Judgment theorem of security boundary for distribution systems.

• Judgment theorems of security boundary are proposed for the first time. • The proposed theorems are verified by mathematical proofs and observations. • Applications based on the proposed judgment theorems are given. Security boundary characterizes the operations range of a distribution system satisfying N-1 security, and this paper proposes three judgment theorems for it. Firstly, the relevant concepts of the security boundary are introduced. The security boundary represents the set of all the critical secure operating points in the state space of a distribution system. Based on the degree of criticality, it can be classified into two types, i.e., strict and non-strict boundaries. Secondly, the load relationships between interconnected feeders are defined, and based on this, three judgment theorems are proposed. Thirdly, the proposed theorems are rigorously proven. Finally, an IEEE RBTS test system is used to verify the proposed theorems and demonstrate their applications. The proposed theorems enable convenient judgment of whether an operating point is a security boundary point and its type. This work reveals the load distribution characteristics of security boundary points, providing fundamental contributions to security boundary theory. [ABSTRACT FROM AUTHOR]