This thesis presents a robust controller design method for a permanent magnet wind turbine generators using the concepts of fractional calculus. Fractional calculus is a generalization of an integer order differentiation/integration that can more accurately describes the dynamics of processes. Recently, fractional calculus has been considered as an alternative powerful tool for modeling and robust control in various applications such as distributed parameter systems, heat diffusion, and viscoelastic phenomena. Fractional order controller has a unique iso-damping property that improves robustness via reducing the sensitivity of the system stability margins with respect to the system uncertainties. The iso-damping feature in fact desensitizes the phase-frequency variations about a gain crossover frequency which increases the robustness of a fractional order control system against uncertainties. In conventional integer order control systems, realization of iso-damping feature requires a controller with very high order transfer function whereas a fractional order system can readily realize this feature in a compact form. The thesis also elaborates the design steps of a fractional order PI controller for a wind power plant and compares the tracking performance and robustness capabilities of this controller with those of justify; TEXT-INDENT: 18pt; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr" dir=ltr To design and investigate the performance of fractional order controllers, a nonlinear dynamical system including a wind power system with a permanent magnet synchronous generator is selected as a study system. It is assumed that the wind turbine generator is connected to a dc power system that eventually delivers the generated power at a power station. The thesis proposes a nonlinear model of the wind power system based on the Hammerstein-Wiener method in which the nonlinearity of the system is modeled by a nonlinear static subsystem followed by a linear dynamic one. Using the proposed model, the thesis presents a procedure to design a robust fractional order controller with emphasis on improving the stability margins and iso-damping feature. The proposed method is applied to the study system and the performance of the fractional order controller is evaluated based on time domain simulation of the study system. The test system investigates the tracking performance of the control system considering the backlash and aging phenomenon within the dynamic model of the wind turbine generator. Backlash is an angular clearance in the gearbox of a wind turbine generator that exists between the gear teeth for lubrication and compensation of the gear thermal expansions. The backlash is a nonlinear phenomenon that can excite the torsional modes of the wind turbine generator rotating shafts which eventually lead to a shaft fatigue. The study results show the superior capabilities of fractional order controller compared with justify; TEXT-INDENT: 18pt; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr" dir=ltr Keywords: Fractional calculus, Fractional order control, Reduced order modeling, Wind energy, Wind turbine-generators.