Since the beginning of the electrification, the fossils have been exploiting for the last hundred years on the generation of electricity. However, now in twenty first century, there is a dilemma that the reserve of combustible fossil fuel has been almost depleted and the combustion has an inevitable consequence on the environment. Hence, the renewable energy sources can be the fuel of choice for the next generation since it is easily available, environment-friendly, and cost effective in all manners. There are several types of renewable energy resources such as solar, wind, geothermal, tides, and biomass. In this paper, the concentration is limited to the wind energy resources and wind turbine. Specifically, this letter is associated with the mathematical modeling of the permanent magnet synchronous generator wind turbine and simulation for the different aspects and cases of the system. After that, the performance of the PMSG wind turbine is analyzed for the different parameters. All of these analysis would contribute in a significant way towards implementing this technology in practical fields. All the results are verified by Matlab simulations with appreciable aftermaths.