This paper deals with the modeling of variable speed wind turbines for stability studies. Using the space-phasor representation and the fundamental relationships governing the operation of the machine quasi stationary model, suitable control algorithms for the simulation of the doubly-fed induction machine (DFIM) as well as the permanent magnet synchronous machine (PMSM) operating on an interconnected system are developed. The control schemes include the pitch-angle/speed control and the decoupled control of the real and reactive power outputs. As an additional modeling option, the generic model for variable speed machine has been introduced. The models were then implemented on a representative test network, and simulations have been carried out to observe the response of the control system to typical abnormal situations such as three phase grid faults to compare the accuracy of the generic models with the detailed quasi-stationary (QSS) models.