In this paper, we propose a comparative study of linear and nonlinear algorithms designed for grid-side control of the power flow in a wind energy conversion system. We performed several simulations and experiments with step and variable power scenarios for different values of the DC-link capacity with the DC storage element being the key element of the grid-side converter. The linear control was designed on the basis of the internal model control theory where an active damping was added to avoid steady state errors. Nonlinear controls were built using first and second order sliding mode controls with theoretical considerations to ensure accuracy and stability. We observed that the first order sliding mode control was the most efficient algorithm for controlling the DC-link voltage but that the chattering degraded the quality of the energy injected into the grid as well as the efficiency of the grid-side converter. The linear control caused overshoots on the DC-link voltage; however, this algorithm had better performance on the grid side due to its smoother control. Finally, the second order sliding mode control did not prove to be more robust than the other two algorithms. This can be explained by the fact that this control is theoretically more sensitive to converter losses.