This paper presents the modeling and design of a 3 kW Permanent Magnet Synchronous Generator (PMSG) used for a variable speed wind turbine. Initially, the PMSG is modeled in the d-q reference frame. Different optimized parameters of the generator are extracted from the design and used in simulation of the PMSG. The generator output power is matched with the power of the turbine such that the generator is not either over-sized or under-sized.