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A novel approach based on genetic search is presented for the design of a supplementary subsynchronous damping controller (SSDC) that is capable of damping out subsynchronous oscillation (SSO) in a parallel AC/DC transmission system. The problem of selecting the parameters of the SSDC is converted to a minimax optimization problem, which is solved by genetic algorithms with an eigenvalue-based objective function. The aim of the proposed control strategy is to choose the best controller parameters in such a way that the dominant eigenvalues of the closed-loop system are shifted to the left-hand side of s-plane as far as possible. Both the eigenvalue analysis and the detailed simulation results demonstrate the effectiveness of the proposed SSDC. Index Terms--Genetic algorithms, minimax optimization, subsynchronous oscillations, supplementary subsynchronous damping controller.