This paper describes the physical characteristics and mathematical representations of large-scale power system states, introduces the concept of dimensional discrete state space in power system, describes the importance and influence of power system components in power system by introducing the weight information of power system components, and gives the structural properties of power system state space under natural order. Using the natural order induced by natural cone, combined with the structural characteristics of power system, the characteristics of partial order and lattice theory were explored. The structural function properties of several types of classical power systems were studied to judge the specific situation of power systems and describe the degree of system failure, and the structural function was explained in detail by taking the system as an example. The properties studied provide basic theoretical and methodological support for the research of multi-objective optimization properties of power system state space, which is crucial for the design of efficient algorithms for power system.