配电系统安全域的数学定义与存在性证明

Mathematical Definition and Existence Proof of Distribution System Security Region

该文从数学上描述了配电系统的N-1安全性,给出了安全域(distribution system security region,DSSR)的严格数学定义,并首次证明DSSR的存在性。首先,从数学上描述了配电系统运行的状态空间与正常运行方式下的约束条件。其次,为描述N-1安全性及安全程度,提出了安全函数的概念,并给出一个具体的安全函数,并证明其具有连续和单调减的重要性质。再从数学上将N-1安全性描述为安全函数满足某个预定临界值的问题。然后,给出了更严格的DSSR数学定义:DSSR是所有安全工作点的集合,该集合具有封闭的边界,边界内部均为安全工作点,外部均为不安全工作点。最后,从数学上证明了对于任意给定配电网,其DSSR一定存在。文中工作对揭示配电网安全域的数学本质具有重要意义,为未来智能配电系统安全高效的运行及规划技术奠定理论基础。

This paper gave the mathematical description of N-1 security of distribution networks, proposed the mathematical definition of distribution system security region（DSSR） and proved its existence for the first time. Firstly, it mathematically described both the operation state space and constrains under normal operation. Secondly, the concept of security function was proposed to describe the N-1 security and security degree. Also, it proposed a concrete security function, which is proved to be continuous and monotone decreasing. Therefore, the N-1 security can be described as whether the security function satisfies a default critical value. Thirdly, it proposed a more strict definition and mathematical description of DSSR： DSSR is the set consists of all secure operation points, and, the set has a closed boundary, inside which all operation points are secure while outside which are all insecure. Finally, this paper mathematically proved that DSSR exists for any structure-given distribution networks. The work in this paper has vast importance to reveal the essence of DSSR, which is the theoretical basis for planning and operation of smart distribution system in the future.