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To alleviate the impacts of stochastic wind generation on stability performance, this paper proposes a novel control design method for coordination and synthesis of damping controllers for conventional synchronous generators (SG) and double fed induction generators (DFIG)-based wind generation in multi-machine power systems. A probabilistic model of wind generation under Weibull distribution of wind speed is first introduced. Based on this model, an extended probabilistic small signal stability analysis (SSSA) incorporating wind power generation is proposed for handling probability density function (PDF) of its power output. The optimization problem for tuning of damping controllers is then formulated, considering the cumulative distribution function (CDF) of the real part and damping ratio of eigenvalues obtained by the proposed probabilistic SSSA as stability constraints. Particle swarm optimization (PSO) is used to solve the optimization problem and to determine parameters of damping controllers. The effectiveness of the proposed method is demonstrated on the modified New England power system with multi-wind farms through probabilistic SSSA and transient stability analysis, and it is compared with conventional deterministic methods. Accuracy of the proposed probabilistic SSSA is also validated by Monte Carlo simulations (MCS).