By the theory of complex functions, a dynamic problem on the edges of a mode I crack subjected to moving unit-step loads are investigated. The Riemann-Hilbert problem is easily formulated by the ways of self-similar f...By the theory of complex functions, a dynamic problem on the edges of a mode I crack subjected to moving unit-step loads are investigated. The Riemann-Hilbert problem is easily formulated by the ways of self-similar functions. The analytical solution obtained is rather simple and concise. After the solution was utilized by superposition theorem, the relevant solution on the case of arbitrary loading can be obtained.展开更多
Sensitivities of eigen-solutions to control variables play an important role in microgrid studies,such as coordinated optimal design of controllers and parameters,robust stability analysis on control variables,oscilla...Sensitivities of eigen-solutions to control variables play an important role in microgrid studies,such as coordinated optimal design of controllers and parameters,robust stability analysis on control variables,oscillation modes analysis on a system,etc.Considering the importance of sensitivities and the complexity of state matrix in a microgrid,parameter perturbations are utilized in this paper to analyze the construction characteristics of state matrix.Then,the sensitivities of eigenvalues and eigenvectors to control variables are obtained based on the first-order matrix perturbation theory,which makes the complex derivations of sensitivity formulas and repeated solutions of eigenvalue problem unnecessary.Finally,the effectiveness of the matrix perturbation based approach for sensitivity calculation in a microgrid is verified by a numerical example on a low-voltage microgrid prototype.展开更多
文摘By the theory of complex functions, a dynamic problem on the edges of a mode I crack subjected to moving unit-step loads are investigated. The Riemann-Hilbert problem is easily formulated by the ways of self-similar functions. The analytical solution obtained is rather simple and concise. After the solution was utilized by superposition theorem, the relevant solution on the case of arbitrary loading can be obtained.
基金supported by the National Natural Science Foundation of China (Grant No. 50595412)the National Basic Research Program of China ("973" Program) (Grant No. 2009CB219700)
文摘Sensitivities of eigen-solutions to control variables play an important role in microgrid studies,such as coordinated optimal design of controllers and parameters,robust stability analysis on control variables,oscillation modes analysis on a system,etc.Considering the importance of sensitivities and the complexity of state matrix in a microgrid,parameter perturbations are utilized in this paper to analyze the construction characteristics of state matrix.Then,the sensitivities of eigenvalues and eigenvectors to control variables are obtained based on the first-order matrix perturbation theory,which makes the complex derivations of sensitivity formulas and repeated solutions of eigenvalue problem unnecessary.Finally,the effectiveness of the matrix perturbation based approach for sensitivity calculation in a microgrid is verified by a numerical example on a low-voltage microgrid prototype.
