Nonlinear Stability Analysis of DFIG Wind Generators in Voltage Oriented Control Operation

In this paper the damping and stability properties of Doubly-Fed Induction Generator (DFIG) wind systems are studied. First the complete 5th order nonlinear system of a DFIG in the synchronously rotating dq reference frame is introduced. Assuming operation under the grid voltage oriented control mode, it is possible to control reactive and active power separately through the d and q controlled voltage inputs, respectively. After that, a simple cascaded controller design is adopted for each input, comprising of proportional inner-loop and proportional-integral outer-loop controllers. A passivity analysis is conducted for both the open-and closed-loop systems with the dynamics of the proportional inner-loop controllers taken into account. The analysis shows that the damping of the system can be modulated by the inner-loop controllers while it provides an appropriate storage function for the nonlinear stability analysis. This constitutes the main contribution of the paper since it is the first time that stability and convergence to the equilibrium is proven for the complete machine model in the face of unknown torque inputs, without needing any estimation or adaptive mechanism. Finally, the analysis and the performance of the closed-loop DFIG wind system are verified through extensive simulation results.