基于断线解环思想的配电网辐射状拓扑约束建模方法

Radiality Constraint Modelling Method in Distribution Network Based on Cutting-line and Opening-loop Idea

配电网采用闭环设计、开环运行的方式,因此在利用数学规划方法解决配电网中的某些优化问题时,需要建立可解析表达的辐射状拓扑约束。该文分析并证明目前使用较多的生成树约束是辐射状拓扑的必要不充分条件,即其无法确保生成的拓扑为辐射状,并给出使其成立的辅助条件。提出基于断线解环思想的辐射状拓扑约束,并证明该组约束是确保辐射状网络的充分必要条件。然后基于该文提出的约束,分别建立配电系统扩建规划和故障恢复问题的混合整数二阶锥优化模型。最后通过配电系统算例测试验证该文提出辐射状约束的有效性,并与常用的生成树约束和单商品流约束进行对比测试,验证该文提出的辐射状约束的优越性。

Distribution systems are usually designed as meshed networks but operate in radial topology.When using mathematical programming method solving some optimization problems in distribution networks,an explicit expression of radiality constraints is needed.In the paper,a set of popular radiality constraints,i.e.,the spanning tree constraint,was proved as the necessary but insufficient condition of radial topology,and the additional conditions to guarantee the radial topology were given and proved.A set of radiality constraints based on cutting-line and opening-loop idea was proposed.It was proved that the proposed constraint was the necessary and sufficient condition of radial topology.Based on the proposed constraint,the mixed-integer second-order cone programs for distribution system expansion planning and restoration problems were built.Case studies validated the effectiveness of the proposed radiality constraint.The comparison tests of the proposed constraint to spanning tree constraint and current single-community flow constraint validate the superiority of the proposed constraint.