The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, th...The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, the multigrid method is extended to the application of solving integral equations which appear in electromagnetic scattering problems. The diakoptic theory is used for this purpose. Compared with other methods, the numerical results show that the multigrid method is powerful to solve electromagnetic scattering problems and can be used to compute electromagnetic scattering problems with electrically large bodies and complex structures.展开更多
随着能源互联网战略的深入实施,可再生能源与微电网的参与度不断攀升,系统中不确定性因素显著增加,各参与主体间的合作与竞争关系变得愈发错综复杂。从垂直和水平两个层面建立了电网、服务商及多微电网混合博弈双层电能交易体系。在垂...随着能源互联网战略的深入实施,可再生能源与微电网的参与度不断攀升,系统中不确定性因素显著增加,各参与主体间的合作与竞争关系变得愈发错综复杂。从垂直和水平两个层面建立了电网、服务商及多微电网混合博弈双层电能交易体系。在垂直层面提出主从博弈的思想,以服务商为主导者、微电网为从属者。构建不确定性问题分阶段优化的分段鲁棒优化模型,实现不确定性的差异化调度,提高鲁棒优化的灵活性。利用布尔-列和约束生成(Bool-Column and constraint generation,B-C&CG)算法求解模型,并把整个模型分为主问题和子问题:主问题优化电价不确定性问题,子问题优化源荷不确定问题。在水平层面搭建纳什谈判模型,通过交替方向乘子(alternating direction method of multipliers,ADMM)算法求解水平层面微电网之间的电能交互模型。利用分布式求解方法得出交易价格策略,再结合拉格朗日乘子法,交替优化各分部并更新乘子,得出各微电网之间的最佳交易电价。仿真结果表明,所提方案兼顾了系统的鲁棒性、经济性及灵活性,缩减了各微电网的成本并充分保护了各微网的隐私。展开更多
文摘The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, the multigrid method is extended to the application of solving integral equations which appear in electromagnetic scattering problems. The diakoptic theory is used for this purpose. Compared with other methods, the numerical results show that the multigrid method is powerful to solve electromagnetic scattering problems and can be used to compute electromagnetic scattering problems with electrically large bodies and complex structures.
文摘随着能源互联网战略的深入实施,可再生能源与微电网的参与度不断攀升,系统中不确定性因素显著增加,各参与主体间的合作与竞争关系变得愈发错综复杂。从垂直和水平两个层面建立了电网、服务商及多微电网混合博弈双层电能交易体系。在垂直层面提出主从博弈的思想,以服务商为主导者、微电网为从属者。构建不确定性问题分阶段优化的分段鲁棒优化模型,实现不确定性的差异化调度,提高鲁棒优化的灵活性。利用布尔-列和约束生成(Bool-Column and constraint generation,B-C&CG)算法求解模型,并把整个模型分为主问题和子问题:主问题优化电价不确定性问题,子问题优化源荷不确定问题。在水平层面搭建纳什谈判模型,通过交替方向乘子(alternating direction method of multipliers,ADMM)算法求解水平层面微电网之间的电能交互模型。利用分布式求解方法得出交易价格策略,再结合拉格朗日乘子法,交替优化各分部并更新乘子,得出各微电网之间的最佳交易电价。仿真结果表明,所提方案兼顾了系统的鲁棒性、经济性及灵活性,缩减了各微电网的成本并充分保护了各微网的隐私。
