This paper presents a computational intelligence technique for optimal coordinated reactive power control between a wind turbine (WT) equipped with doubly fed induction generator (DFIG) and a static synchronous compensator (STAT-COM), during faults. The proposed control model is formulated as a multi-objective optimization problem (MOP) in order to simultaneously minimize two conflicting objectives: 1) voltage deviations at the WT terminal during and after grid faults and 2) low-frequency oscillations of the active power after clearing the faults. For this purpose, it is necessary to achieve the optimal values of control variables, such as the reactive power references for both DFIG and STATCOM controllers. The aforementioned problem is solved by using the stochastic normalized simulated annealing (NSA) algorithm. Since the proposed problem is a MOP incorporating several solutions, the NSA algorithm finds the Pareto-optimal solutions for the proposed control system, based on the assigned priorities (weights) for each objective. For online applications, where the control system needs to act very fast, a fuzzy logic controller (FLC) is used, so that tuning the fuzzy model and fuzzy rules are accomplished offline by the NSA algorithm. To validate the effectiveness of the proposed control strategy, a case study including a l.S-MW DFIG and a l.S-MVar STATCOM were carried out with MATLAB/Simulink.