The growing demand for power and increased environmental concerns gave an impetus to the growth of clean and renewable energy sources like wind, solar etc. There is a remarkable increase in the penetration of wind energy systems in the last decade and this trend is bound to increase at a much faster pace in future. This ever increasing penetration of wind power generating systems pose multi-fold challenges related to operational and stability aspects of the grid. Present day wind energy systems mostly comprise of variable speed wind generators. A large fraction of present day variable speed wind turbine generators use doubly fed induction machine (DFIM). This thesis deals with modeling and grid coordination aspects of variable speed wind gener- ators. In particular, the short coming of the existing steady state equivalent circuit of a DFIM is identified and subsequently, an accurate equivalent circuit of a DFIM is proposed. Relevant mathematical basis for the proposed model is presented. The proposed steady state equivalent circuit of a doubly fed induction machine is further validated using dynamic simulations of a standalone machine. Based on the proposed equivalent circuit, two approaches for computing the initial values of state variables of a DFIM is proposed. The first approach is a linear formulation where the losses due to resistance of the stator and rotor windings are neglected. The second approach is a non-linear formulation which takes the losses into consideration. Further, analysis is carried out on grid connected doubly fed induction generators (DFIG). A framework to incorporate DFIG based variable speed wind farms in the steady state power flow analysis is proposed. The proposed framework takes into consideration important aspects such as voltage dependent reactive power limits and mode of reactive power control of associated converters. Some of the challenges in a grid connected DFIG especially during su- persynchronous mode of operation are identified. The advantages of a non-Maximum Power Point Tracking (MPPT) mode of operation under certain operating conditions is highlighted. Finally, aspects pertaining to coordination of grid connected variable speed wind generators are studied. A trust region framework to determine the reference values to the control loops of converters in a variable speed wind generator is proposed. The proposed framework identifies the reference values considering other reactive power controllers in the grid. Moreover, the proposed framework ensures that the steady state voltage stability margin is maximized. On the computational front, trust region algorithms ensure global convergence. The mathematical models and initialization algorithms proposed in this thesis are tested on standalone systems under various control scenarios. The algorithms proposed to incorporate a grid connected DFIG in steady state analysis tools have been tested on a sample 6-bus system and a practical 418-bus equivalent system of Indian southern grid.