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This paper proposes a design method to coordinate dual-channel supplementary damping controllers (SDCs) of doubly-fed induction generators (DFIGs) and power system stabilizers (PSSs) for suppression of inter-area power oscillations. A dynamic performance index is introduced to measure the dynamics of the conventional synchronous generator and DFIG during the  damping control process. Hence, the proposed method designing the PSS and SDC is formulated as an optimization problem with the objective function being the sum of weighted performance indexes and the constraints indicating the requirements on the damping of the inter-area modes. Solving the optimization problem can obtain the optimal SDC and PSS, which can meet the required damping results as well as optimize dynamics of the controlled plants. Moreover, by adjusting weights in the objective function, the damping control burden …