在“双碳”目标的引领下,可再生能源的消纳需求迎来快速增长。为了实现县域内不同负荷特性的微电网可再生能源优势互补,提高消纳率,提出了基于交替方向乘子法(alternating direction method of multipliers,ADMM)的多场景县域多微电网...在“双碳”目标的引领下,可再生能源的消纳需求迎来快速增长。为了实现县域内不同负荷特性的微电网可再生能源优势互补,提高消纳率,提出了基于交替方向乘子法(alternating direction method of multipliers,ADMM)的多场景县域多微电网交互运行策略。首先,建立微电网独立运行的调度模型,在日前预调度计划中实现最优调度策略;其次,建立多微电网电能交互运行模型,利用ADMM迭代求解各微网间全局交互电量;最后,利用Shapley值法分配微网群系统的收益,降低每个子微网的系统运行成本。算例分析表明,所提方法不仅能提高可再生能源的消纳率,提升经济性,还能降低碳排放量,实现低碳运行。展开更多
For graphs G and H,an embedding of G into H is an injection ϕ:V(G)→V(H)such that ϕ(a)ϕ(b)∈E(H)whenever ab∈E(G).A packing of p graphs G_(1),G_(2),…,G_(p) into H is a p-tupleΦ=(ϕ_(1),ϕ_(2),…,ϕ_(p))such that,for i=...For graphs G and H,an embedding of G into H is an injection ϕ:V(G)→V(H)such that ϕ(a)ϕ(b)∈E(H)whenever ab∈E(G).A packing of p graphs G_(1),G_(2),…,G_(p) into H is a p-tupleΦ=(ϕ_(1),ϕ_(2),…,ϕ_(p))such that,for i=1,2,…,p,ϕ_(i) is an embedding of Gi into H and the p sets ϕ_(i)(E(G_(i)))are mutually disjoint.Motivated by the"Tree Packing Conjecture"made by Gyar fas and Lehel,Wang Hong conjectured that for each k-partite tree,there is a packing of two copies of T(X)into a complete k-partite graph B_(n+m)(Y),where m=■k/2」..In this paper,we confirm this conjecture for k=4.展开更多
An embedding of a graph G(into its complement G~c) is a permutation s on V(G) such that if any edge xy belongs to E, then s(x)s( y) does not belong to E(so G is a subgraph of its complement G~c). Faudree, Rousseau, Sc...An embedding of a graph G(into its complement G~c) is a permutation s on V(G) such that if any edge xy belongs to E, then s(x)s( y) does not belong to E(so G is a subgraph of its complement G~c). Faudree, Rousseau, Schelp and Schuster remarked that all non-embeddable graphs with n vertices and no more than n edges are either stars or contain 3 K or 4 C as subgraphs. For this reason they have conjectured that every non-star graph which contains no cycles of lengths 3 or 4 is a subgraph of its complement. This conjecture would nicely fit with other characterization theorems which specify that all graphs, except a family of forbidden graphs, satisfy a given property or are of a given type. In this article, we prove that the conjecture is true for a family of graphs of girth 5.展开更多
Let B_(n)(X,Y)denote the complete bipartite graph of order n with vertex partition sets X and Y.We prove that for each tree T of order n,there is a packing of k copies of T into a complete bipartite graph B_(n+m)(X,Y)...Let B_(n)(X,Y)denote the complete bipartite graph of order n with vertex partition sets X and Y.We prove that for each tree T of order n,there is a packing of k copies of T into a complete bipartite graph B_(n+m)(X,Y).The ideal of the work comes from the"Tree packing conjecture"made by Gyráfás and Lehel.Bollobás confirmed the"Tree packing conjecture"for many small trees,who showed that one can pack T_(1),T_(2),…,T_(n/√2)into K_(n)and that a better bound would follow from a famous conjecture of Erdo s.In a similar direction,Hobbs,Bour geois and Kasiraj made the following conjecture:Any sequence of trees T_(2),…,T_(n),with T_(i)having order i,can be packed into K_(n-1,(n/2)).Further Hobbs,Bourgeois and Kasiraj proved that any two trees can be packed into a complete bipartite graph K_(n-1,(n/2)).Motivated by these results,Wang Hong proposed the conjecture:For each tree T of order n,there is a k-packing of T in some complete bipartite graph B_(n+k-1)(X,Y).In this paper,we prove a weak version of this conjecture.展开更多
文摘在“双碳”目标的引领下,可再生能源的消纳需求迎来快速增长。为了实现县域内不同负荷特性的微电网可再生能源优势互补,提高消纳率,提出了基于交替方向乘子法(alternating direction method of multipliers,ADMM)的多场景县域多微电网交互运行策略。首先,建立微电网独立运行的调度模型,在日前预调度计划中实现最优调度策略;其次,建立多微电网电能交互运行模型,利用ADMM迭代求解各微网间全局交互电量;最后,利用Shapley值法分配微网群系统的收益,降低每个子微网的系统运行成本。算例分析表明,所提方法不仅能提高可再生能源的消纳率,提升经济性,还能降低碳排放量,实现低碳运行。
基金Supported by the National Natural Science Foundation of China(12071334)。
文摘For graphs G and H,an embedding of G into H is an injection ϕ:V(G)→V(H)such that ϕ(a)ϕ(b)∈E(H)whenever ab∈E(G).A packing of p graphs G_(1),G_(2),…,G_(p) into H is a p-tupleΦ=(ϕ_(1),ϕ_(2),…,ϕ_(p))such that,for i=1,2,…,p,ϕ_(i) is an embedding of Gi into H and the p sets ϕ_(i)(E(G_(i)))are mutually disjoint.Motivated by the"Tree Packing Conjecture"made by Gyar fas and Lehel,Wang Hong conjectured that for each k-partite tree,there is a packing of two copies of T(X)into a complete k-partite graph B_(n+m)(Y),where m=■k/2」..In this paper,we confirm this conjecture for k=4.
基金Supported by the National Natural Science Foundation of China (11871270)。
文摘An embedding of a graph G(into its complement G~c) is a permutation s on V(G) such that if any edge xy belongs to E, then s(x)s( y) does not belong to E(so G is a subgraph of its complement G~c). Faudree, Rousseau, Schelp and Schuster remarked that all non-embeddable graphs with n vertices and no more than n edges are either stars or contain 3 K or 4 C as subgraphs. For this reason they have conjectured that every non-star graph which contains no cycles of lengths 3 or 4 is a subgraph of its complement. This conjecture would nicely fit with other characterization theorems which specify that all graphs, except a family of forbidden graphs, satisfy a given property or are of a given type. In this article, we prove that the conjecture is true for a family of graphs of girth 5.
基金Supported by the National Natural Science Foundation of China(12071334)
文摘Let B_(n)(X,Y)denote the complete bipartite graph of order n with vertex partition sets X and Y.We prove that for each tree T of order n,there is a packing of k copies of T into a complete bipartite graph B_(n+m)(X,Y).The ideal of the work comes from the"Tree packing conjecture"made by Gyráfás and Lehel.Bollobás confirmed the"Tree packing conjecture"for many small trees,who showed that one can pack T_(1),T_(2),…,T_(n/√2)into K_(n)and that a better bound would follow from a famous conjecture of Erdo s.In a similar direction,Hobbs,Bour geois and Kasiraj made the following conjecture:Any sequence of trees T_(2),…,T_(n),with T_(i)having order i,can be packed into K_(n-1,(n/2)).Further Hobbs,Bourgeois and Kasiraj proved that any two trees can be packed into a complete bipartite graph K_(n-1,(n/2)).Motivated by these results,Wang Hong proposed the conjecture:For each tree T of order n,there is a k-packing of T in some complete bipartite graph B_(n+k-1)(X,Y).In this paper,we prove a weak version of this conjecture.
