Study of the Stability of a Direct Stator Current Controller for a Doubly Fed Induction Machine Using the Complex Hurwitz Test

In this brief, a new control scheme is presented for the doubly fed induction machine (DFIM). The proposed control algorithm offers the advantages of proven stability and remarkable simplicity. In contrast to the classical vector control method, where the DFIM is represented in a stator-flux-oriented frame, a model with orientation of the stator voltage is adopted. This approach allows the decomposition of the active and reactive powers on the stator side and their regulation on the rotor side. A main contribution of this brief is the use of the Hurwitz test for polynomials with complex coefficients that has had little prior application in control theory. This results in a proof that a proportional-integral (PI) control regulating the stator currents ensures global stability for a feedback-linearized DFIM. The specific condition that the PI gains must satisfy is derived as a simple inequality. The PI controller has a particular structure that directly relates the d-component of the rotor voltages to the q-component of the stator currents and vice versa. The feedback linearization stage only uses the direct measurement of the rotor and stator currents and is thus easily implementable. Furthermore, it is also shown that the PI controller (without the feedback linearization terms) is also stable for a large range of control gains and does not require the knowledge of the machine parameters. Finally, the control system is validated in simulations and in experiments.