Multi-train modeling and simulation plays a vital role in railway electrification during operation and planning phase. Study of peak power demand and energy consumed by each traction substation needs to be deter- mine...Multi-train modeling and simulation plays a vital role in railway electrification during operation and planning phase. Study of peak power demand and energy consumed by each traction substation needs to be deter- mined to verify that electrical energy flowing in its railway power feeding system is appropriate or not. Gauss-Seidel, conventional Newton-Raphson, and current injection methods are well-known and widely accepted as a tool for electrical power network solver in DC railway power supply study. In this paper, a simplified Newton-Raphson method has been proposed. The proposed method employs a set of current-balance equations at each electrical node instead of the conventional power-balance equation used in the conventional Newton-Raphson method. This concept can remarkably reduce execution time and computing complexity for multi-train simulation. To evaluate its use, Sukhumvit line of Bangkok transit system （BTS） of Thai- land with 21.6-km line length and 22 passenger stopping stations is set as a test system. The multi-train simulation integrated with the proposed power network solver is developed to simulate 1-h operation service of selected 5-min headway. From the obtained results, the proposed method is more efficient with approximately 18 % faster than the conventional Newton-Raphson method and just over 6 % faster than the current injection method.展开更多
A Newton multigrid method is developed for one-dimensional （1D） and two- dimensional （2D） steady-state shallow water equations （SWEs） with topography and dry areas. The nonlinear system arising from the well-bal...A Newton multigrid method is developed for one-dimensional （1D） and two- dimensional （2D） steady-state shallow water equations （SWEs） with topography and dry areas. The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration. The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration, and can handle the steady- state problem with wet/dry transition. Several numerical experiments are conducted to demonstrate the efficiency, robustness, and well-balanced property of the proposed method. The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed.展开更多
文摘Multi-train modeling and simulation plays a vital role in railway electrification during operation and planning phase. Study of peak power demand and energy consumed by each traction substation needs to be deter- mined to verify that electrical energy flowing in its railway power feeding system is appropriate or not. Gauss-Seidel, conventional Newton-Raphson, and current injection methods are well-known and widely accepted as a tool for electrical power network solver in DC railway power supply study. In this paper, a simplified Newton-Raphson method has been proposed. The proposed method employs a set of current-balance equations at each electrical node instead of the conventional power-balance equation used in the conventional Newton-Raphson method. This concept can remarkably reduce execution time and computing complexity for multi-train simulation. To evaluate its use, Sukhumvit line of Bangkok transit system （BTS） of Thai- land with 21.6-km line length and 22 passenger stopping stations is set as a test system. The multi-train simulation integrated with the proposed power network solver is developed to simulate 1-h operation service of selected 5-min headway. From the obtained results, the proposed method is more efficient with approximately 18 % faster than the conventional Newton-Raphson method and just over 6 % faster than the current injection method.
基金Project supported by the National Natural Science Foundation of China(Nos.91330205and 11421101)the National Key Research and Development Program of China(No.2016YFB0200603)
文摘A Newton multigrid method is developed for one-dimensional （1D） and two- dimensional （2D） steady-state shallow water equations （SWEs） with topography and dry areas. The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration. The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration, and can handle the steady- state problem with wet/dry transition. Several numerical experiments are conducted to demonstrate the efficiency, robustness, and well-balanced property of the proposed method. The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed.
