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This paper deals with the problem of nonlinear optimization of proportional-integral (PI) controller in doubly-fed induction generator (DFIG), modeled by the detailed differential-algebraic equations (DAEs), and connected to a power system, where rest of the power system is represented only by measurements in connection point. The basic functions of PI controllers are secondary regulation of speed-active power and reactive power-voltage of multiple DFIGs connected in the same point (typical situation in wind farms). In the presence of PI controllers, stability of the transient responses depends largely on its parameters (proportional and integral part). To calculate optimal parameters of the PI controllers, an 'Extremum Seeking' (ES) algorithm was used, more precisely, its version that assumes that gradient can be calculated [hence the name 'Gradient Extremum Seeking' (GES)]. Optimization of the PI controller parameters is performed for a list of major disturbance trajectories recorded in historical database. The results obtained using the IEEE 14-bus test system show that PI controller parameters must be carefully chosen. Their effect on transient responses and stability of the power system with major disturbance (short circuit, outage etc.) conditions was additionally studied.

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