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An optimal controller for a shunt-connected static VAr compensator (SVC) has been developed for improving the dynamic performance of a power system with wind-turbine generators. The fuzzy-logic control complements the voltage control function, and provides damping in the system. A constrained-optimization design procedure for determining the optimal values of the linguistic variables for forming the crisp output of the fuzzy-logic controller has been developed. A novel aspect of the design is to establish the nonlinear relationship between the power system dynamic performance index (DPI) and the linguistic variables. The nonlinear relationship is represented by a multilayer feed-forward neural network. The inputs to the neural network are the linguistic variables associated with the controller output, and the neural network output represents the DPI. The objective function defined in terms of the DPI is minimized with respect to the linguistic variables, constrained within their bounds, which leads to their optimal values, and in turn gives the optimal fuzzy-controller output. Time-domain simulations confirm the effectiveness the optimized fuzzy-logic controlled SVC. Comparative study performed confirms that the new optimal fuzzy logic controller offers significant improvement in terms of damping of power system oscillations in comparison with the conventional fuzzy logic controller.