This paper presents the steady-state model of a variable-speed wind power machine based on a doubly-fed induction generator (DFIG). Using a fifth order dynamic model of an induction machine, a modified equivalent circuit is derived. It uses the synchronously rotating reference frame in which the q-axis leads the d-axis by ninety degrees. In addition, the relationships between power and rotor-voltages are studied. A strong coupling in the q-axis rotor voltage and active power as well as the d-axis rotor voltage and reactive power is observed. These couplings are analyzed and the ability of the DFIG to produce reactive power is studied. Finally, the power capability characteristic of the machine is described which shows similarities to the capability curve of conventional synchronous generators. Considering the maximum rotor current, the boundary of a safe operation is best described by an elliptical region in the complex power plane. In addition, considering the limits of maximum rotor voltage, stator current and maximum active power the well-known D-curve or capability chart is obtained.