Power system oscillations usually contain multiple frequency components (modes), which are determined by generator inertia, transmission line impedance, governor and excitation control, etc. For generators close to each other (in the same area), the electric link between generators are relatively strong. The oscillations between these generators tend to be at relatively higher frequencies. In the mean time, generators in the same area can also oscillate against generators in the neighboring areas. This is called inter-area oscillation and the frequency is called inter-area modes. Generator groups in different areas are connected through long distance transmission lines, therefore, the electric link is relatively weak. The oscillation frequency is usually lower than local modes.

But i want ti know how can i know this frequency from system eigenvalues

Determine frequency from eigenvalue is trivial. I assume you actually want to know how to tell which engenvalues/frequencies correspond to interarea modes, which correspond to local modes. This can be determined from mode shape, i.e., the right eigenvector. Use the elements corresponding to rotor speeds of the machines in the right eigenvector of a particular eigenvalue, you can see the relative phase (as well as magnitude) of contributions to this mode from each generator. A good example can be found in Kundur's Power System Stability and Control Sec. 12.9.

that what i mean ....thank you DR Shuai Lu

thank you dr. Shuai Lu ,,wish you all the best for your success

Thank you Dr. Shauai Lu. this is perfect definition of local & inter area modes. 

Thank you very much. Dr. Lu. Can you please explain what mean mode? is that mode equal to frequency? Thank you so much.

Prof Lu

What is the physical significance of the left, right Eigen vectors and the participation factor of an Eigen value?

· Local modes (0.7-3Hz); they are associated with the swinging of generating units in a power plant, termed intra plant (1.5-3 Hz), or swinging of a power plant with respect to the rest of power system (0.7 - 1.5Hz).

· Inter area modes (0.1-7Hz); they are associated with the swinging of many machines in one part of the system against machines in other parts connected with weak transmission networks.