In Chapters 2 and 3 of the thesis we propose a self-scheduled control method for a doublyfed
induction generator driven by a wind turbine (DFIGWT), whose rotor is connected to
the power grid via two back-to-back PWM power converters. We design a controller for
this system using the linear matrix inequality based approach to linear parameter varying
(LPV) systems, which takes into account the nonlinear dynamics of the system. We propose
a two-loop hierarchical control structure. The inner-loop current controller, which
considers the synchronous speed and the generator rotor speed as a parameter vector,
achieves robust tracking of the rotor current reference signals. The outer-loop electrical
torque controller aims for wind energy capture maximization, grid frequency support and
generates the reference rotor current. We perform a controller reduction for the inner-loop
LPV controller, which is not doable by conventional model-reduction techniques, because
the controller is parameter-dependent. In simulation, the reduced order controller has been
tested on a nonlinear 4th order DFIG model with a two-mass model for the drive-train.
Stability and high performances have been achieved over the entire operating range of
the DFIGWT. More importantly, simulation results have demonstrated the capability and
contribution of the proposed two-loop control systems to grid frequency support.
In Chapter 4 we investigate the integral input-to-state stability (iISS) property for passive
nonlinear systems. We show that under mild assumptions, a passive nonlinear system
which is globally asymptotically stable is also iISS. Moreover, the integral term from the
definition of the iISS property has a very simple form (like an L1 norm). These theoretical
results will be useful for our stability analysis of wind turbine systems in Chapter 5.
In Chapter 5 we investigate the stability of a variable-speed wind turbine operating
under low to medium wind speed. The turbine is controlled to capture as much wind
energy as possible. We concentrate on the mechanical level of the turbine system, more
precisely on the drive-train with the standard quadratic generator torque controller. We
consider both the one-mass and the two-mass models for the drive-train, with the inputs
being the deviation of the active torque from an arbitrary positive nominal value and the
tracking error of the generator torque. We show that the turbine system is input-to-state
stable for the one-mass model and iISS for the two-mass model. Using our abstract results
from Chapter 4, we identify the iISS gain of this system. We also propose an adaptive
search algorithm for the optimal gain of the quadratic torque controller.