Abstract:The partial order property and optimality of a class of vector sets with state attributes are studied. By abstracting largescale complex power systems into special vector sets with normal and fault state attributes, a class of weighted sum binary relations is considered. Some partial order basic properties of binary relations in vector sets are proved, and some optimality results of special vector sets are obtained. For a class of vector sets with state attributes, a series of theorems such as partial order properties and optimality of binary relations are established. The results can provide theoretical and methodological support for power system reliability assessment.