Renewable power generation from wind and solar are gaining popularity to overcome energy crisis nowadays. A lot of advancement has been focused on wind power generation instead of fossil fuels that are degrading to the environment since last two decades in order to increase electricity generation, efficiency improvement, reliability and cost reduction. The generator used in windmill can be an induction generator (IG), synchronous generator (SG), doubly fed induction generator (DFIG), radial flux permanent magnet synchronous generator (RFPMSG) and axial flux permanent magnet synchronous generator (AFPMSG). Furthermore, due to the variable speed of wind turbine, a fully rated power converter handles the extracted energy in direct drive systems or a coupled geared system. However, with geared system, the cost of the overall system increased a lot and proved to be rather less reliable. In this regard, AFPMSG are most suitable for the direct drive applications due to its disc shape structure. The design of AFPMSG is derived from the design of RFPMSG. By using the desired value of parameters like power, speed, efficiency, number of phases, frequency, rated voltage and by taking some assumptions, inner and outer diameter of the rotors can be computed using sizing equation. Furthermore, in order to get balance three phase output and suitable winding factor a proper combination of the coils and poles is required. A 1 kW dual rotor single coreless stator AFPMSG, with concentrated winding is designed by using sizing equation in this research work. In order to analyze the characteristics of an electric machine analytical method formed on the solution of Maxwell equations and Finite Element Method (FEM) are used. The FEM results are more reliable as compared to the analytical method. However, FEM take long computation time as compared with the analytical method. This thesis presents a 2D analytical method to calculate the no load voltage of the coreless dual rotor AFPMSG. Furthermore, to decrease the no load voltage total harmonic distortion (VTHD), initial model of the coreless AFPMSG is optimized by using the developed analytical method. The back EMF obtained by using the 2-D analytical method is confirmed by time stepped 3-D FEM for both the initial and xi optimized models. Finally, VTHD, torque ripple and output torque are compared for the initial and optimized models by using the 3-D FEM. It is demonstrated that the VTHD and torque ripples of the optimized model are reduced as compared to the initial model. Optimization by utilizing the 2-D analytical method reduces the optimization time to less than a minute. Furthermore, an AFPMSG model to reduce torque ripple is presented in this thesis. The proposed model uses arc-shaped trapezoidal PMs. The proposed model reduced cogging torque and torque ripple at the expense of lower average torque. Time stepped 3-D FEM is performed and the results are compared with the conventional model. It is demonstrated that the torque ripple of the proposed model is reduced as compared with the conventional model. To further improve the performance of the designed machine with proposed magnet shape, it''s PM shape is optimized. The Latin Hyper Cube Sampling (LHS), Kriging Method and Genetic Algorithm (GA) are introduced and employed in the proposed machine for the optimization. Asymmetric magnet overhang, interpolar separation of PMs and axial height of PMs are considered as the design variable for the optimization. The volume of the PMs is kept equal to the conventional shape magnet volume during optimization. It is demonstrated that the torque ripple of the optimized model is reduced and the average torque is increased as compared with the conventional and proposed models. The optimized model shows improvement in terms of the quality of the torque along with average output torque. The proposed coreless AFPMSG presents a suitable alternative to meet increasing energy demand as compared to the conventional AFPMSG due to its reduced cogging torque and torque ripple and increased output power and torque. The research work presented in this thesis seems to be an attractive option in the field of axial flux machine to be utilized for wind power applications.