This paper reprents two types of fully discrete Galerkin algorithm and nonlinear Galerkin algoritlun with variable time steps for solving numerically nonlinear evolution equations, in which spatial discretization is m...This paper reprents two types of fully discrete Galerkin algorithm and nonlinear Galerkin algoritlun with variable time steps for solving numerically nonlinear evolution equations, in which spatial discretization is made by spectral functions and finite elements; time is done by the Euler explicit difference scheme with the first order accuracy and two-step semi-implicit difference scheme with the second order accuracy. According to the stability analysis, we find that for the Euler difference scheme and two-step difference scheme on time discretization the stability of the fully discrete nonlinear Galerkin algorithms is superior to ones of the fully discrete Galerkin a-lgorithms. Finally, our numerical test also shows this fact.展开更多
AC-HVDC-AC energy conversion systems using MMC （modular multilevel converters） are becoming popular to integrate distributed energy systems to the main grid. Such multilevel converters pose a serious problems for H...AC-HVDC-AC energy conversion systems using MMC （modular multilevel converters） are becoming popular to integrate distributed energy systems to the main grid. Such multilevel converters pose a serious problems for HIL （hardware in the loop） simulators required for control, protection design and testing due to the large number of cells that must be simulated individually using very small time steps. This paper demonstrates the advantages of using a very small time step to simulate a MMC topology. The MMC is implemented on FPGA （fiel-programmable gate array） to simulate fast transient with a time step of 250 ns. The AC network and HVDC bus is simulated on the PC, with a slower time step of 10 μs to 20 μs. The simulator architecture and the components simulated on the FPGA and on the PC will be discussed, as well as the method allowing the interconnection of this slow and fast system.展开更多
文摘This paper reprents two types of fully discrete Galerkin algorithm and nonlinear Galerkin algoritlun with variable time steps for solving numerically nonlinear evolution equations, in which spatial discretization is made by spectral functions and finite elements; time is done by the Euler explicit difference scheme with the first order accuracy and two-step semi-implicit difference scheme with the second order accuracy. According to the stability analysis, we find that for the Euler difference scheme and two-step difference scheme on time discretization the stability of the fully discrete nonlinear Galerkin algorithms is superior to ones of the fully discrete Galerkin a-lgorithms. Finally, our numerical test also shows this fact.
文摘AC-HVDC-AC energy conversion systems using MMC （modular multilevel converters） are becoming popular to integrate distributed energy systems to the main grid. Such multilevel converters pose a serious problems for HIL （hardware in the loop） simulators required for control, protection design and testing due to the large number of cells that must be simulated individually using very small time steps. This paper demonstrates the advantages of using a very small time step to simulate a MMC topology. The MMC is implemented on FPGA （fiel-programmable gate array） to simulate fast transient with a time step of 250 ns. The AC network and HVDC bus is simulated on the PC, with a slower time step of 10 μs to 20 μs. The simulator architecture and the components simulated on the FPGA and on the PC will be discussed, as well as the method allowing the interconnection of this slow and fast system.
