The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such op...The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.展开更多
This paper proposes a pattern recognition based differential spectral energy protection scheme for ac microgrids using a Fourier kernel based fast sparse time-frequency representation(SST or simply the sparse S-Transf...This paper proposes a pattern recognition based differential spectral energy protection scheme for ac microgrids using a Fourier kernel based fast sparse time-frequency representation(SST or simply the sparse S-Transform).The average and differential current components are passed through a change detection filter,which senses the instant of fault inception and registers a change detection point(CDP).Subsequently,if CDP is registered for one or more phases,then half cycle data samples of the average and differential currents on either side of the CDP are passed through the proposed SST technique,which generates their respective spectral energies and a simple comparison between them detects the occurrence and type of the fault.The SST technique is also used to provide voltage and current phasors and the frequency during faults which is further utilized to estimate the fault location.The proposed technique as compared to conventional differential current protection scheme is quicker in fault detection and classification,which is least effected from bias setting,has a faster relay trip response(less than one cycle from fault incipient)and a better accuracy in fault location.The significance and accuracy of the proposed scheme have been verified extensively for faults in a standard microgrid system,subjected to a large number of operating conditions and the outputs vindicate it to be a potential candidate for real time applications.展开更多
An efficient and accurate spectral method is presented for scattering problems with rough surfaces.A probabilistic framework is adopted by modeling the surface roughness as random process.An improved boundary perturba...An efficient and accurate spectral method is presented for scattering problems with rough surfaces.A probabilistic framework is adopted by modeling the surface roughness as random process.An improved boundary perturbation technique is employed to transform the original Helmholtz equation in a random domain into a stochastic Helmholtz equation in a fixed domain.The generalized polynomial chaos(gPC)is then used to discretize the random space;and a Fourier-Legendre method to discretize the physical space.These result in a highly efficient and accurate spectral algorithm for acoustic scattering from rough surfaces.Numerical examples are presented to illustrate the accuracy and efficiency of the present algorithm.展开更多
文摘The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.
文摘This paper proposes a pattern recognition based differential spectral energy protection scheme for ac microgrids using a Fourier kernel based fast sparse time-frequency representation(SST or simply the sparse S-Transform).The average and differential current components are passed through a change detection filter,which senses the instant of fault inception and registers a change detection point(CDP).Subsequently,if CDP is registered for one or more phases,then half cycle data samples of the average and differential currents on either side of the CDP are passed through the proposed SST technique,which generates their respective spectral energies and a simple comparison between them detects the occurrence and type of the fault.The SST technique is also used to provide voltage and current phasors and the frequency during faults which is further utilized to estimate the fault location.The proposed technique as compared to conventional differential current protection scheme is quicker in fault detection and classification,which is least effected from bias setting,has a faster relay trip response(less than one cycle from fault incipient)and a better accuracy in fault location.The significance and accuracy of the proposed scheme have been verified extensively for faults in a standard microgrid system,subjected to a large number of operating conditions and the outputs vindicate it to be a potential candidate for real time applications.
基金supported in part by NSF grants DMS-0243191 and DMS-0311915.
文摘An efficient and accurate spectral method is presented for scattering problems with rough surfaces.A probabilistic framework is adopted by modeling the surface roughness as random process.An improved boundary perturbation technique is employed to transform the original Helmholtz equation in a random domain into a stochastic Helmholtz equation in a fixed domain.The generalized polynomial chaos(gPC)is then used to discretize the random space;and a Fourier-Legendre method to discretize the physical space.These result in a highly efficient and accurate spectral algorithm for acoustic scattering from rough surfaces.Numerical examples are presented to illustrate the accuracy and efficiency of the present algorithm.
