Doubly Fed Induction Generators (DFIG) used in Wind Energy Conversion Systems (WECS) differ significantly from Synchronous Generators (SG). In fact, the machine flux rating, the current rating, and the PWM saturation constraints of the grid and rotor-side converters affect the DFIG operation. Furthermore, WECS are frequently installed in remote areas with weak grid connection, so a strong coupling exists between the DFIG voltage and active and reactive power injected into the grid. Therefore, a direct extension of the SG capability curves to DFIGs can lead to unstable or unfeasible operation. This paper presents a comprehensive analysis of the DFIG capability under weak grid connection and for different reactive power control (RPC) and current priority modes. A constrained optimization problem based on the mathematical modeling of the RPC modes, the machine and converters constraints, and the grid limits is formulated and solved under different wind conditions. Numerical analyses for a case study show the superiority of the Voltage Control RPC mode with q-axis current priority for weak grid connections. The proposed analysis can be useful for the design of control strategies that account for the actual limits of the system.