Analysis of global behaviors in a classical power system

The global dynamical behavior of a classical power system consisting of n generators is studied in this paper. Existence and uniqueness of an invariant curve in 2n-dimensional space under suitable conditions are proved. The invariant curve is globally attracting so that the system behaves exactly as a one-dimensional system. Furthermore, a rotation number is defined in the power system and then, it is proved that each generator has one rotation number, but n rotation numbers for the n generators are all equal. Moreover, the rotation number is used to determine the dynamical behavior of the system, in the sense that if it is a rational number, an attractor of the system is composed of subharmonics while if an irrational number, the attractor is composed of horizontal curves. As a consequence the system has no chaotic motion under these conditions. Finally, numerical simulations are used to verify the theoretical analysis.