Doubly fed induction generators in conjunction with frequency converters allow the economic construction of large wind power plants with variable speed drives and a rated power output of up to several MW. Compared to fixed speed generators, the advantages of this configuration are high energy yields despite changing wind speeds, reduced negative effects on the grid and the possibility of reactive-power control. Furthermore, only a fraction of the rated power has to be carried by the frequency converter, which reduces its size and cost. It is vital to the manufacturer of these generators, to reliably predict the operating behaviour by using a suitable mathematical model. This paper elaborately describes such a model for the simulation of the steady state behaviour with a special focus on saturation and losses. Methods for modeling the nonlinearities and for solving the resulting nonlinear equations are described. Simulation results are verified by comparing them to measurement values. Results show that strong saturation of the main field increases the necessary rotor current when the wind power plant has to deliver reactive power to the grid while operating under overvoltage conditions.