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.

[1]  G. Tapia,et al.  Modeling and control of a wind turbine driven doubly fed induction generator , 2003 .

[2]  E. Frank.  On the zeros of polynomials with complex coefficients , 1946 .

[3]  Carles Batlle-Arnau.  Modeling, simulation and control of a doubly-fed induction machine controlled by a back-to-back converter , 2006 .

[4]  Yongzheng Zhang,et al.  Rotor Position Phase-Locked Loop for Decoupled $P\hbox{-}Q$ Control of DFIG for Wind Power Generation , 2009, IEEE Transactions on Energy Conversion.

[5]  Romeo Ortega,et al.  Simultaneous interconnection and damping assignment passivity-based control: the induction machine case study , 2009, Int. J. Control.

[6]  Marc Bodson.  The complex Hurwitz test for the stability analysis of induction generators , 2010, Proceedings of the 2010 American Control Conference.

[7]  Felix A. Farret,et al.  Renewable Energy Systems: Design and Analysis with Induction Generators , 2004 .

[8]  Arnau Doria-Cerezo.  Modeling, Simulation and Control of Doubly-Fed Induction Machine Controlled by Back-to-Back converter , 2006 .

[9]  Joachim Rudolph,et al.  Flatness-Based Loss Optimization and Control of a Doubly Fed Induction Generator System , 2011, IEEE Transactions on Control Systems Technology.

[10]  Marc Bodson,et al.  Analytic conditions for spontaneous self-excitation in induction generators , 2010, Proceedings of the 2010 American Control Conference.

[11]  A. Doria-Cerezo,et al.  A Robustly Stable PI Controller For The Doubly-Fed Induction Machine , 2006, IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.

[12]  T. Thiringer,et al.  Evaluation of current control methods for wind turbines using doubly-fed induction machines , 2005, IEEE Transactions on Power Electronics.

[13]  R. W. De Doncker,et al.  Doubly fed induction generator systems for wind turbines , 2002 .

[14]  Heng Nian,et al.  Direct Active and Reactive Power Regulation of DFIG Using Sliding-Mode Control Approach , 2010, IEEE Transactions on Energy Conversion.

[15]  John Chiasson,et al.  Modeling and High Performance Control of Electric Machines , 2005 .

[16]  Romeo Ortega,et al.  Power flow control of a doubly-fed induction machine coupled to a flywheel , 2004, Proceedings of the 2004 IEEE International Conference on Control Applications, 2004..

[17]  Paul C. Krause,et al.  Analysis of electric machinery , 1987 .

[18]  Hirofumi Akagi,et al.  Control and performance of a doubly-fed induction machine intended for a flywheel energy storage system , 2002 .

[19]  M. Yamamoto,et al.  Active and reactive power control of doubly-fed wound rotor induction generator , 1990, 21st Annual IEEE Conference on Power Electronics Specialists.

[20]  Ion Boldea,et al.  Variable Speed Generators , 2005 .

[21]  Arnau Doria-Cerezo.  Comments on "Control and performance of a doubly-fed induction machine intended for a flywheel energy storage system" , 2013 .

[22]  Jon Clare,et al.  Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation , 1996 .

[23]  S. Peresada,et al.  Power control of a doubly fed induction machine via output feedback , 2004 .