universal Teichmuller union of infinite disconnected components. between different components is 0, and the every other component is 2. space by the derivatives of logarithm is the In this paper, it is proved that the distance distance from the center of a component to
基金the National Natural Science Foundation of China (Grant No. 10671009)
文摘Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.
