Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolatio...Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.展开更多
Gas-fired power generator(GPG)planning in the integrated gas-electricity systems(IGES)is the fundamental guarantee for optimal utilization of natural gas energy.The reliability level is significant for GPG planning to...Gas-fired power generator(GPG)planning in the integrated gas-electricity systems(IGES)is the fundamental guarantee for optimal utilization of natural gas energy.The reliability level is significant for GPG planning to ensure the secure operation of IGES.However,existing planning research considering reliability focuses on the system-level reliability index,which rarely accurately reflects GPG reliability's importance.A set of device-level reliability indices is proposed to consider the characteristics of GPG in IGES,which enriches the reliability index set and provides a complete index system for planning and considering reliability.Furthermore,solving the GPG capacity and location planning model considering the reliability index is time-consuming and difficult to solve directly.For enhancing the solving efficiency,a point-to-point mathematical mapping relationship of the reliability index and the GPG planning is constructed based on bilinear interpolation theory.Based on the proposed mapping relationship and reliability index,a novel GPG fast planning method is established to obtain the optimal planning scheme of GPG meeting reliability requirements directly.This method avoids repeatedly adjusting the optimization scheme to meet the reliability index.Finally,a modified IEEE 24-bus power system combined with an NGS 10-node gas system is adopted to verify the effectiveness of the established model and proposed method.展开更多
基金the National Nutural Science Foundation of China(Grant Nos.10771198,10590353)
文摘Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.
基金supported in part by the National Natural Science Foundation of China(No.51977042)in part by Innovation Project of Guangxi Graduate Education(No.YCBZ2020002).
文摘Gas-fired power generator(GPG)planning in the integrated gas-electricity systems(IGES)is the fundamental guarantee for optimal utilization of natural gas energy.The reliability level is significant for GPG planning to ensure the secure operation of IGES.However,existing planning research considering reliability focuses on the system-level reliability index,which rarely accurately reflects GPG reliability's importance.A set of device-level reliability indices is proposed to consider the characteristics of GPG in IGES,which enriches the reliability index set and provides a complete index system for planning and considering reliability.Furthermore,solving the GPG capacity and location planning model considering the reliability index is time-consuming and difficult to solve directly.For enhancing the solving efficiency,a point-to-point mathematical mapping relationship of the reliability index and the GPG planning is constructed based on bilinear interpolation theory.Based on the proposed mapping relationship and reliability index,a novel GPG fast planning method is established to obtain the optimal planning scheme of GPG meeting reliability requirements directly.This method avoids repeatedly adjusting the optimization scheme to meet the reliability index.Finally,a modified IEEE 24-bus power system combined with an NGS 10-node gas system is adopted to verify the effectiveness of the established model and proposed method.
