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Fast fluctuations in wind farm power produce voltage flicker in the network. One way to mitigate the flicker is to place a static VAr compensator (SVC). Due to the operating delay of SVCs, it is essential to predict the wind farm reactive power. Here, a novel fuzzy nonlinear modeling approach is suggested and used in the one-step-ahead prediction of the power characteristics. The base of the developed fuzzy modeling is the Takagi-Sugeno fuzzy representation and a dual-unscented Kalman filter (D-UKF). In other words, a nonlinear TS fuzzy system is trained online via the D-UKF. The forecasted value is used as the SVC's reference signal. A large number of the actual data gathered from a wind farm are used for the performance evaluation. These data are collected in winter and summer for different climate situations. Using the actual data a current source with changing amplitude and phase which are updated every half-cycle is used to model the wind farm. Numerical results, including the flicker indices, confirm the improvement in the SVC's performance.