Oscillation Mitigation in Electric Power Grids via Semidefinite Programming

Inter-area oscillation of angle differences between groups of power generators is considered the precursor of large-scale blackouts. Because of the wide-area interconnection of generators, merely attenuating oscillation at individual sites is insufficient. In this paper, we consider the design of generator parameters and the interconnection strength such that the spectrum of the power system is assigned to a prespecified region of the complex plane. For identical generators, we obtain an explicit relation between the spectrum of the linearized dynamics and the spectrum of the interconnection matrix. This result allows us to formulate the eigenvalue problem as a semidefinite program, which can be solved efficiently. We provide an example to demonstrate the effectiveness of our approach.