The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is signifi...The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.展开更多
随着新能源发电技术与直流输电技术在大电网中的广泛应用,需要提出含新能源的交直流混联电网静态电压稳定分析方法。为此,该文针对含常规直流输电和多端柔性直流输电的交直流混联电网,采用区间数描述新能源电站出力的不确定波动,建立了...随着新能源发电技术与直流输电技术在大电网中的广泛应用,需要提出含新能源的交直流混联电网静态电压稳定分析方法。为此,该文针对含常规直流输电和多端柔性直流输电的交直流混联电网,采用区间数描述新能源电站出力的不确定波动,建立了交直流混联电网静态电压稳定裕度(static voltage stability margin,SVSM)区间计算的2个双层最优潮流模型,即计算SVSM区间上界的min-min模型和计算SVSM区间下界的max-min模型。计算区间SVSM上界的min-min双层优化模型可直接合并为单层优化模型求解。计算SVSM区间下界的max-min模型需要先通过二阶锥松弛和凸包络松弛等方法将内层模型转化为凸规划模型,并通过对偶优化理论得到内层凸规划模型的对偶规划模型,进而转化为单层优化模型求解。通过对修改后的IEEE-39节点系统和南方电网2个交直流混联电网算例的计算分析,并与蒙特卡洛抽样法和拉丁超立方抽样法的计算结果比较,验证了所提出方法的正确性与高效性。展开更多
基金supported by the National Science Foundation of China (70771080)Social Science Foundation of Ministry of Education (10YJC630233)
文摘The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.
文摘随着新能源发电技术与直流输电技术在大电网中的广泛应用,需要提出含新能源的交直流混联电网静态电压稳定分析方法。为此,该文针对含常规直流输电和多端柔性直流输电的交直流混联电网,采用区间数描述新能源电站出力的不确定波动,建立了交直流混联电网静态电压稳定裕度(static voltage stability margin,SVSM)区间计算的2个双层最优潮流模型,即计算SVSM区间上界的min-min模型和计算SVSM区间下界的max-min模型。计算区间SVSM上界的min-min双层优化模型可直接合并为单层优化模型求解。计算SVSM区间下界的max-min模型需要先通过二阶锥松弛和凸包络松弛等方法将内层模型转化为凸规划模型,并通过对偶优化理论得到内层凸规划模型的对偶规划模型,进而转化为单层优化模型求解。通过对修改后的IEEE-39节点系统和南方电网2个交直流混联电网算例的计算分析,并与蒙特卡洛抽样法和拉丁超立方抽样法的计算结果比较,验证了所提出方法的正确性与高效性。
