In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of commo...In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.展开更多
随着分布式能源和储能容量的增加以及电动汽车的普及,配电网的功率流动由单向转变为双向,且网络拓扑由径向转变为复杂的网状结构。为了高效应对网状配电网的潮流(power flow,PF)分析和最优潮流(optimal power flow,OPF)问题,以及进一步...随着分布式能源和储能容量的增加以及电动汽车的普及,配电网的功率流动由单向转变为双向,且网络拓扑由径向转变为复杂的网状结构。为了高效应对网状配电网的潮流(power flow,PF)分析和最优潮流(optimal power flow,OPF)问题,以及进一步提升现有线性化模型的近似精度、完善对网络损耗等元素的线性近似,该文构建迭代隐式线性化潮流(iterative implicit linearization power flow,IIL-PF)模型及其最优潮流模型(IIL-OPF)。该模型将非线性潮流流形M(Manifold)视为节点电压和节点注入功率之间的隐式代数关系,之后利用切平面对M进行局部近似,并迭代更新线性化点以提高线性模型的近似精度。此外,所提模型充分考虑了支路始/末端潮流、支路潮流平方、支路损耗等因素,并对其进行明确的线性化推导。最后,基于修改的IEEE 33系统,分别在径向和网状运行方式下,验证所提模型可快速收敛,并具有较高的近似精度。其中IIL-PF计算结果、IIL-OPF的目标函数和发电机出力等优化结果与MATPOWER的非线性模型相比,误差均在1%以内,因此所提模型可以满足工程规划或日前运行模拟等应用要求。展开更多
文摘In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.
文摘随着分布式能源和储能容量的增加以及电动汽车的普及,配电网的功率流动由单向转变为双向,且网络拓扑由径向转变为复杂的网状结构。为了高效应对网状配电网的潮流(power flow,PF)分析和最优潮流(optimal power flow,OPF)问题,以及进一步提升现有线性化模型的近似精度、完善对网络损耗等元素的线性近似,该文构建迭代隐式线性化潮流(iterative implicit linearization power flow,IIL-PF)模型及其最优潮流模型(IIL-OPF)。该模型将非线性潮流流形M(Manifold)视为节点电压和节点注入功率之间的隐式代数关系,之后利用切平面对M进行局部近似,并迭代更新线性化点以提高线性模型的近似精度。此外,所提模型充分考虑了支路始/末端潮流、支路潮流平方、支路损耗等因素,并对其进行明确的线性化推导。最后,基于修改的IEEE 33系统,分别在径向和网状运行方式下,验证所提模型可快速收敛,并具有较高的近似精度。其中IIL-PF计算结果、IIL-OPF的目标函数和发电机出力等优化结果与MATPOWER的非线性模型相比,误差均在1%以内,因此所提模型可以满足工程规划或日前运行模拟等应用要求。
